colormaking attributes

This page addresses a single

issue: how can we describe color experience?

Because color occurs in the mind but is a response to light in the world, separate

color descriptions are necessary for the external, physical light stimulus and the

subjective color perception.

The techniques of photometry allow

description of the intensity of a light stimulus as it appears to human vision, and

colorimetry translates the stimulus into a color specification. A standard tool used in

either approach is the spectrophotometric curve, which shows the exact mixture of light

wavelengths emitted from a light source or

reflected from a surface.

The standard photometric units provide a useful framework for learning about the

geometry of light — how light is defined or measured as it propagates through space, is

reflected from surfaces, and registers in

optical systems such as a camera or the eye. Many photographers are aware of these basic

photometric principles, as they help to judge the photographic demands imposed by

contrasts in light intensity. But painters, especially landscape painters, can profit from

a clear understanding of how light behaves.

Color experience, the subjective side of color,

is described by three colormaking attributes — (1) brightness/lightness, (2) hue and (3)

hue purity (colorfulness, chroma or saturation). These permit a sufficient and

reliable description of isolated color areas under simple viewing conditions.

Physical color measurements and subjective color descriptions are only correlated, in the

sense that one approximates but does not define the other. Fundamentally color

depends on context, and context can dramatically change the appearance of lights

color

vision

measuring light & color

radiometry

photometry

colorimetry

the geometry of light

the colormaking

attributes

brightness/lightness

hue

hue purity

optimal color stimuli

are three attributes

enough?

painting saturation &

value

how to judge

saturation

lightness, chroma &

saturation

the painters' "broken

colors"

and surfaces.

Painting is a form of description, and traditional methods of color mixing and

color terminology developed among European

painters as practical equivalents to the colormaking attributes. This page concludes by

explaining these painting methods in the context of modern color description.

The first requirement is a

method to describe exactly the radiant power of the external light stimulus that

creates the perception of light and color. This task is accomplished by three related

methods.

Radiometry is the measurement of radiant

power or energy within that part of the electromagnetic spectrum that is optical,

meaning it is refracted by glass or can be focused by a lens. This includes microwave,

infrared, visible and ultraviolet wavelengths

approximately in the range of 1 millimeter to

100 nanometers (10-3 to 10-7 meters, or

frequencies of 3 x 1011 to 3 x 1016 Hz). Radiometry excludes radio waves, xrays and

gamma rays.

The standard radiometric device is a

vacuum glass bulb with a wheel of paddles inside, each paddle painted black on one side

and white on the other; the wheel rotates when exposed to heat, light or an ultraviolet

lamp.

In radiometry, electromagnetic power is

measured in watts (joules per second), which can in turn be converted into other units of

energy or power. Actinometry is electromagnetic power measured in number of

photons per second. Radiometry provides the fundamental link between our visual sense and

the physics of matter and energy.

(A comment on terminology. Energy is the

potential to cause a change in matter, for example a change in its structure,

temperature, location, speed or direction of movement; it is measured in joules, roughly

measuring light & color

the amount of energy required to raise an apple 1 meter off the ground. Power is

energy emitted within a fixed time interval, equivalent to the potential speed or rate at

which a change in matter occurs; it is measured in watts (joules per second).

Intensity is the quantity of power radiating into a fixed solid angle or projected area of

space.)

the daylight spectral power distribution the spectrum measured in physical units (radiance in

watts) relative to the value at 555 nm

The fundamental radiometric description of a

light source is its spectral power

distribution or SPD, which shows precisely the amount of electromagnetic energy emitted

per second at each wavelength interval (or frequency interval). Shown above, for

example, is the spectral power distribution of typical noon daylight (sunlight plus skylight) at

the earth's surface. The peak energy is at around 450 nm; the energy of each

wavelength is shown as a proportion of the wavelength energy at 555 nm (visual

"green"). (Note that this peak shifts into the

infrared when graphed against wavenumber, a measure of frequency.)

Photometry is radiometry adapted to

represent a single attribute: the average brightness of light as perceived by the human

eye. This is done by weighting the power at

each wavelength by how strongly that light stimulates the photoreceptors in the eye, then

summing the weighted values to get the total

visible energy.

The weighting transforms radiometric watts into photometric lumens, the units of visible

electromagnetic power. Lumens do not

measure brightness specifically, because brightness is a visual sensation that depends

on luminance contrast (for example, the full moon appears brighter at night than during

the day). Lumens simply measure the proportion of radiant power that the eye is

able to see. Your light bulb is rated in watts, because that is how much energy the bulb

consumes per second; the light from the bulb is rated in lumens, because that is how much

of the energy can visibly brighten your world.

The ratio between them is the efficiency of the light source: tungsten light bulbs yield roughly

15 lumens per watt (and lots of invisible heat); energy conserving fluorescent lights

produce around 60 lumens per watt (and very little heat).

These photometric weights define the luminous efficacy of each wavelength, and

they combine as the photopic luminous efficiency function, the light adapted

sensitivity of the cones (diagram, right). Wavelengths outside the visible range, roughly

from 380 nm to 750 nm, negligibly affect the eye and are usually ignored.

The photopic sensitivity curve is scaled so that 1 watt of radiant flux at a wavelength of

555 nm ("green" light) equals a luminous flux of 683 lumens (diagram, right). (This odd

number was chosen to provide continuity with the inherited, historical measures of light — as

emitted from a single burning candle or lamp,

or through an aperture the width of a pencil lead placed over white hot platinum.) The

photopic curve then determines the proportional weights used to convert energy at

other wavelengths into light.

luminous efficacies for

photopic and scotopic

vision

curves show the number of

lumens

produced by 1 watt of radiant

power

at each wavelength between

380 nm and 700 nm

the daylight spectral luminance distribution

the spectrum measured in perceptual units (luminance in

lumens), relative to the value at 550 nm

Here is the daylight spectral power distribution weighted by luminous efficacy to

show the photopic luminous intensity in lumens. The peak luminance has shifted to about

550 nm ("green").

A second curve is available to describe the dark

adapted visual sensitivity of the rods — the scotopic luminous efficiency function

(diagram, above right). The 507 nm scotopic peak sensitivity is shifted toward the short

wavelength side of the photopic efficiency

curve; it is scaled so that it matches the sensitivity of the cones at the photopic peak

wavelength. This raises the scotopic peak luminous efficacy up to 1700 lumens per watt:

the same radiant power, under scotopic viewing conditions, appears roughly three times as

bright.

In fact, the peak scotopic sensitivity is over

120 times greater than the photopic sensitivity, if measured as the minimum

quantity of light necessary to produce a visible stimulus — not the 3 times greater implied by

the photometric scaling. And the point where scotopic and photopic luminous efficacies have

equal light sensitivity is actually in the "red" wavelengths, around 640 nm. Thus, the lumen

is a different psychophysical unit under

photopic, mesopic or scotopic light levels, and it generally understates the luminous efficacy of

very dim light stimuli.

Colorimetry is the measurement of color stimuli using photometric techniques. It does

this by weighting the spectral power distribution of a light or surface using three different

luminous efficacy curves — either standard colormatching functions or the L, M and S

cone sensitivity curves. These values are then used to triangulate or calculate the color

of the stimulus when viewed as an isolated patch; the values are also summed to get the

color brightness. These techniques are

explained in later sections on colorimetry and the CIELAB color model.

The fundamental photometric description of the

light stimulus is called a spectrophotometric

curve, which describes the relative quantity of light (lumens or photon counts) as a proportion

of some standard or maximum quantity across the visible wavelengths (typically 380 to

750 nm, or 400 to 700 nm). These curves come in three flavors:

• a spectral emittance curve describes the light emitted by sources such as the sun or

artificial lights. The quantity of light emitted at each wavelength is expressed as a

proportion of the quantity of light emitted at the most luminous wavelength, or at an

arbitrary standard wavelength (usually 555 nm or 560 nm).

• a spectral transmittance curve curve shows at each wavelength the light that is

passed through or transmitted by the medium as a proportion of the light incident on its

opposite surface.

• a spectral reflectance curve shows at each

wavelength the light that is reflected (not absorbed) by a surface as a proportion of the

light incident on the surface.

Because prints and paintings are essentially

surfaces, the spectral reflectance curve is the standard method to describe the color creating

characteristics of inks or paints on paper.

reflectance curves and cone outputs for

titanium white (PW6) and ivory black (PBk9)

normalized cone spectral curves from Vos, 1978 and

Werner, 1982

The two examples above show the reflectance

curves for the most basic surface colors: black and white. The horizontal dimension identifies

specific light wavelengths in the visible spectrum (symbolized in the diagram as

spectrum colors). The height of the curve shows the proportion (from 0% to 100%) of the

incident light that is reflected by the surface at each wavelength.

The reflectance curve eliminates any effect from variations in the illuminance or intensity of the

light source: a surface that reflects 50% of moonlight will reflect 50% of sunlight too. The

curve is also the same regardless of the color of

the light source, provided only that all visible wavelengths are present in the light in some

amount (though measurement is most accurate using a "white" light standard). When

interpreting a reflectance curve, assume it represents the surface color as viewed under

an equal energy illuminant or "pure" white light, which contains all visible wavelengths in

equal amounts.

The difference between the reflectance curves

for white and black paints shows that the lightness of a paint is proportional to the

average height of the reflectance curve. However this proportion is not easy to

determine from the curve itself, because lightness has a curvilinear relationship to

reflectance; for example, the graphic arts

"middle gray" is produced by an average reflectance of about 19%.

Note also that the average height of a

reflectance curve is never 0%: the blackest watercolors reflect about 10% of the light

falling on them, and black acrylic paints or color

samples reflect roughly 5%.

The trilinear color specification — the relative proportion of L, M and S outputs

produced by the reflected light — can be used to infer the surface color represented by a

reflectance curve, and I provide two aids to help you do this. Each curve is overlaid with the

log sensitivity curves for the L, M and S cones. To show how the curve is actually

interpreted by the eye, most reflectance curves are accompanied by the matching cone

response profile, the level of cone response

created by the light mixture.

a simple method for interpreting spectral

reflectance curves

The key landmarks are the crossover points where one cone sensitivity curve slips below

another. These are conveniently visible in the spectrum as two narrow, distinct bands of

color: the "cyan" boundary between "blue" and "green" wavelengths (at around 495 nm), and

the "yellow" boundary between "green" and "red" (at around 575 nm). These crossovers

divide the spectrum into three sections: blue, green, and red. Within each section, the S, M or

L cone is the dominant receptor. As a rule of

thumb, the proportion of reflected light in each section of the spectrum indicates the

proportional contribution of the L, M or S cones to the color sensation.

It is typically unwise to "read" the color

appearance (lightness, hue or chroma) of a surface directly from its spectral reflectance

curve. For example, the reflectance for a scarlet paint (diagram, right) has peak reflectance in

the "red" end of the spectrum, but where

exactly is its dominant wavelength (hue)? The tail of "blue" and "green" reflectance can have a

a spectral reflectance curve

for a scarlet red paint

significant impact on the hue and chroma of the surface. It is also difficult to assess the

lightness of the surface, as mentioned above. Reflectance curves are most interpretable when

one curve is compared to another — to indicate the relative reflectance difference between two

paints or inks or papers — or to indicate the general color appearance — red versus green,

or saturated red versus unsaturated red.

using reflectance curves to define a color mixture

equal parts ultramarine blue (PB29) and cadmium red

deep (PR108)

Two reflectance curves can also be combined to model the color that would be produced by the

mixture of two pigments, as shown above for a mixture of equal parts of ultramarine blue

(PB29) and cadmium red deep (PR108).

The reflectance curve for watercolor paint

mixtures (of paints having equal tinting strength, opacity and dilution) is approximately

the geometric mean of their separate reflectances computed at each wavelength in

the spectrum. (The geometric mean is the

square root of the product.) For example, if ultramarine blue reflects 80% of a specific

"blue" wavelength (say 480 nm), and cadmium red deep reflects only 8%, then their mixture

will reflect roughly 25% of the 480 nm light (that is, 0.08 x 0.8 = 0.064, where the square

root of 0.064 is 0.25). This averaging must be repeated for every wavelength, then the

apparent color of the mixture is determined from the cone responses to the resulting

average reflectance curve (white line).

For transmission filter mixtures, the simple

product of the two transmission profiles gives the resulting light intensity: 0.80 x 0.08 =

0.064, or 6.4% for the 480 nm wavelength.

The geometrical mean gives more weight to the

absorbance rather than the reflectance of the

two paints: at every wavelength, the reflectance of the mixture is closer to the

darker paint. However, to judge the approximate hue of the mixture or understand

how the two paints will behave when mixed with each other or with light, the visual average

— shifted somewhat toward the darker reflectance curve at each wavelength — may

often work fine. This illustrates that color perception is

dominated by wavelengths emitted or reflected within the center of the spectrum, roughly

between "cyan" and "red orange". Paints that mostly absorb the middle wavelengths and

reflect the spectrum ends (such as deep red and blue violet) produce especially dark colors.

The conversion from a spectral

power distribution to lumens is only the first step toward a useful measure of light intensity.

It is also necessary to specify the spatial

geometry that applies in the viewing situation. The eight elements necessary to define the

spatial geometry of light are:

1. an imaginary point source to represent the spatial origin of emitted light (the radial

property of light)

2. an imaginary measurement sphere

centered on the point source (key element in luminous flux)

3. an imaginary aperture area or surface area (A), defined on the surface of the measurement

sphere that encloses the emitted light (key element in luminous intensity)

4. a straight line defining the average direction of light emitted from the point source into the

solid angle

5. the distance (D) from the point source to

the enclosing spherical aperture area or surface area (radius of the measurement sphere; key

element in illuminance)

(alternately, the solid angle defined by the

ratio between the spherical surface area and its

squared distance from the point source: A/D2;

the geometry of light

see solid angle and inverse square correction)

6. the angle of incidence (θi) of the direction

of light onto a receiving physical surface area (see cosine correction for surfaces)

7. the source area (S) of the physical surface that emits the light (key element in

luminance)

8. the angle of emittance (θe) of the direction

of light from the surface of the light source (see

cosine correction for light sources).

9. the pupil area admitting light to the retina

(key element in retinal illuminance)

The diagram below provides a summary and

visual mnemonic for the various measurement units and the geometric restrictions unique to

each.

the relationships among standard

photometric units

There is a parallel radiometric nomenclature (radiant flux, radiant intensity, irradiance and

radiance, excluding the troland), with identical measurement definitions that are unweighted

for the eye's spectral sensitivity. Luminous Flux is the measure closest to the

fundamental physics of light generation. It is measured in lumens (lm):

1/683 watt emitted = 1 lumen

As mentioned above, the fractional unit of power (watt) was adopted to remain consistent

with historical units of light measurement: one lumen is roughly equal to the light emitted by a

single wax candle.

Luminous flux is the generic term for the visible

power a light source emits per second. Total luminous flux is specifically the light emitted by

the light source in all directions. The spatial geometry is equivalent to enclosing a point

source within a measurement sphere and capturing all the light incident on the sphere's

inside surface (diagram, right). The radius of the sphere — the distance from the light source

to the measurement surface — does not affect the measurement.

Luminous flux can be calculated by measuring the output from a light source from many

different angles at equal distances, then integrating these over a spherical area; or by

measuring the reflected light at one point inside a diffusing sphere, and extrapolating that

quantity to the total surface. In practical

situations, the quantity is usually obtained by measuring the light from a specific direction

and distance (illuminance or luminance), and then calculating backwards from that.

Luminous flux is a "source centric" definition of

light: it describes the source without regard to

the direction, distance or surface area of any surface, camera or eye that might receive the

light. Conceptually it represents the light source independent of a physical point of view, and

corresponds to the sense of physical power we infer from the experience of outflowing light.

luminous flux defined by a

measurement sphere

Luminous Intensity is the luminous flux

emitted from a point source into a radial envelope called a solid angle (explained

below).

The solid angle is essentially a "window" or

aperture cut into the measurement sphere. The average direction of light we want to measure

is centered within the area of this aperture. The

light must be a point source and located at the center of the sphere when the aperture and

direction are defined.

This aperture removes a spherical surface area from the measurement sphere, which is

the area of the solid angle. This aperture area

can be any size or shape, but the standard or

luminous intensity

measured by steradian in a

specific direction

the steradian is the area on

the surface of a sphere equal

unit solid angle is the steradian, equivalent to a square aperture 57° on a side or a circular

aperture 65° in diameter. The steradian defines luminous intensity as lumens per steradian or

candelas (cd):

1/683 watt emitted into 1 steradian

= 1 lumen/steradian = 1 candela

The steradian encloses an area equal to the

square of the radius of the measurement

sphere, or a square radian. It is the unit solid angle because it is defined on a unit sphere (of

radius 1), which makes its area equal to 1. As a result, the steradian aperture area is equal to

1/4π (roughly 1/12th) of the total surface area of a sphere. Thus, assuming a point source that

radiates equally in all directions:

luminous intensity = luminous flux/4π

Luminous intensity captures the notion of a

light source as having a brightness or power in

a specific direction: street lights illuminating the pavement underneath, ceiling lights illuminating

an office work area, a spotlight turned toward a cabaret singer, the sun shining toward the

earth.

However, luminous intensity is still a "source

centric" or abstract measure of light, because we have not specified the distance to a viewer

or illuminated surface, nor the size of a physical surface that receives the light. Luminous

intensity is an abstract measure of the flux density within a standard solid angle.

Viewing Geometry. To make light measurement "viewer centric", we must state

the viewing geometry between light emitting and light receiving objects in space.

The point source or radial property of light is now limited by two measurements in space: (1)

the aperture or surface area receiving the light and/or emitting the light, and (2) the

distance from light source to receiving surface. A cosine correction, for surfaces that are not

perpendicular to the direction of the light, is often necessary.

Solid Angle. The "source centric" measures of luminous flux and luminous intensity require a

to the square of the radius of

the sphere

point source because this permits use of the solid angle. The point source is a

measurement convention, the geometric foundation for the solid angle, and not a

physical description of the light source.

The solid angle is a radial envelope that defines

a projected area that grows larger with increasing distance from a light source, just as

a projected slide image or flashlight beam appears larger when it is cast onto a surface

farther away. The solid angle is analogous to a cone or pyramid, in that it has three attributes

(diagram, right): (1) an apex or point,

corresponding to the point source of light, (2) a central axis, corresponding to the average

direction of light we want to measure, and (3) a base corresponding to the projected area

that encloses the light energy. The area of a circular solid angle whose width is θ degrees is:

However, the solid angle is a measurement unit of projected area, and not a geometrical figure,

in the same way that a square foot is a measurement unit of surface area, and not an

actual square one foot wide. In particular, the

solid angle can represent a surface area or separate areas of any shape — a circle, square,

ellipse, pentangle, only the dark squares of a chessboard, and so on.

Second, the projected area is defined on a

measurement sphere centered on the point

source, and not by a physical surface area that actually receives the light (for example, the

base of a cone). To calculate area on the surface of a sphere, the dimensions of the

projected area must be expressed in radians. This is done by converting the angular

subtense of the area in degrees (ASdegrees

,

its apparent dimensions in degrees of an arc as

viewed from the point source) into radians:

ASradians

= ASdegrees

*(π/180).

Then the spherical solid angle area (in

steradians) can be calculated using the usual formulas for the area of plane figures. For

example, a circular measurement area defines a

elements of a solid angle

the projected area may not

equal the surface area

receiving the light

solid angle as:

solid angle (steradians) = π*(ASradians

/2)

2

and the solid angle for a square measurement area is:

solid angle (steradians) = ASradians

2.

For example, the sun and moon both appear as

circular disks subtending a visual angle (apparent diameter) of 0.5° or 0.0087 radians.

So the solid angle defined by their circular

surfaces is π*(0.0087/2)2 or 0.00006 steradians.

For plane surfaces that are extremely small in comparison to the distance to the light source,

the discrepancy between spherical and plane geometry usually can be disregarded and the

solid angle computed from the plane area and distance expressed in the same units (inches,

meters, kilometers).

Now the crux: because the sides of a solid

angle and beams of light both radiate from the point source like spokes from a wheel, the

quantity of light radiating into a solid angle remains constant regardless of

distance from the point source.

solid angle and standard surface area the solid angle is used to measure luminous intensity,

which does not change with distance; the surface area is

used to measure illuminance, which does change with

distance

This is because the solid angle defines a constant proportion between the spherical area

it contains and the distance of the surface from the point source (both measured in the same

distance unit, such as meters):

A solid angle is always in steradians when both the spherical surface area enclosed by the solid

angle and the radius of the measurement sphere are expressed in the same units (feet,

meters, kilometers). Thus a square meter surface area at a distance of 1 meter defines a

solid angle of 1 steradian.

Although it is not a geometrical figure, the

steradian is a useful perceptual proportion for visual estimates of brightness on a surface

(diagram, right). A "distance wide" circle of surface area underneath a diffuse light appears

more or less evenly illuminated by the light and anchors our judgment of whether the light's

illuminance is adequate to its purpose. A reading lamp looks adequately bright or too dim

according to the amount of light it casts on a 2

foot circle of desk underneath it, and a ceiling light according to the 9 foot wide circle of floor

below.

Inverse Square Correction. Instead of using the angular subtense to calculate the solid

angle in luminous intensity, the solid angle can

also be calculated in terms of a standard surface area that actually receives the light,

such as a square meter or square foot. This is appropriate when we want to measure light in a

human scale — the light falling on a kitchen table or the page of book. But given a light of

constant luminous intensity and a surface of constant area, the surface captures more or

less light depending on whether it is near or far from the light source. So we have to adjust the

luminous intensity contained in a solid angle to

account for actual physical distances.

This relationship between distance and the projected surface area of a solid angle is

described by the inverse square law:

Ib = I

a * D

a2/D

b2

Which means: if the intensity Ia of a light is

measured within a surface area at distance Da,

streetlight and steradian

and the surface is then moved to a new distance D

b, the quantity or intensity of light at

the new distance Ib will be increased or

decreased by the ratio of the two squared distances. In the diagram (above), a surface

area that is 3 distance units from the light

source receives 1/32 or 1/9th the luminous

intensity of the same surface at 1 distance unit. This follows from the constant proportions

required by the solid angle:

Ia/D

a2 = I

b/D

b2.

Cosine Correction. Finally, any physical

surface area corresponding to the solid angle area is always assumed to be flat (a plane) and

perpendicular to the average direction of light.

If the plane surface is tilted at an oblique angle to the direction of light, the physical surface

area enclosed by the solid angle increases, or the apparent size of the surface, as viewed

from the point source, decreases (subtends a smaller visual angle). This is called

foreshortening. Because the surface area as seen from the point source appears smaller, the

surface receives less light.

This problem is solved by the cosine

correction for foreshortening. The light incident on a surface is attenuated by an

amount equal to the cosine of the angle of incidence (θ

i, diagram right) multiplied into the

area of the solid angle:

If a surface is perpendicular to the direction of light then the cosine is 1.0 and there is no

reduction in light intensity. If the surface is at a 45° angle to the direction of light then the

cosine is 0.707 and the intensity on the surface

is reduced by 71%.

Illuminance is simply the amount of light incident on a surface from a light source or

sources of any size at any distance. To specify the concept of illuminance, no information

about the distance or size of the light source(s)

is necessary. However, the standard measurement unit of illuminance is

conventionally defined as the light energy

the cosine correction for

foreshortening

incident on a standard surface area (one square meter) at a standard distance (one meter) from

a point source, in one second. This yields

lumens per square meter (lm/m2) or lux (lx):

1/683 watt incident on 1 square meter

= 1 lumen per square meter = 1 lux

There are several obsolete or nonmetric

definitions of illuminance, including the foot

candle (1 lumen incident on 1 square foot). As there are roughly 10 square feet in one square

meter, the foot candle defines a larger unit of light:

1 foot candle = 10.76 lux.

Two definitions of illuminance start with the previously measured output from a light

source:

Luminous flux is the total output in all directions, so it must be divided by 4π to obtain

luminous intensity. Thus, a nonreflecting 60W incandescent bulb emits about 600 to 840

lumens (and lumens denotes luminous flux); so its illuminance at 3 meters is about 5 to 8 lux.

Recessed or reflector bulbs emit their luminous flux in one direction. The diameter of this light

cone varies with type of lighting, but a handy rule of thumb is that the cone fits within one

steradian (luminous flux = luminous intensity, and lumens = candelas). Thus, illuminance is

equal to luminous intensity: 1 lumen equals 1

lux at 1 meter distance, and only the inverse square correction is necessary: for a 60W

reflector or recessed light rated at 650 lumens, the illuminance at 3 meters is about 72 lux.

If the light is obliquely rather than

perpendicularly incident on the surface, then

the illuminance is less, and the luminous intensity must be multiplied by the cosine

correction for foreshortening.

A third definition is based on the luminance and image size (solid angle) of the light source:

[3] illuminance = luminance * solid angle

S

with luminance measured in candelas per

square meter, and illuminance in lux.

Three key points will help clarify the concept of

illuminance. First, despite the source centric definitions above, illuminance comprises the

total light power incident on a specific surface at a specific location in space. It is equivalent to

the "blind" skin sensation of heat induced by the distant sun or a nearby light bulb. The

sensation, by itself, cannot indicate the size, distance or intensity of the source; similarly, by

itself illuminance does not specify light

sources — it describes the light falling on a surface.

Second, illuminance is not directly visible as

a quantity of light. We only see its reflected

image as the luminance of physical surfaces. If the light source were behind us, and there were

no surfaces in view (or the surfaces completely absorbed light), we would look into total

darkness. If we turned to look directly at the source of illumination, we would perceive the

luminance of the optical image of the light source on the surface of the retina, which

depends not only on the quantity of illuminance but on the visual size of the source that emits

it.

Third, illuminance is very closely related to the

geometry of objects in relation to light sources. For example, on a clear sunny day, a

book held in the shadow of a stop sign on a country road is illuminated by the entire visible

sky; but if we stand in the shadow of a large

building that blocks out half the sky, the illuminance is reduced by half. Similarly, if a

single north facing window illuminates a room, drawing the blinds from a second window

doubles the illuminance. In forests, canyons, alleys or overcast days, the reduction in

illumination from the daylight maximum is equal to the amount of light obstruction.

This dependence on object geometry makes illuminance the key architectural measure of

lighting. The physical dimensions of an interior

space define lighting requirements, because distance has a huge impact on illuminance

through the effect of the inverse square law. At one meter, a single candle (1 candela) yields an

illuminance of 1 lux. At 10 meters, the candle produces an illuminance of 0.01 lux. To get

back the illuminance of 1 lux from a distance of 10 meters, we would have to use 100 candles.

However, the same level of illuminance can be provided by many different lighting systems

(number, power and physical size of light

sources); illuminance provides a specification of what the total lighting system must deliver.

There are many illuminance standards for

the amount of light desirable in different

architectural settings or for different tasks. Office lighting standards require illuminances in

the range of 300 to 500 lux at work surfaces; home lighting levels are typically lower. (See

this section for a broad comparison of illuminance levels.) Many eyestrain problems

are created by the effects of glare (reflected light) or excessive light contrast, and not by

inadequate illuminance levels.

Lighting engineers and interior designers

measure illuminance with an illuminance meter or light meter, which determines the amount of

light through the electric current produced by light energy falling on a photosensitive surface.

Lighting engineers often use a light meter that collects light arriving from a wide area, so that

the measured illuminance corresponds to light sources of any size and shape in any direction;

these all sum to the total light incident on the measurement device. Photographers similarly

use a light meter to estimate the average quantity of light available to alter photographic

film; however, they typically measure only the

light reflected from an average gray card, or the average light reflected from only the

surfaces included in the image.

Luminance is the illuminance incident on a

surface area, divided by the angular width of the source as viewed from the surface. It is the

most context specific definition of light, because it is based on two solid angles, or a solid angle

and a surface area, which gives candelas per

square meter (cd/m2):

1/683 watt incident on

1 square meter at 1 meter distance

= 1 candela/meter2

A surface one meter square at one meter distance is equivalent to the steradian solid

angle. So why isn't luminance the same as

luminous intensity? Because the definition includes two surface areas: the surface area

implicit in the steradian solid angle (used to define the candela), and the square meter

divided into it.

Luminance does not apply to a point light

source but to an extended light source, a light or reflecting surface that has a visible width or

measurable surface area. Since all physical light sources must have a surface area (or angular

size), luminance is a truly "viewer centric" definition of light — the photometric unit that

most closely approximates the perceived brightness of a light or the lightness of a

surface as viewed by a camera or human eye.

It is the fundamental measure of visible light or image brightness.

Luminance assumes a light emitting surface

(such as the diffusing glass over an electric light bulb, or a reflecting sheet of white paper)

that produces all the light incident on a light receiving surface (film, CMOS chip, retina),

which may equivalently be an aperture that blocks the light arriving to the surface from

extraneous light sources. The diagram below

illustrates the basic geometry of luminance in terms of a flat, diffuse light source radiating

into a unit hemisphere.

the basic geometry of luminance luminance is the solid angle of point luminous intensity,

times the surface area of the light

This geometry yields five equivalent definitions

of luminance based on different measurement units:

Formula [1] shows that luminance is defined by three geometrical quantities: the two surface

areas (or a surface and an aperture area) and the common distance between them. Thus, the

surface area of the light source (circular in the

diagram) is defined by π*X2. (The area of a

square light source would be (2X)2.) The

circular area of the light receiving surface (or

aperture) is π*Y2. This surface (or aperture) is at distance D from the source.

It is usually convenient to divide the distance squared into one or the other surface area to

create a solid angle, as in formulas [2] and [3]. The light receiving aperture area defines the

solid angle A, equal to π*Y2/D2 steradians;

the light emitting source area defines the solid

angle S equal to π*X2/D2 steradians.

As always, it is desirable to express X and Y as

a visual angle in radians, as this preserves the spherical area of the solid angle. If Y is the

angular subtense (in radians) of the aperture as measured from a point s on the source and X is

the angular subtense of the source measured from point d at the aperture, then their solid

angles are π*Y2 steradians and π*X2 steradians.

The solid angle A defines the proportion of

luminous flux passing through the aperture from any single "point source" s on the surface

of the light source. The total number of points

illuminating the aperture is equal to the

physical area of the source (π*X2). So the solid

angle A based on the spherical area of the aperture is multiplied by the area of the source,

and this is divided into the luminous flux.

Note that distance is only included once in a

luminance calculation, so two solid angles are never required. In formula [4], luminous

intensity already contains one solid angle (in the "aperture" area of the steradian solid

angle), so this is scaled by the source area only. In formula [5], illuminance only contains a

surface area (the area of the surface/aperture that receives the light), so this must be scaled

by the solid angle to the source (its visual size at the viewing distance).

As before, in any of the formulas above, the luminance quantity can be adjusted with the

cosine correction (diagram, right), when

either the aperture plane (the angle of incidence, θ

i) or the source plane (the angle

of emittance, θe) or both (e.g., a foreshortened

source shines onto a foreshortened surface) are not perpendicular to the average direction of

light between them:

Let's consider the perceptual implications of

luminance. First, luminance describes the image quantity of light, in the sense that the

luminance geometry corresponds to the geometry of an optical image, including the

image formed within the eye. Luminance is always visible, and is therefore complementary

to illuminance, which is always invisible.

Second, luminance defines the "area

intensity" of the light source. It does not simply describe the intensity of light within the

image or the quantity of light reaching the eye, but the degree to which the measured intensity

originates from a visually compact source. As a simple example: you step into a business office

and notice that the floor is brightly illuminated. Simply by looking at the floor and the material

it is made of, you can infer the approximate

level of illuminance, for example as compared to the illumination produced on the ground by

daylight. But you cannot see the luminance of the light source itself.

cosine corrections in

luminance

If you looked up, you might see that the illuminance originates in several "spotlight"

ceiling fixtures, each of which would appear very small from your vantage and therefore

uncomfortably bright to look at (high luminance). Or the entire ceiling may be

covered by diffusing light panels, which spread the light over a large area and therefore appear

comfortably dim (low luminance). Lighting engineers apply this fact in the design of light

fixtures that deliver the necessary illuminance

while spreading the source luminance over a larger visual area.

Third, the "area intensity" of luminance is

constant across distance. Since the

illuminance of a light source is proportional to the inverse square of its distance, the incident

light decreases as a light moves farther away. But the visual size of the light also gets smaller

from our viewpoint, and by the same inverse square proportion. As a result, the ratio

between incident light and visual size remains constant. As lights recede from us, they

become dimmer but also proportionally more concentrated in visual area, so we perceive the

source as having a constant brightness. The

same is true for relative luminance (illuminance times surface reflectance): material surfaces

have approximately the same lightness regardless of distance.

Despite these spatial invariants, luminance and

the perception of brightness/lightness are

only loosely related. Perceived brightness depends on the apparent distance of the light

(lights appear fainter as they move farther away), and the lightness of surfaces depends

on the local contrast with other surfaces; both depend on the level of luminance adaptation.

Luminance & Optics. The luminance of a light

source as imaged in an optical system, such as a camera or the eye, introduces some specific

issues.

the pinhole geometry of luminance the solid angle of the image equals the solid angle of the

light source surface; both are constant across distance

In the simplest case, a pinhole camera contains no lens, only a hole that is extremely

small in relation to the distance D to the light source and the focal length F to the image

plane. The pinhole causes each point s on the source to project a single point image of itself

on the image plane. As the solid angles S and I

are therefore equal, the total light passing through the pinhole is equal to the illuminance

(not the luminance) of the source at the pinhole.

The pinhole is in turn a point source inside the

camera, creating the image at focal distance F. Since moving the image plane away from the

pinhole makes the image area (I) larger by projection, but does not increase the

illuminance into the image, increasing the focal

length makes every part of the image dimmer. So the image luminance is determined by the

pinhole illuminance divided by the focal length

squared (F2):

luminance [image] = illuminance/F2

What happens if we increase the size of the pinhole aperture, to let in more light? This

increases the area admitting light:

luminance [image] = aperture area *

(illuminance/F2)

which produces a much brighter but optically

blurred image. The blurring effect of increased aperture is overcome by a lens (or parabolic

mirror).

the optical geometry of luminance the solid angle of the image is proportional to the ratio of

the distances D/F

The solid angles I and A on opposite sides of the lens are no longer equal — the lens refracts

the light "rays" into a wider solid angle. However, the two solid angles have in common

the surface area of the aperture or lens opening, therefore the ratio of the two solid

angles equal to the ratio of the two distances,

D2/F2. This is the power or light concentrating capability of the optical system.

Assuming D is very large relative to F (as for binoculars or a telescope), then the solid angle

I becomes larger, and the power of the optical system increases, as the focal length F

becomes shorter. When the lens produces a

focused image, then the physical image area is proportional to the physical source area in the

ratio F2/D2 — that is, the higher the optical

power, the smaller the focused image.

Each ratio is a reciprocal of the other, so they

neatly cancel each other out when the solid angle I is multiplied by the image area (or

when solid angle A is multiplied by the source area). As a result, for a completely transparent

lens:

luminance [image] = luminance [source].

This essentially restates the third luminance

property of light sources — luminance remains constant across changes in distance — because

the image of an object in any optical system grows larger or smaller in the same inverse

square relation to the object distance.

The quirk here is that the image illuminance

increases with optical power, just as it does with increased aperture. As aperture increases

(the physical width of the lens becomes larger), it collects more light; as power increases, it

concentrates the gathered light into a smaller image area. Both effects increase the incident

light (illuminance) at any point within the image area and the luminance (brightness) of the

image. A magnifying glass ignites a piece of paper in sunlight, because the sun's heat is

condensed from the aperture area of the lens

(its shadow area on the paper) into the area of the sun's image on the paper. A short focal

length, wide angle lens exposes a photographic film more quickly than a long focal length

telescopic lens of equal aperture.

Luminance & Surfaces. The luminance of

reflecting surfaces is potentially complex and depends on (1) the illuminance onto the

surface, (2) the surface reflectance or albedo of the surface (the proportion of light falling on

the surface that is reflected from it), (3) the angle of incidence of the light, (4) the angle of

view to the surface, and (5) how much the surface diffuses or randomly scatters the light.

These issues are explored on a later page, but a few points should be mentioned here.

There are several alternative luminance measures that attempt to equate the luminance

of a perfectly diffusing (matte) "white" surface with the luminance of a light shining on it. The

most common are the metric apostilb and millilambert (preferable to the inconveniently

small lambert) and the USA foot lambert:

1 candela/meter2 (1 nit) = 3.1416 apostilbs

= 0.3142 millilambert = 0.2919 foot lambert

These are all related to the general formula for the luminance of a surface (perpendicular to the

direction of light):

Note that reflectance is not the lightness (L) but the luminance factor (Y). In most situations

surfaces reflect to the eye only a small portion of the light incident on them. In addition,

surfaces are typically much larger in visual size than the light source. This can confound the

luminance comparison between surfaces and lights.

For example, a perfectly diffusing (matte) "white" surface 1 meter square, placed one

meter below a perfectly diffusing light panel 1 meter square, will appear to be about 1/3 as

bright (or light) as the light source; an "average" or middle gray surface will appear

1/15th as bright. Increasing the distance

between light and surface will cause the light source to appear even brighter than the white

surface; and reducing the visual size of the light concentrates the luminance in a smaller visual

area and increases the brightness disparity even further — well beyond the limits of

luminance adaptation, which can only handle a luminance range of about 1000:1. As a result

all natural light sources (and concentrated artificial lights, such as a bare tungsten

filament) look far "too bright" or glaring

compared to the illuminance they provide. Alternately, a source that is comfortable to look

at directly (such as the full moon, or a candle) typically produces illuminance that seems dark

or feeble.

Paradoxically, glossy or shiny surfaces will

usually appear darker than matte surfaces having the same reflectance, unless the light

source is reflected directly to our eyes. This is why the highly reflective waters of a sea or lake

appear dark in comparison to highly reflective beach sand: the sand diffuses light equally in all

directions, whereas the water reflects light primarily in the direction where the sun's image

is visible on its surface.

Retinal Illuminance is a measure of the

amount of light that actually enters the eye. It is measured in trolands and is derived as the

luminance of the light source multiplied by the area of the observer's pupil in square

millimeters. Because pupil sizes vary from one individual to the next and across different light

intensities, the troland has only an empirical or

observed relationship to source luminance; but at typical indoor levels of illumination (around

300 lux):

1 candela/meter2 = ~10 trolands

Thus, the moon's retinal illuminance in trolands is greater at night than it is during the day,

because at night our dark adapted pupils are larger.

The troland is primarily used in vision research, and to standardize things an artificial pupil

(small hole in an opaque screen), of a fixed width that is smaller than the range of pupil

widths among experimental subjects, is placed in front of the viewers' eyes.

The troland does not take into account most of the perceptual changes involved in luminance

adaptation between day and night, so (like luminance) the troland does not describe very

accurately the subjective sensation of brightness. It simply allows more precision in

the estimate of light actually incident on the retina.

James Calvert has posted a useful Illumination tutorial

that explains the geometrical definitions and standard

formulas for photometric units.

The physical measurement of light must be joined with an accurate description the

subjective color experience produced by the color stimulus. This description is based on

three colormaking attributes: (1) brightness/lightness, (2) hue and (3) hue

purity (chroma or saturation), first defined by

Hermann Grassmann and Hermann von Helmholtz in the 1850's.

Exactly how the three colormaking attributes

relate to the three L, M and S cone fundamentals, the physiology of color vision,

is not a concern. The only goal is to provide an

unambiguous way for individuals to describe a color experience as a number or quantity on

three standardized and easily recognized attributes.

The appearance of a color is a judgment based on context — the setting in which the

color is viewed and our luminance adaptation

the colormaking attributes

and chromatic adaptation to that setting. But at the same time we can make an absolute

color judgment, a kind of color perception in an ideal color space independent of the viewing

context or our visual adaptation. This allows us to compare and recognize colors across

different situations, for example when we perceive that a white piece of paper is brighter

under noon sunlight than midnight moonlight, or that the colors of sunset are redder than

those of noon. The relativistic colormaking

attributes, those influenced by our visual adaptation and the viewing context, refer to

related colors, while the absolute color judgments are roughly equivalent to unrelated

colors.

The three context attributes most important to

color perception are:

• the intensity and color of the illumination — by far the most important context element.

Different terms apply to the two separate

attributes of a light source and their combination:

– illuminance refers to the quantity or intensity

of light incident on the color area, which (via the light reflected from surfaces) determines

the level of luminance adaptation.

– illuminant refers to an abstract relative

spectral power distribution that characterizes the chromaticity of an idealized

light source independent of its brightness; the

actual spectral power distribution of a light determines its color rendering properties and

the chromatic adaptation imposed on the visual system

– illumination refers generically to the intensity

and color of the light incident on the color area

and surrounding surfaces.

• the relative luminance contrast between a color area and its surroundings, which

determines its perception as an emitting light or a reflecting surface. Colors appear self

luminous when their luminance is much

greater than a recognizably "white" surface; they appear as object or surface colors when

their luminances are less than "white". Colors that cannot be clearly identified as either lights

or surfaces are called aperture colors.

Additionally, the chromaticity contrast (the relative luminance contrasts within specific

parts of the spectrum) between a color and the surrounding surfaces often alters color

perception.

• the spatial interpretation of the scene,

which determines the three dimensional relationship between different surfaces, and

between all surfaces and the (usually multiple) light sources in the viewing context.

To make accurate color judgments, these contextual factors (and others, such as gloss,

texture or specular reflections) either must be eliminated (as in unrelated colors) or explicitly

standardized (as related colors viewed on a medium gray background under a diffuse,

moderately bright, full spectrum "white" light).

Physical Stimulus, Perceptible Stimulus

and Sensation. The colormaking attributes provide a flexible and unambiguous description

of color sensations as experienced in lights or surfaces. But this entails that they do not

describe the physical qualities of the color stimulus, and are not equivalent to any

measured quantity of the stimulus.

For example, a subjective quantity of the visual

sensation of brightness (for example, a light that is described as "painfully bright") is not

consistently related to a specific physical quantity of light (say, 10 watts of radiant

power) or a specific perceptible quantity of light

(say, as 6800 lumens). The 10 watts might arrive as "green" or "red" light, which will alter

its apparent brightness; the 6800 lumens might be viewed as a flash of light in high photopic

adaptation or in complete scotopic adaptation, which will alter its visual impact. Many other

qualifications or unique circumstances are possible.

Again, context matters to visual perception. It is important to keep distinct the three

conceptions of the stimulus — as physical quantities, as perceptible quantities, and as

sensations — because a generalization based on one conception may not apply to the others.

The colormaking attributes literally describe color sensations, and nothing else.

Even so, provided the contextual issues are

appropriately limited or standardized, and within a generous allowance for measurement

error and individual differences in visual capabilities, correlates or equivalents to the

colormaking attributes can be computed from the physical or perceptible quantities of a

stimulus. These form part of the color specification in nearly all modern color

models.

Brightness/Lightness. The first and most

important colormaking attribute is the light or dark of a color as it appears in emitted or

reflected light. This is perceived in two distinct ways:

Brightness refers to the relative sensation of light as emitted or reflected from a color area,

given the current level of luminance adaptation. This is a sensory definition; it is weakly

correlated with the perceptible luminance of the color area, as explained below.

Lightness refers to the brightness of a colored surface as a proportion of the brightness of an

area perceived as "white" under the same illumination and light adaptation. This is also a

sensory definition; it is strongly correlated with the physical measurement of the relative

reflectance (luminance factor or albedo) of

surfaces in comparison to the reflectance of a perfectly diffusing ("bright white") surface,

within the photopic to high scotopic range of illuminance and given a wide range of

different reflectances in the field of view.

For objects or surfaces, extremes of lightness

are usually described as dark or black up to light or white; for self luminous areas (lights)

the terms are faint or dim up to bright. The example below shows variations in the lightness

of a dull (low chroma) middle blue hue.

differences in lightness hue and chroma held constant

Lightness is associated with reflectance or

average luminance factor judged against the

reflectance of a white standard (diagram, right), and this contextual "white" anchor

makes lightness a related color attribute. An arbitrarily defined "white surface" is actually the

benchmark that is used to compute correlates of lightness from the measured luminance of

illuminance of a colored surface. Perceptually, a "white" standard somewhere in view is not

essential in order to see lightness differences; we usually have a secure sense of the amount

of light falling on surfaces, and our luminance

adaptation to the light, because of the variety of surface reflectances within a scene.

Brightness and lightness are correlated with the

luminance of a surface or light source. This

means that brightness and lightness usually go up or down as the color luminance goes up or

down, but whether and by how much depends on the viewing context. Let's first review the

relationships among context factors and then summarize how they affect brightness/lightness

perception. (An expanded version appears in color in the world.)

context factors creating the perception of

brightness/lightness

lightness equated with the

proportion of light reflected

in comparison to a white

surface under the same

illumination

We perceive physical environments because of the light incident on material surfaces, which

depends on the source intensity or illuminance of the light source. The

illuminance is the luminous intensity of the light source reduced by its distance from the

illuminated surfaces. Averaged across all directly lit surfaces, this is the scene

illuminance.

Illuminance is separate from the source image

or luminance of the light source, which depends on the source intensity, its distance,

and its visual size from our viewpoint. An extended, diffuse light source, such as an

overcast noon sky or ceiling light panel, can

provide substantial illuminance but, as a source image, appear very dim. This is because, at

equal illuminance, luminance increases as the visual size of the source image gets smaller:

an incandescent filament has much greater luminance than a light panel.

Environmental surfaces reflect more or less light depending on their surface reflectances.

The combination of scene illuminance, shadows and surface reflectances defines the surface

luminance range — the variations in the brightness of the physical enviroment. This is

the anchor of luminance adaptation for two reasons: the luminance of surfaces is constant

across distance (as with lights); and, for diffusely reflecting surfaces, luminance is not

significantly affected by the angle of view or the

angle of incident light.

Exactly how luminance adaptation occurs is not clear, but it apparently requires three

simultaneous adjustments in the visual response: (1) a receptor gain adaptation to the

average scene luminance (the adaptation

gray, Lg,equivalent to a reflectance of about

13%), (2) a cognitive lightness anchoring that links the highest surface reflectance (no

more than 5 times the adaptation gray) to the

perception of "pure white" (the adaptation white, L

w), and (3) a perceptual expansion or

contraction of the lightness range so that a

surface presenting a luminance of about 1/5 of

the adaptation gray is perceived as black (the adaptation black). As a result, color areas

with luminances within the range Lw to 1/20L

w

are perceived as objects varying in

lightness, or color with some gray content.

The lightness range orphans many specific color areas that have greater luminance than the

adaptation white, including areas of spot

illumination (sunlight falling on the floor through a window), gloss or specular

reflections, and secondary or primary light sources. These appear as lights varying in

brightness, or color with some brilliance content. A stimulus darker than the adaptation

black is invisible unless silhouetted against a lighter background, where it appears as a void.

Brightness and lightness are both necessary to perceive the total range of luminances, from

voids to source image, that can appear in

physical environments.

Brightness perceptions are powerfully affected by the level of luminance adaptation and the

luminance of the surrounding area. Lightness perceptions are remarkably consistent and

stable, provided all surfaces are under the same

illuminance; but lightness differences can be powerfully affected by the perceived spatial

geometry of material surfaces and light sources, especially when these define the

perception of average luminance, spot light and shadow.

Within this general context description, the brightness/lightness of a color area depends

on:

• Luminance adaptation. The visual

adaptation to light intensity sets the perceptual boundary between surface lightness and light

emitting brightness, and sensitivity to luminance differences within each range.

In most environments, the anchor for light

adaptation is the average quantity of light

reflected from surfaces — the scene luminance range — which is actually the reflected image of

the scene illuminance. For both surfaces or lights of constant luminance, brightness

decreases as light adaptation increases, and conversely brightness increases as dark

adaptation increases. The lights and colors of a film appear dim as we enter the theater but

brighten after our eyes become adapted to the dark, though there is no objective change in the

luminance levels of the film. Even "gray"

sidewalks or building walls have a high

brightness, and automobile colors appear more vivid, as we exit the movie matinee, but these

effects are muted as our eyes adjust to the light. In the same way, emitting lights appear

to grow dimmer, whites appear brighter, surface colors appear more chromatic, and the

contrast among whites, grays and blacks is greater, as scene illuminance increases,

although these effects partially disappear as we adapt to the new illuminance level.

Under mesopic or scotopic vision (dark adaptation) we also experience a sensory

change in the appearance of lightness: lightness contrast declines and "white" surface

appears perceptually to be gray, as compared

to the memory color of a white surface under photopic illumination. Under scoptopic vision

only light emitting sources (such as the moon) appear perceptually as a "pure white".

• Luminance Contrast. Lightness and

brightness are local contrast judgments, not

direct perceptions of light acting on the retina. So the relationship between a color's luminance

and its perceived brightness or lightness is strongly affected by the visual context.

The key factor is relative luminance contrast.

The light emitting or "brilliance" quality of

brightness is perceived in color areas with 2 or more times the luminance of a white surround,

or roughly 40 times the luminance of a dark gray or black surround. Lights appear brighter

in relative darkness because of the substantially reduced surround luminance and lower

luminance adaptation. And brightness contrast is increased if the brighter color area is made

visually smaller, even when the contrasting color areas are surfaces of constant reflectance.

At night a flashlight appears "bright", and "brighter" than a candle, because the contrast

is with a dark surround a dark adaptation; under a noon sun, both the candle and

flashlight are invisible, because they produce a

negligible luminance increase in relation to the average surface luminance and the eye's light

adaptation. "Bright" also describes specular reflections that are visually much smaller than

the source image, and surfaces whose luminance exceeds the current adaptation white

due to spot illumination.

The reverse is true for lightness: lightness contrast increases with increasing

illuminance (the Stevens effect). More gradations of lightness become visible, and the

visual contrast between lightness intervals appears greater; whites appear brilliant and

darks appear deep black. Lightness contrast is quite pronounced under noon sunlight and

becomes softened or muted at twilight. As illuminance decreases, the visual contrast

between lights and surfaces becomes more

extreme, and even very dim lights acquire brightness. Hence the filmmaker's trick of day

for night, which creates the illusion of night by shooting daylight scenes under reduced

exposure, darkening the image luminance and reducing the image contrast.

So long as the pattern of lights and darks on a

surface remains the same, then lightness appears constant across changes in

illuminance (diagram, right). This is because

lightness perception only depends on surface reflectances (surface luminances) relative to

each other or as a proportion of white. The black print in a book reflects about 10% of the

incident light, and the white paper about 90%, defining a ratio of 1:9; these proportions and

ratio do not change if the quantity of incident light (the illuminance) is increased or

decreased, so the perceived lightness is constant.

A restricted range of luminance contrasts usually creates the lightness scale of grays. It is

sometimes claimed that we cannot see the color "gray" in lights, but this is belied by the grays

in the diagram at right, which are generated by

the pixel sized lights in your computer monitor. We cannot see gray in lights viewed in isolation

or as recognizable sources of illumination; the lights appear veiled or dim instead.

Lightness and brightness are complementary

regions on the luminance dimension: normally

lightness masks direct perception of brightness, and vice versa. The "blacks" in a

television picture have the same absolute luminance (brightness) as the "gray" monitor

screen when the television set is turned off: they produce a black color in the video image

through contrast with higher luminance pixels around them.

context differences

between brightness (left)

and

lightness (right)

Lightness is substantially affected by the contrast between a color area and its surround.

The lightness of a color area can change, sometimes radically, depending on the lightness

of surfaces that are visually next to or behind it (simultaneous contrast). In particular, a dark

background or surrounding color will make a color area appear lighter; a light valued

surround will make the color appear darker. A classic example is the full moon in either the

day or night sky, which appears white although

it is actually very dark (its albedo, equivalent to its reflectance, is 7%).

Finally, as the "radiance" visible on surfaces or

from the source image of lights, brightness

signals a change (contrast) in illuminance or luminance across space, time or context.

Relative luminance differences are perceived as constant lightness patterns across changes in

illuminance, but they are perceptually compounded of a fixed quantity (reflectance)

and a variable quantity (illuminance). In particular, brightness is the sensory token

(the conscious attribute) for (1) a luminance perceived to exceed the lightness range, or (2)

a illuminance change or contrast that requires

an up or down adjustment in the perceptual interpretation of the luminance quantities

associated with whites, grays and blacks. If illuminance is everywhere constant and equal

across surfaces, and we have adapted to the scene illuminance, then we only perceive

surfaces of different lightness; the perceptual quality of brightness is completely absent.

Brightness becomes more salient than lightness

when:

• the scene illuminance changes by a large

amount (the sun comes from behind a cloud; we exit a movie theater)

• the local illuminance changes (we move an object from shadow to light, we turn on a desk

lamp)

• there is a brighter or darker spot illumination

on a surface (cast shadows, volume shadows, a beam of light on the floor)

• we see a surface reflection (the moon on

water, the sun in an automobile windshield)

brightness comparisons

across different grays and

illuminances

are unreliable

• we see a luminous color area against a dark surround, or a void within light reflecting

surfaces.

In all these cases we see light as a distinct

attribute that is more or less separate from surface.

As a result, perceptions of brightness do not

allow a luminance match between surfaces that differ both in lightness (grays) and in local

illuminance. For example, it is difficult to adjust

an indoor spotlight illuminating a light gray paper so that the brightness of the paper

matches the brightness of a dark gray paper in sunlight (diagram, right). The local judgments

of relative luminance under local illumination override the global comparisons of absolute

brightness. (See also the tiled cube example, below right.) However, these brightness

matches are quite easy to do if only the color areas, without any surrounding cues of the

scene illuminances, are visible through small

apertures. • Spatial Interpretation. Relative lightness differences are greatly affected by the spatial

or three dimensional interpretation of an image. This is because the angle of surfaces in

relation to each other, and to the light source, determine the illuminance incident on the

surfaces (which is less for surfaces at a more oblique angle to the light) and in particular the

contrast between light and shadow.

In general, we see illuminated darks as darker

than their actual reflectance, and shadowed lights as lighter than their actual reflectance. In

the example (at right, top), the central "dark gray" tile on the illuminated side of the cube is

the same monitor luminance and measured

lightness as the "white" tiles on the shadowed side, which is evident when all other tiles in the

form are removed (diagram, right, bottom).

The spatial interpretation of illumination

differences between light and shadow, and the apparent match in of surface patterns on all

sides of the object, obliterate a direct comparison of the brightnesses: again,

lightness masks the perception of brightness. The tiles on the shadowed side are perceived to

have a higher lightness because the visual system compensates for the effects of the

lightness judgments

affected by the spatial

interpretation of light

the gray tiles have identical

lightness (L = 60) in both

virtual shadow.

• Spot Illuminance. Finally, the brightness or lightness of surfaces depends on the continuity

of the scene illuminance.

In most cases of spot illuminance (a local area

of increased illuminance), the visual system registers the absolute increase in luminance as

an increase in surface brightness. (Refer to this discussion for the distinction between relative

and absolute luminance changes.) Similarly, a

local are of reduced illuminance is perceived as a shadow. We don't see patches of sunlight

through leaves as white spots on the ground; we see them as brighter versions of the same

lightness visible in the surrounding shadows.

A surface can appear mysteriously darker or

lighter than it normally appears if we cannot perceive the relative illuminance difference in a

visual comparison. If we are sitting in a dark room, and see the sunlit asphalt pavement

outside through a narrow opening in a curtain, the pavement can appear white or light gray

rather than black. In the same way, a black paper hung in complete darkness and

illuminated by a narrow beam of intense light will appear quite white, so long as nothing else

in the room is visible. Its appearance snaps to

black if a gray or white surface is also placed in the beam of light.

It is even possible to contrive situations in

which the spot illuminance cannot be

perceptually separated from the spatial definition of surface patterns or surface edges,

or attributed to visible light sources or cast shadows in the scene. For example, a beam of

light or shadowing form can be arranged so that the edges of the light or shadow

corresponded exactly to the edges of a single white or black tile in a checkerboard floor. In

that situation the discrepant surface luminance will appear as an isolated gray tile, or — if the

spot illuminance change is large enough — as a

square light source embedded in the floor, or as a square hole.

Terminology. Artists usually talk about a

painting without concern for the lighting of the situation where it is viewed, and they interpret

landscape values into paint values that will

appear under different kinds of illumination. For

images

those reasons, the related color judgment of lightness (or the artists' term, tonal value) is

the concept to use when discussing works of art; brightness should be used to describe the

landscape, studio or gallery lighting.

Hue. This is the most familiar color attribute,

the one that answers the familiar question, what color is it?

Hue is identified by a categorical basic color

name such as red, yellow, green or blue; or a

compound of two basic names such as yellow green; or a secondary color name such as

orange. The example below shows several different hues of equal lightness and hue purity.

differences in hue chroma and lightness held constant (colors of equal

nuance)

Hue is usually associated with the average or strongest wavelengths in the light spectrum,

regardless of the total range of wavelengths present in the stimulus (diagram, right). As the

language categories for hue are imprecise and inconsistent, hue is often described by

matching it to the color of a monochromatic light, denoted by its wavelength. This is called

the dominant wavelength of the color: the dominant wavelength of yellow is 575 nm.

However, monochromatic lights change hue slightly if their brightness or chroma changes

(as discussed here), and can shift substantially in contrast to other hues around

them (as discussed here). So the match between a specific hue and a spectral

wavelength is relative to the viewing context.

That is, any color stimulus can be described by a dominant wavelength, but the dominant

wavelength does not define the appearance of the color stimulus in all situations.

If many wavelengths are involved, the hue is

determined as the average or geometric mean

of all the wavelengths on a chromaticity

hue equated with the

dominant

or "average" wavelengths

of light

diagram, not on the linear spectrum. That is, the hue created by a mixture of "red" and

"violet" light (at the ends of the spectrum) is not green (in the middle of the spectrum) but

purple (outside the spectrum, but between red and blue on a hue circle). For these

extraspectral hues, the dominant wavelength is the complementary color ("green"

monochromatic light) that exactly neutralizes the color mixture, denoted by a "c" placed

before the wavelength number. The dominant

wavelength of magenta is c530 nm.

As this matching procedure implies, hues are limited to spectral (prism) colors and the

extraspectral mixtures of spectral "red" and

"violet" light. In English these hue names are magenta, red, orange, yellow, green, cyan, blue

and violet or purple; compounds of these names such as blue violet or yellow green; and

specific names for saturated colors such as scarlet, orange, chartreuse or turquoise.

Hue specifies the location of the color around the circumference of a hue circle, not any color

location toward the center. Names of dull or muted colors such as white, gray, black, brown,

maroon, pink, tan, gold, russet, olive and so forth do not describe spectral colors, and this

rules them out as hue names, even though they may be appropriate answers to the question,

what color is it?

Even so, artists should learn the correct hue

designations for dull colors. "Brown" for example is technically a near neutral, dark

valued orange with a dominant wavelength around 610 nm; "olive" is an dull, mid valued

yellow with a dominant wavelength around 570 nm. You will never be comfortable

describing your coffee as dark orange and your

martini olive as dark yellow, but that is what they are; and accurately recognizing the hue of

any surface color will help you to mix that color using a color wheel and to understand how

the color is likely to change appearance under different types of lighting or from light to shade.

Hue is an attribute of both unrelated and related colors. We can easily identify the hue of

traffic lights at any time of the day or night, and we can judge the hue of any surface provided

that we know whether the illumination is bright or dim, and "white" or tinted.

In general, apparent hue remains constant across wide changes in daylight illumination.

In particular, changes in the sun's light from morning to afternoon, or in cloud cover, don't

significantly affect hue perception. However, the contrast between similar hues, and their

saturation, does appear to increase as illumination increases, and under dark

adaptation (at night) hue perception in surfaces disappears, though we can see hue in lights

(such as the planet Mars and distant traffic

lights).

Reliable hue recognition can go awry in several unusual or extreme situations: (1) the surface

is viewed without surrounding colors and

without an accurate idea of the intensity and color of the light source; (2) the viewer has

been adapted to one colored light source, and the illumination changes to another color or to

white; (3) the hue is viewed in contrast to adjacent color areas of strongly different color

and brightness; (4) the illumination has an intense (pure) color; (5) the spectral power

distribution consists of a broken spectrum that emits only a few wavelengths or many

wavelengths at very different intensities; (6)

colors are viewed at extremely high luminance levels that saturate or overwhelm the

photoreceptor cells; or (7) colors are viewed through a positive or negative afterimage.

Most of us are familiar with the grossly

distorted automobile colors that appeared

under yellow sodium vapor lights, or the dulling effect of fluorescent lights on reds and yellows.

Abrupt changes in lighting color, for example when we step from daylight into the red light of

a photographic darkroom or bar, produce especially inaccurate hue judgments. Color

distortion is obvious in surface colors around sunrise or sunset, but this effect is familiar

enough, and sufficiently minimized by discounting the illuminant, that it has a

trivial effect on hue recognition.

Terminology. Artists use both unrelated and

related color judgments to determine the paint mixtures needed to match colors in the

environment. Related color judgments refer to the "true" or local color as it would appear on a

normally lit surface (which is how artwork is

typically displayed), even when we see the surface under unusual lighting conditions.

Monet's advice, that the artist simply match the hue of a retinal color patch, means a painter

should ignore local color and instead match the hue as it appears under the influence of any

contextual factors.

Hue Purity. The third and last colormaking

attribute is the clarity or intensity of hue, again where hue has the limited meaning of

monochromatic spectral colors and extraspectral mixtures.

Hue purity ranges from intense or highly chromatic for pure hue sensations to neutral or

achromatic for completely colorless (white, gray or black) sensations. However it is common to

find a very chromatic color (such as a "blue" monochromatic light) described as saturated,

pure, bright, brilliant, rich, vivid, luminous or glowing, and an achromatic or near neutral

color as unsaturated, impure, dirty, dull, dead, veiled, dark, pale, whitish or subdued.

The substantial overlap in the adjectives that describe chroma and brightness (and between

both of them and the adjectives that describe vitality and intelligence) signifies the sensory

and "moral" similarity between the two. However it is a parallelism rather than a

polarity: chroma has its null state (gray) and

brightness its null state (darkness). They are otherwise polar opposites: luminance is a

broadband quality while chroma is targeted to spectral subunits; the most saturated

possible hues, spectral lights, appear black if viewed as surface colors; and a strong

luminance contrast by itself can produce both a high chroma and a luminance color

perception.

The example below shows variations in the

chroma of scarlet at constant hue and lightness.

differences in chroma hue and lightness held constant

Hue purity is the most fascinating and

problematic colormaking attribute. Whereas hue is an unambiguous percept that can be

associated with a precise physical property (wavelength), and brightness is a somewhat

complex percept associated with a precise physical property (radiance or luminance), hue

purity is at once the most striking color property in its pure form and the property that

is most difficult to define in terms of specific stimulus attributes. In fact, many definitions of

hue purity are obtained as the residual

dimension in a geometrical color model: hue purity is whatever remains after brightness and

hue are accounted for.

For these reasons, hue purity has gone by

many names — Sättigung, colorfulness, chromaticness, chroma, saturation, excitation

purity, colorimetric purity, chromatic content, brilliance — each defined in relation to a specific

stimulus attribute or color viewing situation. For now I use hue purity to refer generically to the

vibrancy or intensity of a hue, but give the term a specific definition at the end of this section.

The three related definitions of hue purity current in the color research literature are:

1. Colorfulness is the attribute of a visual

sensation according to which the perceived

color of an area appears to be more or less chromatic.

2. Chroma is the colorfulness of an area

judged as a proportion of the brightness of a

similarly illuminated area that appears white.

3a. Saturation is the colorfulness of an area judged as a proportion of its own brightness.

These perceptual definitions of hue purity, despite the obscurities, highlight the sibling

relationship between hue purity and brightness as color sensations. This is an issue addressed

when we consider the context factors that affect perceptions of hue purity.

Stimulus Definitions of Hue Purity. First, let's consider the physical side of color

psychophysics: what is a good color stimulus definition of hue purity?

Start with lights. We know that the most

saturated physical stimulus possible is single

wavelength (monochromatic) light, and the least saturated physical stimulus possible

("white" light) is the approximately equal mixture of all wavelengths across the entire

visible spectrum. So the logical first step is to define hue purity as the spectral breadth of

the elevated part of an emittance curve: hue purity is the number of different wavelengths in

the spectral power distribution of the light (diagram, right). By this principle, a low

saturation color stimulus reflects or emits

wavelengths across a large part of the spectrum. As wavelengths become

concentrated within a single, narrow span of the spectrum, the color's hue purity increases;

but as this happens, invariably, the brightness of the color area decreases.

The problem with the "wavelength purity" definition of hue purity is that the eye does not

respond equally to the "breadth" of wavelength mixtures. The span of "red" wavelengths

labeled "medium" in the diagram would appear just as saturated as a single wavelength of

"orange" light, because the "red" wavelengths do not lose hue purity when mixed. In contrast,

if the "medium" span of wavelengths were

centered on the "yellow green" wavelengths, the resulting mixture would appear desaturated

almost to "white". Emittance and reflectance curves do not represent these quirks of color

perception, so hue purity cannot be inferred from the "wavelength purity" of the color

stimulus.

A second solution: define hue purity in terms of

a standard light mixture. Hermann von Helmholtz, the 19th century surveyor of

colormaking yardsticks, proposed that Sättigung was the proportional mixture of

"white" and pure monochromatic light. This confines all hue purity measures to a single

wavelength standard, creates a constant hue purity "ruler" (a mixing line between 0% at

"white" and 100% at the pure spectral hue),

and defines a practical method to manipulate hue purity in a color vision experiment (mix

"white" and single wavelength lights of equal brightness). Best of all, this method matches an

observer's experience of colored lights, which always appear to whiten as they are

desaturated.

But on the perceptual side there is a fatal

hue purity defined as the

breadth of an emittance

profile

problem with Helmholtz's approach: spectral hues do not create equal sensations of hue

purity. "Yellow" monochromatic lights have a whitish, pale color and a weak tinting

strength when mixed with "white" light; "violet" monochromatic lights are dark,

extremely intense, and very potent at tinting "white" light. These examples reveal that the

perceptual mechanisms that define the sensation of hue purity are not anchored on the

saturation range of lights. Some perceptual

standard other than "spectral purity" is necessary for viewers to say that saturated

"yellow" light, the most saturated yellow light possible, is still not very saturated.

Colorimetric Definitions of Hue Purity. We

clarify these problems by turning to the chromaticity diagram of a uniform color

space, for example CIELUV (diagram, right). This shows that the "yellow" to "red" spectral

hues lie along a straight line, and therefore

retain spectral hue purity when mixed; it shows that "green" spectral hues are bowed, which

brings their mixture closer to the achromatic white point (WP). It also shows that the

distance from the white point to the spectrum locus of "yellow" (Y) is quite small, indicating

that the light appears pale or whitish; while the distance from the white point to spectral "blue

violet" (B) is quite large, indicating that the light appears very intense. (Recall that these

variations in spectral saturation arise in part

because the overlap in cone fundamentals across the spectrum, and in part from the

different proportions of cone types in the retina.)

So we have a third solution: hue purity is the chromaticity distance from the white point

to the color in a chromaticity diagram, in which by definition all colors have equal

luminance. This is an alternative definition of chroma in unrelated colors:

4. Chroma refers to the attribute of a visual sensation which permits a judgment of the

amount of pure chromatic color present, regardless of the amount of achromatic color

(CIE, 1982).

This is a sensible definition in terms of an

established color model or color space, as it creates concentric circles of equal chroma

chroma vs. excitation purity

in the

CIE u'v' chromaticity

diagram

colors C and c, or Y and y,

have equal chroma but

unequal excitation purity;

colors Y, C and B have unequal

chroma but equal (maximum)

excitation purity

centered on the white point (diagram, right); as brightness or lightness go up or down, the

circles become concentric cylinders centered on the achromatic gray scale. But it is a peculiar

peceptual definition: if color is salt and achromatic content is water, it amounts to

saying that you can taste that there is one tablespoon of salt in a glass of water, a bucket

of water, or a swimming pool. Indeed, as more "white" light is added to a stimulus of constant

chroma, the saturation appears steadily diluted.

In any case, we now see that Helmholtz's Sättigung points to yet another definition of hue

purity that requires a color model for its

measurement:

5. Excitation purity refers to the chroma of a color area judged as a proportion of the chroma

of the monochromatic hue of the same brightness and dominant wavelength.

So the chromaticity plane or chromaticity diagram in a color model is used to define the

chroma of the spectrum locus at a given luminance or lightness, and the chroma of the

stimulus is divided by this hue specific quantity. As a result, excitation purity and chroma will

yield very different estimates of hue purity,

depending on the hue of the color (see diagram caption, above right).

Context & Hue Purity. Unfortunately, a

chromaticity diagram is a map of color

sensations, a map that depends on the way we define receptor responses to light and on our

assumptions about how cone outputs are combined and weighted in color perception. In

short, we are still not talking directly about color perception, the psychological side of

psychophysics.

This is a convenient pretext to shift the focus

from lights to surface colors. Because in surface colors, hue purity is affected by absolute

luminance and by relative luminance contrast: it is not a fixed property of a color

stimulus but a relative property of the color viewed in a specific context.

First, consider the absolute luminance of a color

area. The diagram (right) illustrates the

parallels between colorfulness/brightness and

chroma/lightness. At low illuminance, a red color appears relatively dark and subdued, but

as its luminance — the illuminance, for surfaces; the luminous intensity, for lights — is

increased, the colorfulness of the color also increases (the Hunt effect). Colorfulness

increases with increased color luminance, from very low to very high light levels. The Hunt

effect combines with the Stevens effect to produce an overall impression of increased color

vibrancy and contrast. Thus, a floral

arrangement looks more colorful in sunlight than in shadow, and hawaiian shirts produce

the best effect on sunny days.

However, across the normal range of photopic

(daylight) vision (excepting extremely bright surfaces or lights), chroma and saturation

are constant across changes in illuminance provided that all color areas in the scene are

equally illuminated. This is embedded in the definition of chroma as the colorfulness of an

area judged as a proportion of the brightness of a similarly illuminated white. As illuminance

increases, the colorfulness increases, but so too does the brightness of a white area; the ratio

between them remains constant. In the diagram

(right), the surrounding black or white areas, which appear to be similarly dark and only

slightly contrasted under low illuminance, become more highly contrasted under high

illuminance (the Stevens effect); but the red also increases in colorfulness in relation to the

brightness of white, and color contrasts increase to match the increased contrast across

lightness gradations. The result is constancy of the chroma.

Next, consider the relative luminance contrast between the color area and its surround:

increasing color luminance or decreasing surround luminance increases

colorfulness, chroma and saturation. (This was studied by Ralph Evans under the rubric of

brilliance.) The diagram below illustrates the

basic effect.

context differences

between colorfulness (left)

and chroma (right)

luminance contrast effects on hue purity

In this example, which only hints at the actual

impact of environmental luminance contrasts, the violet and magenta color areas each have a

characteristic luminance (CIELAB lightness L*) at maximum chroma, as shown in relation to

the adaptation white or black at left. Each color is shown (center) within a surround of matching

lightness, and then (right) within a surround

that is of a higher lightness (for the magenta) or of lower lightness (for the violet). Although

the effect is small, you should see the violet in the darker surround as more saturated, and the

magenta in the lighter surround as less saturated.

What's more, the contrast between a surface color and a brighter surround induces a quality

of "blackness" in the color that does not appear in colors perceived as isolated lights or

as surfaces brightly lit within a dark surround. Gray and some unsaturated "warm" colors

(such as olive, brown or maroon) only live within the limited luminance contrasts that

produce the appearance of blackened surface colors. Lights viewed against a dark background

do not appear gray or brown but instead as dim

white or orange lights.

In general, provided the color luminance remains constant, minimizing surround

luminance increases colorfulness. Or, if the

illumination on a color area is selectively increased while surrounding color areas are

kept at reduced illumination, the colorfulness of the color area increases. This is a gimmick

widely exploited in "tourist trap" art galleries: by illuminating individual paintings with tightly

vignetted spotlights, in a gallery space that is otherwise dimly lit, the colorfulness and

lightness contrast in the paintings is artificially increased.

Now, it is possible to eliminate most or all of the distorting contrast effects in surface color

displays by viewing them against an achromatic background of the same lightness. This yields a

definition of saturation that is specific to surface colors:

3b. Saturation is the colorfulness of an area judged in relation to an achromatic (gray) area

of equal lightness.

The robustness of this saturation as a

perceptual judgment is that any perceptible difference between the color area and the

surround is, by definition, entirely due to the colorfulness or chromatic intensity. Shown

below is the original red chroma series against an achromatic background of matching

lightness:

differences in saturation hue and lightness held constant

Unfortunately, equating the brightness of monochromatic colors (heterochromatic

brightness matching), or sorting Munsell

color chips into their correct lightness (value) and chroma locations, are perceptually difficult

tasks, where even practiced viewers can give inaccurate and inconsistent results. The reason

is that hue purity appears as a kind of brightness. This is apparent in the red color

series above: the intense red does not seem merely purer than the grayed colors, it seems

brighter or glowing, as if hue contained a chromatic luminance.

Brightness, Whiteness & Hue Purity. Finally,

we can return to the three definitions of hue purity quoted above, and examine the specific

color judgment they specify.

Colorfulness is (like brightness) an unrelated

color attribute, and like brightness it is related to the luminance of the color. To judge hue

purity, a viewer must be able to perceive the colorfulness and the brightness of a color area

as distinct attributes.

perceptions of brightness in hue purity

judgments

In the "colored light" example (above, left), a viewer can judge the saturation of a color

viewed in isolation because brightness and colorfulness are distinct and unambiguous

qualities of the color sensation. The color can be made brighter by adding white light or by

increasing the source luminous intensity, and each has a different perceptible effect on the

colorfulness — the whiteness is perceived as

diluting the colorfulness.

In the "colored surface" example (above, right), colorfulness and whiteness are again distinct

qualities of the color sensation, but its

brightness is now problematic. What part of the chromatic luminance is due to the color's

chromatic intensity, and what part to the illuminance or the absolute intensity of the

incident light? To resolve the ambiguity, the viewer must judge the illuminance by viewing

its undimmed reflection: this is the function of the "brightness of white" in the definition of

chroma. The viewer takes the colorfulness of

the color, and separately the brightness of the white, then combines these qualitatively

different perceptions to judge the chroma of the color. (Implicitly, the white standard is only

chosen after chromatic adaptation to light source, so that the effect of colored light on

colored surfaces is also taken into account.)

As explained earlier, chroma is actually derived

from the measurement conventions inherent in chromaticity diagrams (or tristimulus values),

and the definition of chroma stated above is really a description of chroma measurement

inherited from colorimetry, not a description of color perception.

However, we easily judge hue purity without a white standard, or even a gray standard, in

view. We survey the relative luminances of neighboring surfaces and then anchor an

environmental lightness scale within that context.

This process appears to depend on luminance contrasts (in lightness anchoring), on the

spatial interpretation of the scene, and on memory color — so that, for example, one can

adjust the brightness and contrast on a television image until it "looks right", regardless

of whether the video image is of a sunny or

cloudy day, in color or in black and white. We see through thousands of environmental

variations in illuminance, as we walk from one room to another, look at objects close to or far

from a window, perpendicular or slanted to the light, in light or in shadow.

Because relative lightness remains constant across changes in illuminance, a color's

chroma (relative colorfulness) and saturation (chroma divided by lightness)

also remain constant across changes in illuminance. The saturation of a surface in

shadow is the same as its saturation in bright light.

Optimal Color Stimuli. At this point we can address a new objective: whether it is possible

to define a measure of hue purity that (1) applies specifically to surface colors rather than

light mixtures; (2) is standardized on the maximum possible hue purity for any surface

hue, luminance contrast or absolute illuminance

level; and (3) has a verifiable perceptual

validity, in the sense that colors determined to be at "maximum hue purity" really appear to be

so. This can be achieved by using optimal colors as the perceptual standard of maximum

hue purity.

Recall that the maximum hue purity for light

colors is defined by a monochromatic light chosen from the spectrum locus at the

dominant wavelength of the hue. Spectral lights are the most saturated color stimuli possible,

which means the spectrum locus can be used to define the excitation purity of colors in a

chromaticity diagram or in a Helmholtz Sättigung setup.

However, the maximum hue purity for surface colors has a very different perceptual status,

because luminance contrasts are involved. As surface colors become more and more

saturated, they eventually reach a point where the chromatic luminance no longer appears to

increase: instead the color appears to glow or

fluoresce and then, transform into a light. The basic form of color appears to change. This

zero grayness boundary provides a useful benchmark for maximum hue purity.

These perceptual boundaries, where surface

colors reach the maximum possible hue purity without a fluorescent appearance, can be

equated with optimal color stimuli or MacAdam limits (after David MacAdam, who

developed the concept in 1935 from ideas

advanced earlier by Rösch and by Schrödinger). These satisfy criterion 1, above.

Optimal color stimuli are not actual surfaces or

color samples, but theoretical reflectance profiles that meet two requirements:

• reflectance is either 0% or 100% at every wavelength

• the transition from 100% to 0% reflectance (or the reverse) occurs no more than two times

across the entire spectrum.

These profiles can take only three possible

forms (diagram, right): (A) the color created by an isolated spike or block of reflectance inside

the spectrum (which requires no arbitrary spectrum limits); (B) the color created by a

block of reflectance at either end of the

optimal color stimuli

the three possible profile

forms;

in each case the widths "w"

can be

any size up to the total

spectrum

spectrum (which requires an arbitrary spectrum boundary in either the "red" or "violet"

wavelengths); or (C) the color created by two cliffs at opposite ends of the spectrum (which

requires arbitrary spectrum limits in both the "red" and "violet" wavelengths). In all cases,

the width w represents the reflected wavelengths that define the luminance and

chromaticity of the color area.

Note that no physical substance can absorb or

reflect 100% of the incident light at every wavelength, so optimal color stimuli cannot

exist as physical surfaces. But we've seen that hue purity is dependent on luminance

contrast, so it possible to simulate the

appearance of a MacAdam color in a surface or object (for example by illuminating a patch of

highly saturated paint with a vignetted spot of intense white or chromatic light), and to use

this optimal simulator to represent the physical standard of chromatic intensity in a perceptual

color matching task. The MacAdam limits represent theoretical or ideal colors, but the

perceptual boundary they represent is quite real (criterion 3, above).

In all the idealized profiles the width w is arbitrary. This width affects the luminance

factor of the surface (and therefore its perceived lightness) and its chromaticity (as a

location in a chromaticity diagram). By incrementally increasing the width w in the

reflectance curves, and incrementally moving

each profile across the entire spectrum, a complete inventory of optimal color stimuli can

be generated. These define the hue purity limits of surface colors at every hue and lightness

(criterion 2). In the diagram below, the location of the optimal colors in the CIE u'v' uniform

chromaticity scale diagram, for specific lightness levels, are connected across all hues

to form optimal color boundaries.

width, and for "B" the width

can

be from either end of the

spectrum

optimal color boundaries for surfaces of

different lightness in the CIE UCS diagram; numbers indicate the lightness

of colors at each boundary; from Perales, Mora, Viqueira,

de Fez, Gilabert & Martinez-Verdu (2005)

The shrinking area of the boundaries shows that an increase in lightness causes a

proportional decrease in the maximum possible chroma. A single reflected wavelength would

represent less than 1% of the incident light and

would appear extremely black — yet it is also the surface with the maximum possible hue

purity! If all wavelengths are completely reflected, the surface will appear a bright,

luminous white.

Note that hue alters the link between

lightness and MacAdam limits. Hues in the circuit from green through blue, violet and

magenta to red contract toward the equal energy white point (EE) roughly in proportion to

lightness: any of these hues at 50% lightness is limited to a chroma that is roughly halfway

between the white point and the spectrum locus. But this is not true for hues from yellow

green through scarlet red: a yellow or orange can have the same hue purity as a spectral hue

at any lightness from 0% to 70%. For object

colors from yellow green through scarlet, hue purity is effectively uncoupled from lightness at

moderate to low lightness values. This implies that it is perceptually possible to see a brown

or ochre as an "intense" or "rich" color. (It also may indicate why the unsaturated color

zones, which separate saturated from unsaturated colors based on lightness contrast

alone, are perceptually important for these "warm" hues.)

As we're talking about surface colors, it is more

meaningful to show the optimal color boundaries in a color appearance model

designed for surface colors, for example the

CIELAB a*b* plane (diagram, right). Now the optimal colors, across all levels of lightness,

mesh to form a wedge shaped "basket" extending from a diagonal keel along extremely

dark purple (lower left) upward into blue, green, red and yellow, then closing at the top to form a

narrow crest extending from greenish yellow to white. For comparison I've inserted the CIELAB

location of common watercolor pigments and outlined, in white, the watercolor gamut.

Now a color's hue purity can be defined by a line drawn from the achromatic point through

the location of the color on the CIELAB plane and extended to the optimal color boundary of

equal lightness. This yields two CIELAB chroma

values: for the paint and for the optimal color of matching lightness and matching hue angle.

This yields a measure of hue purity relative to the maximum possible for a given hue at a

given lightness:

6. Hue purity refers to the chroma of a surface

color as a proportion of the maximum possible chroma [MacAdam limit] for a surface color of

matching lightness and hue angle.

As with excitation purity, this procedure standardizes the MacAdam limits so that they

are equally far from the achromatic center at all

levels of lightness and across all hues (that is, the wedge shaped enclosure is morphed into a

cylinder whose axis is a gray scale). If we ignore differences in lightness as a separate

("independent") dimension, the cylinder collapses along the grayscale to form a color

circle. The hue purity of surface colors is then their distance from the center of a circle of

maximum hue purity, as shown below for 130 common watercolor paints.

optimal color boundaries

on

the CIELAB a*b* plane

watercolor gamut in white;

hue purity is defined as

HP = Cpaint

/Cmax

where C is chroma on the

a*b* hue plane

chroma and hue purity compared hue purity standardized to unit radius; CIELAB chroma

markers inserted for comparison, with chroma rescaled

so that chroma and hue purity are equal for hansa yellow

(PY97). (For table of hue purity values, see this page.)

Obviously this procedure destroys the geometry of the CIELAB a*b* plane, with one exception:

the hue angle remains intact. So the diagram superimposes the original CIELAB chroma

markers over the hue purity values, scaled so that the chroma and hue purity of bright yellow

(where lightness differences have the least effect on MacAdam limits) are the same, and

connects the hue purity and chroma markers with a line. This allows comparison of the

relative differences between the two measures

around the hue circle.

The comparison suggests that orange to magenta paints, and blue violet to cyan paints,

should appear to viewers as closer to a pure

hue than their CIELAB chroma values predict. Red oranges should also appear more saturated

than yellow paints or any other paints with the exception of ultramarine blue. Indeed, many

red orange paints achieve more than 80% of the chroma possible in the matching optimal

color, just as a Munsell value of 9 achieves 80% of the possible reflectance for an

achromatic surface. The blues also approach 70% or more of the maximum possible hue

purity, and the disparity in chroma between

reds and blues is altered almost to equality. In

contrast, the hue purity of paints from phthalo turquoise to green gold is consistently below

50%: the most intense green pigments (the phthalo greens) have the same hue purity as a

burnt sienna or iron blue. When I developed this hue purity metric, it seemed idiosyncratic in terms of the CIELAB

chroma scaling. So I was gratified to discover in 2006 that the CIECAM chroma placement of

watercolor paints substantially matches their

locations in these hue purity calculations (separate from the differing estimates of hue

angle in CIELAB and CIECAM). For example, compare the dark blue icons in the diagram

above with the pigment distribution on this CIECAM a

cbc plane. This occurs because the

"basket" of optimal color boundaries is much more regular, and approaches a circular limit, in

the CIECAM chroma and saturation metrics (diagrams, right). This is one reason why I now

use CIECAM as an artist's color wheel. It shows the convergence between my hue purity

metric and modern measurements of saturation.

In fact, hue purity departs from the CIECAM measure of saturation in a significant point: at

maximum hue purity, a viewer can have the perceptual sensation of a surface color that is

pure but not colorful (a "pure pink", a "pure

brown"). This happens because the optimal color boundaries contract toward white as the

color lightness increases, and toward black as lightness decreases, lowering the bar for

"maximum hue purity" in very light or dark colors. The traditional conception of saturation

is chroma divided by lightness, which restricts the "purest" color for each hue to a different

lightness (the lightness with the greatest chroma). But in my hue purity it is possible to

experience a "pure" color at any hue or

lightness: the color would appear as an "ideal" combination of brightness, whiteness and

colorfulness.

In any case, all the definitions of chromatic intensity reviewed here, and evaluated in the

next page, seem reducible to one of three

concepts: (1) the tinting strength of a chromatic stimulus in additive mixture or in

lightness contrast with another color, usually white (Evan's grayness); (2) as the

chromaticity distance of a color from an

optimal color boundaries

on

the CIECAM ab plane

(top) chroma metric,

(bottom) saturation metric;

under EE illuminant, 20%

background reflectance, white

surface

luminance 318 cd/m2

achromatic reference point, either white or gray (saturation, CIE chroma); or (3) as a

chromaticity ratio between the chroma of a color stimulus and the maximum chroma or

saturation possible for that hue, where the maximum is either a physical stimulus

(excitation purity, my hue purity) or an imaginary ideal (colorfulness, NCS pure color).

Terminology. Artists normally work with color relationships in context, and attempt to match

color intensities from the luminance range of a landscape onto the luminance range of a canvas

without regard for the differences in luminance involved. For this reason saturation or

chroma are the most appropriate terms.

Colorfulness can be used to describe the relative color changes observed by changes in

the illuminance level, for example, in the appearance of a painting viewed at higher

lighting levels, or under lights of different color rendering properties.

Are Three Attributes Enough? The final question to address: are more than three

colormaking attributes required to describe surfaces? The answer is, yes and no.

Yes, because color attributes obviously change

according to the overall level of luminance, and

the luminance contrast between color and surround, as we see in our home in the contrast

between early morning and noon light, or in the color change in surfaces illuminated by a shaft

of direct light; and these changes also affect color purity. If we want to describe changes in

color appearance from one illumination context to the next, or between surfaces and lights, or

in an unfamiliar or confusing setting, then five attributes are required.

No, because if we describe lights viewed in darkness or surfaces viewed under daylight

levels of natural illumination, or the color of familiar objects under dim or tinted

illumination, then three attributes are usually

sufficient to describe the color unambiguously. These perceptions are closely attached to our

concept of the "real" colors of unchanging objects, and are closer to color ideas than color

perceptions.

Surfaces can display many other properties

such as gloss, crackelure, texture, grain,

aggregation, opacity, depth, iridescence and pattern, but these are unambiguously surface

or material qualities that are easy to distinguish from color as a global or average

attribute. Three colormaking attributes are the norm because any more are usually

superfluous.

There may be other color attributes reaching

across categories of luminance, hue or color purity that remain unexplored in traditional

color research but are worth further study because they have been important to artists.

One of these is the warm/cool contrast, which I believe emerges from chromatic

adaptation to the color changes of daylight.

Manipulation of the warm/cool contrast is important to the representation of natural light

in landscape painting, and judgments of warm or cool are a convenient and practical way to

characterize comparative color differences in color design and color mixing.

We end up with these five (often three)

colormaking attributes:

the five colormaking attributes

unrelated

colors

related

colorscomments

brightness

relative to light

adaptation level and surround or

background contrast

lightness

lightness = value; independent of

changes in illuminance, but

affected by

surround or background

contrast; white, gray and black are

only visible as related colors

disappears at very low (scoptoic) or

very high (blinding)

These five colormaking attributes

completely define any color sensation: lightness and brightness identify the proportion

of the total illumination that is reflected by a surface; colorfulness and/or chroma describe

the color purity as a proportion of the incident and reflected light; and hue identifies the

average or dominant wavelengths of the light spectral power distribution within the closed

span of a hue circle.

Once again: contextual factors can strongly

affect the colormaking attributes. These three factors must be held constant in order to make

hue

luminance levels;

constant across changes in

illuminance; changes with

change in luminance, with

change in illumination color,

with change in

chroma, or with surround hue

contrast; olive and brown only visible

as related colors

colorfulness chroma

changes with

change in luminance or

illuminance; changes with

surround

chromatic contrast

saturation

equivalent to

chroma for artists' purposes; remains

constant across changes in

illuminance (light to shadow)

excitation

purity

hue

purity

judged by

comparison to monochromatic

hues for lights, optimal color

stimuli for surfaces

accurate color judgments or color comparisons:

• intensity and color of the illumination

• relative luminance contrast with

surrounding colors

• spatial interpretation.

All these phenomena reveal that the

momentary, pixelated retinal image has been extensively adjusted and interpreted to produce

perceptions that are consistent with a lifetime

of visual experience with the real world.

This concluding section looks at the relationships among lightness, saturation and

chroma in terms of traditional painting practice.

How to Judge Chroma. To judge chroma or saturation accurately, the artist becomes

familiar with it in qualitative terms. The trick is to use different perceptual tests for three levels

of chromatic appearance.

• At one extreme — grayed, dull, near neutral

or achromatic colors — the color is difficult to name as a hue. Unsaturated colors are mixtures

of many different wavelengths of light, so the color does not have a narrow, precise location

within the visible spectrum. So the question is whether the surface has a specific hue,

and what that is. Usually the gray appears to be definitely either warm or cool before a

specific hue can be assigned to it.

• At the opposite extreme, when the chroma is

very intense, then the surface hue is quite specific and the best visual cue is how much

the color appears to glow, in comparison to a gray of equal lightness. In paints, this is very

easy to distinguish from the surface gloss. The color has an intensity that seems almost to rise

off the paper. This glowing effect is not related

to lightness: a good quality ultramarine blue applied full strength to white paper has a

pronounced luster when wet, even though the color is quite dark and acquires a whitish

overtone when dried.

painting saturation & value

• For colors at moderate saturation there is a third useful cue: as the chroma increases,

the hue becomes more specific. When John Ruskin wrote that "you shall look at a

hue in a good painter's work ten minutes before you know what to call it," he simply wanted to

say that the good painter's colors are unsaturated. Burnt sienna appears to be a kind

of red orange, but it is not clear whether the color is closer to orange or red.

The chroma or saturation of the color is determined by which test seems most relevant.

If you are debating whether the color is warm or cool, it is very unsaturated; if you know it is

warm but are unsure of the hue, it is

moderately unsaturated; if you know the general hue but not the specific tint, then it is

moderately saturated; if the color presents a specific hue but seems somewhat whitish, dark

or veiled, then it is saturated; if the color appears to glow or shine, it is at maximum

saturation.

Keep in mind that yellow green, the color of

sunlight, is also the color with the smallest perceptual range of chroma, and is the

surface color and light color closest to white. The chroma of yellow paints drops very quickly

as they are mixed with any purple, blue or black; the lightness goes down as well.

Saturated yellows, oranges and reds intermix very well with minimal impact on chroma; blues

and greens tend to darken each other unless

diluted or whitened, and blue will dull almost any other color except purple or magenta.

Chroma, Lightness & Saturation. The next

problem is to understand how chroma and saturation change with lightness or luminance

contrasts. This means the artist know hows to

translate surfaces under light into color changes.

The diagram shows an array of red violet color

samples across the complete range of chroma

and lightness. Lightness or tonal value increases vertically from black (bottom) to

white (top), along equal steps of a gray scale or value scale. Chroma changes horizontally in

equal perceptual steps from achromatic (gray) at left to maximum chroma at right. The

colored rectangles in each row of the diagram are the same lightness; rectangles in each

column are the same chroma.

lightness (L), chroma (C) and saturation (S) for

a red violet hue reduced chroma and reduced light signal reduced

illumination on the surface; this combined effect

produces constant saturation

In this arrangement, lines of equal saturation are represented by a constant proportion or

percentage of chroma in relation to lightness:

saturation = (chroma/lightness)*100

The line S = 100 passes diagonally through the

squares that have equal lightness and chroma,

from black (L =0, C = 0) through a pale purple (L = 7, C = 7). The line S = 200 locates colors

where the chroma is twice (200%) the lightness; S = 50 the colors where chroma is

half (50%) the lightness, and so on.

For a given hue, an illuminated surface has a

specific lightness and chroma. As the surface falls into shadow, the lightness of the surface

decreases down the same column. However, chroma decreases as luminance goes down

under constant illuminance, so the color loses chroma as well, which means the color shifts

leftward across a row in the figure. The combination of these two effects is a diagonal

originating in a pure black value, which is a line of equal saturation for the color.

The diagram below represents in caricature the visual implications of a color change in

lightness, chroma and hue. First look these examples over and consider which ones look

the least and the most convincing as a representation of a shadow on one side of a

dull, moderately light valued red orange sphere.

shadow contrasts in lightness, chroma and

saturation left column: lightness reduced 40%, constant chroma;

middle column: lightness and chroma reduced 40%,

constant saturation; right column: chroma reduced 40%,

constant lightness; middle row: shadow hue = lighted

hue; top row: shadow hue 15° greener; bottom row:

shadow hue 15° redder

The column of spheres at right does not appear shadowed (reduced in lightness) but discolored.

The spheres at left appear shadowed but discolored by the change in hue. The balanced

reduction in lightness and chroma or constant

saturation (middle column) is both the most color neutral and the shadow that shows the

least bias from changes in hue.

The Painters' "Broken Colors". The lightness

of any paint can be altered in one of three ways without altering its fundamental hue. In the

European painting tradition, any desaturating mixture of a pure pigment with another color,

or with white and/or black, was called a broken color, and breaking a color was synonymous

with dulling or whitening it.

In modern terminology these mixtures are

called shades, tints or tones of the pure color, as shown in the figure below for a middle

red.

shades, tones and tints of a middle red

The pure pigment color as raw paint from the tube (or properly diluted when applied to

paper) represents the hue at its maximum chroma and optimal lightness. From that point,

the paint color can be modified by:

• mixing with pure water or a white paint to

raise the lightness up to the value of the paper, or step 10 on a value scale, to produce tints of

the hue

• mixing with a black or dark near neutral paint to lower its lightness close to the darkest value

possible in watercolors, around step 2 on a

value scale, to produce shades of the hue

• mixing with another paint of similar value, either a gray mixture of black and white or a

complementary color, which brings the

mixture color closer to gray; these are tones of the hue.

These changes in lightness and chroma within a

constant hue are typically represented in modern color models as separate "pages" or

sections through the color solid, for example in

the Munsell Book of Color and the Swedish NCS. This presentation mirrors the practice of

altering paints of a specific hue by mixing them with white and/or black paint, a technique

advocated in painting treatises from Alberti to

Chevreul. Here we will look at the color changes produced by these traditional methods

of paint mixing.

Tints. Progressive dilution of a paint with water

produces the tints or lightened, pastel versions of the hue. Watercolor paints can also be

lightened by adding a white paint, such as zinc oxide or titanium oxide, which is especially

effective with very dark or strongly tinting colors. (Note however that mixture with a white

pigment can make some pigments, such as prussian blue [PB27] or dioxazine violet

[PV23] significantly less lightfast.)

Lightening or dilution raises the lightness of the

color. Because white has zero chroma, it follows that tints lose chroma as the lightness

approaches white. In most paints, once the paint has been diluted to its maximum chroma

on paper, any dilution of a paint reduces its saturation by an equal amount: a 50%

increase in value toward white results in a 50%

decrease in paint saturation and chroma.

Note that paints begin to shift toward tints only after they reach their maximum chroma on

paper. For some paints, the dilution needed to produce the maximum chroma causes an

increase in lightness somewhere between 20%

to 50% of the raw paint lightness. This is often the case for very dark paints or moderately dull

paints on the warm side of the color wheel, including: anthrapyramidine yellow (PY108),

all the quinacridone pigments (quinacridone gold PO49, quinacridone orange PO48,

quinacridone maroon PR206, quinacridone carmine PR N/A, quinacridone rose and

quinacridone violet PV19), perylene maroon (PR179), perylene scarlet (PR149), all the iron

oxide (earth) pigments (PBr7, PR101, PY42,

and PY43), dioxazine violet (PV23), indanthrone blue (PB60), the darker shades of

phthalocyanine blue (PB15 and PB16), and both shades of phthalocyanine green (PG7 and

PG36). See the page on the secret of glowing color for details.

Shades. Paints also can be darkened by adding a dark neutralizing pigment such as neutral tint,

payne's gray, carbon black or synthetic black. Darkening a colored paint produces shades of

the hue, and expands the range of color values below the value of the pure paint.

A true black is a pure neutral, so shades lose chroma as the proportion of black in the

mixture increases. They also lose lightness by an equal amount. Therefore the saturation of

the paint should, ideally, remain the same, because lightness and chroma decrease in

roughly equal proportion.

In fact, darkened paint mixtures also lose

saturation slightly, because "black" paints are actually a dark gray, which pulls the color

toward a point above the true black lightness. This causes the mixture to cross saturation

lines as it approaches the neutral color. In perceptual terms, very dark paints typically

seem to whiten slightly as they dry, and this

whiteness acts as it does in tints, to reduce both the chroma and saturation.

If a tinted near neutral is used instead, the

saturation can actually hold constant for paints of similar hue: blue, if payne's gray or indigo is

used; orange or red, if sepia is used; purple, if

neutral tint is used; green, if perylene black is used. In particular, paints named sepia should

not be used to darken blue paints, which are the complementary color the sepia hue, as they

will excessively dull the color; and similarly for the complements of the other near neturals just

described.

Tones. Finally, the lightness of the paint can be

held relatively constant, but shifted toward a neutral gray, by adding a mixing

complementary color of higher lightness or a synthetic black diluted to the same value as the

pure color. This produces tones of the hue.

As with shades and tints, tones lose chroma

as the mixture approaches gray. Tones have approximately the same value as the pure

paint, so the saturation of tones also decreases as increasing amounts of gray (complementary

color) are added.

Mixing complements usually produce a neutral

tone that is darker than the complementary paint, so once a neutral mixture is reached it

must be diluted up to match the lightness of the pure color. Once this is done, tones can create

a complete range of chroma or saturation within a constant hue and lightness.

Hue Shifts. It is common to find that the hue

of the paint mixture changes slightly as it is altered across tones or tints, and especially

across the lightness changes produced by tints. This is both a perceptual and material effect.

The shift is called the Abney effect in monochromatic (single wavelength) lights,

which change hue as increasing amounts of "white" light are mixed with them. The fact that

this effect occurs in light mixtures indicates that it arises in color perception: the y/b and r/g

opponent functions exert different response compressions, which produce different relative

changes in chroma as hue intensity increases or decreases. On an artist's color wheel the

Abney shifts are clockwise for hues roughly

between yellow green to blue violet, and counterclockwise for hues from yellow to

magenta. The effect is largest for blue violet colors, which become violet or purple when

strongly desaturated with "white" light.

In paints, a similar shift is caused by the

differing tinting strength and hue of pigment particles. In general, smaller pigment particles

will have a greater tinting strength and also a different hue (typically yellower) than the

pigment powder as a whole. As paints are diluted with water or white paint, the smaller

particles, with higher tinting strength, exert a greater effect on the color, shifting the hue. On

the artists' color wheel, this shift is usually clockwise for paints roughly from red to yellow,

and counterclockwise for paints from blue violet

to green.

The size and direction of the tinting shift, which is reported as hue shift in the guide to

watercolor pigments, depends on the range of particle sizes in the paint, the hue difference

between small and large particles, and their

relative tinting strengths. In general, the tinting shift overwhelms the Abney effect in paint

mixtures: ultramarine blue and ultramarine violet becomes bluer, not redder, when diluted

with water or white paint.

N E X T : the geometry of color

Last revised 08.01.2005 • © 2005 Bruce MacEvoy

the geometry of color perception

The previous pages have explained three very different methods for

defining a color: (1) the measurement of the color stimulus as a spectral emission or

reflectance curve in colorimetry; (2) the proportional responses to the stimulus by the

L, M and S cones, represented as a chromaticity diagram; and (3) the

subjective description of the color sensation in terms of lightness, hue and hue purity, the

three colormaking attributes. These

methods focus on the physical stimulus, receptor outputs or color sensation,

respectively.

This page describes how these different

aspects of color perception fit together. For example, how is the physical stimulus

(luminance) related to a measure of sensation (brightness)? How can we show that red is

more similar to blue than to green? Does the brightness of a color change as its chroma

increases?

Mapping the quantities of a physical stimulus

onto color sensations is called psychophysics, and it was the earliest form

of color specification. This geometrical approach was innovated by the 17th century

naturalist Isaac Newton, who summarized his experiments in light and pigment mixing as

a hue circle, the first geometrical model of color perception. This evolved into the

painters' many color wheels and is

incorporated into all modern color models.

Another important psychological model was proposed by a physiologist, Ewald Hering, who

tried to deduce the physiology of color vision from subjective color experiences. For several

decades his opponent process theory was

seen as an unsatisfactory alternative to the trichromatic theory, but today both theories

are included in models of color vision.

Hering's model, like Newton's, seems to

assume a mind of geometrical regularity or symmetry. Unfortunately, the functional

relationships between color stimuli, color

color

vision

newton's hue circle

hering's opponent

processes

from cones to colors

the geometry of

colormaking attributes

measuring perceptual

discrimination

luminance

discrimination

hue discrimination

hue purity

discrimination

color attributes

combined

summary of color

geometry

individual differences

in color experience

color & language

receptors and color perceptions are not that simple. Tracking the changes from cones to

colors shows the many complex adjustments that are necessary to create visual experience.

The geometry of colormaking attributes reveals that no single geometry can

adequately unify all the different ways to measure color.

Perhaps the ultimate color description occurs in the translation of color sensations into

color words. Hering's four unique hues have been frequently used in linguistic research in

the hope that the usage of common color words might uncover the fundamental

reference points of human color experience.

One of the most important

aspects of color psychology emerges when we're asked to make judgments of color

similarity.

Color Similarity. If we think in terms of the

visible spectrum, it seems obvious that yellow and green are more similar than red

and green: "yellow" light is closer to "green" light in the spectrum band. Spectral closeness

seems a reasonable way to judge the similarity among colors.

But ask yourself, which hue is more similar to red: green, or purple? Although purple is at

the opposite end of the spectrum from red, most people would answer that purple and red

are more similar.

which hue is more similar to red: green, or purple?

Why? Because of the way color information is

coded by the eye. The extreme "blue violet" end of the spectrum seems also to contain

some "red" light. The reflectance profiles of magenta or purple paints show that these

colors stimulate both the L and S cones in

newton's hue circle

higher proportions than the M cones.

reflectance curves for quinacridone rose (PV19), quinacridone magenta (PR122),

and manganese violet (PV16) see this page for an explanation of reflectance curves

and how to interpret them

Because the L cones are stimulated by red or

purple surfaces, we judge these to be similar

colors — in the same way that yellow green seems similar to blue green, because the M

cones are stimulated by both. However, magenta and red violet, the bridging hues between red and blue violet, are not

spectral lights. They cannot be found anywhere in the spectrum created by a

prism or rainbow, even though "red" and "blue" light, when combined, produce those

colors.

Newton's Opticks. This light mixing

discovery was made by the English physicist and mathematician Isaac Newton (1642-

1726), who first described the many optical and color experiments he performed in the

late 1660's to the English Royal Society in

1672, and after an interval of more study and contentious public discussion published them

in his Opticks of 1704. (That's the English edition; a scholarly Latin translation appeared

in 1706.) Newton had experience grinding his

own lenses and was attempting to understand the problem of chromatic aberration that

introduces fringe colors into optical images. He knew of the "celebrated Phenomena of

Colours" described in experiments with pentahedral (triangular in cross section) prisms

performed decades earlier by Guido Scarmiglioni, Thomas Harriot and Marcus

Marci. But he pursued these studies much further in experimental thoroughness,

observational precision and logical clarity.

The revolutionary aspect of Newton's work was

his emphasis on keeping separate the physical and sensory (mathematical and psychological)

aspects of color — a scientific strategy

advanced in the treatises of Galileo Galilei. Newton demonstrated that each spectral hue

has a unique and measurable refrangibility or angle of refraction when passed through a

lens or prism. In his Experimentum crucis ("decisive experiment") and variations of it, he

showed that this characteristic of light remains constant even if the light is blended by a lens,

sent through multiple prisms, or passed through a colored filter.

He could not explain this refrangibility, which arises from the wave properties of light, but

he concluded that the sensation of color was both separate from it yet intimately related to

it. He first defined refrangibility and color in parallel terms:

The Light whose Rays are all alike Refrangible, I call Simple, Homogeneal, and Similar; and ...

The Colours of Homogeneal Lights, I call Primary, Homogeneal and Simple.

and then, in a famous passage, he declared that color is a sensation in the viewer's

mind, not a property of the light itself or of the materials illuminated by the light:

If at any time I speak of Light and Rays as coloured or endued with Colours, I would be

understood to speak not philosophically [scientifically] and properly, but grossly, and

according to such Conceptions as vulgar [uneducated] People in seeing all these

Experiments would be apt to frame. For the Rays to speak properly are not coloured. In

them there is nothing else than a certain

Power and Disposition to stir up a Sensation of

this or that Colour. ... So Colours in the Object are nothing but a Disposition to reflect this or

that sort of Rays more copiously than the rest; in the Rays they are nothing but their

Dispositions to propagate this or that motion into the Sensorium; and in the Sensorium they

are Sensations of those Motions under the Forms of Colours. [Book One, Part II]

Newton frequently pointed to the similar sensory properties of light and sound and, in

imitation of the diatonic musical scale (produced by the white keys of a piano), he

(or rather a sharp eyed assistant) identified seven "primary or simple" colors of light

in the spectrum — red, orange, yellow, green,

blue, indigo and violet. In Newton's view, spectral "orange" or "indigo" light was just as primary, homogeneal and

simple as "red" or "green" light, because none of these hues by itself could be altered or

separated by refraction into any other colors.

But he found they could be mixed. In

particular, he discovered a region of new colors that were known in isolated natural

exemplars such as gems and flowers but that did not appear in a prismatic spectrum.

Instead, these extraspectral hues — "purple" and "red violet" (magenta) —

appeared by overlapping the "red" and "violet" ends of two separate spectrums (right). And

he found that recombining three or four colors

of the spectrum through a lens reconstituted the original "white" color of sunlight.

The Hue Circle. Newton summarized these

striking observations as an ingenious new color model: he joined the "red" and "violet"

ends of the spectrum to create a hue circle.

This circle still shows the spectrum as a continuous gradation of color from red to

violet, but now red is joined to violet, via the "artificial" or mixed colors carmine, magenta

and purple.

extraspectral magenta

newton's hue circle the original "color circle" (1704) superimposed on the

spectral and extraspectral hues (there is no "magenta"

or "purple" light in the spectrum); capital letters refer

to notes of the diatonic scale

In this diagram, the center of the circle (O) is "white" (colorless) light, and the

circumference represents the "fiery" (saturated) colors of every spectral

hue. The distance from the center to the edge

indicates the range of unsaturated colors — the drab or whitish colors of the everyday

world — between white and homogeneal hues.

The hue circle is not just an artifice to make a

home for extraspectral purple. Newton explained that it provides a geometrical

method to calculate the chromaticity (hue and saturation) of any light mixture. He

declared that two or more spectral "primaries"

combined in specific quantities or "weights" would produce a mixture color that was

located at the "center of gravity" (weighted average) among them all. The method is like

finding the balance point of a circular cake pan with different sized weights placed around the

rim (right).

In Newton's diagram (above), the small circles

underneath each color name indicate the varying quantities or "weights" of each

newton's geometrical

weighting

• the location of each color is

measured on perpendicular x,y

dimensions

spectral color that might contribute to a color mixture: large amounts of red, orange and

yellow, small amounts of "blew", indigo and violet. The color located at "Z", the average of

them all, is the unsaturated red orange color that results. And, to close the circle, Newton

observed that:

If the point Z fall in or near the line OD, the

main ingredients being red and violet, the Colour compounded shall not be any of the

prismatick Colours, but a purple inclining to red or violet, accordingly as the point Z lieth

on the side of the line DO towards E or towards C, and in general the compounded

violet is more bright and more fiery than the

uncompounded.

Newton emphasized that the hue circle only applies to light mixtures. Pigment mixtures

would not depend on the proportional weights or quantities of the pigments in a mixture, but

on "the quantities of the Lights reflected from

them." He verified that colors arise in pigments and in natural surfaces because they

reflect some spectral colors and absorb others.

The Analysis of White. Newton explored

pigment mixtures at length, using the artists'

primaries red, yellow, green and blue (as the pigments carmine lake, orpiment, verdigris

and bremen blue) to explore the origin of white or gray mixtures:

All colour'd Powders do suppress and stop in them a very considerable Part of the Light by

which they are illuminated. For they become colour'd by reflecting the Light of their own

Colours more copiously, and that of all other colours more sparingly, and yet they do not

reflect the Light of their own Colours so copiously as white Bodies do. ... And therefore

by mixing such Powders, we are not to expect a strong and full White, such as is that of

Paper, but some dusky obscure one, such as

might arise from a Mixture of Light and Darkness, or from white and black, that is, a

grey, or dun, or russet brown, such as are the Colours of a Man's Nail, or of a Mouse, or

Ashes, of ordinary Stones, of Mortar, of Dust and Dirt in High-ways, and the like. And such

a dark white I have often produced by mixing colour'd Powders. ... Now, considering that

• the x,y values for each color

are multiplied by the

"weight" (luminance or

brightness) of the color

• the weighted x and y values

for all colors are added

together

• the total x and y values are

divided

by the sum of the weights

• the resulting average x,y

location is the centroid (C) or

mixture point

these gray and dun Colours may also be produced by mixing Whites and Blacks, and by

consequence differ from perfect Whites, not in Species of Colours, but only in degree of

Luminousness, it is manifest that there is nothing more requisite to make them perfectly

white than to increase their Light sufficiently.

... and this Newton accomplished by

illuminating the gray mixtures with a single beam of sunlight in a darkened room, or by

comparing the sunlit mixtures to a shaded piece of white paper.

These mixing experiments with pigments and lights reveal Newton's fundamental

preoccupation with the analysis of "white" into the compounding of different primary colors.

Newton's hue circle implied that different combinations and proportions of primary colors

would equivalently mix to white; white (or gray, in pigments) could be created by many

different combinations of spectral light.

Complementary Mixtures. Newton's play

with "white" mixtures led to one of his most intriguing insights: two hues on opposite

sides of the hue circle could create a near neutral color if mixed in the right

proportions:

If only two of the primary Colours which in the

circle are opposite to one another be mixed in an equal proportion, the point Z shall fall upon

the center O, and yet the color compounded of

those two shall not be perfectly white, but some faint anonymous [diluted and

unnameable] Colour.

This is the origin of the idea of complementary colors and the "mix to

white" criterion for identifying them. But the

passage reveals a few points of confusion. For starters, Newton admitted he could not create

a pure "white" by mixing two or three "primary" colors, but he apparently did not

grasp that this was because he was mixing broad sections of the spectrum as a single

color, rather than mixing single wavelengths. (That is, his hue circle works only if the

calculations are made on the physical attribute of "refrangibility" and not on the

psychological categories of "homogeneal

color", those wide bands of seven spectral

hues.)

Newton also did not explain that some spectral hues are more luminous or have a higher

tinting strength than others, which means

they have inherently more weight in color mixtures and should be either located farther

from the "white" center of the hue circle (as they are in some chromaticity diagrams) or

overweighted in the "center of gravity" calculations. Finally, Newton's parallel

experiments with pigments and lights misled many readers into thinking that pigments and

lights mix in the same way, which only confused 18th century "color theorists".

Newton's Legacy. It is difficult from a modern perspective to grasp the extraordinary

originality of Newton's color theory. Perhaps the most important breakthrough in the

Opticks is the use of geometry — the circle — to explain color mixtures, not as a metaphor,

but explicitly to describe color in mathematical

terms. This linkage between physical quantities and sensory qualities is the

essential principle of psychophysics.

At least seven spectral hues or "simple" colors of light are necessary to describe color

mixtures. The arbitrary distinction between

"real" and "illusory" color is swept away: all color arises in mixtures of light, no matter

whether the light comes from a prism or the reflectance qualities of colored powders. These

ideas went far beyond the dyer's lore that three primary colored paints or dyes defined

color mixing.

A key aspect of Newton's work, as his

contemporaries saw it, was that he refuted the color theory inherited from Aristotle,

in which "light" and "dark" were the two antagonistic primitives that mysteriously

combined, like an oil slick on water, to create the iridescence of color. Newton showed just

the reverse was true: white is not the acme of

all color phenomena but a murky muddled mixture, no purer than dust or dirt; many

different mixtures of three or more spectral colors would produce the same "faint,

anonymous" or near white light. Black was not a "color" at all but merely the absence of light.

Newton insisted that color was a sensation in conscious experience or the "Sensorium". But

this clearly implies that the hue circle is a mental structure, not a property of light. The

psychologist Roger Shepard demonstrated this by asking college students to choose a

numerical rating that described the apparent similarity between every pair of colors in a set

of 14 Munsell color chips whose dominant wavelengths were matched to spectral hues.

(He excluded extraspectral purple and

magenta to avoid inducing a circle where none existed.) He then used a multidimensional

scaling program to translate these similarity judgments into a map, where dissimilarity is

represented as distance. This procedure not only recreated the ordering in the hue circle

but also the perceptual spacing and complementary opponency between hues, as

these are defined in modern color models.

Newton's book was intended for an audience

of Enlightenment naturalists, and it was widely read. The English mathematician and

perspective theorist Brook Taylor (1685-1731), who was also a talented amateur

painter, pointed out in his New Principles of

Linear Perspective (1719) that "the knowledge of this theory may be of great use in painting",

and then explained in general terms how to apply it to mixing paints — though Newton

had cautioned that his circle only applied to mixtures of light. From this misconception all

artists' color wheels have branched and bloomed.

Despite the fact that some Continental scientists found Newton's color mixing

experiments difficult to replicate, or refused to accept his refutation of ancient color theory,

Newton's book had a decisive (and hotly debated) impact on 18th century color

concepts. After centuries of futile and confused speculation about the origins of

color, his book separated the mental from the

physical attributes of color and laid the foundations for its scientific study.

a hue circle formed from

judgments of color

similarity

from Shepard (1962)

The German polymath Hermann Grassmann

(1809-1877) contributed to this work by revisiting Newton's hue circle. Commenting on

recent experimental work by Helmholtz, and adopting principles implicit in Newton's

"center of gravity" method of predicting

color mixtures, Grassmann proposed that:

1. Every color sensation may be analyzed into three mathematically determinable elements:

the hue, the brightness, and the brightness of

the intermixed white.

2. If one of two mixed lights is continuously altered while the other light remains constant,

the appearance of the mixed light is also continuously changed.

3. Two colors, both of which have the same hue and the same proportion of intermixed

white, also give identical mixed colors, no matter of what monochromatic lights they

may be composed.

4. The total luminance of any light mixture is

the sum of the luminances of the lights mixed.

From these principles, Grassmann was able to

prove an important corollary:

For every hue of monochromatic light, there is another monochromatic color which, when

mixed with it, gives colorless light.

Grassmann clarified the principle that

mixtures of light are additive in hue, brightness and chroma (mixture with "white"

light), and therefore that color sensations are

related to light mixtures according to quantitative principles. He also showed that

every monochromatic [homogeneous] hue has a monochromatic complementary color — or

(a point Grassmann missed) a mixture of extraspectral "red" and "violet" hues — which

produce "white" when mixed together (diagram, right).

Today these principles, in a more algebraic version, are known as Grassmann's Laws.

They formed the theoretical framework for color experiments by Helmholtz and James

Clerk Maxwell in the 1850's. These established the trichromatic model of color

mixture, and the modern study of color perception.

One consequence of Newton's

hering's opponent processes

Grassmann's diagram of

monochromatic

complementary colors

dotted line shows a

complementary mixture of

"yellow" and "indigo" light;

letters denote Fraunhofer

spectral absorption lines

from Grassmann (1853)

clarity about the physical attributes of color was that 18th century scientists were able to

identify areas of subjective color experience, in particular the appearance of

complementary hues induced by a strong color stimulus that can be observed in

afterimages, simultaneous color contrasts and complementary shadow contrasts.

These research pursuits evolved into a Romantic color theory emphasizing the conflict

or antagonism between complementary colors,

including light and dark. These themes were famously summarized by the German poet and

bureaucrat J.W. von Goethe in his Farbenlehre (1810) and elaborated in the

early 19th century by German speaking philosophers and scientists, in particular the

Bohemian physiologist Jan Purkinje (1787-1869) in his New Subjective Reports on Vision

(1825).

By the 1850's this anecdotal and speculative

approach to color was largely displaced by psychophysics or the quantitative study of

stimulus and sensation. This discipline emerged in Germany, through the work of

Ernst Weber (1795-1878), Gustav Fechner

(1801-1887), Wilhelm Wundt (1832-1920), Hermann von Helmholtz and others.

Psychophysicists developed the experimental methods and mathematical equations

necessary to link the intensity of a basic sensation to quantitative units of the physical

stimulus — weight in relation to mass, brightness in relation to light intensity, pitch in

relation to frequency of vibration, and so on. At the same time, biologists developed the

laboratory and dissection methods necessary

to understand the physiology of sense organs and the nervous system. As a result

the sensory and biological structure of perception began to be viewed as an

integrated mechanism obeying basic laws that quantify the connection between

mind and matter.

This is the historical moment in which

Bohemian physiologist Ewald Hering (1834-1918) launched a new defense of subjective

color experience and color antagonism, published as the monograph Zur Lehre vom

Lichtsinne (On a Theory of the Light Sense) in 1874 and as a book in 1878.

Hering's Urfarben. Hering's strategy was to start with color experience and from that

attempt to deduce color physiology. He pointed out that the trichromatic theory

advocated by Helmholtz, Arthur König and others, which postulated three types of nerve

excitations produced by three kinds of receptor cells, could not explain several well

established observations in color experience. Hering noted that:

• yellow seems to be psychologically just as basic as the trichromatic red, green or blue,

yet does not seem to contain any of those colors

• dichromats, who lack a "red" or "green" cone, cannot see either a red or green color

yet still can see yellow

• deuteranopia (green colorblindness, caused

by a lack of the M cones) does not cause the point of maximum spectral luminance to shift

from "green" wavelengths toward "red"

• most colors of the spectrum seem to shift in

hue as they brighten or darken (the Bezold-Brücke effect), but these shifts do not

appear in a pure blue, green or yellow.

Based on clues of this kind, Hering asserted

the perceptual primacy of four Urfarben or "primordial colors", known in the USA as the

four unique hues: red, yellow, green and blue. He conjectured that they were produced

by visual substances or processes located somewhere in the visual system outside the

retina. He was vague about the physiology but precise about the "pure" form of the unique

hues, which he equated with the color of monochromatic lights at 470, 500, 570 and

700 nm.

Hering's Opponent Processes. Hering then

turned to color mixtures. He observed that light or surface colors can produce a sensation

of red mixed with yellow (orange) or red mixed with blue (purple), but never create the

sensation of red mixed with green ("reddish

green" or "greenish red") or yellow mixed with blue ("yellowish blue" or "bluish yellow"). This

proved to Hering that the visual substances were organized as antagonistic or opponent

processes.

In one process assimilation of visual substance produced the red sensation and dissimilation

produced the green sensation; the other process produced the opponent sensations of

yellow and blue. When the visual substances were neutralized or in balance, both hues

associated with that opponent process disappeared.

Hering also observed that we commonly lose color vision at night, yet still see light and

dark, which convinced him that luminosity is separate from hue as a color vision process.

So he proposed two additional "colors", white and black, that create the perception of

brightness or lightness and also affect color

chromatic purity by mixing with any of the unique hues to create less intense

(desaturated) colors across the complete range of shades, tones and tints — which

Hering called veiled colors. However, he conceded that yellow and red had an "inherent

brightness", and green and blue an "inherent darkness", which mingled perceptions of hue

and luminosity, and that white and black did not disappear at balance but produced the

positive sensation of gray, which meant that

black and white are not linked as opponent processes.

In summary, Hering proposed there are six

fundamental color processes that are arranged as three visual contrasts, including two

opponent processes. They are:

The achromatic sensation of middle gray results when all the substances or processes

are in balance.

Hering took pains to fit his theory to Newton's

hue circle. Roughly half the hues on the circle can be described as containing some yellow,

and the other half some blue; these semicircles overlap with two opposing spans of

red and green, oriented perpendicular to the

w & k substances (?) - white to black

r/g opponent process - red (+) vs. green (-)

y/b opponent process - yellow (+) vs. blue (-)

yellow and blue like four hue compass points. Binary mixtures of any two neighbor unique

hues (one hue each from the two opponent processes) would explain all spectral hues

between them, including the extraspectral purples between red and blue.

hue circle explained by two opponent

processes combining two illustrations from Ewald Hering (1920),

reversed to match modern color wheel orientation

The outer ring shows overlapping quantities of

neighbor opponent processes. These tapering color bands show that neighboring unique

hues can be blended in any proportions.

Opposing hues — red vs. green, and yellow vs. blue — do not overlap in the outer circle: they

cannot mix. A line through the outer ring indicates the relative proportions of two

unique colors necessary to create the inner hue circle of color swatches. Hering's

examples (in the lower left corner) show that a mixture of 25% unique blue and 75% unique

red produces a crimson red, while a mixture of 75% blue and 25% red produces a blue violet,

and a 50%/50% mixture produces purple.

Other mixtures produce scarlet, orange, yellow green and blue green to complete the circle.

Although Hering did not describe a complete

color system, his color writings suggested the basic geometry for the Swedish NCS color

model.

As explained in the next section, opponent

contrasts have proven to be fundamental to color vision. So it is ironic that most of

Hering's specific explanations of colorblindness and color perception have turned out to be

incorrect, or the data he relied on flawed or incomplete. His concept of "visual substances"

directly causing conscious sensations and working in chemical opponency, like acid and

base, is wrong in several respects. The opponent contrasts that do underlie color

vision are not anchored on the unique hues.

Opponent contrasts can be identified in neural pathways only between the retina and visual

cortex, not in brain areas associated with color recognition or color naming. Hering was an

innovator who uncovered important and valid general principles despite a flawed

interpretation of the facts.

The Opponent Functions. For several

decades after the publication of Hering's ideas, Hering and Helmholtz, and then their

descendant partisans, disputed the theoretical mechanisms and research evidence for the

trichromatic and opponent theories. The trichromatic theory and the opponent

process theory were usually seen as

incompatible explanations of color vision.

By the middle of the 20th century, researchers had concluded that both theories were

necessary to explain the physiological processes of color perception. These hybrid

models were first suggested by Johannes von

Kries and G.E. Müller in the 1890's and were definitively reformulated by Müller in 1930 as

a zone theory of color vision. Zone theories derive the opponent dimensions from the

trichromatic retinal responses by a step by step transformation or recoding across three

or more stages or zones. In 1949 D.B. Judd specified Müller's physiological theory as

testable equations based on cone fundamentals of the CIE standard observer.

Today these opponent dimensions are the

foundation for most modern color appearance models.

recoding opponent dimensions from trichromatic outputs

In the 1950's by Leo Hurvich and Dorothea

Jameson developed a quantitative hue cancellation method to measure the

opponent functions by decomposing monochromatic hues into a mixture of two of

the four unique hues. Their method uses the same color matching techniques developed

to measure the cone fundamentals

championed by Helmholz.

In this procedure, either the viewers or the experimenters chose four wavelengths of light

to match Hering's unique hues. (A mixture of

"red" and "violet" wavelengths must be used to produce a unique red.) The intensity of

each light was then adjusted so that equal parts of red and green matched the brightness

of unique yellow, and equal parts of yellow and blue matched the brightness of unique

green.

Next, a fifth wavelength was chosen as the

test color. Viewers used a light mixing apparatus to blend the test light with the two

unique hues that were nearest complementary colors (opposite on the hue

circle) to the test light, until the mixture produced a pure "white" light. This was

repeated for test lights at regular intervals across the spectrum.

Finally, the proportions (relative luminances) of the two unique hues necessary to cancel a

third monochromatic light at each wavelength were combined as two chromatic response

functions. Representative curves produced by two individual subjects are shown at right;

theoretical curves, based on the CIE 10° standard observer, are shown below.

opponent functions in spectral hues chromatic response functions for the CIE 1964

standard observer; from Hurvich & Jameson (1955);

the unique hues are located at B, G and Y (unique red is

composed of a mixture of "red" and "violet" light)

As shown here, the horizontal zero line represents the balance between the two

unique hues in a single opponent function. The distance of a curve above or below the line

represents the relative quantity of each unique

hue required to match (rather than cancel) the spectral hue at each wavelength (i.e., they are

tetrachromatic color matching functions).

The y/b opponent function is represented by the yellow/blue curve. The area where the

yellow curve is above the horizontal line, with

a maximum in "yellow green" wavelengths, indicates colors that appear to contain some

yellow. The area where the blue curve is below the line, with a maximum in "blue violet",

indicates hues that contain some blue. This y/b function contrasts the long and short

opponent function curves

for

two individual subjects

after Jameson & Hurvich, 1955

wavelength ends of the spectrum.

The r/g opponent function (red/green curve) codes for hues that appear to contain

some red (the areas where the red curve is

above the horizontal line, with peaks in "blue violet" and "scarlet" wavelengths) as opposed

to hues that contain some green (the area where the green curve is below the line, with a

maximum in "middle green"). This r/g function contrasts the middle wavelengths

from both ends of the spectrum.

The unique hues appear at any point where

one opponent function is at the zero line where it cannot bias or alter the hue created

by the other opponent function. Thus, unique yellow appears at the long wavelength balance

point in the r/g opponent function, at about 573 nm, and unique blue at the short

wavelength balance point around 472 nm. Similarly, unique green appears at the single

balance point in the y/b function, at about

492 nm. (The exact location of these unique hues varies across individuals.)

What about unique red? There is no point

where the y/b contrast crosses the neutral line a second time in the visible spectrum —

both contrasts taper toward neutral as the

spectrum fades to invisibility, and near infrared "red" light (beyond 700 nm) actually

appears more yellow (scarlet) as the wavelength increases to 900 nm. To produce

unique red from monochromatic lights, a small amount of "violet" must be added to spectral

"red" light, to neutralize the yellow hue. (This is one reason for the S cone input to the r/g

opponent coding.)

Finally, Hurvich and Jameson adopted the

photopic sensitivity function (gray curve) to represent the whiteness/blackness or

w/k opponent function. Procedurally, they equated the w/k curve with the quantity of

"white" light produced by the neutralizing

mixture of spectral and complementary opponent hues. But this curve glosses over

several problems. It does not account for the additivity failures in spectral mixtures, and

blackness is not a color sensation created by isolated color mixtures — it arises from the

luminance contrast between a color stimulus and the color area around it. Luminance

perception is actually structured as a brightness/blackness (b/k) opponent

dimension: white is its neutral value.

What Are the Opponent Functions? On a previous page I mentioned that a few studies

have analyzed the reflectance curves of a large number of color samples from the

Munsell color system. When the correlations among all these reflectance profiles are

statistically simplified, they result in three

weighting functions (right) that reconstruct the original reflectance profiles with 95% to

99% accuracy, depending on the study. The pattern of peaks and crossings of these basis

functions is extremely efficient in the sense that every surface color can be defined by

a unique location in just three dimensions.

These curves recognizably correspond to the general form of the three chromatic

response functions: curve 1 is the w/k function, curve 2 is the y/b function, and

curve 3 is the r/g function. There are discrepancies in the exact shape and crossover

points of the curves (especially in function 1),

but these discrepancies can be attributed to four factors: (1) reflectance curves are a

physical specification of the color stimulus, not a perceptual specification via the cone

fundamentals; (2) reflectance curves define the color independent of any light source,

whereas the human opponent functions are optimized for chromatic adaptation along

the dimensions of chromatic variation in the daylight phases; (3) the reflectance

variations in the Munsell color samples are

constrained to some degree by the limited number of pigments used to manufacture

them; and (4) by far the largest proportion of natural surface colors are weakly chromatic

and rather dark, which means the Munsell system contains a disproportionately large

number of saturated and light valued colors.

These issues aside, if we plot the size of the

weights assigned to saturated Munsell hues on the second and third weighting functions, the

color samples once again arrange themselves in a hue circle (right) with an accurate pairing

of complementary hues — yellow green across from deep blue, and red across from blue

green. This is persuasive evidence that, as we

weighting functions that

predict the spectral profiles

of 1270 Munsell color

samples

hue circle created by the

spectral weighting

functions

from Lenz, Osterberg et al.

(1996)

would expect, the perceptual structure of color vision is strongly tuned to the reflectance

structure of natural surfaces. Transforming the trichromatic signals into the opponent functions would not be difficult for a

neural network that could flexibly sum, difference and reweight the cone signals. For

example, the diagram (right) shows the Hurvich and Jameson opponent functions

(color) overlaid with curves derived as simple

weighted sums of the linear, population weighted cone fundamentals (gray);

numbers indicate the weight and sign applied to each cone output.

Note the heavy weighting of the S cone outputs necessary to match the y/b

opponent function estimated from hue cancellation experiments. This demonstrates

the perceptual overweighting of S cones in comparison both to their impact on the

opponent dimensions and to their sparse numbers among the much more numerous

rod, L and M photoreceptor cells.

All this implies that the wavelength locations

of the unique hues are a byproduct of the opponent dimensions and not the other way

around. Thus, the fact that very different sets of opponent functions, derived from statistical

reflectance analyses or hue cancellation experiments, can produce the same hue circle,

implies that the orientation of the oppponent

dimensions 3 the location of the unique hues — is of secondary importance. And in fact

there are large individual differences in the choice of unique hues, which strongly suggests

the hues are not structurally basic to color vision in the way the cone fundamentals are.

An exception may be the yellow balance between L and M cones. If the M cone

outputs are approximately doubled (to compensate for the 2 to 1 majority of L cones

in the retina) then unique yellow is located at the null point (L–2M = 0). The S cones

cannot upset this balance because their sensitivity in "green" to "red" wavelengths

(above 525 nm) is nearly zero, and because the S cone peak response (at 445 nm) is the

complementary "violet" hue to unique yellow

(between 565 nm to 575 nm, depending on the color temperature of the light used to

weighted sums of the cone

fundamentals that match

the r/g and y/b opponent

functions

define "white"). Yellow around 570-575 nm is (not coincidentally) the direction of color shifts

in daylight chromaticity and of the yellow tint that accumulates in the lens with age. By

anchoring the y/b contrast on this yellow, both the internal constraints of lens yellowing

and S cone influence, and the external constraints of natural light variations, can be

compensated for by a single mechanism. The r/g dimension would adapt to provide an

approximately independent contrast to the

anchoring y/b dimension. Finally, the spectral hues where the r/g or y/b opponent functions are in balance, as

shown in the CIELUV chromaticity diagram (right), can be contrasted with the white

point or balance point between two photoreceptor outputs that emerge in various

types of colorblindness. In trichromatic vision two areas of reduced hue purity appear

at around 490 nm ("cyan") and 570 nm

("yellow"), and the color white appears as a single point inside the chromaticity diagram.

In tritanopia (missing S cone), the white line extends from 570 nm to 460 nm — in normal

vision a very near visual complement to unique yellow. In protanopia (missing L cone),

the white point changes into a confusion line across the chromaticity diagram from 494 nm

("cyan") to c494 nm: all colors on this line appear neutral or achromatic. In deuteranopia

(missing M cone), the white line extends from

499 nm ("cyan") to c499 nm. Both confusion lines are close to the trichromatic unique red

at c495 nm. This implies that unique red is a somewhat more reliable anchor for the r/g

dimension, as seems verified by the much larger individual differences in the perception

of unique green in comparison to unique yellow or red.

Now we can examine the

specific steps necessary to get from the

Helmholtz cone fundamentals to the Hering opponent dimensions — the process described

by 20th century zone theories.

This problem can be explored with graphical data analysis, which has been used by

multivariate statisticians for over a century. It

from cones to colors

lines of balanced (zero)

values on

the r/g or y/b opponent

functions

after Burns et al. (1984)

lets us examine complex mathematics by means of pictures rather than numbers, and

allows us to show complex transformations in simple geometrical terms.

By making graphical adjustments to the color space — changing the length of color

dimensions, rotating our view of the dimensions, adjusting the angle between

dimensions — we can see the transformations from cones to colors as explicit sculptural

steps.

A Geometrical Color Standard. To start we

require a graphical standard for the geometrical pattern we expect to find in the

color appearance of color samples that have been correctly transformed from the light

excitation produced in the cones.

Since the 1920's, the most commonly used

standard in color research has been the Munsell Color System. The Munsell system

can be used to define colors that are perceived to be evenly spaced in hue and chroma across

equal value (lightness or gray scale) differences. In addition, the Munsell hues 5R,

5Y, 5G and 5B approximately locate the Hering unique hues red, yellow, green and

blue.

The Munsell system arranges colors along

equally spaced, radial hue angles and circular chroma levels from the achromatic point at

each lightness level. This ideal geometry is

most recognizable when viewed in the orientation shown in the diagram below, which

displays all hues within the chroma range typical of artist's paints and at the two Munsell

values 4 and 8.

distribution of munsell color samples

in an ideal perceptual space munsell target colors at 2.5 hue intervals for chroma

values /2 to /12 at munsell values 4 and 8; colors are

illustrative only

This pattern summarizes the expected relationships between color appearance and

measurements of hue, chroma or lightness: chroma differences are equal across all

chroma levels and for all hues; lines of

constant hue are radial, straight and equally spaced around the hue circle; the "compass

point" colors are Munsell hues 5Y, 10R, 5PB and 10BG; and these relationships are the

same across all lightnesses. Another relationship, not visible in the diagram, is that

each hue/chroma plane is perpendicular to the achromatic axis (like a wheel on an axle).

To make these graphical comparisons, the color diagrams must represent height and

width in equal scale units, turn the color space so that our view is directly down the

achromatic axis (the gray scale), and place light yellow (5Y) at the top of the hue circle

and red (5R) on the right. They also depend on the (certainly false) assumption that the

Munsell color system distributes colors with

perfect accuracy.

Cone Excitation Space. The first stage in all zone theories corresponds to the transduction

of light by the cone fundamentals, which

define the relative amount of photoreceptor excitation produced by light of different

wavelengths.

The total stimulation is calculated by

multiplying at each wavelength the L, M and S cone sensitivity by the color's spectral

emittance curve, then adding the products across all wavelengths in the visible spectrum.

This produces a triplet of cone excitations — Le, M

e and S

e — that produce the

geometrically irregular and curved cone excitation space that was introduced earlier

to describe the stimulation of the cones by monochromatic lights.

It is not possible to measure cone excitations directly. Instead, a transformation function

is applied to the XYZ tristimulus values to estimate the L, M and S values for each color

sample.

This space has very different characteristics

when displayed in terms of surface colors, as shown below for Munsell color samples within

the range typical of artists' paints (Munsell values 1 to 9 across chroma levels /2 to /12).

munsell color system in the cone

excitation space munsell target colors for chroma values /2 to /12 at

munsell value steps 1 to 9

In this view the cone excitation space is a cube, with the L, M and S cone excitations

represented as the depth, horizontal and vertical distances from the back left corner

(0); the cube is tilted forward slightly to make differences in the L direction easier to see.

The color stimuli inhabit a small region of the total cubical space, forming a narrow,

elliptical cone with apex at the origin (zero excitation in all three cones). This is the

fundamental topology of human color vision. Hues are oriented with yellow downward (as

yellows produce nearly zero stimulation in the S cones). A plot of the original XYZ values

produces a nearly indistinguishable color

distribution.

Each value plane is almost perfectly flat, hue angles are all approximately straight and

radial from the achromatic point, and complementary hues are radially opposite

each other. The curvature of the color space

produced by monochromatic color stimuli is not visible in surface colors.

However, the distribution of colors displays

some quirks, which are apparent when viewed from the side or above (diagram, right). The

achromatic axis (white line, above), which intersects the pure gray value at each

lightness, forms a rising diagonal across the space, while the luminosity function (green

line, above) lies in the L,M plane. That is, the

S cone contributes to chromaticity but not to luminance; whiteness is not the same as

brightness.

Each Munsell value plane is perpendicular to the L,M plane, so that the projections of all

colors onto the plane form a series of lines

across the luminosity function (gray lines, above), but the hue planes cross both the

luminosity function and the achromatic axis at oblique angles.

Next we orient the colors at values 4 and 8 to match the Munsell ideal standard (above). To

do this, the space must be turned or rotated so that the achromatic axis is aligned with the

direction of view, then turned on its head to place yellow at the top, as shown below.

side and top view of

munsell colors

in the cone excitation space

munsell color samples in cone excitation

space munsell target colors for value/chroma 4/2 to 4/12 and

8/2 to 8/12, after rotation perpendicular to achromatic

axis and placement of luminosity dimension at top

The amount of rotation depends on how the cone fundamentals are weighted (equivalently,

how the white point is defined), but approximately a 45° turn around the S

dimension and then a 30° tilt downward

around the new L–M dimension will bring all the gray points (wp) together over the origin.

In this orientation, the fundamental two part geometry of the cone excitation space is

visible: the L+M excitations define the horizontal dimension, and the S axis the

vertical dimension.

Now we can itemize the asymmetries in the

cone excitation space that must be remedied in order to produce the geometry

of equally spaced color samples:

(1) At lighter values, larger increments in cone

excitation are necessary to shift the lightness to the next Munsell value, although there is a

constant ratio between the cone excitations at adjacent value levels. (See diagram, above

right.)

(2) At lighter values, larger increments in cone excitation are necessary to produce equal

chroma changes, as shown by the increased diameter of the hue plane and of the

innermost (chroma = 2) ring at value 8 compared to value 4.

(3) The hue/chroma planes are not circular but elliptical: the excitation distances between

chroma values are much smaller in the L and M direction than in the S direction.

(4) Hue angles are not equally spaced; instead hue differences are much smaller among some

hues (yellows, oranges and blues) than others (magentas and greens).

(5) Each hue/chroma plane of colors having

equal lightness or Munsell value is not

perpendicular to the luminosity dimension or to the achromatic axis.

Note that the distribution of surface colors in

the cone excitation space is far more regular

than the distribution of monochromatic lights. Color vision is adapted to perceive

surface colors accurately, not spectral hues or rainbows.

Cone Contrast Space. The next step in color

vision actually embraces several color

transformations. In modern color appearance models and chromaticity diagrams, cone

excitations must be adapted through response compression, the definition of preliminary

opponent dimensions, and a complete separation of the luminosity and chromaticity

dimensions.

Physiological and psychophysical studies over

the past few decades have clarified additional early transformations, in particular the

recoding and normalization of cone outputs as a cone contrast space anchored on the

background or adaptation values.

Response Compression. The photoreceptor

outputs actually signal changes in light in relation to the baseline cell excitation.

Photoreceptors do not signal an absolute level of light energy but a relative or proportional

difference or contrast to the amount of light that has come before. Thus, the cone

responses already include some part of

luminance adaptation to the average luminance, and chromatic adaptation to the

average chromaticity, of the visual field. Further adjustments are also made at later

stages of the visual process.

This is specified as a second triplet of cone

values — La, M

a and S

a — which quantify the

baseline response of the cones. (In the early

CIE color models, which are based directly on XYZ tristimulus values, the adaptation

triplet is the illuminant specification XwYwZw

,

where Yw

= 100 always.)

The contrast outputs L∆, M

∆ and S

∆ are then

the contrast ratio of color excitation over

adaptation excitation:

These contrast values can be either positive or negative; the null point or origin of the space

represents the La, M

a and S

a values. The

most important feature of these contrast or

change ratios is that they constitute a comparison between two different stimuli (the

color and the adaptation background), which defines a Weber fraction. Fechner's Law

states that a stimulus contrast will produce an equal perceived color contrast whenever the

color stimulus is a constant proportional difference (∆L) from the baseline stimulus

(La).

This contrast space disguises the absolute

color and brightness of the visual field (because all adaptation states are set equal to

zero), but standard practice is to use the white point to represent adaptation to an

achromatic background perceived as "white" or "gray" (for surface colors) at a specific

luminance level. A thornier problem is that the

dimensions of the space represent relative increases or decreases in cone stimulation,

which are different for different observers, adaptation backgrounds, spatial or temporal

variations in the stimulus, or amount of color contrast. A common procedure is to make

L∆ = (L

e–L

a)/L

a (or ∆L/L

a)

M∆ = (M

e–M

a)/M

a (or ∆M/M

a)

S∆ = (S

e–S

a)/S

a (or ∆S/S

a)

each dimension proportional to the maximum possible stimulation possible in each situation.

In modern color appearance models, which

deal directly with stimulus quantities (in the

form of colorimetric tristimulus values) rather than cone excitations, the response

compression is defined as a power transformation or exponent applied to the

tristimulus values before any other transformations are made.

Different exponents have been used in

different color models and as applied to chromatic or luminance responses. The

diagram (right) illustrates the problem in

terms of the luminance factor (CIE Y) of a surface in relation to its perceived lightness

(Munsell V). At dark values, a relatively small increase in the luminance factor produces a

very large change in the perceived lightness, but at light values a large change in the

luminance factor produces an increasingly smaller change in perceived lightness. As

shown, applying an exponent to the curved stimulus quantities Y causes them

approximately to match the linear perceived

quantities V. (CIECAM uses the exponent 0.43; CIELAB uses the exponent 0.33 and

then, for the lightness L scale, adjusts the intercept and slope of the resulting line.)

exponential compression of

luminance factor to match

perceived lightness

effect of response compression on chroma spacing

munsell target colors for value/chroma 4/2 to 4/12 and

8/2 to 8/12

As shown above, the compression exponent (0.33) has a more complex effect on the

hue/chroma planes. It gives the chroma rings approximately equal diameter at each

lightness level, and somewhat reduces the

elliptical shape of the chroma contours, primarily by changing the relative proportions

along the vertical (S cone) dimension. This changes the geometrical distribution of colors

from an elliptical cone to an elliptical cylinder; but it increases the rightward tilt of the

chroma boundaries.

Note that the chroma spacing increases

substantially in yellow hues at all lightness levels, primarily due to the exponent effect on

the extremely small S cone values. This implies that all cones paradoxically have their

largest relative impact on color discrimination (chroma and hue differences) when their

signals are close to zero. The same effect is visible in the nearly vertical lightness slope of

the Y function at near zero luminance factor

(diagram, right).

Postreceptor Opponent Contrasts. The cone contrast space defined by the L

∆, M

∆

and S∆ provides the framework for the

definition of a preliminary opponent contrasts

of the trichromatic outputs.

This opponent recoding was the second stage

in early zone theories. It pools the contrast information early in the visual system in order

to preserve its signal accuracy and to create separate visual channels for luminance

(brightness) and chromaticity (hue/chroma) information. These postreceptor opponent

contrasts have been measured in early visual pathways and have very different response

and adaptation behavior to visual contrasts across space or time. They are usually defined

as:

Lum = L∆ + M

∆

L–M = L∆ – M

∆

Lum–S = L∆ + M

∆ – S

∆

The version proposed in 1984 by Derrington,

Krauskopf & Lennie (known as the DKL

opponent space) has been especially influential in the neurophysiological stream of

color vision research. It is based on an isoluminant chromaticity diagram devised by

Donald MacLeod and Robert Boynton (diagram, right).

This chromaticity space standardizes all values on the luminance Lum (L+M) response and

gives all three cone responses equal weight. Some color spaces double the M response to

the red/green contrast (L–2M).

The Lum and L–M dimensions are created by

a single orthogonal rotation of about 43° around the S axis of the cone excitation space,

which aligns the luminosity axis with the direction of view toward the color samples.

These new dimensions are simply weighted sums of the original cone excitation

dimensions, as follows:

This procedure also forces a new distinction

between the luminosity and achromatic axes. If the Lum (L+M) dimension includes any S

output, then a second rotation of about 26° around the L–M dimension has been applied

to align the achromatic points with the

direction of view. This defines a whiteness/blackness or lightness induction

dimension (W).

The innovations here are that the cone excitations have been combined according to

specific proportions that establish contrast,

priority and independence among the cone signals; and that four distinct quantities —

Lum, W, L–M and Lum–S are in play.

Separating Chromaticity from Lightness.

The final adjustment addresses the oblique angles between each hue/chroma plane and

W = 0.665*L∆ + 0.610*M

∆ +

0.431*S∆

L–M = 0.676*L∆ – 0.737*M∆

Lum–S =

0.317*L∆ + 0.291*M

∆ –

0.903*S∆

macleod boynton

isoluminant chromaticity

diagram

the achromatic and luminosity axes (see diagram above, right). These angles remain

even after the previous transformations have been applied, as shown below in the opponent

dimensions of response compressed, rotated cone excitation space. (In the original XYZ

tristimulus values, the XZ hue/chroma planes are already perpendicular to the luminance Y

and achromatic axes, so adjustment of L+M+S is not required.)

separating chromaticity from lightness munsell target colors for value/chroma 4/2 to 4/12 and

8/2 to 8/12

The tilt or slope (orange line) along the L–M

dimension arises because the L cones are weighted more heavily than the M cones in

luminance than in chromatic perception; and on the L+M–S dimension because the S cones

are weighted more heavily in chromatic than

luminance perception. The remedy is simple: the separate contributions of the L, M and S

cones to the L+M+S (whiteness) dimension are adjusted by small slope factors (0.32 and

0.47) so that lightness values remain constant across changes in the values of the L–M and

L+M–S dimensions. The solution for this "perpendicular white" (W

p) looks like this:

Wp =

(0.665*L∆ + 0.610*M

∆ +

0.431*S∆) +

This effectively weights the L cone output to

about 2 times the M output and over 50 times the –S output in the definition of the

whiteness L+M+S dimension. Called an oblique rotation, it orients the hue/chroma

planes perpendicular to the achromatic axis,

and aligns the luminosity and achromatic dimensions along the L–M dimension:

saturated red and green are roughly equal in lightness.

In either space, a residual correlation between lightness and chromaticity remains along the

L+M–S (Y–Z) dimension, visible above as the leaning shape of the color distribution. These

are not removed, because it corresponds to the perceptual fact that dark purples are much

more saturated than dark blue greens, and dark yellows and light blue violets are not

strongly saturated.

Perceptual Opponent Space. The third step

in zone theories stipulates that the separate cone contrasts are combined into perceptual

opponent dimensions. These dimensions are presumed to describe the conscious structure

of color perception — in other words, the distribution of colors in the Munsell color

system. In modern color models this stage

constitutes a final adjustment of the postreceptor opponent dimensions (the

"preliminary" ab dimensions in CIECAM).

0.32*(0.676*L∆ – 0.737*M

∆) +

0.47*(0.317*L∆ + 0.291*M

∆ –

0.903*S∆)

= 1.031*L∆ + 0.511*M∆ + 0.006*S

∆

Where have the postreceptor opponent dimensions taken us? After the cone

excitations are response compressed, rotated, made perpendicular to and normalized on the

maximum value on the achromatic (Wp)

dimension, the spectrum locus appears as

shown (diagram, right). The opponent dimensions place "cyan" (495 nm) on the

L+M–S null line and "unique yellow" (570 nm) on the L–M null line; these are the commonly

ascribed balance points for the yellow/blue

and red/green opponent contrasts. The dimensions puts the maximum value of L–M

at a the warmest "red orange" hue (608 nm)

and the minimum at "unique green" (522 nm); and puts the maximum value of L+M–S at

middle "green" (545 nm) and the minimum at "blue violet" (445 nm). These dimensions are

related to the equal area cone fundamentals as:

The large weights given to the L–M contrast are necessary to overcome the narrow

elliptical shape of the color space. The diagram (right) shows the spectral profile of the

chromatic postreceptor opponent functions. The recognition features are the absence of

positive "violet" hue coefficients on the L–M

curve, and the very large negative "violet" hue coefficients on the L+M–S curve.

The diagram below shows the hue/chroma

distribution of surface colors. The L+M–S null line is placed at a distinctive yellow green (leaf

green) and a blue violet (approximately

Munsell 5GY and 7.5P). The L–M null line is placed at blue green and magenta, at Munsell

7.5BG and 10R. These "balance hues" do not correspond to those at the spectrum locus,

especially in the placement of unique yellow (Munsell 5Y): we expect this because human

vision is adapted to perceive surfaces, not spectral lights.

Wp = 1.031*L

∆ + 0.511*M

∆ +

0.006*S∆

L–M = 5.946*L∆ – 6.482*M∆

Lum–

S =

1.215*L∆ + 1.113*M

∆ –

3.454*S∆

the postreceptor opponent

space

(top) plot of spectrum locus;

(bottom) opponent hue

coefficients

munsell color samples in perceptual

opponent space munsell target colors for value/chroma 4/2 to 4/12 and

8/2 to 8/12

Four distinct problems are still unresolved in

the postreceptor opponent contrasts:

• Most important, a pronounced elliptical

distortion remains in the chroma rings: the blue greens are too compressed in comparison

to the yellows, and the hue angles are not equally spaced around the hue circle

(compressed in yellow and blue, expanded in green and magenta).

• The elliptical distortion is itself distorted in the direction of yellow green and red, and this

distortion increases at higher chroma levels, so that the near neutral chroma rings are

roughly elliptical but the saturated chroma rings are clearly wedge shaped.

• Yellows with a distinctly green content are on the "red" side, and blues with a pronounced

red content are on the "green" side, of the L–M (red/green) null line. (That is, the vertical

"compass points" in the geometrical standard are rotated clockwise), However,

this cannot be corrected by rotation, as the

horizontal "compass points" (10R and 7.5BG) are approximately correct.

• The chroma intervals are not equivalent at

different lightness levels; comparing Munsell values 4 and 8, the disparity is especially large

in yellows and blues.

Necessary Additional Transformations.

These four problems remain the most significant obstacles to accurate color scaling

of color samples viewed in isolation (that is, colors that are not significantly affected by

color context). They typically require additional transformations in quantitative color

models that do not, as yet, have a clear connection to the neural machinery of color

vision — we can't explain why they are necessary.

The current level of model sophistication is exemplified by the dimensions of brightness

(Q), lightness (J) and the hue/chroma plane (a

C and b

C) in CIECAM. These are

approximately defined as:

A computational trick was used to derive these weights: the starting or preadaptation R, G

and B values in CIECAM are set to 1.0, with the values on the remaining two cones set to

zero, and these values are passed through the

CIECAM mechanism; the weights above are the final values of these "colors". These

weights will change according to the luminance of the color and the definition of the

viewing context, and the CIECAM cone fundamentals are different from those used in

the previous examples; but the weights do illustrate the modifications necessary to

"improve" the postreceptor opponent space. These are:

• a decrease in the L cone weight, as a proportion of the M cone weight, in all

dimensions

• a substantial decrease in the negative S

cone contribution to the bC (L+M–S)

dimension

Q = 72.08*R'a + 61.99*G'

a + 39.09*B'

a

J = 5.68*R'a + 4.20*G'

a + 1.67*B'

a

aC = 47.08*R'

a – 77.78*G'

a – 7.23*B'

a

bC = 25.07*R'

a + 27.05*G'

a – 24.72*B'

a

• the addition of a substantial negative S cone contribution to the a

C (L–M) dimension

• separation of the achromatic dimension (or

lightness, J) from the luminosity dimension (or brightness, Q) produced by a decrease in the

relative S cone contribution.

In other words, the CIECAM color space

depends on the extensive redistribution of the S cone outputs (equivalently, the effect of

short wavelength light) in the definition of the opponent dimensions. A similar redistribution

is silently effected in CIELAB by the fact that the "red" (X) and "green" (Y) tristimulus

values include a substantial "violet" content.

The diagram (right) shows the spectrum locus and hue coefficients in CIECAM. The key

differences with the postreceptor opponent functions are primarily in the "yellow", "red"

and "violet" (and extraspectral) hues, and in the sharply curtailed "violet" end of the curve.

The recognition features are the positive hue coeffients (and second null point) on the a

C

(L–M) dimension in "violet" wavelengths — which is small in CIECAM but much larger in,

for example, the Hurvich & Jameson perceptual opponent dimensions or in

CIELAB; and the relatively small negative

values for "violet" hue coefficients on the bC

(L+M–S) dimension.

The distribution of surface colors (below)

shows a much more circular outline in the chroma rings, and better placement of the

yellow and blue violet colors in relation to the vertical null line. However, there is still

significant irregularity in the chroma contours, visible as the "wedge" exaggeration of chroma

distances in the yellow green and red

directions, and in the crowded hue spacing in yellow greens, reds and blue greens and the

exaggerated hue spacing in greens.

the CIECAM perceptual

opponent space

(top) plot of spectrum locus;

(bottom) opponent hue

coefficients

munsell color samples in CIECAM ab

space munsell target colors for value/chroma 4/2 to 4/12 and

8/2 to 8/12

At this point, the divergence of the color distribution from the ideal, perfectly circular

distribution runs up against a variety of methodological issues. One is that the

accuracy of Munsell scaling has been questioned; for example, it is generally agreed

that the Munsell hue spacing across green colors is too large, and the chroma scaling

seems to be inconsistent across hues and values.

Nevertheless, the problem with the chroma scaling likely represents a genuine aspect of

color vision. We get a better picture of this problem if look first at the raw data: the

original X,Z tristimulus values in a single hue/chroma plane, with the X dimension

centered on Y and expanded to produce a

near circular ring at chroma 6.

distribution of munsell samples on x,z tristimulus values

for chroma levels 2 to 16 at Munsell value 6

In the 1960's it was discovered that accurate color modeling requires the opponent

dimensions to be rescaled by different exponents within each quadrant of the hue

plane: the distribution above displays the reasons for this. The chroma values for green

extend farther then those for red; the violet chroma values are grossly inflated compared

to the yellow; and there is a linear flattening of the chroma rings along the abscissa, from

chroma 8 and higher for hues between 7.5G

to 7.5YR. (See also the Munsell chroma contours as displayed in these chromaticity

diagrams.)

The geometrical problem appears more clearly in the deviation of each hue sample from the

circular placement in its chroma level. This

produces the diagram below; value 6 is used because it is the only hue/chroma plane that

completely covers all hues out to chroma 14.

deviations from circular chroma deviations of normalized Munsell chroma from a

perfectly circular chroma, for chroma levels /2 to /14 at

Munsell value 6

The undulating curve indicates that the

chroma scaling is too large in the direction of yellow and blue, and too small in the

crosswise direction, toward green and purple, and that the deviations grow larger as chroma

increases. The orange curve shows that the

problem persists in CIECAM.

The hues where the maximum deviation occurs in each quadrant shift slightly as the

chroma increases, but the basic pattern is relatively stable across different lightness

levels, different compression exponents (when applied uniformly to all colors), and different

locations of the achromatic center. The pattern is primarily determined by the cone

fundamentals or color matching functions used

to define the cone excitation space, and by the numerical definition of the opponent

dimensions. The axes of the deviations are also not exactly perpendicular, as shown in the

diagram (right).

The correction for these deviations is probably

a more nuanced specification of the compression exponent. There are at least

three different problems to solve. The first is the increased, eventually linear compression

of chroma spacing along the zero S (=Z) line for hues between 7.5G to 7.5YR at chroma

above 8. This is clearly visible as the flat chroma boundary across the yellow part of the

color distribution in the x,z and opponent

spaces (diagrams above and right).

dimensions of eccentricity

in the

postreceptor opponent

space

The second problem is the spike of inflated b+ chroma values, which is due to the peak

values of the Lum (L+M) sum where they cannot be moderated by subtracting S values

near zero. The effect disappears across the yellow orange and orange hues because these

colors are substantially less luminous. This implies a smaller exponent (a larger chroma

deduction) across the yellow green hues.

The third variation, the g–m+ and g+m–

deviations, suggests a third exponent operating in relation to the sign of both

opponent dimensions: the exponent produces a relatively smaller compression for hues

where the sign product of the ab dimensions

is negative (greens or purples), and a higher compression when the sign product is positive

(oranges and blues).

Perhaps the most significant themes to emerge in this discussion of undefined

additional corrections is the regulatory

importance of the S cones in the specification of an opponent color space, and

the complex interplay of different compression, rotation and normalizing steps

necessary to reach an approximately circular scaling of perceived chroma.

As mentioned earlier, many of the problems described above are minimized by direct use

of XYZ tristimulus values, because these already redistribute the S ("violet") content to

the other dimensions — so that the "red" (X) dimension is actually a magenta, the

hue/chroma planes are already perpendicular to the luminosity dimension, and the exponent

compressed dimensions form nearly circular chroma rings. But this means that many of the

necessary transformation steps are

"precooked" into the XYZ values; alternately, that the XYZ values must be

"uncooked" (transformed or rotated) to get back to the (theoretically) primitive LMS

values.

Starting from the LMS values displays the

essential information processing steps more clearly, and shows that color vision is a tightly

integrated, precisely balanced process. It also confirms that current color models do not yet

describe it accurately.

The various aysmmetries in color space and color

perception described in the previous sections appear across all aspects of color. In this

section we explore how they affect color discrimination on the dimensions of lightness,

hue and chroma.

Measuring Perceptual Discrimination. The

perceptual geometries of vision are identified through judgments of color difference — by

comparing two colors that are different along one or more of the colormaking attributes,

while holding the other attributes constant. The kinds of questions addressed in this way

are:

• What is the smallest stimulus difference we

can perceive on each of the three colormaking attributes?

• Does discrimination ability change as the physical properties or intensity of the stimulus

changes?

• How does change on one colormaking

attribute affect color appearance on another colormaking attribute?

All these questions concern related colors —

one color seen in contrast to beside another. As a bridge between the realm of color

discrimination and the colorimetric definitions

of color matching, I open each discrimination section with the color geometry predicted by

standard chromaticity diagrams, which describe unrelated colors or colors perceived

in isolation.

The "Just Noticeable Difference". For

starters we need a method of measuring discrimination that can apply to any color

attribute we can manipulate by changing a physical stimulus. The metric discovered in

19th century psychophysics and used frequently since then is the just noticeable

difference or jnd.

the geometry of colormaking

attributes

As shown at right, a stimulus is presented at a

starting quantity Q of a stimulus attribute (luminance, chromaticity, or hue for colors).

Once the viewer is adapted to this stimulus, the attribute is increased by varying amounts

and each time the subject is asked, yes or no, if there is a difference in the stimulus. After

repeated trials the increment T that produces a perceptible difference is identified, or the

increment that produces a correct response 75% of the time is used to compensate for the

effects of guessing.

This defines a quantity of stimulus change T,

known as the difference threshold or 1 jnd. When the starting quantity is the stimulus zero

value (complete absence of the stimulus),

then the first jnd value T is called the absolute threshold Q

0. This is the minimum stimulus

quantity necessary to produce any sensation.

The process can be repeated by using the previous value Q as the new starting value,

increasing the stimulus intensity again until a new difference appears, and taking this new

value of T as a difference threshold at that stimlus intensity. By repeating this procedure

across incremental increases in the stimulus

quantity, the subjective sensation produced by any physical attribute can be measured off

using the "yardstick" of the just noticeable difference.

The Weber Fraction (∆Q/Q). At each step

the jnd is the smallest detectable increase T in

the stimulus, given the starting value of the stimulus. It turns out that this increase is

often a constant proportional increase (k) in the stimulus intensity, which is defined by the

Weber fraction (pronounced Veybur):

k = T/(Q + Q0) or equivalently ∆Q/(Q +

Q0)

Weber's law asserts that the ratio k is constant across a wide range of stimulus

quantities, although the value of k is different for different sensory domains or

types of stimulus. If this is assumed to be true, then Fechner's Law allows the

estimation of the sensory intensity (S) from the stimulus quantity, as:

S = a + b*log[Q + Q0]

just noticeable difference in

a stimulus of quantity Q

where a and b are applied to remove negative log values and match the stimulus units to the

perceptual quantities. It is now, especially in color vision research, typical to express this

relationship as a power function, known as Steven's Law, where the exponent 1/e is

typically less than 1 (e=2 or 1/2 is the square root)

S = b*[Q + Q0]1/e

where b is used to fit the stimulus units to a

practical perceptual scale. Similar power functions occur in all sensory domains —

vision, taste, hearing, touch, smell, pain and

muscular contraction (sensations of weight or effort) — although the exponent in each

domain is different. In fact, log or power functions similar to Fechner's Law or Steven's

law are used in many scales related to energetic quantities — stellar luminances in

magnitude, sound in decibels, earthquakes on the Richter scale, ion ratios on the pH scale,

and so on.

I should also mention a generic formula that is

used to model the depletion of photopigment by light (derived from an enzyme kinetics

curve):

where R[%] is the response as a proportion of the maximum possible response, L is the

stimulus luminance (or retinal illuminance), n is the response compression exponent (usually

around 0.70), and σ50

is the luminance value

that produces a 50% response (the half

saturation value), and Rmax

is the maximum

possible response. (Zero is the assumed

minimum response.) This function is discussed in the section on luminance adaptation.

The Power Function in Lightness. What is

the effect of the Weber fraction on perception?

The relationship between the perceived lightness of a surface color and its

reflectance or luminance factor (luminance as a proportion of the luminance of an ideal

"white" surface) shows the perceptual geometry very clearly.

lightness as a function of reflectance relationship between surface reflectance (luminance

relative to the luminance of a white standard) and

perceived lightness (CIE L* scale; divide L* by 10 to

get the Munsell value V)

This power function or nonlinear

psychophysical relationship between lightness and relative luminance is approximately a

square root function for reflectances above

~7% (that is, 1/e is about 0.43). The curve for brightness discrimination is approximately

the cube root (1/e = 0.33) of absolute luminance.

Underlying these sensory power functions is

the common sensory property of response

compression. Fundamentally, response compression represents a compromise

between the physical limitations of an organism and the enormous range of a real

world stimulus. In effect, the organism experiences an increase in the stimulus as a

sensory change proportional to the remaining sensory response — which becomes smaller as

the sensation approaches its physiological upper limit.

The graphic (right) illustrates the perceptual

effect of response compression in lightness. Equal increments of the stimulus intensity

become less and less perceptually potent as

the intensity of the stimulus increases, just as a single lightbulb adds considerably to the

illumination of a candlelit room but in broad daylight makes no impact at all. To raise

lightness or brightness by equal perceptual amounts, the luminance or reflectance must

be raised by a greater absolute amount at each step. Thus an equal interval luminance or

reflectance scale (equal Lum) produces a brightness/lightness scale (B/L) skewed

toward lighter values, while an equal interval brightness/lightness scale (equal B/L) arises

from a reflectance or luminance distribution

(Lum) skewed toward lower values. The effect is to divide the lightness distribution into two

parts — light grays and dark grays — with the proportionately best lightness discrimination in

the light grays (medium to high luminances).

"Less" and "more" luminance is always relative

to our light adaptation around an average luminance (which is usually a 19% luminance

factor for the "middle gray" used in graphic arts but is 10% to 13% for the "gray"

luminance used to meter photographic exposures). For illumination levels above a few

lux the subjective effects of response compression are remarkably consistent.

The sensory response compression displayed in psychophysical power functions is the single

most important asymmetry in color vision. Its effect throughout the visual system is to

create curvatures or nonlinearities in stimulus intensities across steps of perceptual

difference that appear to us as evenly spaced

"just noticeable differences".

Luminance Discrimination. Response compression shows that increasing quantities

of light produce decreasing sensory changes as the light intensity becomes very high.

However, this tradeoff is not consistent across

all luminance levels. Instead, the Weber fraction or "constant proportion" between the

starting luminance and a just visible increase in luminance varies with the average light

intensity.

two sides of response

compression

as defined from

an equal luminance scale (left)

or an equal brightness scale

(right)

In fact, changes in the Weber fraction are apparent just within the range of luminances

that characterize surface reflectances (diagram, right). The first jnd below a pure

"white" surface represents about a 2.6%

decrease in luminance; but at low luminances (low reflectances, or very dark surfaces) the

incremental change in luminance rises to 10% and above. This imposes a hard "floor" or

minimum sensitivity on lightness gradations, which we do not experience because nearly all

surfaces have reflectances greater than 5%.

If we consider difference thresholds in the

brightness of two lights viewed side by side, in the Weber fraction (∆L/L) similarly changes

across luminance levels from .0001 to

10,000 cd/m2 (equivalent to light intensity or illuminance on a white surface of

about .0003 to 30,000 lux), as shown below.

weber fraction across luminance levels adapted from Wyszecki & Stiles (1982)

At scotopic light levels (below 0.005 cd/m2) a

barely visible increase in luminance must be

23% or more greater than the starting luminance. At photopic levels above

100 cd/m2 the sensitivity is much greater, and

luminance need only increase by as little as

1.3% to produce a visible difference.

The kink in the curve at about 0.005 cd/m2 is due to the different response compressions in

cone and rod photoreceptors. It indicates that the cone mediated luminance response

persists to lower light levels than the cone

mediated chromatic response, which is

usually said to disappear at around 0.1 cd/m2

the weber fraction is not

constant across luminance

changes in lightness

perception

or 0.02 lux. On either side of this kink the Weber fraction shifts as two different

exponential functions, one for scotopic vision, and the other for mesopic vision where both

rods and cones are active.

At very low light intensities, it is estimated

that the eye when completely dark adapted can perceive one or a few photons at a time,

so the visual threshold is very close to the physical zero value of the stimulus. Very high

light intensities can completely saturate the photopigments in the eye and make any

changes in intensity impossible to see. This saturation occurs at luminance levels

somewhere above 100,000 cd/m2 — the exact

value depends on the duration of the exposure

— but the chart shows visual sensitivity

already starts to decline above 1000 cd/m2.

At peak sensitivity the eye still responds to a limited luminance range, roughly 1:100

around any specific luminance adaptation

value. Photometric or lightness scales are usually divided into 100 units because, at

photopic light levels, the eye is able to discriminate at most many steps in surface

reflectance when the eye is adapted to the "white" luminance.

50 perceptually equal luminance steps dark lines inserted to eliminate edge contrast

enhancement (mach bands), which reduces luminance

discrimination

For example, the illustration shows 50 luminance steps, from black to white, that

should appear perceptually equal across the entire range. (The contrasts you are able to

see depend on the brightness and contrast settings on your computer monitor.) Note that

the differences between adjacent steps are barely visible with edge enhancement, and

become indistinguishable when separated by a black line.

Now let's step outside the visual range and look at the scope of vision across all light

levels. the graph shows the same compression function across familiar illumination levels.

equal perceptual differences across illuminance levels

What may be unexpected, and is delightful,

about the comprehensive light sensitivity curve is that the visual range defines

similar compression functions at different adaptation states. Two sections of the

illuminance curve, converted to the luminances of a reflecting "white" surface, are

shown as examples: one at twilight

adaptation, the other at late afternoon adaptation. The result of this response

uniformity is that we see the same relative lightness values attached to the corresponding

reflectance factors, even though the level of illumination and the absolute differences in

surface luminances may have significantly changed. The interior proportions of "light

space" remain perceptually constant — the

ultimate benefit of Weber's law.

Finally, the sensitivity of the eye to luminance or lightness changes depends on the

apparent size of the color area. Contrast

sensitivity peaks for surface areas subtending a visual angle of about 0.2° (the apparent

width of a #2 pencil seen from 7 feet, or less than half the width of the full moon).

Sensitivity declines slightly but remains good for areas of much smaller size (such as the

lines forming the letters of this page), and more rapidly for visual areas subtending 1° or

more (a USA dime at 3 feet).

Hue Discrimination. Consider next the ability

of normal trichromats to see the difference between two similar hues, a test of hue

discrimination.

As a template of the hue discrimination we

expect to find, the diagram below shows the hue angle distance between adjacent

wavelengths at the spectrum locus, as measured at the white point, using three

different chromaticity diagrams. The log hue angle difference is used because the hue

angle is made smaller by increased chroma (distance from the white point), and chroma

shows response compression as chroma

increases.

Again, the chromaticity diagrams represent unrelated colors as produced entirely by the

L, M and S cone outputs. So they represent

the hypothesis that the cone outputs define our hue discrimination abilities. If actual hue

discrimination does not match these curves, then hue discrimination must be affected by

additional visual processes.

hypothetical spectral hue discrimination based on the log hue angle difference in 2° and 10°

chromaticity diagrams (from Stockman & Sharpe cone

fundamentals) and CIELUV under equal energy

illuminant; smaller wavelength separation implies

poorer hue discrimination

There is fair agreement among the three predictions. All suggest two points of peak hue

discrimination, around 480 nm ("blue") and 570 nm ("yellow", which is more pronounced

in the foveal model), somewhat diminished hue discrimination in "green" wavelengths,

and steadily weakening discrimination at the spectrum ends, especially in "red"

wavelengths. The result is approximately a W

shaped function with higher vertical bars at

either end than in the middle.

These curves are hard to visualize as a color

circle, so the diagram below presents the CIELUV predicted spectral hue angles

projected to an equal radius (as shown below for the spectral location of "green" at

540 nm). This shows the predicted perceived

spacing of spectral hues as the radial distance between hue markers.

spacing of monochromatic hues in

CIELUV the spectrum locus of the 10° observer in the CIELUV

chromaticity diagram, from 380 nm to 830 nm in 10

nanometer intervals, projected to equal radius; visual

complementary colors are directly opposite on the hue

circle; extraspectral hues shown in black

The two areas of maximum hue discrimination

(at 570 nm and 480 nm) are represented by widely spaced spectral markers, and the areas

of poor sensitivity ("blue violet," "green" and

"red") by crowded or overlapping markers. The lowest "green" sensitivity (at middle

"green", 520 nm) is approximately midway between the "yellow" and "cyan" peaks.

Now here is observed hue discrimination performance, measured as the minimum

wavelength difference necessary to make two monochromatic lights, presented one above

another at equal luminance, appear just visibly different. The three curves represent

hue discrimination ability at three illuminance levels (in trolands) for three stimulus sizes

(angular widths).

spectral hue discrimination the minimum difference between two wavelengths

necessary to create a "just noticeable difference" in

hue; a low score indicates better hue discrimination (2°

curve from Wright, 1941; others from Bedford &

Wyszecki, 1958)

These curves do not correspond very well to the curves predicted from chromaticity

diagrams. Although the experiments show the

distinctive W curve identified in CIELUV

(above), the "basins" of high hue

discrimination are much broader, and the effective wavelength change of 1 or 2

nanometers is smaller, than predicted. Roughly double the hue change (4 nanometers

or more) is required to produce a visible difference in middle "green", much less than

the predicted 10:1 difference between "yellow" and "green" acuity. The decline in hue

discrimination at the spectrum extremes is also more extreme, and closer to "orange"

hues, than predicted. Finally, actual hue

discrimination is very sensitive to stimulus size and brightness, a topic explored in a

later page.

The areas of best and worst hue discrimination differ from the chromaticity predictions. Best

discrimination is around 490 nm ("cyan") and

595 nm ("orange"), which are almost exact visual complementary hues; the "green" peak

of weaker discrimination is closer to 540 nm. There is also a second hump of poor

discrimination at around 450 nm, bounded by a third area of good hue discrimination at

around 420 nm; these are completely absent from the predicted curves.

However, a generally very good match is

obtained in a calculation from the absolute change between two spectral wavelengths in

scores on the y/b, r/g and w/k opponent functions combined (right). The log of this

absolute change represents the "orange" and "cyan" basins approximately correctly, gets

the two peaks of poor "blue" and "green" discrimination, and also catches the third area

of good hue discrimination around 420 nm.

There are a few details where the opponent

dimensions diverge from the experimentally observed hue discrimination curves. But the

overall fit is close enough to suggest that the opponent dimensions, not the cone

fundamentals, define the geometry of hue

discrimination.

In the previous section I explained that the unique hues do not define the opponent

dimensions. A logical corollary is that the unique hues do not explain hue

discrimination, which is easy enough to test.

log hue discrimination

computed from opponent

functions

First the opponent dimensions must be

transformed to show each hue as a proportional mixture of two unique hues, as

Hering required. (This also minimizes the effect of changing brightness or saturation in

the monochromatic lights.) After this adjustment, the opponent functions appear as

shown at right, and their values are called hue coefficients or hue proportions. This shows

that equal mixtures of unique yellow and

unique green, or unique yellow and unique red, are quite close to unique yellow, rather

than halfway toward the other hues.

The unequal spacing occurs because the results are shown along a nanometer scale,

which corresponds to the visual spacing of

hues in a diffraction grid spectrum. This is remedied by respacing the spectrum to

correspond to equal changes on the hue coefficients (the proportional mixtures of two

unique hues). As a result, some parts of the spectrum are perceptually expanded while

others are greatly compressed (diagram below). This new spacing is hue discrimination

acuity predicted from the unique hues.

plot of spectral hue

coefficients

based on unique hue

mixtures

from Hurvich (1997)

spectral hues spaced along a hue coefficient scale

based on hue cancellation with monochromatic lights

It's intriguing that the predicted hue

discrimination curves from hue coefficients

and CIELUV are almost indistinguishable. Again the best acuity is located around

485 nm and 573 nm, with worst acuity at around 520 nm and at the spectrum extremes.

The proportional change in hue discrimination from best to worst is too large (except for the

spectrum ends), and the third area of acuity at around 420 nm is missed completely.

To summarize: Neither the cone fundamentals (chromaticity diagrams) nor the unique hues

predict observed hue discrimination ability as well as a log change score on the three

opponent functions combined. The flaw is that the log opponent curve includes the w/k

function or brightness change, which is

excluded from chromaticity diagrams and was partially excluded from the experimental

results. In fact, predicting hue discrimination is a complex problem that requires several

added assumptions to work satisfactorily. (The discussion in chapter 8, "Chromatic

Discrimination" of Color Vision, 2nd ed. by Peter Kaiser and Robert Boynton provides an

excellent overview.)

However, hue flexes and shifts in response to

viewing or contextual factors, including color luminance, chroma, color contrast, chromatic

adaptation and cognitive interpretation of the scene. It is reasonable to expect that hue

discrimination cannot be explained by a single

zone or mechanism in color vision — though the opponent dimensions, provided they

include luminance (the w/k contrast), do an excellent job.

Hue Purity Discrimination. As explained in the introduction to chromaticity diagrams,

hue purity (chroma or saturation) can be defined as the distance on a chromaticity

diagram between a color and the white point, when all colors are standardized to have the

same brightness.

The diagram below shows chroma measured in

chromaticity diagrams from an equal energy white point to the spectrum locus at each

spectral wavelength. As before, the curves are based on three different chromaticity

diagrams, expressed in log values because chroma shows response compression as

chroma increases. The underlying measurement units were different across the

three chromaticity diagrams, so all have been

normalized to the same maximum and minimum values (which occur in the "violet"

and "yellow" wavelengths).

These curves represent unrelated colors as produced entirely by the L, M and S cone

outputs. So they represent the hypothesis

that cone outputs alone define our chroma discrimination. If actual chroma discrimination

does not match these curves, then it must be affected by additional visual processes.

relative maximum saturation of spectral

hues

based on 2° and 10° chromaticity diagrams from

Stockman & Sharpe (2000) cone fundamentals and

CIELUV, all under equal energy illuminant; scaled to the

same maximum and minimum values

The first point to note is the poor agreement

among the three chromaticity diagrams. All (especially the foveal model) suggest a single

minimum value at around 570 nm ("yellow"), where the spectrum locus comes closest to the

white point. Both the CIELUV and 10° curves

indicate a second chroma minimum or inflection in the curve at around 483 nm

("cyan"), and reduced "green" saturation in between. All models show elevated chroma at

both spectrum ends, but the wide field (10°) and CIELUV curves indicate "violet" chroma is

higher.

What do the data say? Several testing

methods have been used to assess saturation intensity or saturation discrimination in lights,

but many are related to Helmholtz's method for measuring Sättigung (excitation purity)

by the mixture of "white" and monochromatic lights of equal luminance. In these tasks,

viewers:

• judge the amount of "white" content in a

monochromatic light ("yellow" contains much white, "blue violet" none at all);

• count how many "just noticeable" steps of added white light it takes to make the spectral

color disappear completely (about 5 for "yellow"; 20 or more for "blue violet"); or

• measure the minimum quantity of monochromatic light necessary to produce a

just noticeable tint in white light (a lot of "yellow", very little "blue violet").

These tests (especially the last) are analogous to the painter's tinting test and clearly

illustrate the overweighting of B cones in color vision. The geometry below shows the

quantity of pure hue necessary to tint a pure "white" light, or the tinting strength of

monochromatic light at constant luminance.

a tinting test using light mixtures proportional mixture of a monochromatic light and a

"white" light of equal luminance necessary to produce a

just noticeable difference from white; from Priest &

Brickwedde (1938)

These curves show reasonable agreement with the foveal (2°) chromaticity diagram, implying

that the overlap in cone sensitivity curves primarily determines our chromatic sensitivity

(or that Priest and Brickwedde used a foveal presentation of the color stimuli).

The data allow some quantitative conclusions: a 15:1 mixture of "white" and monochromatic

"yellow" light is necessary to produce a just noticeable tint in white, but for "red" light the

mixture ratio is around 170:1, and for "violet" light it may go as high as 1000:1! By this

measure, monochromatic "violet" light has over 60 times the tinting strength of

"yellow" light.

These curves only show the first chromaticity

step from the white point, not the overall geometry of chromatic intensity across the

entire range of saturation values. They also do not indicate the response in surface colors,

which are determined by more complex

perceptual processes. In surface colors, any simple relationship to cone outputs is lost. As a simple illustration,

the diagram (right) plots total chromaticity signal (computed as the ratio between the L,

M and S chromatic and achromatic responses

at each lightness, summed across all three cones) against the CIECAM measure of

saturation for five cardinal Munsell hues (5Y, 5R, 5P, 5B and 5G), across the physically

possible chroma range at Munsell values 4, 6 and 8, into equal area cone fundamentals. The

cone outputs were derived as the transformed tristimulus values for all

colors. The basic feature is a relatively linear response between saturation and cone

excitation across the red, yellow and green

hues, but substantial response compression in the blue and violet hues.

The cone responses also show a very large

initial increment in saturation in relation to the

chromatic signal, a jump that is too large to be traced in detail by the Munsell chroma

intervals. This indicates that the visual system is especially sensitive to small chroma

differences from the achromatic point, and becomes relatively less sensitive to chromatic

differences among strongly saturated colors. Finally, note that the basic function within

each hue is invariant across lightness levels, as we would expect of saturation.

A major perceptual factor affecting the relationship between cone excitation and

perceived saturation is luminance contrast. Ralph Evans used the concept of brilliance to

integrate contrast effects across both self luminous and surface colors. Brilliance

comprises four qualitatively distinct and

mutually exclusive color perceptions — black, grayed (appearing as a surface), fluorent

(appearing as a glowing surface) and self luminous (appearing as a light) — as shown in

the schematic.

qualitative changes across Evans's brilliance

luminance (Y) on response compressed (lightness)

saturation and

total cone chromatic signal

scale; colored dots show G0 values for the unique hues

Evans presented viewers a donut shaped field

of achromatic (white) light, 10° wide and at a

constant, moderate luminance (320 cd/m2),

then projected increasing amounts of highly

chromatic, filtered light into the 2° dark central area. First the area appeared black;

then, as the luminance of the colored light was increased, the shadow changed at threshold

from black to a dark, grayed (dull) surface color. As the color luminance increased, the

color became more saturated (less gray) until

a zero grayness point of maximum hue purity was reached, at a luminance well below

the luminance of white. At still higher luminances the color became fluorent or

glowing, ambiguously between a surface color and a self luminous color. Finally, at a

luminance roughly twice the "white" surround, the fluorent effect abruptly disappeared and

the color appeared unambiguously as a light.

Besides illustrating the importance of

luminance contrast to the perception of saturation, and to the perception of surface

colors as opposed to light colors, Evans's method identifies the luminance ratio between

the color and the white surround necessary to produce the perception of fluorence. In effect,

the "tinting strength" of different hues is now

defined as the power to overcome a luminance contrast.

a tinting test using luminance contrasts log of the ratio between surround luminance and color

luminance where the color reaches zero chromatic

grayness, by dominant wavelength of color stimulus;

from Evans (1974)

Evans's method identifies the two saturation

minimum values at around 485 nm and 570 nm and the suppressed area of "green"

chromatic strength between them (as predicted by CIELUV), but shows a lower "red"

saturation through the end of the spectrum (roughly 10 times stronger than "yellow"

light), and an extremely high chromatic

strength of "violet" light, which is here roughly 150 times that of "yellow" light!

This zero grayness function is similar to the

maximum hue purity or chromatic strength judged by other methods, but again it is not

predicted well from the chromaticity diagrams. However, it is very closely matched by the log

(response compressed) sum of the absolute values of the y/b and r/g functions at each

wavelength, divided by the w/k function to

represent the luminance contrast ratio (right). The fit is very close, and clearly indicates that

the chromatic intensity due to luminance contrast is defined by the opponent

functions.

To summarize: all predicted and observed hue

purity or "tinting strength" geometries show a minimum chromatic strength around 570 nm

("yellow") and maximum in the "violet" wavelengths. Otherwise, the characteristics of

hue purity depend on how it is measured. The evidence suggests that chromatic intensity

conflates two perceptual contrasts: (1) the chromaticity difference between the color

and a white of equal luminance (white as a chromaticity standard), and (2) the luminance

difference between the color and its surround

(white as a luminance standard). The same "brilliance" percept is applied by the visual

system to two different definitions of a "white" contrast.

Perceived chromatic intensity may be determined by the cone fundamentals or by

the opponent dimensions or some combination of the two, depending on the viewing context.

The light mixture tinting curves are approximately predicted by the 10° or CIELUV

chromaticity distances, but Evans's luminance contrast or zero grayness curve is closely

predicted by the opponent functions. In

log hue purity computed

from opponent functions

particular, the cone based chromaticities dominate the saturation perception of isolated

colored lights, while the opponent dimensions dominate saturation perception in related

surface colors.

As explained on the previous page, there are

many definitions of hue purity, each definition linked to a different perceptual

measure, each measure producing a different perceptual geometry. It is probably misleading

to define hue purity as a single perceptual attribute or contextual judgment.

Color Attributes Combined. So far the geometry of the colormaking attributes has

been described in terms of differences in the physical stimulus attributes — luminance and

wavelength in particular. This section considers the geometry created when one

colormaking attribute is described or measured in relation to another.

Brightness and Saturation. The sibling relationship between brightness and hue

purity, described on a previous page, was encountered in the 19th century with a

research technique called heterochromatic brightness matching. In this task, viewers

matched the apparent brightness of two

different wavelengths of monochromatic light, or of a spectral light and a standard white

light, to determine the photopic luminous efficiency function.

It turns out this task is difficult to do, and delivers unreliable results, because the intense

saturation of spectral hues is perceived as part of the color's luminance. This brightness

increased by saturation, which grows stronger as saturation increases, is called the

Helmholtz-Kohlrausch effect. It might better be called chromatic luminance, since

"white" or achromatic luminance is the standard of comparison. It appears in both self

luminous and surface colors, although it is

most pronounced in spectral lights.

the helmholtz-kohlrausch effect in lights observed ratio of luminance (white)/luminance

(color) when both lights appear to have equal

brightness, shown on the CIE 1976 UCS chromaticity

diagram; orange lines show measured ratios, green

lines show ratios extended linearly to spectrum locus;

adapted from Sanders & Wyszecki (1964)

The diagram shows the ratio of "white" luminance to color luminance as actually

measured for partially desaturated hues, and

as projected to the spectrum locus by a straight line. (Tests within single hues show

the HK effect increases approximately linearly with distance from the white point.) This

shows that the HK effect is stronger in some hues than in others: (1) nearly absent in

"yellow green" to "deep yellow" hues, (2) moderately high in "orange", "green", "cyan"

and "blue" wavelengths, and (3) very high in extreme "red", "violet" hues and their

extraspectral ("purple" and "magenta")

mixtures. In addition, the HK effect varies significantly across viewers, quite strong in

some and nearly nonexistent in others.

How large is chromatic luminance contribution to spectral hues? The diagram shows the

increase in the luminance of a "white" color

area necessary to match the brightness of a 10° chromatic color area at a constant

(mesopic) luminance of 20 cd/m2. The

smallest increase is for spectral "greenish yellow" "yellow" light (565 to 575 nm), where

chromatic luminance is equal to about 2 to 3

cd/m2 of "white" luminance; the largest is for

extraspectral "purple" (c541 nm), where the

increase is almost 27 cd/m2. For hues from "violet" to "green", saturation seems to add

about 8 to 14 cd/m2 to spectral hues.

For surface colors, where the lightness of a colored tile must be matched to a gray tile

under the same illumination, the HK effect seems somewhat smaller than for lights and is

more equal around the hue circle; it is also dependent on the chromaticity of the light

source. Under daylight illumination, a comprehensive sample of moderately

chromatic colored tiles produced an average

lightness increase of L* = 7.1 for tiles with an average CIELAB chroma of C = 45.

Chromatic luminance causes substantial

additivity failures in brightness matching. For example, if "blue" and "yellow"

monochromatic lights are separately matched

to a "white" light, the mixture of the "blue" and "yellow" lights is substantially dimmer

than the "white" light at double luminance. This violates the basic algebraic rules of

trichromatic theory. The size of the additivity failure depends on the dominant wavelength of the two lights

in the mixture. This appears in the following procedure. The brightnesses of different

monochromatic lights are matched to a

"white" standard of constant luminance (which in many studies has been an incandescent

source with an "orange" CCT of ~2800°K). Then the luminance of the "white" light is

doubled, each monochromatic light is mixed in turn with a constant "green" (520 nm), and

the brightnesses of the mixture and white light are compared again.

For most viewers, the mixture of "yellow" and "green" lights produces the same brightness

as the doubled "white" standard. However, the mixture of "violet" and "green" creates a

"cyan" that is too bright (enhancement), so the "violet" luminance must be reduced by

40% to restore the brightness match. The

"yellow" mixture of "red" and "green" is much too dim (cancellation), so the "red" luminance

must be increased by 90%. Though not shown in the diagram, mixtures of "violet" and

cancellation and

enhancement in the

additive mixture of spectral

lights

after Guth et al. (1969)

"white" [orange?] also produce cancellation, while mixtures of "red" and "violet" are

strongly enhanced.

In a related procedure, spectral lights are

adjusted to match a "white" standard, then each colored light is mixed in turn with the

"white" light, and the mixture brightness compared to a "white" light at double the

original luminance. This produces a similar curve, but with a slightly greater cancellation

in "cyan" wavelengths. It also shows that lights around 570 nm and 470 nm (unique

yellow and unique blue) have no enhancing or canceling effect on the "white" [orange?] light.

These additivity failures explain several puzzling features of color vision. The

cancellation produced by mixtures of "red" and "green" light, which is very strong no matter

how additivity is measured, accentuates the r/g opponent contrast and likely explains

why mixtures of red and green paints produce

such dark neutrals. The cancellation effect only occurs in the spectral area where the S

cone outputs are effectively zero, so it likely creates unsaturated color zones (darkened

yellow or red color sensations), and explains why a "yellow" sensation in surface colors

cannot be produced by the partitive mixture of red and green dots. And the minimal

luminance change produced when "blue" or "yellow" light are added to "white" light

suggests that luminance adaptation is not

involved in the chromatic adaptation to shifts in daylight chromaticity. Overall, the

chromatic enhancement produced by the S cone, and the cancellation produced by the L

cone, introduce many complexities to color perception.

The HK effect and related additivity failures demonstrate that brightness/lightness and hue

purity are not independent dimensions: one attribute affects the other depending on

the level or intensity of both. We saw a similar interdependence of hue purity and

brightness contrast in measures of brilliance, and it is a general feature of color vision. It

implies that our idea of color as separable colormaking attributes or dimensions, each

varying independently of the others,

misrepresents the integrated and highly dynamic nature of color perception.

Hue and Saturation. A second geometry arises in the linkage between hue and hue

purity, which is the geometry of a chromaticity diagram. This was intensively

studied in an effort to develop a reliable colorimetric measure of apparent color

difference between two similar colors.

How well do we discriminate among more

muted colors defined inside the two dimensional chromaticity plane? These

measurements are much more arduous to collect, but in the 1940's W.D. Wright and

David MacAdam did so for fixed test colors of lights differing in hue and saturation but

having constant brightness. MacAdam took the

novel approach of asking subjects to match exactly a test light with a mixture of primary

lights, then used the margin of error in primary mixtures accepted as a match across

repeated test runs to define the perceptual minimal limits of color difference.

hue and saturation discrimination left: MacAdam ellipses proportional to hue and

saturation discrimination in the CIE 1931 chromaticity

diagram; right: the same ellipses in CIE UCS (1976);

ellipses are shown 10 times actual size for easier

comparison

These error boundaries around the 25 test colors in MacAdam's study are indicated by

ellipses placed in a standard chromaticity diagram (CIE 1931 standard observer, above

left); the size of the ellipse symbolizes the amount of hue and/or saturation change

necessary to produce a visible difference in color.

It immediately appears that the ellipses are not equal in size, shape or orientation of major

axes. The main cause is that the CIE 1931 diagram does not represent equal perceptual

distances as equal distances in the chromaticity space; it grossly expands the

area of green colors in relation to blues and reds. (This is the same problem that causes

Greenland to appear larger than Africa on some world maps.)

MacAdam's approach stimulated several efforts to devise isotropic color spaces or

uniform color scales (UCS) that are perceptually equal in all dimensions and in all

combinations of brightness/lightness, hue and chromatic intensity. In principle, these would

make all MacAdam's ellipses appear as circles

of equal radius, and would provide the framework for accurate and consistent color

difference calculations. The CIE UCS (Uniform Color Space, above right) is a simple version

of these, and it does make the ellipses more equal in size. However, obvious differences

remain, and these appear to be irreducible features of color perception:

• there is a general tendency in blues and purples for discrimination to be weaker in the

yellow/blue direction than in the cyan/red direction (the ellipses are elongated in that

direction); in greens discrimination is worse along a purple/green line; and in reds the

discrimination is worse along a red/cyan line. That is, discrimination errors are elongated in

a Y pattern toward the three corners of the

chromaticity diagram defined by (1) an increase in the S cone outputs relative to the

L+M outputs, and an imbalance of (2) L over M or (3) M or L cone outputs. (That is, the

opponent functions define chromaticity or combined hue and saturation perception

throughout the chromaticity space, as they do separately for hue discrimination and

chromatic strength.)

• discrimination is relatively more sensitive

(the ellipses are smallest) around the white point (gray or neutral colors, where both

opponent dimensions are in balance) and is relatively weakest for each hue at the

spectrum locus (maximum saturation)

• discrimination is relatively more sensitive in

the yellows and oranges where the L and M outputs (the r/g opponent fuction) are in

balance; discrimination is least acute in the extraspectral hues, and is comparable across

other colors

• chromaticity matching is optimal in large

stimulus visual areas (around 10° wide), and grows worse as color areas become smaller,

especially when less than 1° wide (foveal images)

• chromaticity discrimination is much worse

when the color matching is done within a

surrounding area of contrasting chromaticity

• discrimination degrades at low levels of luminance; in particular, sensitivity governed

by the S cones substantially declines at low luminances.

Hue Spacing (Hues Combined). I presented earlier the spectral hue spacing as predicted

by the CIE UCS. That diagram should be applied to the hue spacing of colored lights,

whether monochromatic or broadly emitting.

But what about surface colors? The diagram

below shows the spacing of hues in the chroma based a

CbC plane in CIECAM, an

opponent dimension color appearance model. Hue is indicated by (1) colored circles for

spectral hues at 10 nm intervals as defined by the CIE 10° observer (wavelength indicated

in italics); (2) black dots for average hue angles of target colors the Munsell Color

Order System; and (3) colored dots for the

approximate location of the four unique hues.

hue spacing on the CIECAM acbc plane

under illuminant D65; inner circle: consensus location

of the four unique hues (Kuehni, 2001); middle circle:

markers for Munsell hue angles averaged across 9 color

targets (V = 5, 6 and 7 at chroma C = /8, /10

and /12); outer circle: spectral hues in 10 nm intervals

based on 10° observer; percentages refer to proportion

of 410 nm "violet" in extraspectral mixture with 680 nm

"red"

The overall even spacing of the Munsell hue markers suggests that CIECAM aproximates

quite well a perceptually uniform spacing of surface hues. The spectral hues corresponding

to the ends of the a-, b+ and b- opponent dimensions — at 445, 493 and 575 nm —

agree well with the spectral unique hues or function peaks found in the theoretical

opponent functions. But other landmarks — unique blue at 473 nm, or the peaks of the r/g

function at 524 nm and 610 nm — are

orphaned.

Another difficulty is that the visual complementary hues identified in the CIE UCS

(and other CIE chromaticity diagrams or cone

excitation diagrams) do not match the complementary hues in CIECAM, which is

evident when we connect the location of spectral blues with their yellow or orange

visual complements in the CIECAM acb

c plane

(diagram at right). All the lines are sharply

bent rather than straight, and the same displacement appears in CIELAB. This is not a

displacement of spectral

visual complementary hues

in CIECAM

flaw, because the hue circles in both CIECAM and CIELAB reproduce quite well the visual

complements defined in Munsell (lower diagram, right). (The slight bend in the

CIECAM complementary lines is almost entirely due to the difference in hue spacing

between the Y and PB parts of the hue circle, which are difficult to scale accurately.) Thus,

surface colors and light colors scale differently, and CIECAM scales surface colors accurately.

The diagram above also makes clear that (always with the exception of yellow) the

Hering unique hues do not define the ends of the opponent dimensions. The opponent

functions are important in accurate hue

scaling, but the unique hues are not.

These observations underscore the important structural differences between light and

object colors, and the crucial fact that, contrary to Hering's conjecture, the structural

foundations of color vision do not intrude

themselves into color experience as "fundamental" colors or universal color

concepts.

reproduction of Munsell

visual complementary hues

in CIECAM

What should we adopt as the "correct" standard of hue spacing? Obviously, in a

perceptual system that is dependent on context, there is no single standard. CIELUV

describes light mixtures, which is useful in video or computer related applications but is

not of much interest to painters. The Munsell

color system is free of theoretical or geometrical distortions, but includes small

empirical inaccuracies in the spacing of hue and chroma, especially in greens and violets,

that are revealed in CIECAM; the CIECAM model is based on opponent dimensions that

seem to compress the spacing of Munsell blues and greenish yellows. The overall

disagreement between the Munsell and CIECAM systems is relatively small.

Summary of Color Geometry. Response compression exerts its effects throughout the

visual system. In lightness perception, response compression expands lightness

contrast in low reflectance surfaces, minimizes lightness contrast in high reflectance surfaces,

and represents most of the increments of an

equal interval luminance scale as values above a medium gray. In hue purity perception,

response compression expands chromatic contrast in saturated colors, minimizes

chromatic contrast in dull colors, and represents most of the increments of an equal

interval excitation purity scale as colors below medium saturation.

Color measurements are normally made with the color presented against a background

neutral gray, the adaptation gray. Small color differences are especially noticeable in the

contrast between adjacent color areas. Large color differences or differences between

visually distant color areas may be compressed or distorted in order to render the

complete range of colors in a visual context.

As shown below, there is a bewildering

number of landmarks identified in color vision, including the white points or "balance hues" in

the various types of dichromacy (gray circles), the points of maximum hue discrimination

(white squares), the opponent dimensions,

and so forth. At present we lack two forms of description that can make sense of these

landmarks: (1) a process explanation, starting with photoreceptors and ending with color

appearance, of how color vision can adapt and transform cone excitations into a stable color

perception, regardless of the type of visual stimulus; and (2) an ecological explanation,

anchored in the physical facts of surfaces and species survival, of why human color vision is

adapted to emphasize certain types of visual

information over others.

hue anatomy based on Stockman & Sharpe cone fundamentals

Color measurements are normally made with the color presented against a background

neutral gray, the adaptation gray. Small color differences are especially noticeable in the

contrast between adjacent color areas. Large color differences or differences between

visually distant color areas may be

compressed or distorted in order to render the complete range of colors in a visual context.

Color geometry demonstrates the limited

direct effect of the photoreceptor cells on color experience. The trichromatic mechanism

determines how radiant energy is made

palpable, describes the color of light mixtures, predicts when two different color stimuli may

appear the same (metamerism), and accounts for chromatic intensity; it cannot explain the

location of hue boundaries, hue discrimination in lights or in surface colors, or the Helmholtz-

Kohlrausch (HK) effect. The cone fundamentals and chromaticity diagrams

define the perceptual limits and basic quantities of color; the opponent dimensions

transform these into a geometry that is much

closer to color experience.

Two opponent dimension balance points, one around 470 nm, and the other near unique

yellow (570-580 nm), consistently emerge as perceptual landmarks in studies of hue

discrimination, chromatic intensity and the HK effect. However, the location of these balance

points, and the locations of peak trichromatic hue discrimination at around 590 nm, 480 nm

and 420 nm, strongly suggest that the unique hues are not fundamental landmarks in color

perception.

Nevertheless, there is strong support for a

stable visual balance point at around 570-575 nm ("yellow"). This represents both the

equillibrium point between the L and M cones and the composite brightness/lightness value

(L+M) that is balanced against the S cones (with a peak at round 445 nm). These also

mark the extremes of low (yellow) and high

(violet) chromatic intensity in spectral colors, and S cone outputs have a very large weight

in chromaticity/brightness perception but a less important role in lightness perception.

These relationships are probably adaptations of the y/b opponent function to the task of

chromatic adaptation under natural variations in daylight.

The colormaking attributes are not independent perceptual dimensions. Hue

discrimination and the HK effect show that hue and chroma, and chroma and brightness, are

functionally interdependent at several stages of color vision. The colormaking attributes are

meaningful when used in combination to describe, model or predict the conscious

experience of color, but they are weak when

considered as abstract dimensions of color — especially when used to describe lightness or

brightness separate from hue and chroma.

Finally, the difference in hue spacing between monochromatic lights and Munsell/CIELAB

surface colors, and the qualitative stages in

Evans's brilliance, emphasize that colors of light and surfaces are perceived very

differently. In particular, luminance and spatial contrasts have a dominant role in the

perception of surface colors. Isolated light mixtures are easier to manipulate and

measure as color stimuli, and in principle can stimulate to the limits of the visual system,

and many generalizations about color vision are based on them. But care must be taken to

distinguish clearly between spectral colors and

surface colors when reading or thinking about color, or using color principles in design.

a more natural chroma benchmark? munsell hues at chroma 10 at lightness 62 (outer ring,

average CIECAM chroma 54) and 45 (inner ring,

CIECAM chroma 56); background lightness 50

(periphery) and 30 (center)

As a single example, measures of hue purity

(chroma or saturation) have traditionally used the spectrum locus as the outer limit of

chromatic purity. But if we rarely perceive

spectral hues, this limit is not relevant. Surface colors are the ultimate framework for

color perception, so it makes more sense to anchor chroma contrasts on the optimal

color limits, as I demonstrate with my measure of hue purity. As most natural

surfaces are quite dull or gray, and none are as intense as optimal colors, we may

habitually judge the intensity of color in relation to a more muted reference, as shown

above.

For reasons of historical research convenience,

analytical precision and practical measurement, the color matching foundations

of colorimetry are derived entirely from light mixtures. Yet, given the proportion of

developmental years that humans spend

looking at objects rather than lights (including "soft copy" lights such as televisions or

computer monitors), there is no question that

surface colors are the fundamental visual context that color vision is adapted to

represent accurately. Despite the fact that physical color appearance is very far removed

from the original cone excitations, surface colors are the framework within which all color

phenomena must be rationalized or modeled. Many color appearance phenomena are

properly adaptations to the goal of surface color recognition or inescapable inefficiencies

or compromises to that end.

Perhaps the most significant and

underreported fact to emerge from color research is the large individual variations

that characterize our collective color experience.

These variations have been justifiably suppressed in the color vision literature in the

pursuit of a consensus or "average" color description that can drive standard models of

color vision and standard methods of color measurement. For artists, who must work

within a personal esthetic vision and color

sense, individual differences in color vision are less easily dispensed with. Let's see what we

can infer from the scraps of evidence available.

One occasionally finds in the color research literature mention of the size of this problem

in specific contexts. Peter Kaiser and Robert Boynton, in their discussion of hue

discrimination, observe that

Comparisons between different observers,

whether in the same or a different experiment, present a discouraging picture. Although

observers agree on certain major trends, individual differences are best described as

enormous (Human Color Vision, 2nd ed., p.343).

Günter Wyszecki and W.S. Stiles, writing on studies of the MacAdam ellipses, say that

When one confines the intercomparison

[between subjects] to a particular location in

individual differences in color

experience

the chromaticity diagram, the ellipses of different observers are quite often not in close

agreement. Rather, larger discrepancies are noted in the orientation, size and shape of the

ellipses (Color Science, 2nd. ed., p.323). Individual differences appear clearly in

opponent hue cancellation experiments. The exact shape of the opponent curves and the

resulting hue discrimination differ significantly from one person to the next, probably because

of individual differences in the proportions, distribution and photopigment chemistry of

the L, M and S cones, and in the optical density of the lens and macular pigment.

The example at right shows hue cancellation curves produced by Hurvich and Jameson

themselves, who presumably knew what they were doing. One researcher, compared to the

other, required roughly twice the amount of "yellow" unique hue to produce spectral

matches from middle green through red.

The contours of photopic sensitivity also

show large variations across individuals with normal color vision. The example below, from

an early study, shows the range of individual

variation across all wavelengths.

individual variations in photopic

sensitivity results for 52 individuals, based on heterochromatic

step by step brightness matching; from Gibson &

Tyndall (1923)

opponent function curves

for

two individual subjects

after Jameson & Hurvich, 1955

I have indicated for three wavelengths the size

of individual differences as a percentage of the average value. For an orange hue (600 nm)

the variation is 58% of the average value; this is smaller in the "green" span of the spectrum

but becomes large again in the "blue" span (below 500 nm). The range in peak values is

roughly 540 to 570 nm. The method used, in which the brightnesses of similar spectral hues

are matched, step by step, across the entire

spectrum, is not the most reliable, but comparable variability appears in other

methods. For example, in a study using flicker photometry, the range of peak values was

between 549 to 570 nm.

individual variations in rgb tristimulus values

10° color matching data for 49 observers, from Stiles &

Burch (1949)

Similarly large differences appear in one of the most carefully controlled color matching

studies by Stiles and Burch, both in the primary color matching functions (above) and

in the location of the spectrum locus in an r,g

chromaticity diagram (below). In general these show large variations in the tinting

strength of the red primary light, especially in the "out of gamut" hues between "green" and

"violet" that must be desaturated (negative r

values) by added "red" light.

individual variations in scaling of

spectrum locus 10° color matching data for 49 observers, from Stiles &

Burch (1949)

An irrefutable and disconcerting example is in the large variation in unique hue choices

across individuals in different color perception studies. Here viewers are put the simple task

of choosing, for example, the specific yellow that appears to contain no tint of red or green.

The general picture, illustrated at right, is not the same for all hues. The narrowest

variations occur in the choice of unique yellow,

and second for unique red, which indicate generally better agreement across individuals

on the "warm" side of the color space. Much larger variations appear in the choices of

unique blue and unique green.

The variation in green, which covers one

quarter of the hue circle, deserves a closer look. Illustrated below are the results from a

single study in which 50 men and 50 women viewed moderately bright monochromatic

(maximally saturated) green color patches that were 1° in diameter (twice the apparent

size of the full moon) and seen against a white background; patches were viewed for one

second with a 3 minute rest period between viewings to eliminate chromatic adaptation

effects. The subjects were asked to indicate

whether each green contained some yellow or

CIELAB hue angle range of

unique hues chosen by

individual subjects in

different color studies

dots show average or

consensus location of unique

hues; after Kuehni, 2004

some blue, and the color adjusted accordingly until their unique green was located.

individual choices of unique green black square indicates average unique green; data from

Volbrecht, Nerger & Harlow (1997)

As a whole, the color vision literature is also

vexed with inconsistent results of the same visual effect or mechanism across different

research methods. This certainly means

context matters: in most cases the variation in responses across different studies is much

larger than the variation in responses by the same individual in the same study. But it is

often difficult to account for the variation in terms of the study methods or a generic

model of color vision. It may be that individual differences in the same situation mean

individuals adapt differently to different situations, and color experience is actually

more diverse than it seems in a single study.

These large individual variations in color

perception compromise the specific claim that "colors have meanings". To "communicate",

colors must have a consistent stimulus

specification (the red in all traffic lights is the same) and must be used in well defined

contexts to declare a conventionally preassigned meaning. These helps are less

available in the visual arts. Artists can impose a consistent personal specification, context

and meaning through the painting habits called a "painting style". But a new and

unfamiliar style of art will use color in a new way, communicate very different things to

different people, and thereby stimulate

pointless debate about what color in art "really means".

color and language

To conclude, we look at how color

appears in words, and whether the language shape of color provides insights into

fundamental properties of color perception.

Most of the evidence comes from color

naming studies conducted by anthropologists and cognitive psychologists

across different languages. The anthropological data (called the World Color

Survey) records the names assigned to

Munsell color samples by 2700 native speaking respondents in 110 different language

cultures. The psychological data includes measures of consistency and reaction time in

the choice of color names in color naming tasks, and tests of color discrimination in

infants and children.

Results from these investigations have been

sadly underutilized, because they are largely embroiled in the debate between two opposing

theories: (1) color names depend entirely on the need for color distinctions imposed by the

environment or culture; or (2) some colors are perceptually more basic than others, are

named first, and must be defined in the

language before other color words can develop. The developmental scheme proposed

by the second theory is shown in the following schematic.

development hierarchy in color terms

According to this scheme, there are two kinds of colors and color words: (1) basic

colors, which cannot be reduced to any other color name or color mixture, and which are

the six unique colors (red, green, yellow, blue,

white and black), and (2) binary colors, which are mixtures of two basic colors or color

words ("red+yellow" for orange, "red+black" for brown). The hypothesis is that languages

develop basic terms through opposing contrasts and binary terms through overlap or

combination. The scheme is largely validated by stages in the development of modern

English:

• Languages first of all represent light+warm

(white plus all "warm" colors, positive) and dark+cool (black plus all "cool" colors,

negative) as opposing concepts. All languages can describe variations in lightness or

brightness, and subsume many other color

variations under that basic distinction. (See for example the Aristotelian color theory.)

In Anglo Saxon or Old English (c.600-1150

CE), and from there back into the reconstructed Indo-European lexicon,

light/dark was the predominant sense of color

related words; God, intelligence, intellect, insight, the sun, light, flashing reflections,

metals and fire were all described with the "white (bright)" word.

At this stage the concept of "color" as a

perceptual attribute does not really exist. For

example, the ancient Greeks defined color as a material attribute, so other material qualities

or physical changes were also identified with color names — especially "black" or "white".

Color words also denoted surface qualities ("black" was due to roughness), optical quality

("white" translucence), reflectivity (a "white" mirror), color intensity or chroma (a "white

red" was an intense red), physical composition ("blue" was associated with air, "black" with

earth), or chemical origin (pigments made by

a similar method of manufacture, regardless of hue). Indeed, Greek color words appear so

haphazardly in ancient texts that the 19th century philologist W.E. Gladstone concluded

that the Greeks were colorblind!

• Next, languages separate the "light+warm"

into two terms, dividing "light" (white) from warm (red+orange+yellow+brown) but

keeping the dark+cool term (black and green+blue); purple hues may belong to

either category. Thus the primitive distinction between hue and lightness emphasizes the

warm hues.

• The separation of grue (green+blue) from black comes next. This contrast also implies

that surface values can now described as

graded mixtures of two bipolar attributes: light/dark and warm/cool.

• "Warm" is split into red and yellow before

"cool" is split into green and blue. (There is a consistent trend for lexicons to provide a

greater number of color labels for "warm"

colors than "cool" colors.)

• All the Hering unique hues (red, yellow, green, blue, black and white) are contrasted

and named before other color names are added.

The etymological roots for all these color names go back to the Indo European lexicon,

but they achieve separate hue meanings only in Middle English (1100-1500).

• If there are seven or more color concepts, the words for purple, brown, orange, pink

(all warm colors) and gray are all added before green or blue are divided further (for

example, into "ultramarine," "turquoise" or "chartreuse"). These are all binary colors

compounded from the six unique hues: purple

is a red blue, brown is a yellow black, orange is a yellow red, pink is a white red, and gray is

a white black.

In English, these compound hues — names for mixtures of the basic hues — do not begin to

appear until late Middle English (1350-1500).

• Finally, the linguistic marking of chroma or

intense versus dull colors appears only relatively late in a color lexicon. In English,

this marking does not appear until the late

1600's (Newton's "fiery hues"), and we find the 19th century English art critic John Ruskin

still struggling with it.

Perceived color similarity also appears in the alternative or mistaken names that

children and adults apply to an ambiguous

color. It's very easy to find a color that some people will call green and other people will call

blue, but it's not possible to find a green that anyone with normal vision will call red. These

color labeling tasks again support Hering's exclusion of red/green or yellow/blue hue

compounds. In addition, people in many different cultures can name "pure" examples

of the Hering hues more quickly and consistently than compound or borderline

colors. And when asked to pick the "best" yellow, red, green or blue from a large array

of colors, individuals choose the color that most closely match their perceptual unique

hues as measured with a hue cancellation

or color comparison method. Not surprisingly, in the same way we still rely on the ancient wheel more than the modern

computer, the earliest words to appear are also the most frequently used today, with a

few qualifications. Frequency counts of words in written English (right) show black and dark

(plus white and light) leading the parade. The only hue terms equal to these are red, blue

and green. The remaining hues are all "warm"

hues — brown (dull orange), yellow, pink, orange and the gold not found in the business

section. When these are added to red, their "warm" total (0.031%) is greater than the

combined "cool" total of blue, green and purple (0.022%).

The cadre of academics who dispute any version of the Berlin and Kay hypothesis tend

to focus on the fact that the research methods do not reveal how color terms can refer to a

variety of appearance attributes, such as succulence or gloss, and can be used in a

variety of metaphorical ways — red with rage, green with envy. But it is hardly reasonable to

reject the anatomical study of dogs because

anatomists ignore the fur and fleas. The task of naming colored chips seems to be easily

done by people in all cultures, and the surface uniformity of the chips limits the salient

attributes to color differences.

The perception of color always appears

attached to objects, so it is practical and sensible for cultures to make distinctions

among objects in terms of attributes that are more important than color — the rotten apple

rather than the brown apple, the spring leaves rather than the yellow green leaves, my shirt

vs. the red shirt, etc. — or the attributes of size, shape and spatial location that distingish

objects in context. If necessary, similar

black 0.024%

white 0.023%

red 0.015%

dark 0.012%

blue 0.0106%

green 0.0105%

light 0.0099%

bright 0.0072%

gray 0.0056%

brown 0.0050%

yellow 0.0048%

pale 0.0041%

pink 0.0034%

dull 0.0021%

orange 0.0017%

silver 0.0014%

purple 0.0013%

gold 0.0013%

white/light/bright 0.043%

black/dark 0.036%

warm 0.031%

cool 0.022%

gray/pale/dull 0.012%

frequency of color terms

in modern written English

percentage occurrence in

100 million words

objects can be distinguished using relative differences in lightness or brightness, surface

texture or pattern, or differences in ownership or condition.

Even in western cultures, color words are almost never essential for day to day work and

chatter. Abstract color concepts seem to become necessary, and emerge in a language,

only after a new cultural practice, task or skill — such as fashion, ornament, manufacturing,

art, agriculture or medical diagnosis — makes color distinctions within the same types of

things (textiles, gems, masonry, paints, plants, wines or skin lesions) important.

Indeed, it appears that several cultures have

actually lost color terms, although this seems to happen by discarding color names that are

relatively more complex in the Berlin & Kay scheme.

If we accept that human vision can distinguish

as many as a million unique colors, then our

lexicon codes less than a fraction of 1% of that diversity. This means that color terms

inherently carry a stupefying level of imprecision: we cannot expect to request a

"white" paint and buy a color that will actually match our walls. Instead, every language

culture (and technical subculture) has developed a complex system of conventions

that dictate how color perceptions and color discriminations are to be defined, described

and communicated in relation to objects or

task purposes — in English, for example, a "red" wine, a "red" sunset and a "red" face are

not at all the same color. These complex rules are not assessed at all in the color literature.

Finally, not all color disciminations or labeling

tasks are equal. The opponent gradations of the light/dark distinction may be fundamental

because they are instantiated in the solar light cycle, and because they fit with the universal

semantic capability to define opposition or

negation. In contrast, categorical distinctions such as hue or "color" require the recognition

of combined attributes, which may have been sharpened or ignored because the culture

places more or less emphasis on certain color discriminations. Finally, chroma distinctions

are not well researched in color vocabularies (perhaps a cultural bias of the color

researchers), although the best conclusion is

probably that they are relatively unimportant in most languages; here the natural

environment, which is overwhelmingly populated by dull colors, may make chroma

distinctions inconsequential.

When we tally up all these complicating

factors, however, it seems to me we strengthen rather than weaken the case for

the perceptual saliency of the unique hues. After all, if they were not salient, consistency

in the experimental tasks would be overwhelmed by the cultural complexities. The

fact that patterns emerge despite the cultural idiosyncracies proves that there is a universal

foundation, whatever variations there may be

in the cultural edifices.

The decisive point: agreement is poor across different language cultures in the perceived

boundaries between one color term and another: the same orange may be grouped

with red in one culture but with yellow (or

"tan", or "warm", or "light") in another. But across all cultures, the focal color or best

exemplar for a color, when chosen from a complete array of saturated color samples, is

consistently located within a small area of the color surface, as shown below for the most

saturated Munsell color samples across different hues and lightnesses.

Munsell locus and scatter of focal colors

The academic debate about the primacy of the unique hues seems to me largely to depend on

how the problem and evidence are considered. On that note I have my own observation. The

fact that colorblindness was not recognized until the late 18th century indicates the

relatively trivial role that color recognition plays in routine human life and in any

technical tasks common to human history up

to that point. Paradoxically, this color triviality is the reason colors can be used

as arbitrary symbols in many different areas of a culture — cuisine, cosmetics, institutional

uniforms, ceremonial or ritual dress, fashion, interior furnishings, architectural decor,

advertising ... and of course, art.

The most recent review of research on language and

color is the edited volume by C.L. Hardin and Luisa

Maffi. There is a favorable academic presentation of

linguistic color research with examples of confirming

and contradictory findings posted by Robert

MacLaury. For deep drilldown, see also the dissenting

views by Barbara Saunders and Jan van Brakel.

N E X T : basic forms of color

Last revised 08.01.2005 • © 2005 Bruce MacEvoy

basic forms of color

The previous pages have

described color vision as a process defined at

the sensory end by the photoreceptor cones and rods, and at the perceptual end by the

three colormaking attributes.

This traditional or "old testament" model of

color vision, inherited from the 19th century, describes the perception of isolated color areas

in impoverished situations at moderate to low luminance levels. In caricature, it assumes

that color is equivalent to the trichromatic mixtures produced by light.

This page and the next describe the "new testament" view of color perception in context

with other colors and in more natural viewing situations. In modern terms,

color is a context judgment of surfaces under light in space.

To an amazing extent, color is defined by

the patterned, illuminated and three

dimensional context. It is not an illusion that is factually unreliable, but a complex judgment

expressed as a world of interrelated sensations. This is the specific meaning

intended by the claim that color is in the mind, not in the world.

Context defines basic perceptual categories or basic forms of color that we implicitly use to

judge color stimuli. This page explains the dependence of color perception on visual

context and illustrates the most important mechanisms. Across all the basic forms of

color, contrast is a key perceptual element. In many ways, contrast is the fourth

and most important colormaking attribute.

Color appearance is not usually

defined by the physical attributes of the stimulus alone, but depends on the

surroundings in which the stimulus appears,

basic forms of color

color

vision

basic forms of color

unrelated

vs. related color

self luminous

vs. surface color

local vs. veiled color

plane vs. depth color

summary of

basic forms of color

the adaptation of our eyes, and our recent visual experience. We encounter examples of

this every day, and habitually ignore them, because the purpose of our visual experience is

not to identify colors but to understand the world.

The visual context actually shapes or moulds the color, in the sense that the color must fit

into an interpretation of the world. The color is part of a whole. I use the idea of forms

of color to emphasize that color is formed or shaped, or that color is transformed and made

qualitatively different, depending on the visual context.

In my study of the research literature on this topic it seems to me there are eight basic

forms of color. These forms are antagonistic or mutually exclusive, in the sense that

opposing forms of color cannot define the same color stimulus in the same context at the

same time. They can be grouped into four

perceptual contrasts that determine the appearance of any color area:

(1) Unrelated vs. Related Color. The most

fundamental contrast in color perception is between a single color perceived in isolation or

two or more contrasting color areas,

differing in brightness or chromaticity or both, appearing together:

An unrelated color is perceived by itself,

isolated from any contrasting color areas or

any visible physical context.

A related color is perceived in the same visual field as one or more contrasting color areas;

the color areas form edges or patterns with one another or against a contrasting

background.

(2) Self Luminous vs. Surface Color. The

primary contrast among related color areas is in relative luminance — one color appears

brighter than the other. This perceived luminance contrast between contiguous

color areas, or between an isolated color area

and its background, is used by color vision to distinguish surface colors from light sources:

A self luminous color is perceived as radiating

(emitting or transmitting) light and therefore

as having brightness.

A surface color is perceived as a physical surface reflecting illumination and therefore as

having lightness.

Surfaces are normally perceptually distinct

from lights, but in some contrast situations a color area may appear ambiguously like a

glowing surface or a disembodied light. In the current color appearance terminology this is

called an aperture color.

(3) Local vs. Veiled Color. The most

important perceptual contrast regarding surface colors is whether they are their own

color or the color of something else. The perception of at least one tinting source is

the criterion difference:

A local color appears completely free of

distortion from the intensity or chromaticity of the illumination or from any interposed tinting

layer such as a surface reflection, colored

glass, shadow, fog or smoke.

A veiled color appears to be altered by an unusually intense or colored light source

and/or an interposed tinting layer, including shadows.

Lights are not normally tinted by other lights or by surface reflections, and therefore do not

appear as veiled colors. However they can be tinted by transmissive media such as colored

glass, a mist or a colored liquid, and in these situations the color of the light and/or tinting

medium may seem to merge or mix. In the

current color appearance terminology this is called volume mode.

(4) Plane vs. Depth Color. The final contrast

among surface colors is in spatial geometry.

The perception of illumination in space, whether created by three dimensional

materials or by viewing a two dimensional pictorial or stereoscopic illusion, is the

criterion difference:

A plane color appears as color areas in two

dimensions — without recession, binocular disparity or shadow; the illumination, if

noticeable, appears diffuse and directionless.

A depth color displays recession and binocular disparity indicating unequal distance from the

viewer; or specular reflections, the direction of cast shadows and spatial variation in the

illumination intensity define the direction and relative intensity of one or more light sources.

The color vision literature often refers to the spatial properties of an image, but often as

not this actually refers to its two dimensional structure. I use the term spatial exclusively to

describe an image interpreted as a three dimensional space, and use the terms spatial

frequency, pattern or image to denote the two dimensional structure.

Crank alert. My use of form of color rather than appearance mode is nonstandard and

idiosyncratic. I use it to highlight the fact that the current color terminology is more

convenient for describing color vision experiments than for distinguishing the

perceptual factors that influence color

perception.

In a viewer's experience, the perceptual interpretation of the context is expressed in

the color itself; we usually cannot, or only with unreasonable effort, separate the "real" color

from its context. In particular, we are normally

completely unaware of the "cognitive" aspects of color perception — discounting the

illuminant, spatial perspective, shadows, memory, object concepts, available color

labels, and so on.

My slogan for this perplexity is: we cannot

describe how we look at color, we can only describe how a color looks.

The simplest possible color context

is one where we can provide a color description, or a color name, for the color we

see. This context is created in color vision experiments by the display of a single small

color area against a large neutral background that fills the field of view, as

illustrated below.

unrelated vs. related color

unrelated color presentation

The diffuse border represents the limits of the

visual field as the viewer looks through an eyepiece or peephole into a gray, featureless

chamber. Inside the chamber, color samples are presented through a circular window

(called a reduction screen) as (1) colored light projected from behind onto a colorless,

diffusing glass; or as (2) colored surfaces

under diffuse, moderately bright illumination. The walls of the chamber are curved and the

edges of the window are disguised so that the stimulus appears to the viewer as a floating,

intangible, moderately bright disk of color. The surrounding gray area is usually illuminated to

an equal luminance as the color stimulus, and its flat reflectance profile contributes no

chromaticity.

This is the standard presentation for an

unrelated color or a color seen in isolation. (The purpose of the gray background is

explained below.) In the presentation illustrated above, most observers would report

(with confidence) that they see an orange color of moderate brightness and saturation.

Perception of an unrelated color strips away nearly all the cues that normally define color

judgments in the real world. Even so, color vision always responds to or "recognizes" this

primitive stimulus situation in three ways (diagram at right):

• a trichromatic response to the color area as a stimulus of specific brightness and

chromaticity

• a luminance adaptation to the photometric intensity of the entire visual field

on the retina, which acts to shift the apparent brightness (B) toward the middle of an open

ended brightness range; and

• a chromatic adaptation that reduces the

saturation or chromatic intensity of the color in view by shifting the neutral point (N) of a

chromatic range toward the dominant color — in the example, toward the color orange.

These three color processes — a conscious "color" response, equivalent to naming or

describing the color — and involuntary chromatic and luminance adaptations —

continually adjust color vision to the viewing context.

The main characteristic of unrelated color sensations is that they suppress the

luminance and chromatic contrasts that shape color through the opponent functions.

This means unrelated colors are completely described by the L, M and S cone sensitivity

curves (or their practical equivalent, the colormatching functions of the standard

observer). If the color has been created by light mixtures (for example, an orange created

by mixing "red" and "green" light), the

mixture is described by the mixing line in a chromaticity diagram.

Color sensations in unrelated colors are very

close to our cognitive color concepts or color

categories — our ideal colors. Assuming the brightness and chromatic adaptations are in

balance, a color always looks like itself.

A lack of colorfulness or saturation in unrelated colors is perceived as a whitening of

the color, and an increase or decrease in the

luminance is perceived as a brightening or dimming of the color. The color appearance

can be completely described using the colormaking attributes of brightness, hue

and colorfulness.

There are two visual illusions that appear in

the unrelated form of color. The first is metameric colors, where two different

spectral emission or reflectance profiles appear to be identical emitting sources or

material surfaces (that is, two physically

visual responses to

an unrelated color

trichromatic response

luminance adaptation

chromatic adaptation

different lights or surfaces have the same tristimulus values or location in a

chromaticity diagram). Metamers are created by the reduction in spectral information

caused by the principle of univariance in just three color receptors. The second is

afterimages caused by abrupt, large changes in brightness or chromaticity at the same

location in the visual field.

The terms aperture color or film color

describe the perception of color as coming from a source viewed through an aperture at

an ambiguous distance. Aperture color is sometimes used as synonymous for unrelated

color, but an aperture appearance is possible

in related colors, for example in a color matching experiment. The concept might be

better used to describe the special case of an adaptation where the viewer cannot decide if

the color is a surface or self luminous and appears as "color from an immaterial area."

For example, Ralph Evans found a fluorence quality, ambiguously between surface and

light and therefore an "aperture" color, in the luminance contrast between a highly

chromatic stimulus and a "white" surround.

A minor qualification: any color that appears

within a surround, even a gray or black surround, is actually a related color. This is a

trivial issue if the surround (background) is adjusted to provide minimal contrast with the

color area (usually a medium gray), because

the surround suppresses adaptation.

The logical alternative — just make the color area very large — is perceptually unstable. If

the color area partially fills the visual field, adaptation will cause the color to desaturate

and shift toward an average brightness. If the

color completely fills the visual field and lacks visible texture, this ganzfeld color or "whole

field" color will (within a minute or two) completely extinguish color sensation. (For

many viewers this state can be induced by cupping one half of a colored ping pong ball

over each eye.) This is the most impoverished possible wakeful visual state, equivalent to

blindness. It is normally disrupted by blinking or by involuntary movement of the eyes

(nystagmus).

Related Color. If a second color area is

displayed nearby in the same context, customarily in the upper or lower half of the

circular window, the viewer perceives two contrasting color areas at the same time,

as shown below.

related color presentation the original orange stimulus presented with a second

color area (bottom of circle)

Now the viewer can compare the first color

stimulus to a second color in the same visual field. Any display of two or more colors in the

same visual field, including a single color against a contrasting background, creates the

second basic form of color: a related color perception.

Related colors cause a shift in the three responses that characterize unrelated colors

(diagram at right):

• The second color changes the total

luminance of the visual field; so the luminance adaptation shifts up or down in response to

the combined luminance, weighted by visual area (larger areas are more important);

• The colors differ in chromaticity, so

chromatic adaptation shifts toward the

average of their mixed chromaticities, weighted by visual area. In the case of an

added green light, the combined orange and green would produce a yellow mixture, so

chromatic adaption would move toward yellow, decreasing sensitivity to yellow and

increasing sensitivity to yellow's visual complement, blue violet.

Related colors also introduce three new

visual responses:

• The combined luminance and chromaticity

difference between adjacent color areas causes a chromatic induction, which alters

the perceived colors in relation to each other. In chromatic contrast the perceived

difference between adjacent color areas increases on both lightness and chromaticity,

visually separating the color areas; in chromatic assimilation the perceived

difference between adjacent color areas is reduced on both lightness and chromaticity,

causing the colors to appear more similar or

visually blended.

• The luminance ratio between two adjacent colors, or between a color and the

background, may induce a brightness induction, so that the lighter color appears to

glow or shine, or a lightness induction

(discussed below), so that the darker color shows more blackness.

• The colors form a border along a shared

edge, which may cause edge contrast effects between them.

Chromatic induction, brightness/lightness induction and edge contrasts emerge from a

new level of perceptual structure that corresponds to the opponent functions and

opponent contrasts between groups or

clusters of receptors across the retina. These effects do not arise from the basic

photoreceptor outputs. They are created when receptor outputs are differenced, summed,

suppressed or enhanced by the secondary cells in the retina or the visual pathways in

the brain.

The spatial frequency (visual size) of color

areas, which is determined by the physical size of the color areas as viewed from a

specific distance, and is affected by the local spacing between receptors on the retina and

the perceptual grouping of color areas into patterns, plays a major role in determining the

direction and size of chromatic induction effects in two dimensional color displays.

The principal visual illusions in related colors

added visual responses to

related colors

trichromatic responses

average luminance adaptation

average chromatic adaptation

simultaneous contrasts

border contrasts

are the color shifts produced by chromatic induction. As a simple example, the three

color areas in the diagram below differ only in visual size between a low frequency (large) or

high frequency (small) contrast patterns.

color shifts produced by chromatic induction

(top) a low spatial frequency produces chromatic

contrast, and (bottom) a high spatial frequency

produces chromatic assimilation; in both diagrams the

dotted bars have the same lightness

In each example, all four color bars above or below the small dots are identical image colors

on your computer monitor. However, the wide (low frequency) bar on the dark background

appears lighter than the wide bar on the light background, because chromatic contrast

makes color and background appear more different. At high spatial frequencies, the thin

(high frequency) bar on the dark background

appears darker than the thin bar on the light background, because chromatic assimilation

makes color and background appear more similar. Roughly, color vision enhances

contrast between color areas large enough to count as different objects, and suppresses

contrast between color areas small enough to be texture on a single surface.

The activity of the opponent functions also produces hue dependent differences in edge

contrast. The y/b dimension produces weaker edge contrasts than the r/g dimension, as

shown below in the standard related color presentation.

differences in chromatic contrast and

assimilation on the y/b and r/g opponent functions (top) edge contrast in the standard related color

presentation; (bottom) chromaticity pattern contrasts in

alternating colors 1, 2 or 3 pixels wide

The top of the image shows this difference in

edge contrast in the familiar related color presentations. The bottom of the image shows

an identical color pattern presented in a black/white version (example b), or in

yellow/violet (a) or red/green (c) at equal lightness and chroma. The r/g stimulus still

produces color separation at high spatial frequencies when lightness or chroma

contrasts are minimal; a comparable

yellow/violet stimulus produces assimilation — an apparently solid color area.

However at maximum chroma for each hue

(an adjustment that also alters the lightness of

the colors), the yellow/violet contrast (d) has greater clarity than the red/green contrast (f).

This contrast also causes a significant desaturation (whitening) of the yellow color,

which is visible if the identical yellow is used in

a contrast with black instead of violet (compare d with the top half of e). The violet

color is less affected, as visible when the identical violet is used in a contrast with white

instead of yellow (compare d with the bottom half of e). This is a demonstration that the S

cone contribution is less affected by pattern contrasts: most of the chromatic contrast

effects arise from interactions between the L and M cones or their outputs.

The term "related colors" is sometimes used as equivalent to object or surface colors, but

this is inaccurate. All related color effects occur in whether or not the color areas can be

identified as lights, surfaces or objects in three

dimensions.

The third basic form of color appears in the perceived difference between

lights and surfaces. This powerful perceptual contrast is produced by the luminance ratio

and relative area between a target color area and the surrounding or background color

(s). Ratio and area induce two opposing color mechanisms:

• a brightness induction that creates the appearance of a self luminous color, which is

strongest when a small, high luminance color area is viewed against a much larger and

darker (lower luminance) surround or average background, or

• a lightness induction that causes the appearance of a surface color, which is

strongest among many contiguous color areas of similar luminance and size.

self luminous vs. surface color

The figure at right illustrates both perceptual

effects in a single figure. The three blue dots

at the center of each cube face have exactly the same luminance on your computer screen.

(That is, if the colors are sampled with the Photoshop color picker, they yield identical

hexidecimal or RGB values.) However, the upper face of the cube appears the most

brightly illuminated and therefore the blue dot within it, because it has a much lower

luminance relative to the yellow dots around it, and so appears darkened and attached to

the surface. The cube face on the right is in deep shadow, and therefore the same blue dot

has a much greater luminance relative to the shadowed surface around it, causing it to

appear to glow dimly as a light.

The physical proportions that underlie this

perceptual discrimination are discussed in the section on the constants of light. The

perceptual mechanisms are discussed in a later section. The subjective color qualities

involved in brightness and lightness perception are:

1. The opponent primaries of brilliance (the visual quality of shining or emittance) or

blackness (the visual quality of absorptance or partial reflection) define the opposing

perceptions of self luminous or surface color — colors that appear to arise from the emittance

properties of lights or the reflectance properties of surfaces.

It is important to grasp that brilliance and blackness are perceptual qualities or

symbols attached to relative luminance contrasts, and not physical quantities of light

intensity that we perceive directly, just as red or blue are perceptual qualities attached to

relative proportions of long or short

wavelength light, and not physical colors that we perceive directly.

2. White is the transition point between

brilliance and blackness — that is, white is

only surface color that appears to have both zero blackness (light absorptance) and zero

brilliance (light emittance).

A point of comparison is the ganzfeld color that appears under constant visual

stimulation. This might be described as a

dimensionless, colorless, enveloping fog. It also lacks both sensations of blackness and

brilliance, but does not appear "white". Brilliance and blackness, white and black, are

perceptual symbols for changes and inequalities in visual stimulation across related

colors: they disappear when visual stimulation is equal and constant across the visual field.

simulation of lightness and

brightness induction on the

faces of a cube

the contrast is enhanced by

viewing

the image in a darkened room

from Purves et al. (2002)

3. The brightness range or perceived

luminance variation in self luminous colors is

bounded by the physiological limits of light

perception under the current luminance adaptation. Self luminous colors cannot be

perceived has having less brilliance than a "white" surface in their local area, but the only

upper limit is the point where the luminance completely depletes the cone photopigment

or the light intensity causes visual stress — light blurring, intrusive afterimages, physical

discomfort or blindness. However brightness is normally scaled to the current level of

luminance adaptation: a candle flame appears

quite bright in complete darkness, but is invisible in daylight.

In contrast, the lightness range is a

perceptual scale of grays closed at opposite

ends by the sensation of whiteness or blackness. These comprise a range of physical

luminance values that are defined in color appearance models as lightness values from

0 to 100, although for physical surfaces the actual luminance ratios are never greater than

1:33 and in most natural or artificial environments are less than 1:20.

These two luminance related contrasts operate simultaneously in color vision

(right). The average illumination determines the luminance adaptation, and the relative

brightness of lights; the variations in luminance factor (reflectance) determine a

lightness range anchored on white. The status of both adaptations is signaled by the quality

of white and the chromatic intensity of

surface colors.

4. Typically, lightness perceptions contain grayness or the "dulling" quality of a diluted

blackness, the symbol of surface light absorption that is perceptually inferred from

relative luminance differences. Similarly,

brightness perceptions contain luminosity or an "outflowing" quality of brilliance, the

perceptual symbol of light emittance.

5. The intensity purity of blackness or

whiteness, or of luminosity in relation to background, depends on the relative area

and spatial relationship between color areas. Brilliance or blackness are increased by

(1) reducing the visual size of the color area, (2) increasing the size of the surround, and

(3) increasing the luminance contrast between color and surround.

added visual responses to

surface colors

trichromatic responses

average luminance adaptation

average chromatic adaptation

simultaneous contrasts

border contrasts

lightness induction

inferred illuminance

These context factors can be experienced through aperture or fluorent colors, which

appear "very bright" or "brilliant" but ambiguously between light emitting and light

reflecting. To see this, draw a curtain over a sunlit window in an otherwise unilluminated

room: the large rectangle of illuminated floor or wall in the daylit room becomes a narrow

band of brightly shining light in the darkened room. By moving the curtain back and forth to

adjust the width of the light beam, the

illuminated wall or floor can be made to appear either reflecting, emitting, or glowing

(simultaneously reflecting and emitting). A similar effect occurs in the luminance

variations inside your home barbecue, where some coals appear in early afternoon light as

orange lights, while others appear as surfaces painted a dull orange. Because these

variations in illumination are common, near neutral surfaces with reflectances of 90% or

less appear "white" in most situations. Thus,

visual context plays an unusually important role in how white and fluorent colors are

perceived.

6. A corollary to this is that grayed or

blackened colors can only appear as surfaces, not as lights. Colors such as gray, ochre or

brown only appear as surface colors. The corresponding stimuli, when presented as self

luminous colors, appear to be dim white, yellow or orange lights.

7. The colormaking attributes for self luminous and surface colors therefore become

different: self luminous colors and surface colors are still described by the attributes of

brightness, hue and colorfulness (chromatic intensity or hue purity); but lightness contrast

additionally induces the attributes of lightness and chroma (both judged in relation to the

surface white).

8. Importantly, the direction, intensity and

chromaticity of a light source does not appear in surface color perception: all color

and lightness is imputed to the material the creates the color areas. The most luminous

surface in the visual field becomes a "white" anchor (it may, in fact, be colored or dark

gray), and the range of grays (surface color

lightnesses) is distributed below this anchor in a way consistent with a single source of

illumination.

Surface color can be perceived in the absence of specific information about the location or

character of a light source. The color appears

through limited contrast between color areas (the apparent absorptance or blackness of

surfaces), within a constant luminance adaptation.

A color stimulus called a color mondrian is

used to study color constancy, corresponding colors or context effects in

related, surface colors. The mondrian is a quiltlike array of variously sized, overlapping

rectangles that produces complex color

contrasts within a limited luminance range (right). Originally (circa 1920) these were

actual physical surfaces illuminated by diffuse, white light at moderate intensity; now they

are increasingly presented to viewers as digital images on a flat panel computer monitor. In

both cases, the colors appear as surface colors and there is no recognition of a remote source

of illumination.

The major visual illusions in surface colors

or self luminous colors arise from a discrepancy between the actual and apparent

illumination. This occurs through "false" luminance ratios produced by light

vignetting or inexplicably large light contrasts. Thus, a computer monitor is really a pattern

created by millions of faint lights, not a

surface; the moon appears as a light at night and a pale surface during the day; a spotlight

that is vignetted to match the borders of a color area can make the color appear to glow.

Another "illusory" effect occurs in fluorescing colors, which absorb invisible ultraviolet

wavelengths of light and partially emit the energy as visible wavelengths, which makes

the color appear to glow (emit more light than is shining on it). The effect is enhanced by a

"black light" or light source relatively high in

short wavelength emittance.

As long as the location and chromaticity of a light source are perceptually

unspecified, all related colors appear as if illuminated by an ideal "white" or equal energy

local vs. veiled color

a mondrian stimulus

diffusely illuminated to

eliminate the perception of

illumination in space

light source. This means we adopt the attitude that we see the material color as it "really is".

Luminance contrast determines whether the color areas appear as lights, as surfaces, or as

an ambiguous state in between, but the light does not seem to have a specific chromaticity

or come from a specific direction.

The fourth basic form of color occurs when a

notional or categorical illuminance and chromaticity is imputed to a light source that

makes surface colors visible. This divides surface colors into two contrasting forms:

Local color is perceived as a surface or material body illuminated by a "pure white"

illumination. We tacitly accept the good color rendering quality of the illumination at the

same time that we perceive the surface color. This is the common perception of color under

noon sunlight, or colors examined under balanced artificial light, and of the

remembered or memory colors of objects.

Veiled color is perceived as the visual

mixture of the local (material) color and one or more spatially distinct tinting layers. This

perception is distinctive because it automatically separates into two "local" colors

— the color (lightness and chromaticity) of the

surface and the color of the tinting layer.

These opposing forms of color define a level of color complexity where several new factors

are active.

First, a spatial interpretation of color

sources is essential to a veiled color perception. A veiled color is appears as some

combination of (1) a translucent material in front of an opaque local color, (2) an opaque

material behind a translucent local color, (3) a

source of colored illumination in front of an opaque or reflecting surface, or (4) a source of

colored illumination behind a translucent or transparent local color. Veiled color requires

the cognition of two or more sources of color separated in space; this divided color is

inherent to the color sensation. The examples (right) show that this may depend on the two dimensional

configuration of edges and color areas, or on

visual cues identifying a light source at a

specific location, or both. Veiled colors are usually perceived in relation to three

dimensional surfaces: color vision studies have shown that humans can reliably discriminate

the difference between a three dimensional blue chamber illuminated by white light and a

white chamber illuminated by blue light. But the examples at right show that the two

dimensional structure of the image is by itself sufficient to create the appearance of a tinting

source separate from a local (surface) color,

which we interpret as transparency or cast shadow.

Second, veiled color is perceived as a

nuisance, in the sense that color vision works

to eliminate or isolate the tinting layer in order to retrieve the local color of the surface. This

adjustment is usually automatic or, if it depends on knowledge of the viewing

situation, is not easily reversed once our knowledge of the situation is changed.

Third, it's my conjecture that essentially the same perceptual process or combination of

processes are involved in the recognition of very different kinds of tinting layers. These

include:

• a global chromaticity arising from one or

more light sources, including the principal light source (the color of sunlight at sunset, or

skylight through a north facing window)

• shadows cast by objects interposed between

the light source and the color area

• a change in the level of illumination (as in the change between the colors at night of an

illuminated living room and an unilluminated outdoor patio)

• reflections onto a surface from a nearby illuminated surface (such as a color reflected

from a wall into a nearby shadow, or the image of sunlight reflected from window glass

onto the wall of an adjacent building)

• reflections from a surface, either from the

color area itself (such as the sky reflected in a lake or the hood of a car) or from a

transparent reflecting surface inteposed between the color area and the viewer (the

colors of a city street reflected in front of the

a transparency illusion

congruity of color areas and

inconguity of edges creates the

perception of a tinting source

(a film layer)

a tinted color mondrian

the appearance of a luminance

gradient and a contiguous

darkened area creates the

perception of a tinting source

(a cast shadow)

objects in a store window)

• semitransparent tinting media located between the color area and the viewer (such

as tinted windows, screen doors, sunglasses,

photographic filters, smoke or mist).

Obviously most of these situations involve a three dimensional interpretation of the image,

and therefore fall under the next form of color (plane vs. depth color), but my conjecture is

that the spatial interpretation exerts a

controlling function on processes that work equally well in two dimensions.

The illustration below shows the minimal

related color presentation necessary for the appearance of veiled color: two contrasting

color areas (orange and white) displaying two

contrasting chromaticity areas (neutral and tinted violet), with the color and tinting areas

distinguished by separate (differently aligned or shaped) edges or boundaries.

local and veiled colors caused by a tinting source, with white standard

The simplest or most literal interpretation of

the image is that it shows two semicircular color areas fitted inside two identically shaped

and symmetrically placed rectangular arches. But we don't see it that way: the pattern is

much more likely to appear as a white square containing a large orange circle that is crossed

by the boundary between light and shadow, or

as a square and circle illuminated by two light sources, one a bright white and one a dim

violet. Either judgment — of a shadow edge or two contrasting sources of illumination — requires

a "cutting away" or scission (a term coined by Fabio Metelli) of the color discrepancy as a

tinting layer within the image. Scission attempts to retrieve a stable color judgment

by peeling back a layer of distracting color to retrieve the layer of local color underneath

(right).

Two observations here. The spatial location of

the shadowing edge or second light source is undefined, because there is an infinite number

of geometrical arrangements that would result

in the same visual appearance. So although veiled color creates a three dimensional

perception of one material in front or behind another, the actual spatial distances involved

(the location of a shadowing object, or the thickness of a tinting layer) can be undefined.

Second, the perception of surfaces as white or very light valued seems to play a crucial role.

On the one hand, it is very unusual to perceive a color seen as a white or light valued surface

as being actually tinted or veiled. This is because the color of a surface and the light

illuminating it mix subtractively, meaning that any tint in the light is perceived to darken the

surface. At the same time, a smoke or fog often appears as a partially transmitting white,

and the whiteness makes it visually distinct

and lightens and desaturates any objects glimpsed through it. This implies that

lightness contrast is a key factor in determining a scission.

But anything that allows the extent and

density of the tinting layer to be recognized

and "pulled away" from the surface color can function as a scission tag. Key scission tags

include: (1) specific edge or gradient boundaries that do not match the edges

between background color areas (a diffuse edge crossing sharp edges, or a sharp edge

over diffuse edges, or a straight edge across a complex pattern, etc.); (2) a separate tinting

shape that cuts across the color areas of a surface pattern or recognizable objects

(reflections in a window superimposed on

objects behind the window); (3) a uniform color shift that produces an equal

visual response to

a tinting source

trichromatic responses

average luminance adaptation

average chromatic adaptation

simultaneous contrasts

border contrasts

lightness induction

inferred illuminance

tinting scission

proportional change in the lightness or chromaticity of a group of color areas; or (4) a

global color shift due to the color of the principal illumination. In many instances, (5)

deviations from memory color, our expectation of the local color that a familiar

object or surface material should have, are also important.

Veiled color arises from a complex perceptual inference, a visual hunch. With few

exceptions — the perception of object shadows or relative changes in illumination — we are

nearly always aware of a scission when it first occurs, often as a fleeting sense of intrusion or

ambiguity or "recognition" of something

blocking our view, as if the perceptual process must get conscious approval for its

identification of a reflection, colored light source or tinting medium. This may occurs

even with familiar tinting layers, such as reflections in water.

Extremely large changes in apparent reflectance ("luminance errors") can occur if a

tinting layer (or its pictorial representation) is altered in a systematic way, and these form

the main category of visual confusions between local and veiled colors.

"erroneous" lightness perceptions produced by

an illusory tinting layer a "wall of blocks" pattern with simulated color changes

caused by transparent bars (center) or shadow bands

(right); adapted from Logvinenko (1999) and Kingdom

(1999)

In the wall of blocks visual pattern (left), the

horizontal diamonds veiled by the sharp edged or diffuse edged "transparent" bands have the

same luminance (lightness in the image) as

the horizontal dark diamonds across the center, but they appear much lighter (center)!

The effect is enhanced when the bands have diffuse rather than sharp edges (right).

These effects are produced by a scission

error. The trick is revealed in the bottom examples: the separate tinting layers were

actually "cut out" in Photoshop along edges that exactly match the diamonds, which left

the diamonds at their original lightness.

However, the bands appear to be continuous between their horizontal top and bottom

edges, which makes the diamonds appear "covered" by their tint. Peeling away this dark

tint causes the color to appear lighter valued. The top examples show how the horizontal

diamonds would appear if a truly homogeneous tinting layer were placed over

them: now the diamonds appear slightly darker, but at the same time the "same color"

as the middle row of diamonds in the main

example.

In the even more dramatic "chess pieces" illusion (right), the pieces again have exactly

the same pixel by pixel lightness in both images, but their apparent reflectance is

almost completely reversed, from luminous

white to dark gray, by greatly increasing the lightness of a tinting layer of "smoke" swirling

around the pieces while again performing a cutout or deletion of the tinting layer in front

of the pieces. Amazingly, in this illusion the "luminous" chess pieces appear even lighter

valued than the light background glimpsed behind them.

There is a cute scission error in Steven Spielberg's film Terminal, when the reflection

of a man's head in a mens' clothing store window seems to merge with a suit displayed

behind the window, because the reflected head and headless shirt collar exactly

correspond. The combined form of the torso and head fuse as a familiar single form (a

human figure) which suppresses the scission.

These examples demonstrate the extreme

the "chess pieces" illusion

after Gilchrist (2005)

added color or edge

congruity

disrupts the illusion of a

tinting layer

importance of corresponding or overlapping edges or disjointed forms as a scission tag.

But scission can also be disrupted by coloring or contouring, for example using a contrasting

color for the tinting layer, or by shaping the border of the achromatic "tinting layer" to run

parallel to the dark diamond edges (right). In both cases the tinting layer illusion is

destroyed. Without a scission tag the "tinting" attaches to the surface as a discoloration, or

separates as an overlaid pattern.

Perception of a tinting source is not a form of

simultaneous chromatic contrast but a form of spatial perception. The lightness shifts

produced by chromatic contrast appear in the

achromatic diagram of parallel edges (right), and this lightness shift is much smaller than

appears in the tinting layer with diffuse edges (above); and even minor color discrepancies

can destroy a scission error that is very potent in an achromatic version. The difference in the

achromatic or color keyed contrasts indicate that we are dealing with different contrast

processes.

The real significance of veiled colors does not appear until we consider the

fifth and last basic form of color, which

appears as the contrast between two dimensional and three dimensional colors.

A plane color appears as a color area on a

flat surface seen from a specific direction and

made visible by illumination arriving from a specific angle of incidence to both the surface

and the direction of view.

A depth color appears as a color area on a surface that appears among other surfaces

seen as objects in space, which create many

different angles of view and incident illumination and create contrasts between light

and shadow. [I use the label depth color to avoid confusion with the use of "spatial" to

describe two dimensional color stimuli.]

The point of this contrast is that plane colors

are seen under approximately the same illumination from the same point of view.

There are geometrically simple changes in

plane vs. depth color

color appearance that, for surfaces illuminated by a distant light source (such as the sun), are

due to changes in the viewing angle alone, or for surfaces illuminated by a nearby light

source (such as a light bulb), are due to the joint effects of viewing angle and the distance

and direction of the light source. However, there are fairly simple constants in viewing

geometry that account for variations in plane colors.

Depth colors introduce two crucial new problems: they define objects, which occupy

a specific volume of space and create different angles of view and light incidence across their

different sides, and they define shadows,

which affect both the color of the object's dark side and the color of other surfaces or objects

it shades. These variations in light and shade are perceived as the modeling of the object

and the location of the object in space.

In the previous section I pointed out the

importance of overlapping or aligned edges as a scission tag. By far the most frequent

examples of veiled colors are shadows cast on surfaces, which turn up everywhere under

nearly all types of illumination. Shadows mean that surface colors must be compared across

significantly different levels of illumination. However the modeling of objects permits

these veiled colors to be peeled away through the three dimensional perception of the

objects itself. The cognition of objects

illuminated in space becomes the scission tag for its own variations in light and dark.

Spatial colors are just scission tags that correspond to objects.

The cognition of objects illuminated in space

extends to all the common sources of veiled

colors: light reflected into shadows from nearby surfaces, shadows on an object,

shadows cast by the object, highlights or reflections on an object, and changes in

luminance or texture relief (surface gradients) due to changing distances or angles of

incidence between a surface and a light source. All these veiled colors more or less

disappear into the unified perception of material objects in different locations within a

three dimensional scene.

The diagram (right) shows the additional

visual responses active in spatial vision, the most complex form of color. This is admittedly

a parody of an actual inventory, because the visual processes involved in spatial colors are

very poorly understood — for example, we cannot simulate them in robotic vision.

However, it seems fair to assert that all aspects of our visual sense are unified in the

experience of spatial color, the representation of a three dimensional material world under

natural illumination.

This might be called the principle of spatial

dominance: vision strives to interpret a visual image as material surfaces illuminated

in space. Spatial colors can only be disrupted

by grossly and systematically impoverishing the visual image or by contriving an image

that is inconsistent with a simple (parsimonious) spatial interpretation.

The principle of spatial dominance is the basis

of all visual illusions in depth colors. The

diagram below shows the difference between two arrangements of identical color areas.

a complex color stimulus organized as

plane color or depth color

When the colored diamonds are arranged randomly (left) they appear as flat color areas

inserted into a flat blue field. Each diamond is an autonomous color area and there is no

layer tag that color vision can use to identify and adjust veiled colors: as a result the color

variety is quite large.

When rearranged to form a depth illusion

(right), the same colors are interpreted as opaque colored blocks and their cast shadows.

This cognition allows rapid and silent

visual response to

a spatial image

trichromatic responses

average luminance adaptation

average chromatic adaptation

simultaneous contrasts

border contrasts

lightness adaptation

lightness contrasts

shadow/light balancing

object recognition

chromatic adaptation to light

identified reflections

identified direction of light

perceived distance/direction of

objects

adjustment in the colors interpreted as shadowed or as lit by grazing illumination: the

variety in the colors is muted, and the illuminated and shadowed surfaces appear to

be the "same" color.

An achromatic depth illusion (below)

demonstrates how depth color can strongly alter surface color to match or consolidate a

three dimensional perception.

a spatial illusion alters lightness

appearance

In both figures the basic pattern is a 5 x 5 matrix of identically shaded achromatic "tiles",

with the shape of some tiles changed in shape or orientation to create the illusion of a surface

folded vertically (left) or horizontally (right). This is sufficient to produce contrasting depth

illusions and color changes: (1) each column

appears as a flat surface crossed by alternating bands of color (left) or as a band of

continuous color at different angles to the light (right); and (2) the apparent lightness of any

single facet changes depending on the spatial interpretation: compare between figures the

second and fourth facets of the middle column. These discrepancies are not noticed

as conflicts or changes in color: they disappear into the spatial illusion. The modeling of the

folded surface, the idea of its geometrical form

in space, acts as a scission template functioning across its entire surface.

Depth colors can induce changes in

chromaticity as well as lightness. In the depth mondrian diagram (above), the trio of colors

of the same hue appears more varied when

viewed as isolated, flat diamonds (left) than when viewed as the three sides of a cube

(right). At right, an orange color palette is shown two ways: with chroma (and saturation) changing

across the vertical faces of the polygon and lightness changing across the horizontal bands

(top figure), or with lightness changing across the faces and chroma across the bands

(bottom). The positions of the color areas have simply been flipped around the righthand

diagonal.

Color vision interprets this geometrical picture

as an object in space, working from the color changes to infer an illumination that will make

the continuous stripes around the sides of the

polygon appear to be the same local color.

For the bottom polygon this is straightforward: the constant chroma within stripes and

changing lightness across the faces suggest the illumination comes from the right. But the

top polygon is not consistent with a single light

source, because chroma but not lightness changes across the figure, which makes the

lefthand face look too pale and desaturated. To account for this spatial variation in local

color, color vision imputes a second light source. Both polygons appear illuminated from

the right, but upper polygon appears additionally illuminated by a faint bluish light

shining on it from the upper left.

In the real world, shadows do not by

themselves alter the reflectance profile or chromaticity of a color, they just reduce its

luminance; so any change in shadow hue or chroma is perceived as arising from the

chromaticity of a second light source. Colors are most strongly desaturated (shifted toward

gray) by their complementary color, and

saturation is strongly enhanced by lights with a hue similar to the hue of the physical color.

Red orange is most strongly desaturated by its complement, blue, so a blue color is attributed

to the inferred light in order to reconcile the decrease in chroma (but not in lightness) on

the lefthand side of the figure.

The diagram summarizes the relationships among the four forms of color

summary of basic forms of color

a solid modeled in two

ways with identical colored

areas

described above. See below for the current standard terminology.

summary of basic forms of color

If we summarize the forms of color as perceptual attributes, then colors are primarily

contrasted as: (1) an isolated color area or a combination of different color areas, including

a target color against a background color (contrasting color areas?); (2) a luminance

contrast between adjacent color areas that causes brightness induction or lightness

induction (high or low luminance contrast?); (3) the perception of color distortion by a

colored light source, shadow, reflection or

transparent medium (tinting source?); and (4) the perception of related surface colors as

forming a three dimensional pattern of light and shadow across physical surfaces

(illumination in space?). Current Terminology and Concepts. To avoid confusion I describe here the standard

color nomenclature and my impression of its shortcomings.

The simple distinction between unrelated and related colors illustrates the main problem. In

my sampling of texts published in the last decade, I find related colors defined as (1)

colors seen against surroundings of similar luminances that usually appear to be reflecting

or transmitting objects, usually having a gray content in their color (my paraphrase of

R.W.G. Hunt); (2) a light viewed in the context of at least one other light (S. Shevell);

(3) color perceived to belong to an area or object seen in relation to other colors (CIE

official definition); or (4) surface color (P. Kaiser & R. Boynton). None of these

definitions identify the essential perceptual

attribute — two or more contrasting color areas — and most muddle up the definition of

color with the description of a color stimulus.

In the color research literature, a color

appearance mode usually refers to the viewer's interpretation of the color context.

The mode is an inferential, judgmental state in the viewer — a kind of "viewing assumption"

about the visual field that fuses the perception of color onto a perception of physical reality.

While cognitive factors are essential to explain color perception, the problem here is that

viewers rarely perceive how they look at colors: they just perceive how colors look.

As a result, the color appearance modes are usually defined in terms of the viewing

situation — the experimental setup or physical description of the stimulus — in which

cognitive assumptions can be expected to emerge, not in terms of the perceptual

attributes that comprise the basic forms of

color. Thus, a white surface that is illuminated by a red light is in illumination mode, and a

red surface illuminated by a white light is in surface mode (or object mode); but if either

surface is viewed through a reducing screen or eyepiece, then it is in aperture mode. This

strikes me as a Borgesian way to anatomize color perception.

In small field color perception, the spatial arrangement of color fields — especially as

patterns and small color areas — strongly affects responses in the retina or early visual

pathways. In wide field colors, visual grouping or a three dimensional interpretation of the

scene have an equally large effect. All are spatial effects, but the meaning of "spatial" is

very different in small or large field colors. In

both domains, the spatial effects are typically discussed as dozens of discrete color

appearance phenomena, each defined by a prototypical visual illusion; some important

visual properties, such as small field iridescence, are orphaned in this approach.

These areas of color vision terminology date from the middle of the 20th century and seem

to me badly in need of a comprehensive review and new terminology. For reference, I list here

the standard appearance modes and my interpretation of them as basic forms of color:

• Illuminant mode describes colors that appear to be or actually are lights. I prefer self

luminous color to allow for the perception that results from strong luminance contrasts in

surfaces, not just from light sources, and to avoid confusion with the technical use of

illuminant to mean the spectral power distribution of a light source.

• Illumination mode for surface or object colors that appear to be distorted by the color

of the illumination. I prefer the terms local color to denote the appearance of a surface or

transparent body seen under a recognized "white" or unbiased illumination, and veiled

color to denote the perception of any kind of tinting source, no matter whether the tinting

source is perceived to be the chromaticity of

the light source, shadows cast by the illumination, a tinting reflection, or a filter or

other semitransparent material.

• Surface mode denotes colors that appear

illuminated by a "white" light source. I prefer surface color to indicate a luminance contrast

that induces the appearance of a material surface without imputing a specific quality to a

light source, whether white (local surface color) or tinted (veiled surface color).

• Object mode for surface colors that appear as physical objects in space. I prefer plane

color or depth color to indicate that the surface colors induce the perception of a continuous

surface or objects in three dimensions.

• Unrelated Color and related color are not

considered modes because there is no cognitive contribution to the color perception;

but for related colors this requires that there are no spatial or illumination cues created by

the color stimulus.

N E X T : adaptation, anchoring & contrast

Last revised 08.01.2005 • © 2005 Bruce MacEvoy

adaptation, anchoring & contrast

This page continues the

"new testament" view of color described in the previous page on the basic forms of color.

I describe how color vision copes with changing levels of illuminance in the environment (luminance adaptation), anchors our relative sense of white and black in surface colors (lightness anchoring), and compensates for any color bias in the illumination (chromatic adaptation). These adaptations maintain our experience of color as a stable attribute of objects, and minimize our awareness of changes in the intensity or chromaticity of the illumination.

I then outline the processes of chromatic induction, including simultaneous and successive color contrast. Both are shaped by the complementary color relationships of the opponent dimensions. Finally, I review some of the changes in color appearance produced by changes in luminance intensity or luminance contrast.

As in the basic forms of color, contrast is the key perceptual element. In many ways, contrast is the fourth and most important colormaking attribute.

The human visual system has an astonishing capability to record images across an enormous range of illumination, producing an apparently consistent picture of light, shadow and color despite changes in environmental light intensity. This is usually called light adaptation or sensitivity regulation, but it is more accurately termed luminance adaptation, to separate it from the opposing processes of light adaptation and dark adaptation.

The mechanisms that accomplish luminance adaptation are not completely understood. The general goal of the adaptations can be

luminance adaptation

colorvision

luminance adaptationsize of the challenge

the form of adaptation adaptation mechanisms light & dark adaptation

mesopic color appearance

brightness, lightness& anchoring

chromatic adaptationphotoreceptor

adaptation successive color

contrast complementary colors corresponding colors

chromatic inductionchromatic contrast

chromatic assimilation

luminance & color changes

color constancy

described (for example, by analogy to photography), and some specific mechanisms in the eye (such as pupil contraction and photopigment depletion) have been isolated and described exactly. But these early mechanisms are only part of the story; other mechanisms are involved in later visual processing.

Size of the Challenge. Before delving the processes that produce luminance adaptation, it is useful to look at the range of light levels that vision must accommodate.

Light is usually quantified in two ways: as (1) the light incident on a surface of constant physical size (the illuminance), or as (2) the light emitted into a solid angle of standard area (the luminance). Illuminance (in lux) is the appropriate measure of the quantity of light provided by a light source, while luminance (in candelas per square meter) is the appropriate measure of the brightness of a visual image. (Retinal illuminance, in trolands, estimates the light actually incident on the retina, compensating for the light reduction due to pupil size.) Recall that illuminance (including retinal illuminance) is not directly visible: we only see the luminance of the light source viewed directly, or the luminance of the light source as a diffuse or specular reflection from physical surfaces. The illuminance in light environments is commonly measured in lux (left) or foot candles (1 foot candle = 10.8 lux). As the table shows, the human eye must cope with an enormous variation in light across natural light environments — from the illuminance of the noon sun (which can be anywhere from 60,000 to 130,000 lux) to the illuminance provided by the planet Venus or an overcast

night (about 10-4 lux). The sun provides a quantity of illumination equivalent to 13 billion planets or bright stars, 130 million starry nights or 1.3 million full moons, yet our vision can adapt to light environments anywhere within this range.

If we take indoor (architectural) environments as a direct expression of human visual preferences, then human vision is most comfortable under illumination levels of

around 100 to 1000 lux, depending on activity — 100 lux for restaurants, churches or auditoriums, 300 lux for business offices, 500 lux for medical laboratories, kitchens and manufacturing areas; and 1000 lux for surgical theaters. The "white" of computer monitors is designed to simulate the appearance of a sheet of white paper illuminated at office lighting levels of about 300 lux (about 28 foot candles.)

Most people can easily negotiate a night environment under the light of a full moon; many people prefer to wear sunglasses in the brightest outdoor daylight. This implies a latitude of behaviorally comfortable

illuminances from 10-1 to above 104 lux, or 5 log units.

In many task environments eyestrain is a potential problem. Eyestrain generally arises when illuminance is too dim to perform detail tasks (such as reading or sewing), or the visual field includes areas that are too bright in comparison to the surround luminance. Illumination that is too bright (windshield glare, a television viewed in a dark room, sunlight reflected on open water) can cause tearing, irritation or burning of the eyes; inadequate illumination can cause headaches, double vision or blurred vision.

Luminance benchmarks are harder to pin down because luminance depends on how the viewing geometry is defined and how the visual sizes of various sources are standardized; natural sources such as the sky, moon or sun vary dramatically by weather, geographic location or elevation from the horizon. Independent references provide very different luminance values for the same light stimulus, and the conversion to trolands is somewhat arbitrary. The table below is my best guess for a representative selection of luminance values, laddered on the appearance of a white paper (reflectance ~90%).

total range of human visionand effective light adapted

response range

after Paul Schlyter (2005); Handbook

of Space Astronomy and Astrophysics (1982)

Here the range in values is even larger, from a lightning flash (above 10 billion candelas, or

1010 cd/m2) to the minimum possible visual

stimulus (one millionth a candela or 10-6

cd/m2). At both extremes, the duration of the exposure influences visibility.

The behavioral comfort zone for surface luminances, as defined by a sheet of white

paper, is in the range of 101 to 104 cd/m2, or about 3 log units, which is a much smaller relative proportion of the total range than is found in illuminances. This is consistent with the fact that our visual system does not adapt to the actual illuminance but adapts to the average (gray) luminance of natural surfaces — the diffuse reflected image of ambient light.

Note that a diffusing 60W light bulb is about the brightest light source that can be looked at continuously without risk of eye damage. The connection between bright appearance and a potentially dangerous light intensity is anchored on daylight levels of illumination. A candle flame appears very bright in a dark room but is completely harmless. Lights perceived as "bright" in daylight are almost always hazardous; the setting sun, until it has turned deep orange, should be admired in glances.

The Form of Adaptation. The basic adaptation task is to compress the enormous range of natural light intensities into a consistent (and limited) perceptual range of surface lightnesses and self luminous brightnesses.

How informative are these contrasting surface and self luminous forms of color? Lightness, the relative luminance of surfaces, provides rich information about physical objects — their density, surface texture, molecular structure, mineral content, even life content. Every substance has a characteristic reflectance "signature" that includes its average refractive index, reflectance, chromaticity, homogeneity, pattern, surface texture and surface relief.

Brightness, or luminance in excess of "white" surface reflectance, is much less informative. It adequately renders lights such as smoky fires, translucent or specular materials, and the moon and planets; but the dominant natural light source (the sun) is dangerous to look at.

So the most informative luminance adaptation should center the best contrast discrimination

on the luminance variations of illuminated surfaces, inclusive of the somewhat brighter luminance variations of filtered or specular light.

A standard method for examining the relationship between stimulus luminance and perceptual response is the characteristic curve, which plots log scene luminance against linear response, as a proportion between the minimum and the maximum possible response. The characteristic curve is used to describe the density response of photochemical reaction in photographic film or the photoelectric response of light sensors, but the same curve describes the response of animal vision.

a generic characteristic curve comparison of an ideal luminance to response function

(blue curve) with a generic characteristic curve representative of most imaging media (adapted from

Hunt, 2004)

The characteristic curve is fundamentally defined by the density response of the imaging medium to light, which ranges from the zero response baseline or response floor to a maximum response ceiling. Outside these limits, luminance variations are imageless. The threshold stimulus is the smallest light energy necessary to produce a just noticeable shift from the baseline (zero) response, and the saturation stimulus is the light energy that produces a response indistinguishable

from the maximum possible. In photographic film, the response is the proportion or density of dye or silver halide crystals converted by light (from 0% to 100%); in the human eye, it is the total response range of the whole retina.

Within this four sided space, the characteristic curve takes a diagonal path inflected by a curve at the low end (the toe) and at the high end (the shoulder or knee). However, as described here, the shape of the characteristic curve changes radically depending on whether log or linear units are used for the stimulus and/or response axes of the graph.

Two metrics are commonly used to describe contrast. The first is the contrast ratio between the luminance of the brightest and darkest areas in the scene, or between the response density of the "whitest" and "blackest" areas of the image. For lightness values in scenes or in images, the contrast ratio is defined as:

contrast ratio = L*max/L*min

Most fully illuminated surfaces (exclusive of specular reflections or directly imaged light sources) and computer monitors have a contrast ratio of about 1:20. That is, the peak "white" reflectance is rarely more than L = 95 and the "black" reflectance no lower than L = 5. (Artificial materials can achieve a range from 98% to less than 0.05%.) Daylight cast shadows reduce surface luminances by about one log unit, or 90%, amplifying the need for light and shadow contrast to something like 1:200. Modern cinemas have a contrast ratio of about 1:80, which is necessary to offset the contrast reducing effect of the dark viewing environment and to convincingly approach the actual human response range (described below).

As the line between log luminance and linear response gets steeper, the image contrast or luminance discrimination becomes greater. This maximum contrast is in the approximately straight middle section of the S curve, which is usually centered in the contrast range. The measure of maximum image contrast is gamma, the slope of this middle or straight portion of the log/linear S

curve:

The slope must be calculated in units that contain the characteristic curve in a square, so that the slope defines an equivalent proportional change on each dimension; alternately, the slope is the tangent of the angle of a line that fits the central slope of the curve. In the generic diagram above, using pixel addresses of the "white" and "gray" points:

gamma = (185 – 96)/(247 – 195) = 1.71

Gamma is literally the denominator e in the exponent fraction 1/e that defines a nonlinear response compression; to find e, take the reciprocal of the gamma. A gamma of 1.0 indicates a 45° slope in the semilog plot. A higher gamma defines greater contrast, but across a more limited span of luminance. A gamma value of about 2.3 (1/e = 0.43) is typical of computer monitors and the human eye.

The characteristic curve describes primate contrast perception very well. For example, when primate cones in vivo (in an intact retina) are first adapted to different levels of background luminance and then exposed to contrast flashes of increased or decreased luminance, the receptor potential (cell electric discharge) describes a series of characteristic curves, as shown below.

cone sensitivity and luminance adaptation

changes in late receptor potential of rhesus monkey cones produced by short flashes of increased or decreased luminance (white squares) against an

adaptation visual surround of constant retinal illuminance (blue circles), for different levels of

adaptation illuminance (adapted from Valeton & van

Norren, 1983; and Boynton & Whitten, 1970)

This graph clarifies a number of perceptual changes across mesopic vision. First, the total response range remains roughly constant, from about zero to 700. Second, the cones at any fixed adaptation level respond to a contrast ratio of about 3 log units, or 1000:1 trolands, which is fundamentally the limit imposed by photopigment bleaching (or, in photography, silver crystal or dye depletion). Third, the response curve shifts to higher or lower luminance levels, across a range of 7 log units, due to the effect of the adaption intensity — a large visual area of constant luminance. Fourth, the position of the adaptation response to this constant background shifts, as luminance increases, from the toe to about the middle of the characteristic curve. Finally, the gamma or contrast of these curves remains approximately constant across luminance levels, although the area of peak contrast (relative to white or middle gray) seems to darken as luminance increases, because the adaptation response shifts toward the toe of the characteristic curve. The position of the adaptation intensity in the

middle of the visual characteristic curve may seem incorrect if compared to the normal placement of "white" within a photographic characteristic curve. But if we take a semilog (log/linear) plot of luminance on lightness, it is obvious that surface luminances lie in the lower half of the actual visual response range, and that the effective response is larger than 3 log units of luminance (diagram, right). Although lightness does not describe self luminous colors, the upper bound of the full characteristic curve would plausibly come at about L* = 200, which is proportionately about 1000 times the luminance of the adaptation white. Human vision seems to perform optimally (and lightness discrimination is typically measured) at

luminances no greater than 320 cd/m2 or 1000 lux (equivalent to late afternoon daylight), which implies a maximum luminance sensitivity of about 3.2 to 320,000

cd/m2. Note that the upper limit is a hazardous level of luminance exposure for human eyes.

Full moonlight is illustrative, as we can see brightness contrasts both on the light source (the "man in the moon") and on the illuminated surfaces (the ground). The full moon's typical luminance is about 3000

cd/m2; its illuminance is therefore about 0.2 lux, so surface luminances range from about

0.06 (white) to 0.012 (medium gray) cd/m2. The total luminance range is therefore 3000 to 0.01 or 300,000:1, which is equivalent to about an 18 stop range in photography and is about 30 times greater than the contrast ratio produced by photopigment with pupil contraction (~4 log units).

These two examples document that the human visual range is about 5 to 6 log units with a 95% contrast ratio of 10,000:1 and a gamma of about 2.4. To achieve this response range, photopigment depletion and pupil area must be dynamically amplified by other adaptation mechanisms (such as cellular adaptation and response compression, described below) in the moment to moment luminance changes of visual experience.

semilog plot of luminanceagainst lightness

As a result, the dynamic range of human vision is strongly clipped by conventional

imaging media. This is the motivation behind high dynamic range images (HDRI), which merge the contrast information in three or more photographs taken at different f stops, or are generated whole cloth in computer animation or simulation. The fused images can

capture a 105 luminance range (or more) and, displayed on high dynamic media, reproduce the impression of light, space and luminance contrast experienced in normal vision. Unfortunately HDR images appear somewhat distorted in low contrast media such as photographic prints or computer monitors (image, right), but HDR enhancements have been effectively used in cinema, which has an 80:1 contrast ratio, and in digital animation and computer game effects.

A final issue is flare, defined as any contrast reducing light (brightness) added to an optical image. In all imaging systems, flare reduces both chromatic and brightness/lightness contrast, and sometimes reduces image detail as well.

In photography, flare has many sources, including: scattering from the diaphragm edge, lens aberration, aperture vignetted images of the light source reflected from refraction boundaries (the surfaces of lenses), light scattered inside the camera body (including light reflected from the film or sensor surface), the "spreading" or "burn out" of the brightest lights due to overexposure, overexposure of the film or fogging of the developed print, surface reflections from glossy prints or monitor screens, and the "show through" of white paper under inks. Analogous sources cause flare in animal vision.

To offset flare, contrast must be increased by increasing gamma — so that the straight section of the characteristic curve has a steeper slope (blue curve in the diagram, above). This shifts the toe and knee toward the center of the luminance range, causing dark colors to shift toward black and near white colors to appear almost luminous; the range of luminance discrimination is reduced.

Because surfaces are only imaged through differences in the absorptance of incident light, flare is light that obscures surface

8 bit simulation of ahigh dynamic range photo

from Wikipedia (2007)

contrasts. This is almost always unwanted reflections or light that is too bright: the glare of sunlight reflected from water or snow, gloss reflectance from polished surfaces, the whitening or desaturation of surfaces viewed in bright sunlight after coming out of a darkened movie theater, the excessive depletion of cone photopigment at high illuminance levels. These produce visual flare artifacts identical to those found in imaging systems. Adaptation Mechanisms. Environmental luminance varies over an enormous range, approximately from 1 to 10 billion, so the image luminance will change over an equal range.

The first nonlinear response to luminance variations begins in the photopigment reaction to light. Photopigment bleaching follows a nonlinear equation that produces a "hockey stick" curve in a log luminance/log response plot (diagram, top right). This curve provides a suitable characteristic curve (adequate

image contrast) for luminances between 103

to 106 cd/m2, which is only 3 log units out of the total luminance range of 10 log units. So additional adaptation mechanisms are necessary.

The first is the addition of second photopigment that has a slightly different response range but which is adjusted, through response compression rather than photopigment saturation, to have a much lower effective response range (diagram, bottom right). In mammalian eyes, this is provided by the rod photoreceptors used for night vision, which anchor the scotopic

sensitivity range from about 10–4 to 10–1

cd/m2.

The second strategy is aperture regulation, or adjusting the quantity of light striking the photopigment. In human eyes this is the pupillary reflex, which can expand the aperture area of the pupil by about 10 times or 1 log unit. In photography, these two strategies are represented by changes in film speed and the adjustable diaphragm.

As the diagram shows, these two mechanisms

mechanisms of luminance adaptation

(top) luminance response range provided by

photopigment alone; (bottom) expansion of luminance

response by pupil contraction and second photopigment

(rods)

would provide at most an increase of visual response to 7 log units, which leaves 3 log units of adaptation unexplained in the middle

or mesopic luminance levels between 10–1 to

102 cd/m2.

The remaining adaptation is believed to come from two processes. Response compression causes an equal increment in luminance to result in a smaller proportional change in response as the total response level increases. It is the primary adaptation mechanism in the rods, because only 10% of the rod pigment is bleached at 1000 trolands. Cellular adaptation is a shift of the entire response curve to more intense stimuli, primarily by raising the adaptation response rate. This mechanism is active in the cones and retinal ganglion cells, but apparently does not occur in the rods; rods are "pegged out" by response compression at around the mesopic threshold, and only begin to desaturate in the mesopic range.

How these four separate mechanisms — photopigment depletion, pupil contraction, cellular adaptation and response compression — coordinate luminance adaptation is not yet known. However, Peter Kaiser and Robert Boynton provide a quantitative illustration of how the four principal processes might interact, as shown below.

processes of light adaptation in iris and cones

for luminances from 0.01 cd/m2 to 1,000,000 cd/m2, with quantitative markers for white paper luminance, pupil area and photopigment depletion; adapted from

Kaiser & Boynton (1996, Table 6.1)

I've displayed these adaptation processes as if they were independent, variable density filters that may transmit from 100% to 0% of the imaged luminance. The net signal reduction is the filter product or cumulative effect of all adaptation mechanisms. These have more or less "pegged out" at a retinal illuminance of about 500,000 trolands, so a frosted (diffusing) 60W incandescent light bulb (which

yields about 105 cd/m2) is a "safe" and commonplace stimulus to illustrate the upper limit of luminance sensitivity.

Two things happen as the adaptation luminance increases. The first is a radical reduction in the scale of the luminance variance. If scotopic luminance (at about 0.01

cd/m2 or 0.28 trolands) is the point where no photopic adaptation mechanisms are operating, then adaptation reduces the luminance signal at extreme photopic levels

(around 1 million cd/m2 or 3.5 million trolands) to only 0.00016% (1/633,000) of its

scotopic efficacy. As an illustration, this signal reduction is equivalent to the difference in the sound of an automobile horn as heard at a distance of 10 meters or 8000 meters (5 miles). Second, the adaptation mechanisms somewhat undercompensate as luminance increases, so that a criterion perceptual effect (such as a just noticeable difference from the adaptation luminance) requires a proportionately smaller luminance difference at higher luminances. This causes the Weber fraction of incremental luminance response goes down as luminance increases, from about

25% at .01 cd/m2 to about 1.3% at 100

cd/m2. In other words, contrast increases about 100 fold from scotopic to low mesopic vision; thereafter, it remains relatively constant through the upper mesopic and photopic range. This is apparent in the divergence between a proportionally constant threshold response and the adapted signal (diagram, right). It also appears in the migration of the adaptation stimulus from the toe to the slope of the characteristic curve, as shown in the diagram above.

Pigment bleaching provides the outer limit of the curve, evident in the parallel curves for photopigment (purple) and adapted signal (black). Bleaching occurs because the retinal photopigment molecules are decomposed by light, and until photopigment is regnerated light cannot affect the photoreceptor response.

At luminance levels below 100 cd/m2, the process of replenishing photopigment can keep ahead of bleaching, so the pigment is "transparent" to light. At luminances above this point, bleaching occurs at a faster rate. The proportion of unbleached photopigment under stable adaptation is about 50% at 5,000

cd/m2 and less than 0.2% at 1 million cd/m2.

The most gradual reduction occurs through contraction of the iris and reduction in the area of the pupil aperture. This is a reflex reaction and quite prompt; failure of the pupillary reflex is a sign of severe brain trauma or death. Starting at a full scotopic

dilation of about 28 mm2, it reduces light by

about 50% at a luminance of about 50 cd/m2, and reaches its maximum effect, a reduction

sensitivity reduction produced by each

adaptation process

baseline signal defined by response threshold; adapted

from Kaiser & Boynton (1996)

of 87%, at luminances above 10,000 cd/m2.

How does the visual system determine the appropriate adaptation level, especially for pupil contraction and cellular adaptation? It appears that rods and/or S cones in the periphery of the visual field (along the sides of the eye) play an important role, and that there are secondary cells in the retina that are photosensitive (respond to light) but do not contribute in any way to the optical image transmitted from the cones.

Two additional adaptation processes are common but rarely described in conjunction with the physiological mechanisms. The first is the many forms of behavioral adaptation — turning lights on or off, moving toward or away from a light source, averting the eyes from glare or bright reflection, shielding the eyes with a hand or sunglasses. These tactics are used primarily to reduce flare and minimize changes in adaptation, or to create a task comfortable illuminance.

The second is lightness anchoring, the perceptual interpretation of high and low luminance areas as white or black surfaces, which is a "local adaptation" determined by the relative proportion of high and low luminance areas in the image, separate from the "global adaptation" to the average luminance of the whole visual field. By shifting the relatively lightest areas toward white, lightness anchoring adjusts the image luminance range within the highest contrast part of the characteristic curve. Lightness anchoring can produce instantaneous color shifts, which implies a cognitive rather than sensory adaptation process.

The changes in visual contrast are summarized in the schematic below.

schematic of color vision contrast by adaptation level

Peak contrast in both lightness and hue purity

occurs around 104 candelas/meter2 (under an illuminance between typical daylight shade and full sunlight), and declines in both directions; daylight shade provides an optimal illuminance for reading that summer novel.

Around 101 cd/m2 contrast is reduced from the peak by about 15%. Then contrast begins to fade (the visual gamma gets smaller) under low mesopic illumination (below 100 trolands), and "white" surfaces appear distinctly grayed

or dimmed. From 10–1 cd/m2 downward contrast declines further up to the scotopic threshold; scoptopic "white" surfaces appear to be a middle gray, and lightness discrimination of dark surfaces is lost. (Compare with this diagram of luminance response exponents.)

Light & Dark Adaptation. Although photopigment depletion, pupil area, cellular adaptation and/or response compression are the major mechanisms of luminance adaptation, they function together differently when adaptation shifts toward a higher or lower illuminance environment. These shifts are described as light adaptation and dark adaptation respectively.

Light Adaptation. Light adaptation decreases the sensitivity of the eye to light sources or light environments that have a higher luminance than the previous (adaptation) level. These are, for example, the processes that act as we step out of a darkened movie theater, dimming the superabundant daylight to a more comfortable level.

The principal feature of light adaptation is that it occurs relatively quickly in a sequence of reactions: first behavioral avoidance of extremely bright lights or glare, accompanied by pupil contraction within 2 seconds; then depletion of photopigment to a new steady proportion of maximum; and finally cellular adaptation to the higher response level. The time course depends on the starting point and size of the luminance change, but light adaptation is typically well advanced within one minute, and stabilized within 10 minutes.

Light adaptation is accompanied by a temporary loss in contrast sensitivity at higher luminance levels, as these are shifted into the flattened "knee" of the characteristic curve. There is a complementary increase in the discrimination of very dark surfaces, provided they can be viewed without flare.

photopigment depletion across luminance levels

At high luminances photopigment depletion becomes the major component of photopic light adaptation. The other adaptation mechanisms do not completely saturate, so cone photoreceptor variance can still be transmitted; meanwhile the remaining photopigment is never completely depleted, and is regenerated at an exponentially higher rate as it approaches saturation. For this reason we do not become completely insensitive to light, even beyond eye

damaging light levels.

As they are fundamentally the same type of molecule, both the rod and cone photopigments bleach at about the same luminance levels; both have a half saturation point at about 20,000 trolands. Why then don't the rods contribute to photopic vision? The answer is that the response compression in rod photoreceptor signals, which is probably due to the different anatomy of the rod cell, effectively saturates at around 1000 trolands, or 6 log units above the luminance threshold. Above this point, any change in the photopigment produces no visual signal. Yet at this luminance only about 2% of the rod photopigment has been depleted.

One consequence of cone bleaching is self screening, or a decrease in the optical density (absorptance) of the visual pigment in the eye because it has been converted into the more transparent bleaching products.

A second effect is a spreading of the cone sensitivity curve under very high light intensities, which raises the relative response contribution from the tails of the cone sensitivity curve in relation to the peak. This causes a decrease in the kurtosis (peakiness) of the sensitivity curve, which decreases the separation or difference among the L, M and S signals and therefore decreases the perceived saturation of colors. The third and most intricate effect is a shift in the yellow balance — it might be called the Wright-Brindley effect. This shift, which occurs in both foveal and wide field vision, changes the wavelength that is exactly complementary to a "blue violet" primary (mixes with it to produce a pure "white").

Günter Wyszecki demonstrated the effect with a standard Maxwell matching task. First, three "red" (R), "green" (G) and "blue violet" (B) primary lights are mixed as a criterion light that matches illuminant D65, which has the property of remaining perfectly achromatic ("white") at all luminance levels. Then this criterion "white" is matched by a second mixture of a target light (T) of any wavelength plus the two primary lights sufficient to desaturate it. The diagram (at

right) shows the example of a "yellow" (572 nm) target light mixed with the B and G primaries. The luminance of the "white" criterion is increased, and the second mixture adjusted to restore a color match, in incremental steps up to 100,000 trolands.

At a retinal illuminance of 1,000 trolands

(about 100 cd/m2), a "yellow" target light at 570 nm by itself makes a pure achromatic mixture with the B (445 nm) primary light: any added R or G light will destroy the "white" color. The 572 nm target light is very slightly too red, and therefore must be shifted toward green by a small amount of the G primary. But at a retinal illuminance of 100,000 trolands

(about 25,000 cd/m2), the complement of B shifts toward a "yellowish green" at 555 nm. As a result, the original "yellow" wavelength T appears much too red and creates a distinct pink or magenta mixture with the B primary. This magenta tint must be neutralized by adding a larger quantity of the G primary and reducing the amount of target "yellow", as shown below.

shift in yellow balance at high luminance levels

the visual complement of "blue violet" shifts from "yellow" to "green" wavelengths at high luminances

In tandem with this shift in the yellow balance is (1) an increase in the relative tinting strength of average long wavelength light (long wavelength target colors must be reduced by a greater amount at high illuminances), and (2) a shift in the peak tinting wavelength, which is about 605 nm at low luminances but 595 nm at high luminances.

change in achromatic mixture caused by shift in

yellow balance

adapted from Wyszecki & Stiles (1982)

For a "green" target wavelength, such as 550 nm, the shift in the yellow balance causes a sharp decrease in the quantity of R primary, and a slight increase in the target color, required to neutralize any green tinted mixture with "blue violet" (diagram, above). However there are negligible shifts in "blue" or "violet" target wavelengths (below ~492 nm) at high luminances, because both the criterion and matching mixtures contain the same quantity of R and G primaries. Nearly all of the adaptation shifts occur between 8,000 and 50,000 trolands, and they indicate a failure in the proportionality requirement of Grassmann's Laws. The shifts implicate the r/g but not the y/b opponent balance in the proportionality failures.

These changes in the yellow balance are measurable in lights but not in surface colors or in perceptions of the illuminant. In that respect they resemble the color shifts described as the Bezold-Brücke effect. However, the yellow shift is very large, so it probably contributes to global changes in color appearance, in particular the hue bias of greens and changes in color saturation, that characterize changing illuminance levels.

Dark Adaptation. Dark adaptation increases the sensitivity of the eye to light sources or light environments that have a lower luminance than the previous (adaptation) level. These are, for example, the processes that engage after we step from summer sunlight into a darkened movie theater. The principal features of dark adaptation are that it occurs relatively slowly and in two distinct stages. There is a prompt increase in photopic (cone) sensitivity, corresponding to a sharp drop in the faintest perceptible luminance, which is completed within about 5 minutes; then a more gradual increase in scotopic (rod) sensitivity, corresponding to a gradual perception of luminances as low as

10–6 cd/m2 (about 1/36,000 of a troland), which is completed within about 30 to 40 minutes (diagram, right). These changes are accompanied by behavioral adaptations — restricted or cautious movement, and reliance on touch or sound — for the first few minutes.

As these curves imply, complete photopigment regeneration occurs over 3 times more rapidly in cones than in rods. However, the initial prompt increase in dark sensitivity is assisted by increased pupil dilation and a shift in cone cellular adaptation, processes that do not affect the rod sensitivity.

Dark adaptation imposes a relatively prolonged loss in contrast sensitivity at low luminance levels, as these are shifted deep into the flattened "toe" of the characteristic curve and, for very dark surfaces, below the adaptation threshold. There is a complementary increase in the discrimination of very light valued or bright surfaces and reflections, for example in the surreal and romantic clarity of moonlit clouds and water reflections as one leaves the mountain lodge for a midnight stroll.

Mesopic Color Appearance. For artists in particular, it is instructive to consider the effects of luminance adaptation on the perceptual quality of lights, darks, colors and contrast, especially in the dark light, storm light, twilight, moon light, candle light environments of mesopic vision.

The color literature too often suggests that vision divides into separate scotopic and photopic regimes. This supports the application of colorimetry by assuming that Grassmann's Laws are valid far into the mesopic range. In fact, especially for wide field (>10°) vision (the standard observer measured with full photopic "primary" mixtures), as luminance decreases through the mesopic range, luminance adaptation and threshold responses are averaged over a larger area of the retina, and trichromatic color matches breaks down due to additivity failure.

Among the obvious effects, low mesopic vision desaturates hue, shifts the white point toward blue, and constricts the perceptible differences in a reflectance gray scale toward white. The appearance of white surfaces changes from an almost luminous brightness to a veiled, shimmering gray; foveal detail disappears and the world dissolves into a quilt of large, low contrast shapes. These changes are hardly captured in the usual description of

rod and cone components of

dark adaptation

minimum visible luminance for cones (red) and rods (green); from Wyzecki & Stiles (1982)

the Purkinje shift as "an increase in the brightness of blue and green colors".

Mesopic Color Matching. Recently there has been renewed interest in mesopic color matching and color appearance changes under low luminance adaptation, particularly the naming or identification of colors under mesopic illumination. I describe both my personal observations and some current research findings.

I first examined mesopic and scotopic contrast perception by viewing a photographer's gray scale late at night, from full studio lighting to moonless night adaptation. The diagram shows that contrast is substantially reduced under scotopic adaptation, somewhat reduced at around the mesopic threshold, but is relatively constant as illuminance increases into the photopic range.

appearance of gray scale at different illuminance levels

The degradation in the gray discrimination and darkening of the "white" standard is consistent with the shift in adaptation luminance toward the toe of the characteristic curve as adaptation luminance decreases, which puts the maximum contrast at luminances above surface luminances. On a moonless night we perceive surface lightness differences only coarsely, but have a delicate sensitivity to brightness differences among stars. In

daylight the adaptation gray and white shift into the middle of the characteristic curve, and the contrast in bright lights is much reduced compared to the contrast in surface grays. To examine mesopic changes, I viewed a sheet of 24 color swatches about 1" square painted on white paper, under sky/horizon illumination from sunset until 1 hour after sunset, and then at night under complete dark adaptation. The swatches included 17 colors equally spaced around the hue circle, all at maximum chroma for their hue/lightness, plus 1 green gold (dull lemon yellow) and 6 "earth" colors (ochre, siennas and umbers). The sheet was viewed at a second story bay window admitting the southwestern sky. Illuminance figures below were estimated from an illuminance graph and local time of sunset. The illustration (right) suggests the color appearance changes:

• 0 minutes (sunset, A) (solar altitude 0°, illuminance ~200 lux). There was a full range of color against the white background that appeared somewhat subdued, like a book under a reading light.

• +15 minutes (B) (–4°, ~20 lux). The white paper begins to dim and soften, appearing slightly luminous; magenta, red and orange become slightly lighter valued and more saturated, as if glowing; red violet, purple and blues darken slightly. Greens acquire the softened appearance of the whites, and a few minutes after the reds appear to brighten, yellow green and middle green appear also to brighten slightly. Yellows lose their sunny, floral character and begin to shift toward a tan or ochre.

• +30 minutes (C) (–8°,~2 lux). Bright yellow colors disappear and become indistinguishable from ochre, raw umber or green gold; the relative green or red content of yellow comes to the fore, causing yellows to appear either green or pinkish tan. Blues and greens begin to merge; dark purple appears jet black. The colors show a much reduced chroma, but still appear relatively saturated because lightness is also substantially reduced.

• +45 minutes (–12°,~0.2 lux). All colors

subjective color appearance changes from photopic to scotopic vision

have been reduced to three percepts — tan, grue and a warm (reddish) dark gray. The darkest blue or green colors turn to black. Brown appears very dark but warm.

• +60 minutes (D) (–16°, ~0.02 lux). Near the limit of color vision. The paper appears a silky grayish blue and lightness contrast is much reduced; all reds and browns collapse into a generic "warm" that is much darker than the photopic colors. All greens and blues appear as a grayish "grue" (green blue) that is lighter (greens) or darker (blues) than the photopic colors. Yellows, ochre and green gold drop to a mid value with a faint orange cast.

• +90 minutes (E) (<0.001 lux). Under complete scotopic vision color is objectively lost (tested by looking at unfamiliar magazine covers), but some trace of color remains in the familiar sheet (especially for colors with a very light or dark scotopic value), probably due to memory color and/or rudimentary hue perception based on "grue" rods and "red" L cones.

Current research methods ask subjects to identify a representative selection of color chips (by naming colors or by grouping together similar appearing colors), or to match mesopic colors viewed with one eye to photopic colors viewed with the other eye (haploscopic color matching). These studies, in addition to my observations above, suggest the following sequence of color changes, which I have summarized as four mesopic stages in the schematic (right): • the transition from photopic to scotopic vision is nonlinear — color shifts are rapid and dramatic in the range of about 5 to 0.05 lux, but are more subtle above or below that range.

• chroma grows smaller, in approximately the same proportion for all hues, down to the visual limit; some hue (and therefore chroma) persists until scotopic vision, and then after — either as memory color or as the hue associated by experience with each scotopic lightness.

• reliable color discrimination, including accurate identification of yellow shades,

four mesopic stages in color appearance across

low mesopic illuminances

persists down to illuminances of 10 to 1 lux [yellow mesopic stage]; nearly all color disappears at illuminances below 0.003 lux [scotopic].

• at around 5 lux, a bright yellow percept disappers (yellows become confused with ochres or green golds), but greens and blues remain distinct [green mesopic stage].

• below 1 lux, discrimination between blues and greens fails or is determined by the color's scotopic luminosity — relative lightness as perceived by rods alone; sienna, red, orange and magenta remain recognizable [red mesopic stage].

• below 0.1 lux red, orange and brown become indistinguishable, red violet and purple appear black, but a weak warm/cool contrast still functions [warm mesopic stage].

Related studies suggest that most of the hue changes in mesopic vision occur at the opponent stage rather than the trichromatic stage, and that color shifts occur separately on the y/b and r/g channels.

The current research reports disagree on the transition points in mesopic color appearance by as much as 1 log unit of illuminance, which is probably due to large observer individual differences in adaptation, differences in stimulus presentation or adaptation preparation, or inaccuracies in illuminance measurement. The low mesopic sequence of discriminations between yellow and ochre/green gold, green and blue, and scarlet and brown have been sufficiently replicated to serve as adaptation benchmarks.

Rod/Cone Interactions. The source of mesopic color shifts lies in the transition from cone based color vision to rod based color vision. During this shift cones and rods dynamically collaborate in color perception. From the prejudice of colorimetry, this was considered a disruption or complication of trichromatic color matches; thus it was traditionally called rod intrusion. Mesopic color changes are now studied as rod/cone interactions. There are four major differences in color

appearance between rod and cone vision. The first is in rod chromaticity. Rod sensitivity is usually equated with the "blue green" peak in the scotopic luminosity function at around 505 nm, but if the curve is interpreted as a transmission profile "filtering" a white photopic illuminant, its chromaticity corresponds to a CIECAM or CIELAB hue angle of about 210, or a spectral hue of 480 nm, which is a cerulean or turquoise blue. The brightening of green or blue green surface colors (the more common description of the Purkinje shift) corresponds instead to the union of the photopic and scotopic sensitivity curves (the wavelengths that stimulate both functions), which has a CIECAM hue angle of 154 matching a middle green wavelength of 520 nm.

The second difference is in rod lightness contrast, which is qualitatively darker and softer. I cannot find a scotopic lightness function in my references, however the sensation of scotopic white equates with a photopic gray of about 75% reflectance (diagram right), and the foveal contrast function seems to have a much lower gamma (a Weber fraction above 20%) with contrast shifted into the highest reflectances, as illustrated above.

The last differences between rod and cone vision are a change in the quality of white, which in scotopic vision has a ghostly, silky sheen, and a reduction in spatial resolution (especially in foveal vision), which softens edges and internal details. The shift to scotopic vision produces a visual field tinted a pale, gray greenish blue, in which lighter valued forms are characterized by outline, and darker forms lose almost all internal (low contrast) detail; very small forms cannot be discriminated, and rapid movements are greatly blurred.

As light dims into the middle and lower mesopic range, the cone responses do not "fade out" equally. There is instead a shift in chromatic sensitivity toward the extreme "red" wavelengths. This is measured using color mixtures contrived to display differences between photopic and scotopic brightness, while retaining a constant chromaticity during the mesopic transition. This allows differences in light sensitivity between scotopic and

relative chromatic sensitivity under scotopic

(λ') and photopic (λ) adaptation

photopic vision to be mapped into a standard chromaticity diagram, as shown below.

the contours of rod intrusion

The isobars in the diagram show that the extreme values concentrate in the "red" corner of the chromaticity space, and contract more quickly from the "green" than from the "violet" corner, especially at moderate mesopic levels. Thus, at near scotopic light levels, the cone sensitivity to "red" light is roughly 14 times higher than the rod sensitivity to the same chromaticity. This is why astronomers and submariners use red lights to perform photopic tasks (such as reading) without disrupting their dark adaptation.

Tetrachromatic Color Matching. Given the fact of rod intrusion, mesopic vision is actually tetrachromatic: its color mixtures are the result of four "primary" inputs — L, M, S and V'. To assess the mixture characteristics of this four color or tetrachromatic color space, Pat Trezona provided her viewers with four adjustable "primary" lights at wavelengths 470 nm ("blue", B), 510 nm ("green", C), 590 nm ("orange", Y) and 645 nm ("red", R) that were used in the maximum saturation

color matching method to match a range of monochromatic target lights (Q). One or more of the "primary" lights could be mixed with the target light, to desaturate it. Viewers first mixed the R, Y and B "primary" lights to match the target light (with one or two "primary" lights mixed with it) at mid mesopic luminances (400 trolands). Then the mixtures were reduced to scotopic luminance (< 2 trolands), the viewer was allowed to dark adapt, and the C "primary" light was added to the dimmer mixture to restore a scotopic (brightness) match. Then the lights were returned to photopic levels and the match was adjusted again. This alternation was repeated up to three times until mixtures were obtained that did not change color or brightness between mesopic and scoptopic levels. The results for all target lights were four "primary" matching functions with 1, 2, 3 or 4 inflections or peaks across the spectrum (diagram, right). Negative values indicate the "primary" light was mixed with the target color.

Two mixtures, for "blue violet" and "green", are shown in the diagram to illustrate that Trezona's color matching method essentially defines two near neutral or achromatic mixtures of matching brightness. The "blue violet" criterion is desaturated by the "yellow" mixture R+C, which then is matched by the similar achromatic mixture Y+B. Similarly, the "green" criterion is desaturated by the dull "blue red" (R with a tint of B), which matches the feeble "green" mixture Y+C. The exceptional mixtures are in the long wavelengths, where only the R primary has a nonzero value because the long wavelength criterion lights appeared "red" (rather than achromatic) even at scotopic luminance levels.

The unexpected effect was that these brightness/chromaticity matches remained metameric (visually identical) across all intermediate levels of scotopic or mesopic luminance. In other words, the mixtures define brightness confusion lines in spectral mixtures that are unaffected by changes in luminance adaptation. Note that these curves are not color matching functions (because chromaticity was in most cases very low) but adaptation balancing functions.

trezona's original tetrachromatic

color matching functions

adapted from Wyszecki & Stiles (1982)

The functional implications are easier to understand when they are transformed into a trichromatic color space (the "primary" matching curves can have no more than three inflections), as shown below.

trezona's tetrachromatic color matching functions

projected into trichromatic space (adapted from Wyszecki & Stiles, 1982)

Two of the curves seem familiar. One is a blue violet (B) function, which matches the shape and peak of the S cone sensitivity curve (tristimulus Z), which represents the brightness contribution of the S cones. The V function, which resembles the shape and peak of the photopic luminosity function (tristimulus Y) but, because of the negative values in the "violet" wavelengths, actually has an intense "yellow green" chromaticity; this probably compensates for mid spectrum brightness differences in the luminous efficiency (brightness) of mesopic and scotopic lights.

The two largest curves are visual complements (they form an achromatic mixture in the right proportions), and they account for nearly all of

the adaptation balancing. One is a supersaturated, luminance destroying magenta (M) that resembles the r/g opponent function, and the second is its mirror image — a supersaturated, luminous middle green (G).

I conjecture that Trezona recovered a luminance dependent shift in a mesopic green/magenta balance that is analogous to the luminance dependent shift in the photopic yellow balance. Shifts in the yellow balance are believed to be caused by bleaching differences in the L and M photopigments that define the r/g opponent function. The green/magenta balance would be caused by rod signals that are transmitted through cone pathways and are interpreted as M and/or S cone signals. Under photopic and high mesopic vision, luminance sensitivity is defined by the L+M signal in a weighting of about 1.5 L to 1 M. However, under mesopic illuminance the rods begin to stimulate the cone pathways in ways that resemble "green" light, which inflates the M component of the cone luminance and chromatic signals. At the same time, the rods stimulate the S cone pathways to produce a phantom violet sensation, which combines with the persistent L cone chromatic signal. These define the contrasting "green" and "magenta" components in mesopic color.

Whatever the actual mechanisms of mesopic adaptation may be, the green/magenta balance can be vividly experienced in the negative afterimage of a "white" light. In a dark room, first expose both eyes to the view of a 60W light bulb for one minute. Then turn off the light and look into a completely dark corner of the room. The positive afterimage of the bulb first appears as a bright yellow green enclosing a dark violet core. After a few moments this changes to a negative afterimage — magenta with a yellow green or yellow penumbra. The magenta and green oscillate slowly, until the image shifts into into a saturated violet surrounded by bluish green.

positive and negative afterimages of a bright light

the positive afterimage is yellow green (left), which turns into an oscillating magenta/green or purple/green

contrast

The intense light exposure bleaches the rods and cones, and the oscillations in darkness display all the colors identified in Trezona's matching method. They appear to be different contrast mechanisms seeking an objective balance point, as the oscillations are suppressed by the image of exterior objects.

Suggestions for Painters. Translating the colors of twilight or night into a painting that is viewed at gallery lighting levels is a complex problem.

A dark background or mat and a dark frame are essential, as it reduces the image contrast. The painting should hang in subdued lighting, keyed to barely reveal the darkest value differences.

No color vision is purely achromatic, so a night painting in pure black and white appears colorless. It is customary to represent night scenes with a dark blue violet sky, very dark silhouetted objects and deep yellow emanating from windows viewed from outside. Color research indicates that the scotopic tint cast over all colors is probably best represented as a very dull cyan or cerulean blue. However, the trezona primaries suggest that magenta, deep blue and green, at very low chroma and contrast, form the color foundation of a scotopic palette.

Warm grays or browns should be used to render red or orange objects, dark blue green to represent greens and blues, and a pinkish gray to represent yellows, ochres and yellow greens. The value contrast between light and dark colors should be cut by at least half, and the lightest surface colors should appear to be

a medium to light gray. White and light valued colors should stand out with greater contrast from black and dark colors than they do under daylight illumination — by reducing the number of intermediate grays. Dark purples should appear the same value as black.

Scenes that represent mesopic luminance levels, such as twilight, should represent approximately the normal color range, but biased according to the color shifts described above. Reds remain relatively more prominent until close to the low mesopic threshold. All yellows and yellow greens turn ochre just below the upper mesopic limit, where oranges, reds and magentas appear slightly brighter and whites take on a delicate pinkish hue.

For landscape painters, it is very useful to examine the mesopic and scoptopic color changes in a set of color swatches, or in color photographs or magazine reproductions of landscape scenes, to memorize the color shifts it is necessary to capture in paint mixture. The green/magenta balance is often important to guide color choices and color harmonies to represent darkness, but also atmosphere.

Painters and graphic artists will want to read the article Night Rendering by Henrik Jensen et al. (2000).

The previous section explored adaptation related changes in color appearance that are produced by changes in the photoreceptors and the early visual pathways. This adaptation creates a new problem: how to consistently recognize white or black in surface colors across a varying range of luminance values.

Because of luminance adaptation, the absolute luminance of any isolated surface provides a very poor cue of its reflectance properties. The diagram below illustrates the remarkable range of luminances that masquerade under the seemingly consistent appearance of white and black contrast.

brightness, lightness & anchoring

luminances in the perception of black and white

Under noon sunlight illuminance, the black shirt has the same luminance (about 2600 candelas per square meter) as white paper in daylight shade. In the shade, the black shirt reflects more light than the white paper under

a reading light (about 84 cd/m2); and the black shirt under the reading light reflects over 100 times more light than the white paper under full moonlight. Yet these transformations do not affect our recognition of the gray scale.

Lightness Induction. The visual system has approximately a 10,000:1 contrast ratio within 95% of its response range that can shift to enclose almost any naturally occuring luminance levels. Surface reflectance produces about a 150:1 luminance ratio, which is compressed into roughly a 20:1 lightness ratio. However shadows darken surfaces by as much as 60%, producing a 300:1 luminance ratio and the tinting layer necessary to define textures, shapes and objects.

The illuminance from noon to midnight varies by a billion to one or more. But because of the absorptance properties of physical surfaces, object luminance from diffusely reflecting surfaces varies by a factor of no more than 33:1 and in many settings by less than 20:1. Hence grays stand for the surfaces that predominate in the visual image but lie within a narrow luminance range. Vision adapts to this luminance level.

This luminance span, defined almost entirely by outputs from the L and M cones, is structured as a brightness/blackness (b/k) opponent dimension, ordered on increasing luminance (diagram, below).

the brightness/blackness opponent dimension

On this dimension, white is the neutral or adaptation point, the perceptual quality that has both minimal brightness (self luminous quality) and minimal blackness (absorptance quality). Nearly all our visual experience is shaped by the lightness of surfaces, clouds and sky — that is, in the blackness half of the opponent contrast. This is why white and black, unlike the chromatic unique hues of opponent theory, can mix with each other: white is the neutral ("gray") luminance color, so it mixes with brightness and blackness in the same way that gray mixes with the opponent hues yellow and blue, or red and green. And, in the same way that a gray area takes on the complementary hue of a surrounding chromatic field, a small white area can appear to glow if surrounded by a large field, or appear grayed if surrounded by a large bright field.

Paradoxically, this means our luminance experience of the world is radically "monochromatic" — weighted toward the lightness side of the b/k opponent dimension. It is as if all surface colors were experienced as various shades of red, and only lights or bright reflections appeared green.

These blackness colors are produced by a negative luminance contrast between a

lightness induction

color area and its surrounding or background areas. The diagram (right) illustrates what happens when viewers examine a circular target light projected within a background that is either completely dark or moderately bright.

Against the 0 cd/m2 background, the apparent brightness changes in proportion to the luminance of the target light from 100,000

cd/m2 to 1 cd/m2, and consistently with a quality of shining or brightness. No matter how dim it becomes, the light appears self luminous.

However, when the target is viewed against

the 300 cd/m2 background, it acquires the quality of blackness when its luminance is less than the background luminance. It loses its self luminous quality and turns gray, finally becoming black. This change from the quality of self luminous brightness to surface blackness is called lightness induction.

The third aspect of lightness induction is that it anchors on the lightest values in the visual field. These are perceived as "white" or "bright" depending on their visual size and luminance contrast with the background. This is dramatically demonstrated with the Gelb staircase effect, as simulated below.

simulation of the gelb staircase effect a black surface appears white if illuminated by itself in a dark surround, but instantaneously appears darker as

lighter valued surfaces are revealed next to it

A piece of black paper, suspended in midair and illuminated by a spotlight, appears white because it is the brightest luminance in the

from Wyszecki & Stiles (1982)

visual field (A). If a medium gray square is added, it appears white and the black square now appears light gray (B). If a white square is added, the previous two squares appear darker again; but the black square never appears darker than a middle gray (C). The illusion is very convincing although the lighting conditions necessary to produce it will vary across settings. (It's highly instructive to experience lightness anchoring for yourself. See instructions by Alan Gilchrist for reproducing the Gelb staircase effect.)

The fact that a surface of very low reflectance (black) appears to be a middle gray occurs because the Gelb staircase reflectance samples occupy only a small part of the total visual field: the fourth aspect is that vision adapts to a spatial luminance distribution, in which relative luminance ratios are reconciled with their relative visual area, as explained below.

The fifth aspect of lightness induction is that it is strongly affected by the spatial structure of the visual field — where "spatial structure" is somewhat confusingly used to indicate both the two dimensional pattern of color areas in the visual image and the three dimensional arrangement of objects in relation to light sources. A variety of two dimensional demonstrations of this are possible, but the example below is easy to construct.

spatial structure and lightness perception stimulus consisting of a horizontal white square with a

horizontal black tab attached, and a vertical black square with a vertical white tab attached, illuminated from above and viewed at a 45° angle; after Gilchrist

(1977)

The stimulus display consists of a white square and a black square, of equal size and at right angles. Extending from each square, in the same plane, is a small tab of the opposite color. The display is illuminated so that the horizontal square and tab receive 30 times the illumination of the vertical square and tab; the black paint has only 1/30th the luminance of the white paint, so the tabs have equal luminance. When a naive viewer examines the array monocularly (through a peephole), the tabs seem to be painted onto the large squares behind them, and contrast is defined by them. But viewed binocularly, the tabs appear connected to the opposing planes, and this single spatial change is enough to literally reverse the perception of both tab colors, from a dark gray (around L = 35) to a near white (L = 80).

The spatial pattern of lights and darks is so important to lightness induction that it appears even at the binocular fusion between the two eyes. The strength of this rivalry can be experienced in the following diagram, after the two images are "free fused" or overlapped through a visual contortion.

opponent rivalry in luminance perception (1) relax the focus of your eyes, and cross your eyes

until the two images overlap as a single central image, then (2) refocus on the central image, causing it to fuse

The matching circles on the left and right differ by the same lightness difference (∆L = 20), but are in the opposite direction for the central circles. As a result these do not fuse to form

an average lightness percept — instead they seem to hover and slip, one over the other. This effect is present in iridescent or fringe colors, which the two eyes view at slightly different angles and therefore see as two overlapping colors. It illustrates that spatial consistency is fundamental to our luminance perception. White Anchoring and Light Area. The contrast study (described above) showed that the apparent brightness of a light viewed in a dark surround is proportional to some power of its luminance. This power is defined by the Weber fraction or the luminance increase necessary to produce a just noticeable difference in brightness. For illustration this proportional brightness weight (W

B) (ω). Under lightness induction,

a disproportional blackness weight (WK) is

added to all related colors whose luminances are lower than the white standard, causing them to darken into grays (diagram, right top).

This perceptual shift has the paradoxical effect of making surface luminances appear lighter valued than their equivalent brightness, while adding the perceptual quality of blackness that makes them appear as shades of gray.

When both lightness and luminance are displayed on log scales, the blackness weight appears to contract the luminance response by about 1 lot unit (diagram, right bottom). This reduces the contrast ratio from 1:1 around whites to 10:1 at grays below L=10, which effectively increases the gamma as a flare compensation in dark values. (Flare in light values is minimized by luminance adaptation.)

If we imagine an ideal surface that by reflectance creates an equal visual area for every luminance value, and distributes these values randomly as pixels below the fusion threshold, then the brightness weight alone would anchor the average luminance at Y = 31 and the perceived lightness at L = 61. The blackness weight increases the luminance further, to Y = 51, corresponding to a lightness of L = 75. Thus a surface that reflected any random, flat distribution of

very low luminances are underweighted in lightness

contrast

luminances would appear on average as light valued. Intriguingly, the average brightness weight corresponds to the luminance of a perfectly diffusing white surface expressed as a ratio (0.314) of the incident illuminance; and the average blackness weight (0.51) corresponds to a 50% reflectance. In effect, the "deficit" of natural surfaces is counterbalanced by the blackness weight (diagram, right) so that actual surfaces are shifted closer to their ideal values. They are made to appear brighter than they actually are.

In addition, shadows cast by full sunlight represent the illuminance of a clear sky (12,000 lux), which is as little as 10% of the illuminance from the sun (~60,000 to 120,000 lux). This 1:10 ratio means that the lightness of a white surface in cast shadow has the same lightness as a dark gray in sunlight.

This is the average shift: no shift occurs for white colors, and a tenfold shift occurs in very dark colors. The apparent luminance of near white surfaces corresponds to a perfectly diffused illuminance, while the average gray also increases the strength of lightness contrast or compensatory overweighting of darker grays, and a curbing of the lightness function that causes and increasing contrast with black. This increases the perceived darkening of surfaces and the contrast among reflectance values.

The final step is to cognitively shift the perceptual lightness scale until the brightest luminance value has the property of white. Color vision assumes that the lightest valued color areas have minimal absorptance, but also minimal brightness. As a result, white is the adaptation neutral value of lightness judgments. It produces luminance perception without any upward pressure on the luminance adaptation (which would darken all colors). The highest luminance rule, proposed by Wallach, is that the highest luminance value perceived as a surface is linked to the color concept white. Then grays are assigned by the ratio rule.

These rules were explored in an elegant series of experiments by Alan Gilchrist and

key luminance ratios

colleagues, who asked viewers to look at a whole field (180°) achromatic pattern of a medium and dark gray, presented on the interior of a 30" (76 cm) hemisphere illuminated from below, by diffuse lighting

(medium gray luminance of 11 cd/m2). Viewers then assigned lightness values to the two grays, from memory, using a Munsell value scale viewed in a separate room under brighter lighting (medium gray luminance of

135 cd/m2). The diagram below shows the hemisphere area as a circle, the experimental patterns, and the contrast between the average perceived gray values.

lightness anchoring the interior of a hemisphere was painted in different contrast patterns with a dark and medium gray (2.5

and 5.5 on a Munsell value scale); the perceived gray values were shifted lighter, so that the lighter value appeared white (Munsell value ~9.0); after Lee &

Gilchrist (1999)

From this and previous research, Gilchrist & colleagues derived the following lightness heuristics:

• in every visual field the lightest value of surface colors (areas of moderate to low luminance contrast) appears as white (CIELAB L* = 90 to 95); this is the highest luminance white anchor

• other gray values are perceptually related to

a gray scale in approximately their luminance ratio to the white anchor.

The researchers proposed a relative area rule to account for the variations in lightness contrast once the white anchor had been established, as shown below.

relative area rule for lightness anchoring after Lee & Gilchrist (1999)

If the darker area represents less than 50% of the visual field, then vision simply reports the luminance ratio. As the dark area becomes larger, the white field is pushed to appear more luminous, and the dark area becomes lighter behind it. This only applies when the second color appears as a decrement or darker value than white. If it is an increment, then the higher value appears self luminous. Self luminance appears when the brightest area is very small and appears against a very large, dark background. However, it appears that the amount of contrast with white is also affected by the global spatial pattern of figure/ground (diagram, right). Thus, the peripheral edge produces greater contrast reduction than the light dot, even though the dark area is larger behind the light dot; the complementary elliptical fields produce the same contrast, even though the ellipse is one third smaller than the peripheral ring.

The highest contrast — the darkest dark and the lightest white — is produced by a central dark dot (1.4° wide) and by a visual field split by a single edge; these produce the largest lightness contrast, with the dark dot or dark edge below middle gray. The smallest contrast is produced by a peripheral edge, such as the horizon when we look up at the sky, which also produces the lightest visual field. Below this is a light dot, which produces the twilight sensation of a luminous disc within a glowing sky. A large elliptical field (91° by 118°) centered within a peripheral ring produces the same contrast regardless of which field is light or dark, and this contrast matches the stimulus contrast — from white to a gray above middle gray.

lightness percepts that remain constant across changes in total illumination are illumination invariant, and lightness percepts that remain constant across changes in luminance ratios with adjacent or background areas are background invariant. backgrounds must be integrated across large retinal angles. these must appear to "belong together," for example to lie in the same spatial plane.

reflectance edges indicate changes in surface absorbance; illumination edges define shadows. this determines how areas in the image belong.

figure/ground effects on contrast

from Lee & Gilchrist (1999)

White Luminance Tokens. The lightness measurements used by Gilchrist confound two different visual judgments: (1) that an achromatic contrast appears relatively the same under two different levels of illumination; and (2) that a "white" at one level of adaptation is perceptually identical to a "white" at a different level of adaptation. The first statement is empirically true: the second statement is obviously false.

The example (right) is offered as a reminder that the common experience of a white piece of paper is qualitatively different when the paper is viewed under different levels of illumination. A variety of cues seem to influence the perceived color. The is an obvious difference between light and shadow, but this difference is qualitatively unique at different illuminance levels.

luminance dependent changes in "white"

appearance

The perceptual issue here is similar to color constancy under a chromatic illuminant. If we examine a familiar room under a colored red or green light, we seem able to perceive the "true" colors of the objects at the same time that we can perceive that the illuminant has its own hue. In a similar way, we are able to see white as a fixed color, even though the perception "white" differs qualitatively across illumination levels. Under scotopic vision, whites appear to be a middle gray, and blacks are quite dark. Under daylight illumination, whites appear quite bright and darks are induced by contrast. The illustration (right) suggests the variations that are encountered around my home on a sunny day.

We can divide the luminance range into seven zones:

• Star scotopic (below 1 troland). The value range is collapsed, with foveal blindness, and there is no color vision.

• Moon scotopic (1-10 trolands). The value range is large, there is no color vision, with foveal blindness.

• Twilight Mesopic (10-300 trolands). The value range is large, with expanding chromaticity and foveal acuity, but the light appears subdued.

• Intimate Light (300-3000 trolands). The value range is large, with expanding chromaticity and foveal acuity, and the light appears ample.

• Public Light. (3000-8000 trolands). Limit of mesopic metamers; colorfulness and luminance contrast at maximum.

• Task Light. (8,000-80,000 trolands). Hue shift from green to red; colorfulness and luminance contrast align with the y/b opponent function.

• Sky Light. (80,000+ trolands). Lower limit of photopic metamers; colorfulness and luminance contrast peak, as in rainbows; luminance only achieved by light sources.

• Sun Light. (80,000+ trolands). Lower limit of photopic metamers; colorfulness and

luminance contrast peak, as in rainbows; luminance only achieved by light sources.

The fact that these qualitative changes in "white" surfaces exist means both that they are one outcome of visual processing, and that they are also one benchmark for color recognition.

links between white, bright and "brightness of white"

The diagram shows a solution. A "minimal brightness" quality attaches to the standard perceived as white in any environment. The white itself has an apparent brightness which is determined by the luminance adaptation.

The phenomenological range of whites is an excellent example of a very broad color change that is unmarked by language: a case where color terminology does not track color appearance. The Whiteness of Whites. A final point is that the qualitative "color of white" is itself problematic. Technically, white is a color area that appears completely to lack any chromaticity or grayness. If measured under standard conditions, the range of surface colors accepted as "white" is quite small (compared to the range of all possible colors), but it does shift with the color of the illuminant — a warm incandescent light causes yellowish surfaces to be accepted as white, while typical daylight shifts the achromatic point toward blue violet. Walls that appear to be a clay yellow during the day can appear perfectly white at night, under incandescent lights.

However, in specific preference situations and under consistent illumination, the identification of a "true white" or "ideal white" varies considerably across individuals and, in many cases, varies in the same individual from one time to the next. According to Wyszecki & Stiles people differ by "a large amount", in what appears to be a combination of color vision differences, habitual exposure to white surfaces of one type or another, and personal preference.

A large number of colorimetric formulas have accumulated in commercial applications (including textiles, plastics and consumer appliances or "white goods") where the precise control of color is important. These differ quite a lot from each other, but seem to converge on three perceptual standards:

• the luminance factor or overall level of photopic lightness of the color in comparison to a perfectly diffusing surface; and

• the blueness or relative proportion of the emittance or reflectance in "blue" light (around 445 nm) as compared to "yellow" or "red" light (above 570 nm); or alternately

• the chromaticity or deviation from zero values on opponent dimensions (a* and b* in CIELAB), or deviation from the white point established by the illuminant and a "pure" white reference, such as magnesium oxide.

Blueness is common in historically earlier formulas; most current measures use some combination of luminance and chromaticity distance from the white point.

Chromatic adaptation, as defined by Wyszecki & Stiles (1982), is a change in the visual response to a color stimulus that is caused by (1) previous exposure to a conditioning stimulus (such as a luminous colored light or intensely colored surface) or (2) simultaneous presentation of the color stimulus against a surround or background of a different color.

These are different visual processes. The first

chromatic adaptation

is described below successive color contrast. The second defines the situation discussed in the next section as chromatic induction. There is also a third process, usually introduced as part of color constancy: the visual system adapts to the illuminant (the chromaticity of the illumination) by shifting the appearance of all colors to restore the neutral appearance of a white surface. In fact, many studies of chromatic adaptation manipulate the illuminant rather than the surround color or the viewer's exposure to a conditioning field. So this seems to be a third case.

How do you compare colors before and after chromatic adaptation? One method is memory matching: viewers study the appearance of colors in a color atlas, then rely on memory colors to describe the appearance of adaptation colors. A second is binocular matching or haploscopic matching, in which the "before" and "after" color stimuli are presented separately to the left and right eye, aligned to appear side by side. A third is to use prompt color matching during the brief period of successive color contrast.

An important point is that chromatic adaptation is not simply a "color shift" equivalent to changing the chromaticity of the color stimulus. That is, if a test color can be exactly matched by a mixture of three real "primary" lights before chromatic adaptation, the appearance of the test color after chromatic adaptation sometimes cannot be matched by any mixture of the "primary" lights or even by any physical color stimulus of any kind.

The problem with haploscopic matching can be illustrated by example. The problem with memory matching can be illustrated by analogy: we turn the color matching task into a geography matching task. Viewers first memorize a map of the USA, then use their memory of the map to name the state underneath "adapted" geographic locations. The problem is that viewers can sensibly locate a state, but cannot by that procedure describe a fundamental change in the map.

Photoreceptor Adaptation. A significant part of chromatic adaptation appears to take

place in the photoreceptors, either as a change in the individual sensitivity curves of the L, M and S cones, or in the response of the retinal secondary cells to the cone outputs. That is, the adaptation occurs before the cone outputs are transformed into the opponent functions.

The simplest way to represent this effect was first suggested in 1902 by Johannes von Kries and known today as a von Kries transform. His concept is based on two assumptions: (1) the adaptation in the normalized sensitivity curve of a photoreceptor L

a, M

a or S

a is expressed as

the ratio of the previous level of cone stimulation over the maximum stimulation; and (2) this adaptation occurs separately in each type of cone. For surface colors, the maximum stimulation is produced by a bright white surface, so the basic adaptation function is the ratio:

La = L/L

white

Ma = M/Mwhite

Sa = S/Swhite

A white surface takes on the color of the illuminant, so the basic adaptation can be expanded to represent the shift in the chromaticity of a white surface produced by the shift from one illuminant to another, for example by the daylight shift from illuminant D65 to illuminant A:

La = (L/Lwp(D65))*Lwp(A)

Ma = (M/Mwp(D65))*Mwp(A)

Sa = (S/Swp(D65))*Swp(A)

The adjustments. The diagram below shows the type of shifts that occur as the illuminant changes from daylight D65 to incandescent A. The increase in long wavelength light bleaches proportionately more L and M photopigment, lowering the L and M cone response probabilities, while the decrease in short wavelength light allows more S photopigment to regenerate, increasing the probability of response by the S cone.

receptor chromatic adaptation changes in relative cone sensitivity curves by shift from

D65 to A illuminant

When confronted by a sudden change in illuminant, the time required for this adaptation to complete can be relatively short, on the order of 5 minutes. As this is an evolved response to the gradual changes in daylight phases, we normally notice color discrepancies only in unusual circumstances, such as quick storms, overhead smoke, or fire. Fortunately, we have a system that describes visual complementary colors precisely (the opponent process algebra). And we can use it to describe and explain complementary color contrasts.

And more of the same.

Successive Color Contrast. Subjective or psychological color effects were of interest in the 18th century, and among the most important of these were afterimages, which Michel-Eugène Chevreul and most modern color researchers term successive color contrasts.

These early studies produced conflicting results (summarized by Chevreul) because there are in fact three different physiological mechanisms involved in successive contrast, and several different ways to produce the afterimage experience. Each produces a diffferent visual effect.

Positive Afterimages. Positive afterimages result from brief, intense stimulation of the cones. The effect is easiest to see at night, in a room illuminated by a single, naked, light bulb. First look directly at the light blub, then quickly turn off the light. A glowing yellow or

yellowish green image of the bulb will form in the darkness. Other common sources of positive afterimages are photographic flashes and specular solar reflections.

These images form because of receptor afterdischarge. The intense light momentarily consumes a large proportion of the photopigment in the outer segments of individual cones, which causes a prolonged synaptic discharge (up to several minutes) from the affected cone while the photopigment is slowly replenished. Until this happens, the positive afterimage appears to mask or displace any new images in that area of the visual field.

Photopigment in the L cones replenishes slightly faster than photopigments in the M or S cones, which causes the L receptor afterdischarge to attenuate more quickly. This produces an apparent change in hue (usually, a shift toward green or blue) as the afterimage disappears.

Negative Afterimages. Negative afterimages result from prolonged, moderately intense stimulation of the cones. These produce far more complex and interesting visual effects.

As simple demonstration: stare for 20 seconds at the white dot in the colored square on the left, then look away to the black dot on the right. After a moment (it helps to blink your eyes), a faint afterimage of the colored squares will swim into view — but the colors will be different. What colors do you see?

demonstration of negative afterimages Stare at the center of the colored square for 20

seconds, then look at the black dot on the right.

For most people, the colors in the afterimage are almost exactly reversed: the green turns magenta, the blue turns yellow, the magenta

turns green, and the yellow turns blue. These illusory colors are the visual complements to the hues in the original image. This complementary afterimage also works for most other colors: an orange square will produce a blue afterimage, lime green will produce violet, and so on, all the way around Newton's color circle.

Complementary Colors. Newton's hue circle implicitly requires that every spectral hue will have a single spectral opposite (or mixture of two opposite spectral hues) that can combine with it to create white light.

Newton did not state this rule definitively because he could not consistently produce white mixtures with the broad spectral bands he was able to isolate with his prisms. But it was derived logically from his color circle by the German physicist Hermann Grassmann in 1853 as one of the basic color mixing principles known as Grassmann's laws, which were experimentally confirmed by Helmholtz and Maxwell in the 1850's.

These paired hues are now called complementary colors. These arise naturally from the geometry of Isaac Newton's hue circle and his observation that colors opposite each other on the hue circle create a "faint anonymous" (neutral) color when mixed. They suggest that all opposing colors are created equal, in the sense that they all can be mixed to the same "color" of white light.

Complementary colors are also the point where hue sensation gives way to hue relation, which means a cognitive process is now interfering with the sensation in a way that symbolizes more than a simple hue contrast, such as the difference between red and yellow. These illusory hue changes are visible as simultaneous color contrasts. They show that we do not see the world as it is, because we see color differences where the physical stimuli are the same. Only their context changes.

Newton stated the definition of complementary colors that is still used today: any two hues that, mixed in the right proportions, produce a neutral (pure white, gray or black) color.

If we specify Newton's basic concept in terms of Hering's yellow/blue and red/green opponent processes, then we transform the hue circle into a kind of compass, with four cardinal points representing the four color sensations produced by one side of each opponent process. (For now, we ignore the w/k opponent process that gives us lightness variations, and focus only on hue.)

r/g and y/b opponent processes within the hue circle

the opponent color dimensions in the hue circle, and the location of Hering's unique hues

How do we determine the exact complementary color for any color we choose? The simplest way is to determine a weight or quantity of the two opponent processes that determine the chosen color, then identify the color that is produced if we apply the same weights to the opposing process hues.

As an example, we might start with a yellow red (scarlet), and determine that this color can be matched by a quantity c1 of the r process

and a quantity c2 of the y process. In that

case, the complementary color for scarlet will be the color produced by a quantity c

1 of the

g process (the opposite of red) and a quantity c

2 of the b process (the opposite of yellow).

This gives us the complementary color to

scarlet: a blue green (cyan).

visual complementary colors defined by the r/g and y/b opponent

processes

Complements defined in terms of the opponent processes are called visual complementary colors because their "mix to gray" relationship is determined by our visual system and the mixing of lights. Thus, a monochromatic (single wavelength) light that matches our scarlet hue will produce a "white" mixture with a second monochromatic light that matches our cyan.

Now we can specify any complementary color relationship using one of four algebraic formulas:

c1*r = c1*g

c1*r + c

2*y ("warm") = c

1*g + c

2*b

("cool")

c1*y = c

1*b

c1*r + c2*b (purple) = c1*g + c2*y

(green)

Again, we would also have to specify the w/k opponent process if we want to determine the complementary colors according to lightness as well as hue and chroma. This is how colors are specified in the Swedish Natural Color

System.

Let's pursue two points. Hering claimed that the entire hue circle could be explained by binary mixtures of the four unique hues, which represented the "pure" sensation produced by one end of the opponent processes. In fact, Hering was both right and wrong.

Imagine that we march through the spectrum, one monochromatic hue at a time, and for each wavelength we determine the wavelength of its exact visual complement. (This has actually been done, many times.) For nearly all green hues, we have to simulate the visual complement by a mixture of a "red" and "violet" wavelengths, but we can determine the proportion of r and b required to neutralize each green hue, and so measure the entire hue circle.

Now we take a group of people with normal color vision and ask them to choose the wavelengths that best represent their unique hues. The diagram shows what we find.

the unique hues and opponent processes compared

location of the unique hue visual complements (cR, cG and cB) shown in gray

First, we discover that the unique hues are not visual complements. If we combine the "yellow" and "blue" chosen as unique hues,

what we get is not a "white" mixture but a pale green. If we mix the unique "red" and "green" in the same way, we get a pale yellow.

In other words, the Hering unique hues do not define the opponent processes. The r process seems to be anchored at a bluish red similar to carmine. The g process in contrast is not an actual green but closer to a turquoise or teal blue. The b process has a small amount of red mixed in it, similar to a cobalt blue. Only the y process seems to match the unique hue. The following table summarizes these differences as contrasting paint colors.

The second point is that language is the worst form of color specification. Most people would probably call the scarlet hue in the example a "red" color. The complement to it would probably be called a "blue" color. So, in simplest terms, one would say that the visual complement of red is blue. But we've just seen that the opponent process green is closer to a teal blue or turquoise, so we'd be equally justified to say that the visual complement of red is turquoise. However, many people refer to a magenta as red, and the complement of magenta is a green: so we have the visual complement of red is green.

Many attempts have been made to develop a hue circle that accurately represents our judgments of the perceived difference or contrast between hues, and most of these

paint exemplars for opponent and unique hues

as defined on the CIELAB a*b* plane

hue opponent unique

redquinacridone carmine

pyrrole red

yellowbenzimida yellow

benzimida yellow

green cobalt teal bluephthalo green YS

blue cobalt bluecerulean blue RS

were developed without explicit consideration of the opponent contrasts. In all these hue circles, the unique hues are not opposing or complementary colors. But the unique hue names — red, yellow, green, blue — are the common coin for describing and explaining complementary colors in art textbooks. This leads to gross inaccuracies in talking about color.

The complementary color relationships of negative afterimages are determined by the opponent coding of color receptors, as summarized in the basic rules of color vision. The simplest way to identify the visual complement of a color is to reverse its location on the r/g and y/b opponent contrasts (or the underlying LGN opponent curves). This is done simply by reversing the signs or polarity of the color's opponent coding. Orange (coded by the visual system as r+y+) is the complement of blue (coded as r-y-); middle green (r-y+) is the complement of red violet (r+y-), yellow (y+, rg=0) is the complement of blue violet (y-, rg=0) ... and so on around the color wheel.

Two different neural processes are shaped by this opponent coding. The first, photopigment depletion and receptor adaptation, arises because prolonged stimulation to a cone depletes the normal amount of photopigment in the cone, which suppresses the neural response from that cone to new light stimulus. When this cone is then turned to a new color area, its response is momentarily reduced, so the new color area appears depleted of the color represented by the outputs from that cone. (This is also a mechanism in visual adaptation.)

However, as Ewald Hering pointed out, negative afterimages appear at luminosity levels too low to produce receptor bleaching, and appear even when the eyes are closed and there is no contrasting background to make the receptor bleaching visible. So a second mechanism, neural rebound in the visual pathways of the LGN and visual cortex, appears to be involved. A general property of nerve cells is that, after a prolonged stimulation is ended, the cells "rebound" into an opposite state of inhibition. These effects produce changes in the apparent

visual field even in the absence of successive visual stimulation.

Negative afterimages do not displace or mask subsequent images in the visual field, so in all cases the background color of the successive visual field affects the apparent color of the afterimages. The normal situation is to view the afterimage over a gray or white background, which produces an undistorted color impression. Viewed over a colored background, the afterimage and background color will mix visually: a magenta square will produce a green negative afterimage, but seen against a deep blue background this green will appear to be a cyan or turquoise blue. To see this for yourself, try viewing the afterimage squares above over different sheets of colored paper.

Afterimages and Color Harmony. It's worth mention that the phenomena of negative afterimages was one of the cornerstones of 19th century color theory. Shown a patch of yellow, the eye retained the image of blue. This was taken to represent a fundamental tendency of the eye to "seek balance" or to make a color compensation. On this basis the concept of "color harmony" as a balance between these antagonisms arose.

The opponent process explanation for contrasts was unavailable in the 18th and 19th centuries, so it is typical to find instead an "eye animism" or eye volition, for example in J.W. von Goethe's claim that complementary color afterimages arise because the eye seeks "to experience completeness, to satisfy itself."

The erroneous assumption that the eye was demonstrating a desire or need for color balance invited the conclusion that complementary colors are the most harmonious (satisfying) color pairings possible. The fact that they canceled to make gray was taken as proof of the inherent balance. Indeed, in the 19th century it was suggested that all the colors in a perfectly harmonious painting, if spun rapidly like a color top, would produce a perfectly gray blur.

Suppression and Enhancement of Afterimages. If afterimages can happen so

easily, why do we not see them all the time? The answer is that afterimages are simply suppressed or written over by new images formed in vision. However, they can be enhanced by a successive image similar to the first.

suppression and enhancement of successive contrast

In the example above, the afterimages of the colored squares appear clearly when seen over the gray background. They disappear when seen over the conflicting colored background (at left), as this simply overwrites the previous image. But the afterimage is enhanced — appears more quickly and brightly — when viewed against a background image of similar gray squares (at right).

In normal visual experience, succeeding images on the retina are sufficiently different from the previous ones that afterimages don't conflict with what we see in the present.

Corresponding Colors. The fact that the same color can appear to be a different color under a different illumination or adaptation invites the location of two different colors that will appear to be the same color under different illuminations, that is, metamers produced by adaptation. These are called corresponding colors. The thumbnail at right shows measurements of human color perceptions under two tinted illuminants, a bluish "daylight" illuminant known as CIE illuminant D65 (for daylight at a correlated color temperature of 6500°K), and a yellowsh incandescent tungsten

illumination (with a correlated color temperature of about 2860°K), known as CIE illuminant A.

Viewers used memory colors learned by study of the Munsell color system

This graphic is an attempt to render the colors for comparison with a background tint to suggest the illuminant hue.

color changes under chromatic adaptation 31 Munsell color samples at value 5, as they appeared to subjects when presented under CIE illuminants D65

(daylight, left) and A (incandescent tungsten, right)

Principles of Chromatic Adaptation. In his 1879 book on color science, Ogden Rood suggested a simple method to anticipate these color changes. This is adapted from the more general principles laid down by Michel-Eugène Chevreul and embodied in his color hemisphere.

You first of all need to identify a target or key color that is the source of the color shifts. For example, you may be painting a Buckingham Palace Guard in his bright red coat, and want to know the effects this color will have on adjacent colors in the image — the guard's face, gold epaulets, the foliage green background, the blue sky, whatever.

predicted CIELUV shift in Munsell color samples

perceived color shift between daylight (D65, blue) and

incandescent light (C, red); after Bartleson (1978)

To do this, you imagine the visual color wheel shifted away from the key color along the hue angle of the key color (the line from the key color to the center of the wheel). Then you interpret the hues in their new positions in the shifted wheel (shown in faint colors, below) using the original wheel as a frame of reference. The shift in the color positions indicates the hue and chroma shift that would

be caused by a simultaneous color contrast. (Note that shifts due to lightness are not considered.)

apparent color shifts in simultaneous color contrasts

shifts are shown in contrast to a middle red key color

These color effects are of the following four kinds:

• Analogous hues. Colors of a similar hue to the key color show little hue shift but will appear desaturated (shifted toward the center of the color wheel). A middle red will make red orange or magenta appear duller.

• Quadrant hues. Colors at approximately 90 degrees on either side of the key color will show little change in apparent chroma, but large hue shifts away from the key color toward the key color's complementary hue. A middle red will make blue violets shift toward blue and yellows shift toward yellow green.

• Triad hues. Colors diagonally opposite from the key color will hue shift away from red and increase in chroma (shift away from the center of the wheel). A middle red will make a green or middle blue appear more intense and cooler.

• Complementary hue. The key color's complementary hue (teal blue) will show no hue shift, but will appear more intense.

So goes the theory. In practice, this calculation is not equally accurate for all hues around the color wheel. To take one example, middle yellow is already one of the most intense watercolors, and its complementary hue (close to cobalt blue) is typically darker and relatively dull. For these reasons, the simultaneous contrast shifts experienced in yellow placed next to blue will be relatively muted, because yellow is already near the visual limit in chroma. Similar complications arise across the same hue at different values or intensities.

Because chroma and lightness are so important, the better approach is to visualize the two contrasting colors as located in the three dimensional CIELAB color space. The general rule is then: simultaneous contrast moves colors farther apart on the L*, a* and b* dimensions. The difference in lightness (L*) and chroma between colors will always increase, especially if their values are similar; colors will appear to separate in hue. In general, the eye adapts to increase the perceptual contrast or apparent range of any gamut presented to it, to make the most of perceptible color differences in the scene.

A light emitting computer color monitor is less effective to display these color shift effects than reflective artists' materials viewed under room lighting. For that reason I urge you to conduct your own complementary contrast experiments with colored papers. I find that common origami papers are brightly colored and varied enough for many interesting color contrast experiments; these papers can be mixed and matched with the heavier weight and traditionally more unsaturated colored construction papers (craft papers). Always test different color combinations or color constructions under different types of lighting: sunlight, incandescent and fluorescent light provide the most variation.

The second major area of subjective color experience, researched primarily in the 19th century, is the simultaneous color contrasts produced

chromatic induction

by differently colored areas viewed side by side at the same time. These effects are among the easiest and most convenient to reproduce from household materials, and for that reason many classic "color theory" books, from Chevreul to Albers, describe them at great length.

Chromatic Contrast. The observation and explanation of simultaneous contrasts in the traditional "color theory" literature are distorted by two serious flaws.

The first, experimental flaw is that these effects were traditionally analyzed by opposing some "colors" to other "colors," without separating the three colormaking attributes — lightness, chroma and hue — as independent contrast elements. Underlying this approach was the prejudice that hue was the key component to the contrast effect. In fact, when the three colormaking attributes are considered separately, we find that hue is the least potent visual contrast of all.

The second, logical flaw is in the assumption that the "tension" or "conflict" between one complementary color pair is pretty much the same as any other. As we will see, this is simply not true. The supposed fundamental "tension" between two colors has a qualitative impact that depends a lot on the specific values, intensities and hues involved, and is highly sensitive to the overall color context.

Lightness. By far the most powerful example of simultaneous contrast is the apparent shift in lightness of identical mid valued squares surrounded by a color of darker or lighter tonal value. If the surrounding color is darker, the central square appears lighter; if the surrounding color is lighter, the central square appears darker. (To enhance this and similar illusions, focus your gaze between the two large squares.)

color shift in a simultaneous lightness

contrast all large and small squares have the same hue and

chroma

This illusion is normally demonstrated using different shades of gray, to cancel the effects of hue and chroma. But the example shows that it also works for shades of blue (or any other color) that have exactly the same hue and chroma, but differ widely in luminosity.

Within each large square, the average lightness is based on the outer and inner squares. Contrast is increased around this local average, shifting the apparent value of the smaller squares in opposite directions. This also means that the two larger squares both appear darker than they would in other settings, because they are shifted to contrast with the white background of the page.

This value shift is the easiest visual illusion to elicit. In fact, many people will not believe that the two central squares are really the same lightness. The illusion is so powerful because value dominates our visual experience, a fact we will explore later.

Crispening Effect. A special case of lightness contrast is the crispening effect, which increases the apparent contrast between two colors of similar lightness against a surround lightness of value between them. The schematic at right shows the basic effect: the perceived lightness contrast between grayscale steps amplified around the average lightness of the background. All the lighter values are compressed slightly toward white, and match the nominal white at the lightest step of the scale; the darker values are compressed slightly toward black. This shift is strongest within a one half Munsell value step on either side of the background value, and then becomes constant for the rest of the scale.

crispening effect in visual displays

the apparent contrast is greatest around the value of

the background

the crispening effect the contrast between two areas of slightly different

lightness is greater against a background with a lightness value between them

In the diagram, the pair of rectangles differ slightly in value, but have the same values across all examples. However, the differences between them are most visible when they are displayed against a gray background; when the background is white or near black, these differences are obscured.

Bartleson-Breneman Effect. A related effect appears in the perceived contrast among areas of different value within an image when the image is viewed against a light or dark valued background.

The Bartleson-Breneman effect is well known in imaging studies: as the background becomes darker, the induced lighteneing in the image (called the "complex stimulus") causes all the values to appear lighter; but this has the greatest impact on the darkest values, which compresses the value range and makes the steps between gray values appear smaller. Against a light valued background the lightness contrast causes the image values to appear darker, but again this has the greatest impact on the darker values, causing them to darken and causing the value steps between grays to widen.

the bartleson-breneman effect a dark background compresses values toward white and

reduces apparent contrast across value steps

In this example, the value series on the left appears closer together because the background or surround is very dark. On the right, the same values appear more greatly contrasted because the surround is relatively light valued. Note that the induced change becomes more noticeable as the values get darker.

Watercolor painters, especially those who build up images through several layers of paint, are familiar with this effect. The first, light valued glazes on white paper appear to have darker values and greater contrasts in value than desired. However, as the image is built up, and these first layers are surrounded by darker valued areas, the original layers become compressed toward the lighter end of the value scale. They appear lighter valued, and the value steps among them appear more subtle. Painters who apply the first layers so that they appear "just right" against the white paper are usually disappointed to discover that they become faded and too light once darker values are added to the painting.

What is the optimal illumination level for the best overall sensitivity to reflectance differences, for example in the gray values of

an etching, photograph or halftone image? The graph (above right) indicates this is around a

surface luminance of a few hundred cd/m2, which as it happens is the approximate maximum ("white") luminance emitted by a typical computer monitor or the average luminance emitted by a brighter color television set, which are both best viewed under subdued ambient lighting. To get similar luminances from reflecting surfaces, an ambient illumination level of several hundred to 1000 lux is necessary — the typical illumination used in "high demand" task settings such as microelectronic assembly or surgical theaters. Noon sunlight can actually be too bright, as you can verify by viewing a low contrast photographic print or a faintly smudged piece of white paper under direct sunlight, shade (skylight) and indoor light at different times of the day.

Chroma. The next strongest visual effect is the apparent shift in chroma of identical colored squares. In the illustration, the central squares are moderately unsaturated (chroma 55), and the surrounding colors are either dull (chroma 30) or intense (chroma 100). All squares have exactly the same lightness (L = 60) and hue (red violet).

color shift in a simultaneous chroma contrast

all large and small squares have the same hue and lightness

The difference in chroma alone is enough to cause an obvious color shift: the small square on the right appears darker and duller, while the square on the left appears lighter and more intense. (Some readers may also see a slight hue shift, with the square on the right appearing somewhat bluer.)

These unexpected apparent value shifts — unexpected because the larger squares are exactly the same lightness and hue — occur

because the violet on the right seems to be a brighter color. The eye incorporates this information in the darkness it attributes to the inner squares because value and chroma are often confused in color perception.

lightness shift in a simultaneous chroma contrast

inner and outer squares are matched on lightness

This confusion is apparent if we replace the central, moderately saturated violet squares with a pure gray of slightly lower lightness (L = 50) to enhance contrast between the squares at left. The chroma contrast between the two outer squares induces a small simultaneous lightness shift in the gray squares, which have no chroma: the square surrounded by the high chroma red violet appears darker valued than the square surrounded by dull red violet, as if the higher chroma were equivalent to a higher lightness. (Again, fix your gaze on the space between the two large squares to see this effect most clearly.) As I mention in my review of Michel-Eugène Chevreul's Principles of Color Harmony and Contrast, the effects of lightness and chroma were often confused in painting terminology and practice from the Renaissance through the early 19th century. Painters could certainly tell the difference between intense and dull colors, and could reproduce colors within the range of their historical pigments; but chroma and lightness changes were manipulated by "breaking" the colors with some combination of black and white paint, which altered both lightness and chroma at the same time.

You may notice a fuzzy or vibrating quality at the border between the high chroma and gray squares (at right). Although I know of no research to confirm this, I believe visual edge detection is much less effective at the boundary between chroma contrasts than

lightness contrasts, especially if the lightness contrast between chroma differences is small (as in the example above). In fact, this indistinct boundary seems to contribute to the "glowing" effect of high chroma color fields.

Helmholtz-Kohlrausch Effect. We can bring into this overview of luminosity shifts in color the fact that increased chroma increases apparent color luminosity, which is known as the Helmholtz-Kohlrausch effect. This applies both to lights and to object colors, and is a kind of reciprocal statement of the Hunt effect.

The Helmholtz-Kohlrausch effect is especially confusing when artists attempt comparisons of color lightness or value between two intense hues or between an intense and muted color. For that reason it is explored further in the discussion of hue, lightness and chroma.

Finally, the central square can be surrounded by colors contrasted in hue but identical in chroma and lightness. According to "color theory," a complementary shift in hue should appear. In practice, I've found this hue shift is hard to demonstrate. After a lot of experimenting, I found a contrast that does seem to work: a smaller square of green within larger squares of yellow and turquoise (all squares have a lightness of 90 and chroma of 80).

color shift in a simultaneous hue contrast all large and small squares have the same chroma and

lightness

These hue shifts can often involve complex changes on both hue and chroma, but these can be conveniently worked out on a standard color wheel, according to the simple rule of the mixture of contrasted complements enunciated by Michel-Eugène Chevreul: if two colors are placed side by side, each color shifts as if mixed with the

visual complement of the contrasting color. Thus, the green square surrounded by yellow should hue shift as if it were mixed with the visual complement of the yellow, or blue violet; the green square within turquoise should hue shift as if mixed with the visual complement of turquoise, or middle red. (Both the yellow and turquoise should shift as if tinted with the visual complement of green, or purple.)

Unfortunately, I don't see anything like those hue shifts here; the central squares seem roughly the same hue to me. In fact, the small green square on the left looks more intense, lighter valued, and shifted slightly toward yellow — even though "color theory" predicts it should appear less intense and shifted toward blue violet. This color shift is what we would expect in a chroma contrast, and it may happen because the chroma of 80 is enough to make the yellow appear duller than the turquoise, even though the lightness of the two colors is the same.

color shift in a simultaneous hue contrast all large and small squares have the same chroma and

lightness

Here is another example, this time with red violet against orange or blue. In this example the hue does seem slightly bluer within the orange square, but again the predominant effect seems to be a lightness or chroma shift, making the left square appear brighter and more intense than the right.

The difficulty in finding a hue contrast that works on its own arises because the relationship between chroma and lightness changes radically from one hue to the next, and the eye tends to overestimate the lightness of some hues (deep reds and blues) and underestimate the lightness of others (yellows and greens). With all that going on at the same time, it's not easy to find

three contrasting hues that can be subjectively equated on both chroma and lightness. With few exceptions, the "color theory" books you'll encounter do not bother with these distinctions, and therefore mislead you on the true nature of visual contrasts. But I repeat: hue is the weakest component of visual contrast, when compared with the impact of lightness and chroma.

Some of the early color texts (including Michel-Eugène Chevreul and Ogden Rood) are careful to explain that these contrast effects tend to appear in certain situations but not others. (Modern texts rarely bother to mention these subtleties.)

According to Rood, the shift color (the color in the central square, which can be expected to shift) should be unsaturated and mid valued, and it should be surrounded by a single strongly saturated color. If the shift color has a high chroma or is either very light or very dark valued, the apparent shift is usually reduced. Hue contrasts will also vary depending on the relative color distance between the two contrast colors (in this, case, between the central square and its background): a greater color distance should produce a larger color shift.

color shift in a simultaneous hue contrast central squares set to low chroma and mid value; outer squares are both at lightness of 70 and chroma of 90

Here's the previous hue shift in "enhanced" form — complementary background colors, and neutralized central squares — so you can judge the difference for yourself. I see primarily an apparent value or chroma contrast between the two central squares, with a small hue shift toward blue in the square surrounded by orange, and toward yellow in the square surrounded by blue. But, again, the hue shift by itself is very small. It seems to me a measure of the ignorance and

bias inherent in the writings of Johannes Itten, Faber Birren and other popular "color theory" writers that they make so much of "color" effects that depend so little on hue.

Chromatic Assimilation. Assimilation.

We are familiar with the experience of going from daylight into a darkened room or theater, and then returning into bright sunlight again: our eyes require a few moments to adapt to the light changes. I discuss these effects of visual adaptation in the page on color in the world, but it seems appropriate to conclude this discussion of color contrasts with a look at luminosity contrastsas well.

effects of illuminance or luminance contrast

A baseline illuminance of a light gray/dark gray contrast pattern; B illuminance selectively increased on part of the pattern; C illuminance increased across the entire

pattern

The example shows a simple contrast pattern under moderate to low illuminance from a single source. If illumination is selectively increased on only part of the pattern, the lightness of that part appears to increase, as does the contrast with the background. A similar increase in contrast occurs by increasing the illumination across the entire pattern. Method B amounts to a visual illusion and is commonly used in art galleries to increase the apparent contrast and colorfulness of works of art.

luminance & color changes

The main conclusion to emerge from these constancy illusions is that artists typically "overpaint" color contrasts, whether of hue, chroma or lightness.

Stevens Effect. As light becomes more intense, the perception of lightness contrast increases. This contrast increases visual acuity, especially of fine detail, within the normal range of daylight illumination. The Stevens effect is the perceptual basis for our linguistic association of light and intellect: we shed light on a problem, see the light, are "bright" (intelligent), and symbolize an aha! or creative insight with a light bulb. The example at right shows the general effect of increased brightness on lightness contrast. Example a shows the case where a target color is much lighter than the surround. In this case, as the illumination is increased in brightness, the relative contrast between the two areas increases, with the surround appearing to become darker and the target color appearing to become lighter. Example b shows the case where the target color and surround are similar in value; as brightness is increased this relationship is maintained. Example c shows the case where the target color is much darker than the surround; again, as the illumination is increased, the contrast between the two areas increases, with the target area appearing blacker.

Painters are especially familiar with these effects in landscape lighting. The example a is well known to backpackers, who notice the increased brilliance of a white shirt against a gray scree as sunlight breaks through after a storm. (Thomas Girtin captured a related effect in his White House at Chelsea.) The opposite effect is common in adobe houses, whose windows appear as a similar gray to the walls in the morning, but darken to black during the hot light of afternoon.

Hunt Effect. As light becomes more intense, the perception of colorfulness or chroma also increases. This is called the Hunt Effect, after the vision scientist who measured and described it in 1952 by asking participants to match the chroma of two colors presented separately and at different luminance levels to the two eyes. It applies both to lights and to

variations in the stevens effect depending on

relative values

surfaces.

The Stevens and Hunt effects are both changes in the gamma or contrast function of the characteristic curve. The size of the effect is not large: using an indoor daylight illuminance of about 1000 lux as the benchmark, contrast decreases by about –7% at an illuminance of 20 lux and increases by about 7% at an illuminance of about 10,000 lux.

However, it is easy to observe the Hunt effect. First find a large, brightly colored image in a magazine or book, but do not look at it closely once you have chosen it. Instead, go outdoors on a bright day, wait a few minutes for your eyes to adapt to the light, then leisurely study the image and the color contrasts it contains. Then go indoors to a windowless room illuminated by an incandescent (tungsten) light, let your eyes adapt for five minutes, and study the image again.

Landscape painters must cope with both the Stevens and Hunt effects when they work outdoors. It is common to see novice plein air paintings that have relatively dark, dull, subdued color — and for the painters to feel disappointment in the appearance of their landscapes in the studio. What went wront? The problem is: they were painted in bright outdoor light! At high luminance levels outdoors, the Stevens effect makes paint value contrasts appear very strong, and the Hunt effect makes the colors appear very intense. To match the landscape colors, the painter subdues his paint mixtures. But when the same colors are viewed under gallery level lighting, they appear muddy and dark. This problem left many footprints in the landscape tradition, and is especially obvious in the rather dark, muddy landscapes by Corot, Pissarro and others. Monet's famous paintings of the Rouen cathedral, viewed through the window of a north facing and relatively dark room, were probably in part an attempt to understand and grapple with this problem.

To get around these problems the painter must learn two tricks:

• overpaint chroma and value contrasts compared to the color contrasts that appear in

the landscape;

• make the overall key or average value of the painting lighter, compared to the brightness that appears in the landscape.

How much should the value key, contrasts and chroma be exaggerated? This depends on the weather, time of day and landscape, but as a general rule a one third increase in the middle values (for example, from a mid valued 5 to a lighter valued 6.5), and a 50% increase in chroma and lightness contrasts, is a reliable baseline for daylight on most clear days. On overcast days, or when the sun is low, the exaggeration should be reduced.

When these "exaggerated" works are viewed under comparatively subdued gallery lighting, the Stevens and Hunt effects will pull the colors back toward the values that the painter wanted to capture in the landscape. This is the painter's paradox: to bring the landscape indoors, you must not "copy" the landscape colors!

Bezold-Brücke Effect. As light becomes more intense, the perception of wavelength hues also changes. This effect is called the Bezold-Brücke Effect after the two 19th century scientists who described it.

the bezold brücke effect in spectral lights adapted from Wyzecki & Stiles (1982) and Hurvich

(1997)

The main effect is a significant expansion of the wavelengths that appear yellow or blue, with a corresponding decrease in the wavelengths that appear green or red, as

retinal illuminance increases from 100 to 1000 trolands. This is roughly equivalent to stimulus

luminances of 8 and 130 cd/m2, a contrast that straddles the boundary between mesopic and photopic vision. Although rod vision may be partly involved, most of the shift is attributed to different adaptation curves for the y/b and r/g opponent processes. This produces a corresponding shift in the elevation and spread of the hue cancellation curves. The r/g dimension is apparently more sensitive to luminosity changes and adapts to a greater degree than the y/b or w/k dimensions, lowering its relative response at high light levels. The Bezold-Brucke effect mimicks the color shift that we saw in the hue cancellation: hue discrimination increases from the yellow green through the red orange part of the spectrum, with a complementary (though much smaller) increase in blue discrimination. (The shifts can also be described as a collapse of hue perception around unique green, a small expansion of hue perception around unique blue, and a much large expansion around unique yellow.)

It is instructive to compare this figure with the analysis of hue discrimination using the hue cancellation method with unique hue mixtures. This seems justified by the fact that the three spectral unique hues are constant across luminosity changes, and by the similar expansion of the "yellow/orange" and "blue" sections of the spectrum and the corresponding compression in the "blue violet," "green" and "red" sections in both the hue cancellation and hue shifts.

bezold brücke shifts in relation to the y/b opponent function

Abney Effect. If chromatic intensity appears as a form of brightness or luminosity intensity, we might wonder whether an increase in chroma produces hue shifts similar to the Bezold-Brücke Shift. The answer is, they do, and these apparent chroma induced changes in apparent hue are known as the Abney Effect. // hue angle changes as lightness increases. due to change in the exponent on the S input, which rotates counterclockwise munsell as exponent increases. //

The Abney applies to both surfaces and lights.

Contrast can justifiably be called the fourth colormaking attribute. Both luminance and chroma are strongly influenced by local contrast, and sensitivity regulation can be thought of as a kind of contrast adaptation, in the same way as chromatic adaptation.

Contrast is a fundamental reference space, centered on a dark valued (reflectance 20%) neutral gray and extending across a luminance span of roughly 100:1 in physical units, which vision continually adapts to maintain. Color constancy is, first of all, a matter of a constant contrast environment.

Qualitative Contrast Differences. If we use our judgment and contrast painting colors on chroma and lightness as well as hue, then placing visual complements side by side can create a very powerful tension within an intricate pattern or between large areas of color. In particular, pattern contrasts often produce a kind of color vibration or energy between the two colors, especially at the boundary between two intense colors that are relatively similar in value.

However, this "tension" or vibration is not the same for all complementary hue contrasts, as the following examples demonstrate.

complementary color contrasts are not created equal

As you examine these color patterns, look at four things: the crispness or distinctness of the edge between colors at the thinnest color bands; the overall visual harmony or conflict

between the color pairs; the ability of the colors to invoke a representational illumination or mood; and the relative power of the contrast to convey a three dimensional form (a fluted column).

Some of the strongest (and to my eye, most unpleasant) color tensions arise between red and turquoise or magenta and blue green (top and bottom rows, far left), colors that are at opposite ends of the very powerful r/g opponent contrast. This contrast seems also to be visually the most unstable, as it produces a kind of visual fluttering or vibration when the colors are closely spaced — the reason why intense reds and blue greens are rarely used against each other in text.

By comparison, the combination of violet and yellow green (bottom row, right) seems visually much less active and emotionally more stable and restful. And natural light seems invoked by the contrasts with yellow or orange (top row, right and center). (For further discussion of color contrasts and visual design, see the pages on full color harmonies and near neutrals and color design.)

"Color Theory" Conclusions. After playing around with color contrasts using both computer images and colored papers, I've reached these basic design conclusions with regard to simultaneous contrast effects:

• Simultaneous contrast effects due to either value (lightness) or chroma are much stronger and more common than contrast effects due to hue alone.

• Most "color theory" demonstrations with colored squares confuse the colormaking attributes, attributing to hue effects that are created primarily or entirely by differences in lightness or chroma.

• The strength of simultaneous contrasts is dependent on hue: the contrast between blue green and red is different in strength and subjective effect from the contrast between yellow green and violet.

• Much depends on the visual context and the actual materials; simplistic "color theory"

generalizations will fail in many specific applications.

The last two points deserve emphasis. Nothing is gained through simplistic, geometrically symmetrical rules of color combination. Nothing is gained by ignoring the unique effects possible by combining different hues.

The eye's contrast enhancing behavior surely indicates that artists must attend to color contrasts when making a picture. But what exactly have we inherited from traditional "color theory"? As explained in the section on Newton's color circle, the phenomenon of complementary spectral hues — colors that mix to white — seemed to offer an objective "color logic" that could clarify color relationships after centuries of color confusion. These contrasts also appeared spontaneously in carefully contrived simultaneous contrast patterns, in successive contrast or afterimages, and in chromatic adaptation, so their effect was recognizably significant. All this contributed to make complementary color contrasts an idée fixe with 19th century "color theorists" and their Bauhaus progeny.

More than a century later, we can ask: how much of that emphasis is deserved? To my mind, the fixation on complementary color contrasts above all other color contrasts seems misplaced and overblown. We no longer need to be panicked by color confusion or resort to simplistic geometrical contrasts to build color ideas. These ideas should never distract us from actually looking at color to evaluate its impact — for example, a more general pattern of color harmony appears in triadic hues separated by roughly one third the circumference of the color wheel. And finally, in actual paintings, these simultaneous contrast shifts in hue, chroma or lightness can be easily negated by adjustments in paint mixtures and by the overall color context.

In short: relax the grip of "color theory" dogma on your mind and experience color effects without preconceptions. Simultaneous color contrasts don't indicate visual biases that must be compensated for, or rules that must be obeyed: they identify one among the many aspects of color that can be used to enhance

an already effective design.

Books that intelligently address color design issues are hard to come by. Wucius Wong's Principles of Color Design (John Wiley & Sons, 1997) is one of the more comprehensive, with discussion of electronic (computer) design issues. However, it suffers from adherence to the traditional color wisdom, which I've just shown is an inadequate approach to color effects.

It turns out that humans do not have color constancy, if that means the ability to recognize or distinguish colors across a wide range of illuminants. Instead, a rich system of beliefs about the world — the behavior of light, colors at different times of day, remembered colors of familiar objects — impose themselves on color sensations in a way that is typically involuntary and unconscious.

Our color experience seems consistent even though it is changing all the time, minute to minute. Simply by looking from a computer monitor toward a sunny window, or by walking from a doorway into the open air, or by watching heavy clouds clear into radiant moist sunlight, we discount color change by experiencing it as a change of light or context.

Color becomes inseparable from form or illumination. It condenses onto physical forms or dissolves into lights. Greens become lawns and blues become skies; color fuses with the material world. But color must also keep its place. It must still follow the principles of related colors and colormaking simplification. If it is lawn, the green must stay lawn even when it is in shadow or raked by reddish light. It has a visual identity akin to its color under the best light, even when that light changes.

This is color constancy. Humans absolutely do not have color constancy in the sense that "colors look the same" all the time, because otherwise we would not notice that light had changed. But we do have color constancy in the specific sense of altering or interpreting changes in color as changes in light — specifically as changes in the color and intensity of illumination, or changes caused by transparent or filtering media such as fog,

color constancy

smoke or tinted glass.

Color recognition is anchored fundamentally in a range of ideal colors that have the status of abstract concepts: the color invoked when someone asks you to imagine the color red. Ideal colors are necessary for managing the translation of sensations into color labels and color labels into a decision or behavior, but they are not sensations and they have a very vague relationship to color experience. For example, once you have imagined the color red, it is rather odd to be asked "how bright is it?" And the word "red" can be applied to very different colors — an apple, a sunburn or a glass of wine.

In contrast, attached to many objects is a remembered color or memory colors that participates in recognizing the object or noticing a change in its appearance or condition. Memory colors can be quite specific (the color of your partner's hair or skin), or rather general (the color of grass, or the color of cheese); they are also dependent on the illumination under which they have typically been seen. Memory colors are not attached to language but to object concepts, so they often cannot be described precisely because they do not match the ideal color categories of our language. It is perfectly natural to say "how bright" is the color of the sun, and it is not unusual to use the memory color of one object to describe another object — a school bus may "be the color of" a California poppy, or a good cheddar.

The Ambiguity of Images. When color becomes the world, it divides into four primary forms. The first and dominant is the ambient light source or illuminant. Without the illuminant, nothing else would be visible. It is almost always the largest and brightest light, even if it is diffuse, indirect, or dim. And it is always colored, because it has a unique spectral power distribution.

But surfaces are what we see, and surfaces can and do transform the color of the illuminant. Light and surfaces mix subtractively, just like paints. These mixtures tell us both about surfaces and light, but our vision is designed to ignore the effects of the illuminant as much as possible, which is why

we may not notice we are in a dim room until we try to read, or not notice that the light is red until we see the sun is low in the sky. In most natural environments the brightness of surfaces is substantially brighter than the sky, and surfaces at a middle gray lightness (around 20% reflectance) usually determine the light adaptation.

sources of ambiguity in the visual world perceived colors depend on the color of the illuminant, the surface or local color of objects, and the color of

any intervening transparent media such as air, glass or chromatic adaptation

The third color quality, the transparent medium, is both the quality of air and scattering substances such as water, fog or rain, smoke or dust, or artificial materials such as glass or plastic. This may darken, whiten, iridesce, hue shift or hue enhance the colors of surfaces under light, and is typically a quality we attribute to the atmosphere or tinted glasses.

There is however an additional kind of "transparent medium," which is our beliefs about the consistent or enduring properties of the world, which is usually called memory color. Evald Hering made the connection with tinted media explicit:

All objects that are already known to us from experience, or that we regard as familiar by their color, we see through the spectacles of memory color.

A key part of this process is discounting the illuminant, which occurs when we can

consciously perceive that a color area has a changed because of the color of the illumination or a transmitting filter, yet we are able to ignore the color change because (1) the color change is global and constant, and (2) the surface color, or the color change in context, is familiar to us.

The simplest example of discounting the illuminant occurs when we put on sunglasses. These change both the lightness and color of surfaces, and we are immediately able to ignore these changes, then forget we are ignoring them. (As this example shows, discounting the illuminant is a misnomer, since we can also discount tinted media.) More dramatic examples can be manufactured by radically shifting the color balance of photographic images or simulations of images that we have never seen before. Here for example is the same multicolored cube viewed as if under light or through a transparent medium tinted either yellow or violet.

demonstration of discounting the illuminant

a tiled cube viewed under simulated yellow or violet light, or behind a yellow or violet transparent medium; the same gray color can appear to be either a yellow or a blue tile, and different orange and purple colors can appear to be the same red tile (adapted from the Dale Purves web site and from American Scientist, May-

June 2002)

There are several remarkable aspects to this. We immediately achieve a very firm conviction about the "real" colors of the cube, even though we know the colors are distorted and we have never seen the cube before. We are

fully conscious of the strong overall tint, yet ignore it. And our actual sense data contradict our color interpretation: we see the "same red" in tiles that are either orange or purple. In fact, astonishingly, we see "different yellow or blue" in tiles that are an identical, perfectly neutral gray! Seems impossible, yet there it is.

However, if we place these impossible color shifts in their general relationship in a hue circle, with white at the center, a pattern emerges. The red, green and white have all shifted from yellow to blue, or warm and cool, and the opposing yellow and blue have radically increased or decreased in chroma.

color changes under chromatic adaptation

So we disregard the local color changes because they conform to a simple scheme: colors along the path of the hue shift change in chroma, while colors on either side change in hue. This is the general pattern of an illuminant color shift, and is produced every day by daylight phases, from dawn to noon to dusk.

Equally powerful deceptions appear when the principal contrast is in illumination. The example at right shows a cube tiled with yellow dots, with a blue dot at the center of each face. What is remarkable is that the blue dots have an identical lightness and chroma in the image, while the contrasting values of the cube faces make the dot appear luminous on the dark side and close to black on the bright side. Despite these strong apparent differences, the lightness of each blue dot is the same, as you can confirm by downloading the image into an image processing program and measuring the dot values with a color picker.

These are changes in light that arise from the intensity and direction of light, whose color effects we also see clearly and ignore. They are interpreted into the shape of objects and their ability to occlude light. Thus, color constancy is primarily concerned with the coloring and shadow casting effects of illumination.

The example chosen by Purves is to some extent special pleading, because the recognition of colors is most accurate when they are displaced along the y/b opponent function. The example below shows the same cube under simulated magenta or cyan illumination, which has a significantly different effect.

color change between magenta and green illuminant

perceived colors under simulated illumination with a strongly magenta or cyan color (partially obscured

"white" image provided as reference)

The magenta illuminated cube, remarkably, retains the hue contrasts and makes some colors more chromatic. It also makes the colors more equal in lightness, which obscures value contrasts. The cyan illuminated cube darkens or lightens colors in a way that increases the value contrasts but obscures the hue differences: green, yellow and white, or blue, brown and red, now resemble one another.

color changes under different illuminants

Again, a crude hue circle presentation of the contrasts shows this effect as well. In general green is a value enhancing illuminant, distorting hues but making lights and darks stand in stronger contrast, while magenta is a hue enhancing illuminant, distorting value relationships but keeping the hue differences relatively unchanged.

N E X T : additive & subtractive color mixing

Last revised 08.01.2005 • © 2005 Bruce MacEvoy

additive & subtractive color mixing

The previous pages have

described the fundamentals of color vision.

Now the focus narrows to a single issue: how color mixtures can be explained.

Painters mix their paints to shape the light reflected from a painting, and the viewer's eye

interprets this reflected light as color in space. These two extremes of color experience — the

mixed paints, and the interpreting eye — are described by two separate and unequal color

mixing theories.

Isaac Newton's hue circle, a geometrical

arrangement of the different colors seen in a solar spectrum, is the original statement of

additive color mixing. Newton explained that the chromaticity (combined hue and

saturation) of a light mixture could be predicted as the weighted average of the

ingredient hues around the hue circle. However, the most important feature of

additive mixing, as specified by Newton's

averaging method, is that the chromaticity of ingredient lights always determines

the chromaticity of their mixture.

Newton explicitly stated that color is a perceptual property, not a physical

attribute, which meant that the light mixtures

occurred in the eye, not in the light. Today we define the chromaticity of light mixtures as the

proportional stimulation induced in the separate L, M and S cones relative to the

stimulation across them all (the color's brightness). Three red orange, green and

blue violet (RGB) lights are used to demonstrate additive color mixing, because

they are the most direct way to stimulate the separate L, M and S cones.

However, painters and dyers had long experience with paints and dyes, and they

affirmed that material color mixtures behaved very differently from light mixtures: they get

darker rather than brighter, and they seem

defined by red, yellow and blue primary paints (now replaced by the modern choice of cyan,

yellow and magenta or CYM). In

color

vision

additive color mixing

subtractive color

mixing

substance uncertainty

"theory" vs. experience

subtractive color mixing, colorants absorb or subtract wavelengths from filtered or

reflected light. This was pointed out by several 18th century artists and naturalists, including

Jakob Le Blon in 1725, Brook Taylor, Moses Harris, Philipp Otto Runge and

Thomas Young. But it was only in the late 19th century that material color mixtures were

understood as an indirect form of additive color mixing. Until then, artists were taught

that light mixtures and paint mixtures were

both produced by the same red, yellow and blue "primary" colors.

Unfortunately, the color mixture "predictions"

made by subtractive color theory are often

inaccurate, because the light absorbing properties of a colorant are affected by its

physical state — its particle size, transparency, density, dispersion or medium,

the color of the substrate, the other colorants it is mixed with, the thickness of the color

layer, and so on. I call these problems substance uncertainty: because of them,

the color of ingredient substances does not determine the color of their mixtures.

Often, colorants must be physically mixed in

order to find out what their mixture color will be.

Even among artists today, misconceptions

about additive or subtractive color mixing are the cause of many misleading ideas about

color. Most of these misconceptions are taught

to artists as "color theory." I explain why artists should rely on mixing experience

instead.

Additive color mixing explains how the eye interprets light wavelengths in

the perception of color. It describes the color structure of light perception from four

cardinal lights: red orange, middle green and blue violet, plus the white light (or white

point) defined by mixing the three colored

lights together. This trichromatic foundation is in turn the basis for all modern

chromaticity diagrams, the identification of visual complementary colors, and the

definition of modern trichromatic color models.

additive color mixing

Additive Mixtures Occur In The Eye. The beauty of additive color mixing principles is in

their narrow scope. They are limited to a single sensory process for the explanation of

color mixtures: the average or typical responses of the L, M and S photoreceptors

to light.

These LMS cone outputs can be predicted

fairly accurately from the light's spectral emittance curve and the cone sensitivity

curves. In fact, the LMS cone sensitivity curves are actually only a mathematical

restatement of the quantities of three "primary" lights necessary to mix a specific

wavelength of spectral light — the RGB color

matching functions. This close link between light energy and cone outputs allows us to

describe accurately the resulting color perception for those with "normal" color

vision.

But wait ... isn't additive color mixture really a

theory of how light mixtures behave? No, it is not. This misconception arises because light is

obviously the only stimulus that the eye normally responds to, and because lights of

various colors are explicitly manipulated in color matching experiments used to

measure additive color mixtures. But light is the stimulus, and additive color mixing

describes the response of the eye to a light stimulus.

This description only applies to unrelated colors — that is, a light stimulus perceived

without any surrounding physical context. Unrelated colors can be created by shining a

diffuse light directly into the eye, or by reflecting the light into the eye from a

colorless (white or gray) surface; the source of

the light in an unrelated color does not matter, because additive color mixing happens in the

retina, not in the light. Special steps must be taken to reduce the effects of a visible

context. When this is done the connection between light stimulus and color response is

predictable.

Color scientists diagram this connection

between cone responses and perceived color using the trilinear mixing triangle devised

by James Clerk Maxwell. This triangle defines the chromaticity (hue and saturation)

of any unrelated color as a proportional mixture of the three cone outputs; the

"white" brightness is approximately equal to their sum. These outputs, in turn, can be

exactly reproduced by a specific mixture of three actual (visible) "primary" lights —

typically red, green and blue violet. All modern color models are based on additive

trilinear values that specify both the chromaticity and luminance of a color. In fact,

many late 19th and early 20th century artists

learned the basics of color theory in terms of a mixing triangle — not a color wheel.

The Additive "Primary" Lights. Now, how

do we illustrate, verify or measure the rules of

additive color mixing? Obviously, by manipulating the outputs of the separate L, M

and S cones. How do we manipulate these outputs? By stimulating them with three

colored lights — red, green, and blue violet (RGB). Necessarily, these lights create

a fourth "primary": the "white" light mixture of them all. So "white" light can be

substituted for any of the colored lights in a color mixing demonstration.

The basis of additive color mixing is trichromatic metamerism: the color

produced by any spectral emittance curve, no matter how complex the curve may be, can be

exactly matched by the visual mixture of no more than three lights: either three strongly

saturated (single wavelength or

monochromatic) lights, or at most two monochromatic lights mixed with a "white"

light. All physically possible light colors can be reduced to the mixture of just

three simple lights. Here, for example, are the "primary" RGB colors of your computer

monitor. Note that the green primary contains too much yellow, and the blue primary not

enough violet, dulling all purple and blue green mixtures.

There is an important limitation to the use of

trichromatic primaries: we can't mix all

possible colors with the same three lights, as explained below. Even so, the

incredible complexity of light in the physical world is reduced by the eye to just four

primaries — three independent cone outputs, and the "white" light that defines their

achromatic mixture.

How do color scientists create the strongly

saturated RGB lights used in color matching experiments? For precise color measurement,

the primary lights are single wavelength or monochromatic lights, isolated from the

visible spectrum by a system of prisms, that are mixed by shining them onto a diffusion

glass or white surface visible through an eyepiece. Less saturated but higher luminance

lights have been created by passing three

separate beams of "white" light through separate broadband red, green or blue

transmission filters, and mixing the colored beams as before. A third (and relatively weak)

method uses partly overlapping disks of colored or painted paper that are visually

mixed by spinning them rapidly on a color top.

additive color mixtures as demonstrated with filtered lights; note that each pair

of RGB primaries mixes one of the CMY primaries

The illustration (above) shows the typical

demonstration of additive light mixtures, made by shining three overlapping circles of filtered

light onto an achromatic (gray or white)

surface. If the surface is illuminated by both the red and green lights, but not by the blue

light, then the eye responds with the color sensation of yellow. A magenta color results

from the mixture of red and blue violet light, and cyan from the mixture of blue violet and

green. In additive color mixing, yellow and blue don't make green — they make white!

The "White" Color Theory. It's handy to think of additive mixing as the "white" color

theory. Mixing light wavelengths from the "red," "green" and "blue violet" parts of the

spectrum adds luminosity and negates hue to shift the mixture color of lights from dim

pure hues toward bright whites. The key principle is that the eye always adds together

all the wavelengths of light incident on the

retina — nothing is lost — and it is this total light sensation that the eye interprets as color.

This additive behavior leads to an important

constant in color vision: the chromaticity

and brightness of lights always predicts the chromaticity and brightness of their

mixture, for lights from moderately dim to bright but not dazzling. This is true regardless

of whether the lights are monochromatic (a very pure hue, as we see in homogenous or

single wavelength light) or complex (as we see in a mixture of many different spectral

wavelengths, for example a "white" light passed through a colored filter). In additive

color mixing, for both normal and colorblind vision:

• the brightness, saturation and hue of any two or more lights predicts the brightness,

saturation and hue of their mixture

• any two lights that appear to be the same

color will mix identical colors with any third light — even if the spectral emittance profiles

of the lights are different (that is, they contain different wavelengths in different proportions)

• if two separate light mixtures have an identical color, then adding a third light in the

same quantity to both of them will result in

identical color mixtures

• these points are true, even though is not possible to deduce the spectral profile of a

light from its color alone; for example, the

chromaticity (hue and saturation) of any spectrally complex light can always be exactly

matched by one or two monochromatic wavelengths mixed with some quantity of

"white" (achromatic) light.

These principles summarize the metameric

mixture rules of additive color mixture. They were first stated by Hermann Grassmann in

1853 and are known today as Grassmann's laws, though in fact they are not laws but

generally accurate descriptions of color mixing in mesopic and moderate photopic light

sources.

We will discover that equivalent subtractive

metameric rules do not exist in the many examples of material color mixing, and that

lack of predictable consistency in substance mixtures is the most important difference

between the additive and subtractive color mixing frameworks.

Real Lights and True Primaries. Let's examine further the additive color mixing

demonstrations with colored lights, as they are probably the main reason why artists believe

that the RGB primary colors can reproduce all color mixtures, or that the additive primaries

are "real" colors (that is, visible physical

lights), or that the lights used in additive color mixing demonstrations must be RGB lights

and no others — the choice of lights is fixed rather than arbitrary. All three beliefs are

false. The Additive Primaries Are Invisible. The

diagram at right shows the location on the

CIELUV chromaticity diagram of three monochromatic lights (at 460nm, 530nm and

650nm) that have frequently been used in color vision research to analyze trichromatic

color matches and opponent color mixtures.

The focus here is on the white triangle or

gamut that connects the three primary lights. This defines the range of actual additive color

mixtures it is possible to make with those three primaries. This gamut encloses most,

the gamut of RGB primaries

used in color vision

research

but not all, of the chromaticity area, which defines the area of all physically possible light

colors. A significant portion of the chromaticity diagram is outside the gamut. In other words,

the "real" RGB primary lights cannot mix all visible colors.

Thus, the "green primary" gives full mixing coverage along the red to yellow colors, but it

cannot mix (with the "blue violet" primary) the most intense greens, blue greens and blues.

In addition, the "blue violet" and "red" monochromatic primaries cannot mix the most

intense purples and red violets.

The true additive primaries, the only

"primaries" that can mix all possible colors, are the outputs from the L, M and S cones.

We are never aware of these outputs directly and therefore they are invisible. We only

experience them as the tendency toward a red, green or blue color sensation that results

from the combination and interpretation of

these outputs in the visual cortex.

How Do We Choose the RGB Lights? Some artists think that these primary lights are the

same hues that most stimulate the three receptor cones. This also is false. The cones

are actually most sensitive to "greenish

yellow," "green" and "blue violet" wavelengths, as shown below. Red orange,

green and blue violet lights are used by convention and convenience, and it is from

these color matching lights that we get the names red, green and blue assigned to the

additive primaries.

additive primary colors are illustrative

only

additive light mixing gamut

defined by lights at 460, 530

and 650 nm

the wavelengths of maximum sensitivity for the L,

M and S cones (top) are unrelated to the colored lights

used to simulate the cones in additive color mixing

demonstrations (bottom)

There's a simple logic for choosing these

primary lights. Almost any light wavelength that stimulates one cone will also stimulate

one or both of the other cones, because the cone sensitivity curves (especially L and M)

overlap. To explain color mixing as the result

of three independent types of photoreceptor response, we need three light wavelengths

that each stimulate one cone much more than the other two. In other words:

An ideal additive primary color must stimulate

only one type of receptor cone (L, M or S) as

strongly as possible, and stimulate the other two types of cone as little as possible.

So, within each section of the spectrum

where the L, M or S cone is the dominant

receptor, we pick a wavelength that creates the greatest difference in response between

that cone and the other two. This occurs at around 420 nm in "violet" light and above

680 nm in "red" light. However, these monochromatic lights are very close to the

spectrum extremes, and are therefore visually quite dim. In practice, the hues of the R and B

primary lights are often shifted away from the extreme ends of the spectrum to provide more

luminance in the lights, given the method used

to generate them. The G light is always bright enough, so it is usually positioned at the point

where it achieves both a high relative contribution and the most saturated yellow

when mixed with the R light. This is usually a green with a dominant wavelength between

510 nm to 530 nm. Sometimes a very small quantity of "violet" light is mixed with the red

primary, to eliminate the yellow tint in spectral "red" light.

Does Additive Mixture Require RGB Lights? Many artists assume that red, green

and blue violet lights must be used to explain or demonstrate additive color mixing. Not

true. The choice of lights is arbitrary, and one selection of primaries is better than another

only if we require the mixture gamut to be as

large or comprehensive as possible.

We could just as easily demonstrate additive color mixing with colored lights representing

the subtractive primary colors cyan, yellow and magenta, although most of the blues,

greens and reds that we could mix with these lights would appear quite whitish or

unsaturated.

Again, the somewhat arbitrary procedures for

choosing the additive primary lights are acceptable because the real lights are not the

actual basis of additive color mixing. The true additive primary colors are the

photoreceptor outputs. We use RGB colored lights to symbolize the LMS receptor

outputs, because they are also the most

effective way to manipulate those outputs. A Scientific Theory of Color Vision. For many centuries, the behavior of color mixtures

was difficult to explain because material colors, which seemed to be anchored in "real"

objects of the external world, was not

conceptually distinguished from the "illusory" colors in rainbows or prisms. The two types of

mixtures behaved differently, but the reason for the difference was unknown.

The trichromatic theory provided the clarifying explanation and prediction of all color

sensations as arising in the behavior of the eye. Because the L, M and S receptor

responses can be predicted mathematically from the summed intensity of all wavelengths

in a light stimulus, the additive primaries empirically connect a measurable light

stimulus to a measurable (matchable) color sensation — at least, in experimentally

restricted viewing conditions. This is what

makes additive color mixing, in the scientific sense of the word, a theory of color vision.

Subtractive color mixing is,

in comparison to additive color mixing, a flawed attempt to describe the colors that

result when light absorbing substances are mixed. It is not a rigorous theory at all, but

rather a description of the way colors should mix in the ideal case. Subtractive mixing

theory imitates the main features of additive color theory, and to understand why

subtractive color mixing

subtractive color mixing does not accurately describe the colors of substance mixtures, we

need to unmask these points of imitation one by one.

Subtractive Mixtures Occur in Substances. First, let's get clear on what subtractive mixing

rules are trying to explain. All subtractive color mixing occurs in the external world,

in a wide variety of material substances.

In principle, subtractive color theory ought to

be able to explain the color changes that occur in any kind of material mixture. In fact, it

should also be able to explain the color changes that occur when a surface is

illuminated by different illuminants (colors of light). And this is the fundamental difficulty

with subtractive mixing theory: it must explain the behavior of too many

different substances. This problem is minimized, but not at all eliminated, by

limiting the application of subtractive mixing

principles to manufactured colorants. Even here, the variety of materials would include

light reflecting substances (such as powders, paints, dyes or inks) and light transmitting

substances (such as photographic filters, stained glass or tinted liquids).

If we are only interested in the color of a pigment or dye in isolation, then we can define

its material color attributes by measuring its spectral reflectance curve. This defines the

light mixture that is reflected to the eye — in fact, all reflectance curves define the

subtractive mixture of a pigment or dye with "white" light. The reflectance profile in turn

defines the photoreceptor responses under normal viewing conditions, or the material's

color. So long as we only consider the

spectral profile of the light entering the eye, or the mixture of spectral profiles as light

mixtures entering the eye, we are in the domain of additive color theory and predicting

the color produced by the reflectance curves and their mixture is a straightforward

problem. But when two or more colors are physically mixed, or combined as light filters,

all the physical qualities of the substances interact, which can cause their reflectance

curves to combine in unexpected ways and

produce an unexpected color in the mixture. The most important of these physical mixture

issues are:

1. The apprarent color does not define a unique reflectance curve. The same green

color of paint can be produced by many

different reflectance curves, and these different curves will produce different blue

colors when each is mixed with the same purple paint. This is the problem of material

metamerism. The apparent color, not the reflectance curve, is all that a painter has to

work with. The painters' subtractive mixing rules are not stated in terms of reflectance

curves, as "this reflectance curve mixed with that reflectance curve yields this apparent

color", but in terms of categorical color labels,

as "yellow and blue make green". 2. The reflectance curve changes with the physical state of the colorant. A pigment

such as quinacridone violet (PV19) does not have fixed, unchanging color attributes. The

reflectance curve, and hence the apparent color under standard viewing conditions,

changes with the physical state of the pigment — the pigment may be dry or wet, it may be

suspended in water or oil, it may be diluted or

concentrated, it may be displayed as a thin or thick layer (diagram, right). In most colorants,

each of these physical changes will alter the reflectance curve significantly.

3. Separate colorant reflectance curves do

not specify the color of the physical

colorant mixture. This problem arises because there are many more physical

attributes to a colorant than its reflectance properties. The same reflectance curve can be

produced by substances that differ greatly in particle size, refractive index, transparency

(hiding power) and tinting strength, and these all can affect how the colorants will appear

when dispersed in a vehicle, or which colorant will dominate when used in a mixture with

other dyes or pigments.

4. Mixture colors are different in different

types of subtractive mixture. Even if we find out the mixture color of two colorants by

actually mixing them, that color does not necessarily predict the color that will result if

they are mixed in other ways — there are

different kinds of subtractive mixture. Subtractive mixtures of reflecting paints or

reflectance curve changes

with physical state

the masstone reflectance

curve of quinacridone violet

(PV19) changes shape, not

just overall level, when it is

diluted into a tint

dyes obey different mixing rules than subtractive mixtures of transmitting filters;

paints applied to highly absorbent white paper appear duller and whiter than paints applied to

heavily sized white paper; pigments applied as watercolor (which does not form a paint

layer) appear different from paints applied as oils or acrylics (which do form a paint layer).

Of all these issues, material metamerism (1) is probably the most troublesome. In additive

color mixing, metamerism does not conflict with our ability to describe the unrelated color

perception that results from light mixtures, because the visual chromaticity of a light

predicts its mixing behavior with other lights.

But in subtractive mixtures it is not the color of the substance but its reflectance profile and

physical attributes that determine its behavior in physical mixture, and this information is

simply discarded when we define substances indirectly, in terms of visual color categories

such as blue or yellow.

Even if we do know all the important physical

attributes of the colorants we mix, the prediction of their subtractive mixture from

their separate reflectance curves is mathematically complex. A paint layer is

essentially a physical object (it has thickness, surface, transparency and so on), so the

prediction must significantly limit or simplify the paint's material characteristics. (See

comments on the Kubelka-Munk theory

below.) These arbitrary limitations and lost complexities mean there are usually more

practical and reliable ways to guide color mixing decisions. As a color chemist in the

automotive industry explained to me, you mix the two pigments and look at color you get. Or

as I like to say, subtractive color mixing concepts are only useful as a compass to

color improvisation.

I give the name substance uncertainty to

these confusing connections among a colorant's reflectance curve, physical

attributes, apparent color when prepared in a specific medium, and mixture color with other

colorants, and I explore these issues in more detail below. For now, the essential point is

that we can't reliably use the color

appearance of two paints to predict the color appearance of their mixture. This is

the most important point of difference with additive color theory, where the color of two

lights of moderate brightness can predict the color of their mixture.

The Subtractive "Primary" Colors. Subtractive color mixture is fundamentally

about substances, and for that reason it has also been the color mixing practice with the

longest commercial application. Additive color mixing has been technically important only

since the advent of color television 50 years ago. Subtractive mixtures have been

recognized and used in dyers' and painters' trades since ancient Greece. That long trial

and error practice fixed on blue, yellow and

red as the best subtractive primary colors, which achieved the form of a published

"theory" in the 18th century.

In fact, the historical choice of primary colors was limited by the historical availability of

suitable pigments, which until the late 19th

century were comparatively dull and dark. Color choices today have been greatly

expanded by modern industrial chemistry, so that the modern subtractive "primary"

colors are cyan, yellow and magenta (CYM), as shown in the figure below. The

traditional and grade school subtractive primaries — blue, yellow and red — are relicts

of 18th century color theory and are best forgotten.

subtractive color mixtures as demonstrated in overlapping sheets of transparent

colored plastic (transmission or filter mixture)

These primaries produce the mixtures familiar

to us in paints. When we mix together a yellow and magenta paint, the resulting

mixture is scarlet or orange; the mixture of magenta and cyan yields purples and blues,

and yellow greens and blue greens result from the mixture of yellow and cyan.

Here are exemplars of the yellow, cyan and

magenta subtractive primaries in your

computer monitor colors:

What Is "Primary" About Subtractive Primary Colors? The subtractive cyan, yellow

and magenta primaries are presented as the

basic or elemental colors in subtractive color mixing, no matter what kinds of materials —

paints, inks, dyes, pigments or filters — are used to embody those colors.

This substitutes apparent color, the color

sensation in average or individual eyes, for the

chemical and physical attributes of paints or inks that determines the reflectance curve.

Apparent color sweeps under the rug all the material qualities of paint pigments, especially

mineral and opaque ones.

The "Black" Color Theory. The first question

to address is: what is the universal visual effect on color that happens when we mix

material substances?

The answer: when we combine paints, dyes or

filters, we do not increase their light reflecting (or transmitting) behavior but their light

absorbing behavior. A subtractive mixture absorbs all light wavelengths that each

colorant absorbs by itself. Subtractive mixture always increases darkness in material

colors.

This makes subtractive color mixing the

"black" color theory. Mixing all three subtractive primaries produces a dark neutral,

the opposite of white, because each paint subtracts or absorbs light that might be

reflected by the other. Subtractive color mixtures can only be made lighter by diluting

the amount of pigment in the mixture with white paint or water; either remedy weakens

the color saturation. So subtractive mixture typically also reduces the hue purity (increases

the grayness) in the color of mixed substances.

Multiplicative Darkness Mixture. The second point of difference with additive color

mixing has to do with how the colors combine in subtractive mixtures. This is always some

form of multiplication or product of the separate reflectance curves, as shown below

for two common paint colors, categorically

labeled magenta and yellow, assuming that the two paints have identical tinting strength,

particle size, refractive index and hiding power and are mixed in equal proportions.

subtractive color mixing of yellow and magenta

white line shows reflectance curve of subtractive

mixture; high reflectance remains only where both

paints reflect light

In this mixture, the yellow absorbance

subtracts light from the "blue" reflectance in magenta, and the magenta absorbance

destroys the "green" reflectance in yellow. The common reflectance, the light reflected by

both paints, is largely in the "red orange" and

"red" part of the spectrum, which is the approximate hue of the mixture. It is

specifically this mutual antagonism among light absorbing substances that subtractive

color mixing tries to explain.

As explained above, this mutual antagonism

depends on many physical attributes of the colorants, so there are no "Grassmann's Laws"

for material color mixing. However, for most paints and dyes in most applications, the

reflectance resulting from a physical mixture of pigments is usually close to the geometric

mean of the separate paint reflectance curves across each wavelength in the spectrum. (The

geometric mean of two numbers is the square root of their product.) For example, if a white

paint reflects 98% of the light at 452nm, and a black paint reflects 10% of the light, their

mixture (in equal proportions at equal tinting strength) will reflect approximately 31% of the

light at that wavelength.

However, because subtractive mixing behaves

differently in different substances, we have to use a different mixing rule for filters, or for

pigments in solution, where the mixture color is usually equal to the product of the separate

transmission profiles. That is, two filters that

separately transmit 98% and 10% of a wavelength will transmit about 9.8% of the

light when they are combined.

When we apply these mixing calculations to the reflectance or transmission profiles, we

find that the mixture profile is always closer

to the darker profile in the combined total reflectance curve, or darker than the

darkest profile in the combined total transmission curve. Mixing white and black in

equal proportions does not reduce the luminance of white by half, but by at least two

thirds. As a result, sequentially (transmissively) combining any two colorants

always results in a darker mixture than physically mixing the two same two colorants;

and physically (subtractively) mixing two

colorants always results in a duller, darker color than visually (additively) mixing the

same colorants, for example on a color top!

Double Cone Stimulation. We've identified the multiplicative combination of light

darkening (absorbing) qualities as the two

universal traits of subtractive color mixture. But we haven't identified the attributes that

define the subtractive primary colors cyan, yellow and magenta. What is the material

attribute of "yellowness" that occurs in all yellow colored substances? Why do we choose

those visual colors, and not some others?

The answer begins with the fact that

subtractive mixtures always destroy ("subtract") the material luminance, making

color both darker and duller. To compensate for this, painters should start with colors that

are both light and bright (that is, light valued and highly saturated).

However, if we play around with various light

valued, high chroma paints, as the ancient

painters and dyers did, we discover that some do much better as subtractive primary colors

than others. Why? Because the key to subtractive primaries is not in their light value

or high chroma alone. It's in how that color intensity affects the eye:

An ideal subtractive primary color must stimulate two types of receptor cones (L and

M, or M and S, or L and S) as strongly and equally as possible, and stimulate the third

type of cone as little as possible.

In other words, the subtractive primaries

are only an indirect way to specify the L, M and S cone responses of additive color

mixing! Once again, these cone outputs are the "true" color mixing primaries.

Some texts express this point in negative terms, saying that each subtractive primary

absorbs or "subtracts" from "white" light the wavelengths representing a single additive

primary. These are often written (or diagrammed) as subtractive formulas,

including both white (W) and black (K):

C = W – R

M = W – G Y = W – B

K = W – (R + G + B)

Thus cyan subtracts "red" light from the total

"white" light spectrum; magenta subtracts "green" light from the spectrum, yellow

subtracts "blue" light; black subtracts all light from the spectrum.

This way of defining subtractive primaries is helpful to remember their complementary

hues, but it is essentially a definition that allows for dull "primary" hues. Thus, raw

umber almost completely absorbs "blue" light, and iron (prussian) blue almost completely

absorbs "red" light, so they can be used as a primary yellow and blue, even though they

also absorb light from other parts of the spectrum and therefore appear relatively dull

or dark.

Ideal Subtractive Primaries. Once we have determined that the best subtractive primary

colors will produce the maximum possible stimulation in two types of cones and the

minimum possible stimulation to the third type of cone, we simply choose the colorants that

achieve those receptor effects as far as possible in a physical color stimulus.

To guide our search, it turns out that we can match those criteria by means of an ideal

reflectance profile. The ideal profiles we look to are optimal colors, which define the

theoretically brightest possible colors in a nonfluorescent physical surface. These colors

always have the maximum possible saturation

or hue purity of any surface color at a given hue and lightness, and the maximum possible

lightness of any surface color of a given hue and saturation.

The diagram below (top row) shows the

spectral reflectance curves and cone

responses produced by these three idealized subtractive primaries.

ideal spectral reflectance curves for

subtractive

primary colors each subtractive primary reflects or transmits the light

representing

two additive primary colors

To qualify as an optimal color, a reflectance

profile must have two attributes: (1) the

reflectance (or transmittance in filters or dissolved dyes) must be at 100% or 0% at

every wavelength across the entire spectrum, and (2) the reflectance curve may change

from 100% to 0%, or from 0% to 100%, no more than two times within the spectrum

(arbitrarily, 400 nm to 700 nm).

By these criteria, there are roughly 90,400

unique (but not necessarily visually different) optimal colors. If we sort through these until

we find the reflectance profiles that stimulate two of the three types of cones as much and

as equally as possible, while reducing stimulation to the third type of cone as much

as possible, we have the reflectance curves for optimal primary paints (top row in the figure).

The cone response profiles (middle row) show

how these optimal subtractive primaries affect the eye. For example, the ideal yellow

colorant transmits or reflects all the "red," "yellow" and "green" light and omits all light in

the "blue" and "violet" wavelengths; this

spectral profile results in high stimulation to the L and M cones, with low stimulation to the

S cones. The bottom row shows the perceived colors that result from the cone responses in

additive color mixing: "red" and "green" reflectance, with no "blue" reflectance,

appears as a bright yellow (Y). The idealized profiles, cone responses and perceived color

for magenta and cyan are presented in the same way.

These optimal colors are the physical ideal case. So it is instructive to see how the

chromaticity of these ideal subtractive primaries compares with the chromaticity of

common pigment choices for subtractive primary colors in watercolor paints or printing

inks. Note the unexpected result that cobalt teal blue (PG50) has the closest hue match to

the ideal cyan primary, and cobalt violet (PV49) is the closest hue match to the best

magenta.

However, the phalocyanine and quinacridone

pigments actually work very well as "primary" colorants, because they have a much smaller

particle size, higher tinting strength, higher transparency and greater chroma in tints than

the mineral cobalt pigments, especially when

used as inks.

subtractive primary colors

defined as optimal stimuli with

real CYM pigments in the

CIELAB a*b* plane

Observe, in the ideal cone response profiles above, that all three physically ideal

subtractive primaries stimulate to a significant degree the third or "unwanted" L, M or

S cone. (Note in particular the M response in magenta.) In each case we cannot achieve a

visually pure primary hue of paint, because of a physiological limitation: the overlap between

the M cone and L cone fundamentals. We just can't stimulate the L cone with "red

orange" light, or the S cone with "blue violet"

light, without also stimulating the M cone, just as if we stimulated it with "green" light.

Paradoxically, the "invisible" quality of the true additive primaries is partly responsible for

the "impure" quality of the material subtractive primaries.

Mixing Subtractive Primaries. What happens when these ideal primary paints are

mixed? Because any two subtractive primaries will share reflectance in either the "red,"

"green" or "blue" wavelengths associated with a single additive primary color, the mixture

of two subtractive primaries holds constant the response of a single

photoreceptor. Yellow and magenta share

"red" reflectance that stimulates the L cone, yellow and cyan share "green" reflectance that

stimulates the M cone, and magenta and cyan share "blue" reflectance that stimulates the S

cone.

mixing two ideal subtractive primary

colors reflectance representing a single additive primary

remains high; other parts of the spectrum also reflect

light (white line shows cone response to a 50:50 paint

mixture), and this flatter cone response profile is

perceived as a grayer color

What about the other two photoreceptors? In any subtractive mixture, the remaining two

additive primaries must compete with each other. As shown above for the mixture

of yellow and cyan, the "red" light that primarily stimulates the L cone is reflected by

yellow but absorbed by cyan; the "blue" light

that stimulates the S cone is reflected by cyan but absorbed by yellow. So both are

substantially darkened. The common or shared additive primary (that is, the eye's M response, in the case of cyan

and yellow) remains roughly the same, but the other two additive primaries (the eye's L and

S responses) work against each other: like a seesaw, as "blue" reflectance goes up, "red"

reflectance goes down, and vice versa. The

resulting light mixture is interpreted according to additive principles as containing mostly

"green" reflectance, but ranging from a blue green (when "blue" reflectance greatly

exceeds the "red" reflectance) to yellow green (when "red" exceeds "blue").

These tradeoffs also mean that mixtures of two subtractive primaries reflect light

from all parts of the spectrum. The result is a flatter cone response profile (shown in the

middle diagram of the figure), which creates the perception of a less saturated color

mixture — a color closer to gray. This explains the saturation costs in subtractive mixtures

— the tendency of paint mixtures to be darker and grayer than the original paints.

These saturation costs — the unwanted third cone stimulation in ideal colors and the added

"white" reflectance in real colors — are the fundamental reason why primary colors are

either imaginary or imperfect, as explained here. There is no combination of

three real primary colors in a specific medium

(dyes, paints, phosphors, filters) that can mix every possible color in that medium. And any

set of primary colors that can mix every possible (visible) color must be imaginary —

they cannot be embodied in any material substance or light source, so they cannot be

experienced as colors by the eye.

Don't Confuse Additive & Subtractive Mixtures. I hope you now understand why all

color mixing involves the retinal response to light; the only issue is whether or how we let

the physical properties of substances muck with the behavior of the light stimulus.

Because subtractive color mixing (in materials) is actually an indirect manipulation

of additive color mixing (in cone responses), the two types of color mixture can be

demonstrated in superficially similar ways. To avoid confusion, remember that the

fundamental difference is whether light wavelengths are excluded by the colored

substances before the light reaches the eye

(the light mixing occurs in the external world), or light wavelengths are separately able to

reach the receptor cones (the light mixing occurs in the eye):

• colored transmission filters – in the

additive mixing demonstration, a colored

yellow filter is placed over one beam of white light, and a blue filter over a second beam of

white light, and the two colored beams are overlapped on a reflective surface. Because

each filter is placed over a separate beam of light, the blue and yellow lights are separately

reflected to the eye, where they both affect the receptor cones to create the sensation of

"white" light. In the subtractive color mixing demonstration, the same blue and yellow

filters are both placed over a single beam of

light. Then the two filters act in combination before light ever reaches the eye; the only

wavelengths that can pass through both filters at the same time are in the "green" section of

the spectrum, so green is the color we see.

• mixing paints – in the additive mixing

demonstration the two paints can still separately reflect light to eye when they are

visually mixed on a spinning surface (a color top) or as closely spaced dots of color (in

visual fusion); but they cancel reflectance in each other when they are materially mixed as

paints.

Finally, it should be clear why red and blue

are not subtractive primary colors. A red paint reflects light only from the "red" end of

the spectrum; it stimulates primarily the L cones, but not the M or S. Most blue paints

reflect mostly "blue" and some "green" light, stimulating the S and M cones, but not the L.

So their mixture creates a very dull purple, because the two colors have no reflectance in

common: most wavelengths reflected by one color are absorbed by the other.

The same considerations explain why the RGB additive primaries are effective only in light

stimuli, such as televisions or computer monitors, but not in paints or inks. There is no

shared reflectance in the reflectance curves of red orange, green and blue violet paints, so

these produce very dull, dark colors when mixed subtractively. The additive primaries

are only effective when the mixing occurs in

the retina.

By the same token, the CYM primaries are ineffective in televisions or computer monitors.

There is a large overlap in the emittance curves of cyan, yellow and magenta lights, so

that their additive light mixtures appear

whitened and bright — the equivalent of dark and dull in subtractive mixing. The subtractive

primaries are only effective when the mixing occurs in materials.

Partitive Mixture. A special case of additive

color mixture presents a confusing paradox for

some readers. In partitive mixture, an image composed of small, separate but closely

crowded color dots or pixels are fused by the eye into a visually smooth or continuous color

area. Thus, the text and every image in this web page are generated on your color monitor

as thousands of tiny RGB lights that are blended into color by partitive mixture.

Visual fusion results when a surface texture, such as the spacing between the tiny lights in

your computer monitor, is too small for the eye to resolve optically or retinally; this is the

process that makes color areas appear from a field of halftone or overlapping colored dots in

printed books and magazines or in the tiny

dye molecules of color photographic papers. Additive (retinal) color mixing then resolves

the differences in light stimulation between adjacent RGB cones in the eye. Yet all

photographs and printed color images use the CYM subtractive primaries. So the question

arises: why aren't the additive RGB primaries used instead?

To grasp the answer, it will help first to print the diagram below on your color printer.

subtractive color primaries as subtractive

colors and as additive RGB pixels

In this image, the CYM color areas in the

upper row are actually created on the computer monitor by the visual fusion and

additive mixture of two of the three RGB

monitor lights. These are physically distinct but barely too small for the eye to resolve into

distinct dots. The color areas in the lower row are created by the visual fusion of alternating

RGB pixels. Each pixel contains three monitor lights, so this doubles the amount of black

(unilluminated) area within each color. (Examine the two areas with a magnifying

glass.) This doubled black spacing between lights coarsens the screen texture enough to

make it visible.

the subtractive inks and additive

mixtures printed on paper

The printed copy looks quite different (image above), first of all because the printer silently

substitutes a pure yellow ink for the "yellow" R+G monitor light mixture. However your

computer screen is fundamentally a light source, despite the illusion (created by the

subdued "white" luminance and the slight blackening effect of the monitor light

interstices) that it is a surface. The printed paper is a true surface, and therefore the inks

printed on it have the absorptive grayness that characterizes surface color perception. If

you hold the printed diagram next to your

computer monitor and illuminate the paper to a matching brightness, you will see that the

inks appear to be darker and less saturated than the monitor colors — especially in the

cyan and magenta. Absorbing inks are inherently a less effective source of luminance

than emitting lights.

If you next look at the printout by itself, you

see that the yellow created from the pure Y ink (top row) is much brighter than the yellow

created from the visual fusion of alternating, printed R and G dots. Your printer renders the

pixels without black space between them, so the darkening is not the same as on your

monitor; rather, visual fusion averages the

luminance (reflectance) of adjacent dots; it does not add them together as it does in

blended light mixtures. The average lightness of red or green inks is far lower than a pure

yellow ink, so the visually fused and additively interpreted yellow appears much darker and,

therefore, closer to a dull ochre or brown. A similar dulling and darkening occurs in the

cyan and magenta mixtures.

Thus, the RGB primaries suffer from three

handicaps when applied to surfaces: (1) they lose the inherent brightness of light sources,

and (2) RGB inks are much darker (lower luminance) surface colors than pure yellow,

cyan or magenta inks. This severely compromises their effectiveness in the

additive color mixing induced by visual fusion.

Since RGB inks make drastically dark subtractive mixtures — think of mixing a

yellow color from a red and green paint — (3) they would have to be printed as separate,

nonoverlapping dots, which would double the visual texture of a printed image and greatly

increase the registration (dot alignment) precision necessary for a clear image.

Because subtractive colors can be overprinted in a single dot or pixel location, to produce

subtractive mixture with each other and with the white paper, they produce a much finer

visual texture with less registration precision. The overprinting also subtractively creates the

span of orange, green and violet colors necessary to complete the hue circle. These

dots of subtractive mixture are effaced by visual fusion, and averaged together by

additive color mixture. This provides an

acceptable simulation in printed surfaces and photographic papers of the brightness and

contrast experienced in the light images of monitor phosphors, projective transparencies,

and the surfaces of the real world.

The Computer Sciences department at Brown University

hosts a Color Theory Library with several Java applets

that allow you to explore additive and subtractive color

mixing, color metamers and more.

So far we've explored subtractive color mixing by looking at idealized

reflectance curves. But, as we've just seen, there are differences between subtractive

mixing using idealized spectral profiles and actual color mixing using paints. As an artist,

you will forever be confused by paint mixtures

until you understand this difference in depth.

Reflectance curve and Visual Color. The kernel of the problem lies in the distinction

between material color, the light wavelengths that a paint actually reflects, and visual color,

the color we see with our eyes.

The material light absorbing and light

reflecting attributes of a pigment are exactly described by its spectral reflectance curve,

and for that reason the guide to watercolor

pigments provides the reflectance curve of all major pigments, linked from the spectrum

icon .

Using the methods of colorimetry, the reflectance curve can be translated into three

colormaking attributes that describe our

visual color perception under normal conditions of lighting and display. These

colormaking attributes fit the way we naturally

substance uncertainty

think about colors, and are much simpler to interpret than reflectance curves. However

different reflectance curves can produce exactly the same color appearance, and

this metamerism means we cannot identify the material reflectance curve of the pigment

from its visual color alone.

And here is the problem. As explained

above, the color of a paint mixture depends on the combined reflectance profiles of the

paints being mixed. When the material reflectance curves of two visually identical

colors of paint are different, they will produce different reflectances, and appear as visually

different colors, when mixed with a third paint.

But we can't tell, just by looking at the color, which wavelengths a paint absorbs or reflects.

So we can't tell, just by looking at the color, that two paints with the same color will mix

with other paints in the same way.

Visual Color Can't Predict Material

Mixture. For painters, metamerism is the single most important cause of substance

uncertainty, because the color of a paint does not define the color of mixtures

made with the paint.

There is an idealized and a practical way to

demonstrate the depth of the metameric problem. Let's start with idealized

photographic gel (transparent) filters, which we design to pass either 100% or 0% of the

light at each wavelength. In these examples, there are no constraints on the wavelengths

we are able to filter, and two filters are placed in front of a single beam of "white" light. Then

the apparent color of the transmitted light is the additive (retinal) mixture of all the

wavelengths passed by the subtractive

(material) mixture of the separate spectral transmittance profiles.

subtractive mixtures of different yellow and orange filters

The example above shows five pairs of ideal

filters that appear yellow and orange to the eye — they would all have the same

"color" (that is, hue), though they would differ somewhat in lightness or chroma. Yet, as the

examples show, the same "yellow plus orange" mixture can produce very different

mixing results depending on the specific

overlap in their transmittance profiles. Yellow and orange can combine to make yellow,

orange, red or black ... yellow and orange filters could even mix to make green!

And in principle (though I have not worked through every variation), it is possible for two

hypothetical transmission filters of any apparent color to create by mixture any other

color. The example below shows how two "neutral" gray filters can mix an intense red

(or green, or blue...).

how the subtractive mixture of two gray filters can

produce an intense "red" color the first gray filter passes all even numbered

wavelengths in the spectrum; the second gray filter

passes all odd numbered wavelengths below 600nm,

and all even numbered wavelengths above 600nm

The point of these abstract examples is to

show you that there is absolutely no logical or necessary connection between the

visual color of two substances and the

color of their subtractive mixture. If the only thing we know about two substances is

their visual color (not as spectral reflectance curves, but as the way they appear to our

eyes or as the lightness, chroma and hue measured by a spectrophotometer), then the

material mixture of those two substances can potentially make any other color. There can

never be universal or invariable color mixing rules in subtractive color mixing — they simply

don't exist.

Substance Uncertainty in Paints. But let's

get practical. The extreme, idealized variations I've described are implausible. We certainly

can't mix a red color from two gray paints! In

fact, regularities or patterns often appear in the way colored substances mix. Why is that?

Because we live in a real world of atomic

substances, and the atomic causes of color follow the organizing patterns of chemistry

and physics. These tend to produce

transmission or reflectance curves in most substances that follow more regular patterns,

such as the "warm cliff" profile typical of saturated red, orange and yellow paints and

filters. In addition, painters work with a very limited range of colored substances — their

paints — and modern colorants belong a fairly well behaved family of reflectance profiles.

So I have to turn to paint color mixing demonstrations to assess the practical extent

of the metameric problem for painters (or anyone else mixing paints, dyes or inks). To

do that, let's see what happens with the most explicit paint mixing test possible (and the one

most beloved in "color theory"): making a pure gray mixture from two complementary

paint colors.

The test is simple (though tedious) to do.

First, using the visual color only, arrange all the available "warm" colored paints in a

series, from greenish yellow to purple, on one side of a page. Then arrange all the

complementary "cool" colored paints, from blue violet to yellow green, on the opposite

side. Align the paints so that they are approximately matched as mixing

complement pairs — blue violet across from yellow, blue across from deep yellow, and so

on. Then mix all possible combinations of these warm and cool paints to identify the

pairs that produce a neutral (gray or black) mixture. Finally, connect these mixing

complement paints with a dark line.

If complementary paint mixtures are

determined by the visual color of the paints, and if all the paints have regular, simple

reflectance curves, then lines connecting these

complementary pairs should be roughly parallel (diagram, right). As the hue of the

warm paint changes from deep yellow to violet, the hue of its mixing complement

should change from blue violet to green by an equal amount.

This is precisely what does not happen, as shown below!

idealized subtractive

mixing complements in

watercolor

paint mixtures

substance uncertainty in watercolor paint

mixtures mixing complementary colors as measured on the a*b*

plane in CIELAB: pigments that make "pure gray"

mixtures are joined by dark lines, "near gray" mixtures

by light lines (see this page for more information)

Instead, the mixing lines from each pigment

fan apart, or skew up or down haphazardly. The mixing complement of teal blue can be

anything from a bright scarlet red to a dull maroon — and there are even paints between

scarlet and maroon (such as quinacridone red, PR209) that do not mix a close gray with teal

blue! And that is obviously the typical case for every pigment shown in the diagram.

The limiting rules of physics and chemistry take us out of those idealized transmission

filter examples, where subtractive color theory doesn't exist, but they don't take us all the

way to a perfect world where all pigment "colors" mix in a consistent way or where the

reflectance curve of the paints is apparent in the visual color. So we end up in the middle,

in a fuzzy, messy real world where subtractive color mixing is a real fuzzy mess.

This diagram also shows why a subtractive or mixing color wheel can never be

defined precisely: the mixing behavior of pigments or paints is only weakly predicted by

their hue relationships, or the relationships are too complex to be summarized as a simple

wheel. Substance uncertainty is an important

reason for the color wheel fallacy.

Couldn't we avoid substance uncertainty if we used real world colorants that had regular and

simple reflectance curves? The answer is no: because the second reason for substance

uncertainty arises from the many invisible

differences in pigment material attributes: refractive index, particle size, crystal form,

hiding power and tinting strength. Thus, the pigments cadmium yellow medium (PY35)

and hansa yellow medium (PY97) have almost identical reflectance curves, yet they

produce visibly different mixtures with other paints because their refractive indices

(appearance in paint vehicle) are so different.

Suppose we could somehow make paints so

that every apparent color had the same reflectance curve, and made sure every paint

had exactly the same material attributes — wouldn't that solve the problem? Again, the

answer is no: because the third reason for substance uncertainty arises in the material

attributes of the support and the paint

application methods. The qualities of different papers or canvas supports have a significant

impact. A glossy, highly reflective white paper can show up to 24,000 distinct color mixtures

using modern process inks. The same inks, printed on ordinary newsprint, generate a

much smaller range of perhaps only 2,000 distinct colors. In watercolors, a highly

absorbent paper (which pulls the pigment particles into the cellulose mat) will produce

duller color mixtures than a heavily sized,

nonabsorbent paper. These effects occur because applying paint to paper effectively

mixes three light reflecting substances — the two paints in the mixture and the paper —

which means the material attributes of all three will determine the apparent color.

Color mixtures also depend on how the paints are applied. A familiar example for

watercolorists occurs when paints are mixed by glazing or layering one color over another:

cadmium yellow over phthalo green is a lighter and less saturated mixture than phthalo green

glazed over cadmium yellow, even when the two mixtures have exactly the same hue.

These problems of metamerism, physical composition, support attributes and

application methods all contribute to a single result: paint color appearance cannot

predict mixture color appearance. And this happens because subtractive color mixing

"theory," by trying to imitate additive color mixing theory, bites off much more than it can

chew.

True, a complex mathematical model called

the Kubelka-Munk theory has been used with some success to anticipate color mixtures

in manufacturing and printing industries, but even there it has not replaced the empirical

methods of mixing by eye or according to

predefined recipes (as found in the Pantone™ or process color systems used in printing). The

Kubelka-Munk equations require information about paint reflectance, the scattering power

and hiding power of pigments across all wavelengths (which is often hard to come by

for the specific pigments being used for a particular job), and they assume a

homogeneous layer of paint vehicle containing very small pigment particles of identical tinting

strength that do not affect the color

reflectance of the other pigments — restrictions that are often unrealistic.

In the situations that matter to watercolor

painters, watercolor paint on paper does

not form a continuous paint "layer" at all, and does not distribute pigment on the support in

the same way that acrylic or oil mediums do, so theoretical models are even less applicable.

There is no way to escape the real and practical in order to reach the abstract and

ideal.

The Color Is In The Mixture. Substance uncertainty is such an insurmountable problem

for popular "color theory" books and color wheels that they deal with it the only way they

can — they ignore it! (Or, even worse, they assertively deny it by presenting their color

mixing explanations within perfect, idealized triangles and circles.) The artist tries to mix

paints according to these idealized, perfect "color theory" rules, and is only confused by

the many messy exceptions that result.

Experienced painters work with a more

intuitive rule: the material color of paints appears in their mixtures. They put

emphasis on the mixture colors that a paint

produces with all other paints on the palette. They pay more attention to the chroma and

lightness of paints, not just their hues — whether they are intense or dull, light or dark.

They learn, by trial and error, how the paints behave when they are diluted, and mixed with

every other paint on the palette, and they prefer paints that are versatile, rather than

pretty by themselves.

This is an important reason for the greater

mixing skill in experienced compared to novice painters. Novices think about the pure color

of the paint as it is painted on the paper, and attempt to judge mixtures in terms of the

visual color. These painters, who often learn "color theory" in terms of the visual colors of

paints arranged on a color wheel, learn how

to mix hues — "yellow and blue make green".

Where does this leave us? The fundamental issue is this: the artistic

control of "color" can be pursued through experience or theory. The diagram shows

the basic process tension.

"theory" vs. experience

approaching color through painting experience

or "color theory"

If we take a specific part of a painting, such as a green color patch in a landscape, then we

can either view it as the outcome of a material process that involves the

manipulation of paints or pigments on specific supports using specific mixing and application

techniques, or as the outcome of an intellectual process that assumes planning

based on traditional principles of contrast and harmony based on abstract color ideas and

fictional primary colors, or geometrical color

models used to "predict" color mixtures.

The material process is guided by painting experience, which tends to be a very long,

trial and error labor of exploration and imitative training that develops the painter's

understanding of the best materials and

techniques to produce a specific finished appearance — though why that result occurred

is often a mystery. The intellectual process is guided by "color theory" dogma, which

provides sometimes accurate and sometimes inaccurate explanations for why colors appear

a certain way, though it does not explain any of the process techniques necessary to

produce the desired effect.

I have tried hard to assure you that substance

uncertainty renders all the abstract rules

based on artists' color wheels or primary colors imprecise or arbitrary. There is no

"there" there. At the same time, color mixing is so inherently complicated that some kind of

conceptual framework is essential to keep one's bearings and learn efficiently.

The key is striking a personal balance between practical experience and

abstract rules, which every student can achieve by studying and painting with the

following in mind:

• color is fundamentally a subjective

experience that differs considerably from one person to the next;

• "color theory" rules consist of limited

preconceptions based on past experience with

specific artistic media, not predictive rules based on abstract scientific principles;

• experience with materials the ultimate

standard of best painting practice and the

preconceptions you have about how materials behave;

• "color theory" principles are useful when

they accurately summarize your painting and color experience;

• always consider "color theory" guidance when you are confused by a basic painting

problem or design difficulty;

• avoid the empty intellectual game of talking

about "color theory" separate from a specific design or painting problem in relation to a

specific design or painting; and

• keep your eyes always open to the effects

your materials create, so that theory does not become a limitation to your artistic growth.

Eventually, accumulated experience makes futher experience easier to acquire and

understand, and makes theory less of an issue. Intimate knowledge of your paints,

supports and technique is the key to effective color control. It is always more difficult to

look at the actual behavior of the paints you use than to memorize the simplifed rules

of "color theory." But experience, not memorization, is where learning actually takes

place.

N E X T : do "primary" colors exist?

Last revised 04.20.2008 • © 2008 Bruce MacEvoy

do "primary" colors exist?

For the past 400 years, the drug

of choice to combat the headachy symptoms of color complexity and substance uncertainty has been the primary color scheme.

The painter's three primary colors are the foundation of academic "color theory" (which is not really a theory), and some art school graduates develop a rigid attachment to primary colors and the formulaic approach to color mixing that goes with them. So it seems surprising to ask ... do "primary" colors exist? Even more surprising to learn that the answer is — no!

This page examines the history of painting, from ancient color theories to modern colorimetry, to identify the guiding principles of color mixture used by artisans.

A major theme is that "primary" colors are either imaginary or imperfect. That is, primary colors are either imaginary sensations you cannot see — and "colors you can't see" aren't really colors — or they are actual lights or paints that cannot mix all possible colors, which means they aren't really "primary".

I once received an email from an artist and "color theorist" who insisted that the subtractive (CMY) primaries were "the primary colors of the universe." The best antidote to that kind of fuzzy color worship is a historical review of how "color theory" developed, and why primary colors — imaginary or imperfect — were conceived.

We can pick up the story in 1613, when the Jesuit mathematician François d'Aguilon (1567-1617) of Brussels published his Opticorum libri sex (Optics in six chapters), illustrated with seven handsome engravings by the Flemish painter Peter Paul

the ancient primaries

colorvision

the ancient primaries

the painter's primaries

Newtonian color confusions

material trichromacy

comprehensive color models

perceptual trichromacy

colorimetry

imaginary orimperfect primaries

Rubens (1577-1640). D'Aguilon discussed the optics of the eye, linear perspective, surveying instruments, and the behavior of light and color, using practical demonstrations that would be of interest to painters. (For example, he describes partitive color mixing, a technique Rubens used with great skill.) When he touched on the origins of color and the rules of color mixing, d'Aguilon endorsed the medieval view that yellow, red and blue were the basic or "noble" hues from which all other colors derived.

françois d'aguilon's color mixing theory (1613)

the "primaries" are white and black (light and dark)

From a modern perspective, the most peculiar feature of d'Aguilon's theory is that these three "noble" hues were themselves created from the mysterious blending of white and black, or light and dark (upper curved lines in the figure), so that light and dark were the two "simple" or primary colors. The "composite" hues green, orange (gold) and purple (lower curved lines) were mixed from the "noble" triad colors. D'Aguilon's diagram was reprinted by the Jesuit scholar Athanasius Kircher in his optical treatise Ars magna lucis et umbrae (The Great Art of Light and Shadow, 1646). Both sources were widely read in the 17th century and shaped the explanation of color mixing dominant during the Baroque.

This light/dark color theory was inherited from medieval books on optics, which in matters of color borrowed from ancient Greek philosophical texts: an extended account in Plato's (c.390 BCE) creation poem Timaeus, scattered and inconsistent passages in the

writings of Aristotle (c.350 BCE), and the De Coloribus (On Color), sometimes attributed to Theophrastus (c.330 BCE), Aristotle's commentator and Lyceum administrator.

Three points to keep in mind about the ancient texts. First, color was a quality of substances or the surfaces of things, or of surface appearance altered by transparent media such as smoke, haze or water. Second, many Greek texts assert that sight was a kind of touch, produced by rays emanating from the eye, and (like touch) responding to the qualities of physical bodies. The ancients seem to have made no distinction between sight and light, so that distance, darkness or disease produced an equivalent "weakening" of colors. Third, the ancients had by modern standards a very erratic color nomenclature. In particular, the Greek words for white seem to have covered meanings such as white, light valued, bright, saturated, glowing, transparent, metallic, reflective (as in a mirror or water) or smooth, while black referred to black, dark valued, shadow, darkness, dull, opaque or rough, more or less. The modern color terms white and black, or light and dark, introduce different or more restrictive meanings than the ancient authors intended.

Aristotle's On Sense and Sensible Things observes that color only appears in reflected or filtered light that is not as bright as the illumination but is brighter than darkness. From this came the "conceivable hypothesis" that all colors appear due to variations in a "common nature or power", translated in English as the translucent, which allows sight to reach across space or into transmissive bodies such as the air or ocean. The translucent facilitates sight (which is equated with light), and an absence of translucency is produced by haze, smoke, shadow or darkness. The opacity and color of objects might arise from a fixed blending of invisibly small particles of white and black. And the purest or most intense colors might result from a whole number mixture ratio of light and dark, similar to the whole number divisions of a vibrating string that produce musical notes or harmonics:

Such, then, is a possible way of conceiving the existence of a plurality of colors besides the

white and black, and we may suppose that many are the result of a ratio; for they [white and black] may be juxtaposed in the ratio of 3 to 2, or 3 to 4, or in ratios expressible by other numbers; while some may be juxtaposed according to no numerically expressible ratio, but according to some incommensurable relation of excess or defect; and that those involving numerical ratios, like the concords in music, may be those generally regarded as most agreeable, as for example, violet, crimson and some few such colors, their fewness being due to the same causes which

render the concords few. [439b]

D'Aguilon's figure adopts this musical analogy as arcs over a straight line, like stops on a vibrating string. The clearest statement of the proportions of light and dark that produce colors appears in Aristotle's discussion of the rainbow (On Meterology):

White [bright, pure] color through a dark medium or on a dark surface (it makes no difference) looks red. We can see how red the flame of green wood is: this because so much smoke is mixed with the bright white firelight; so too, the sun appears red through smoke or mist. ... When the sight [light] is relatively strong the [color] change is to red; the next stage is green; and a further degree of weakness gives violet. No further change is visible, but three completes the series of colors. ... The appearance of yellow [in the rainbow] is due to contrast, for the red is whitened [lightened] by its juxtaposition with green. ... Bright dyes too show the effect of contrast. In woven and embroidered fabrics the appearance of colors is profoundly affected by their juxtaposition (purple, for instance, appears different on white and on black wool).

[374b]

These are almost the only colors which painters cannot manufacture, for there are colors which they create by mixing, but no

mixing will give red, green or violet. [372a]

Aristotle apparently preferred the rainbow or veiling media as examples of "natural" colors because they represented a "pure" display of color variation; paint mixtures just muddled different colors together. This preference was

maintained by the later Peripatetic philosophers who taught at the Lyceum. Thus, the De Coloribus advises that:

We must not proceed in this inquiry by blending pigments as painters do, but rather by comparing the rays reflected from the aforesaid known colors [white, yellow, and black], this being the best way of investigating the true nature of color-blends. ... [Thus], the different shades of crimson and violet depend on differences in the strength of their constituents, while blending is exemplified by the mixture of white and black, which gives

gray. [792a-792b]

And still later, the exclusion of subtractive mixture was expounded by Alexander of Aphrodisias (c.200CE), whose writings were well known in the Middle Ages and Renaissance. His commentary on Aristotle's On Meterology reveals a very fuzzy knowledge of painters' pigments and dye manufacture:

That the ... colors of the rainbow cannot be compounded or imitated by painters, and that red is closer to white than green and violet, is clear from the following. The natural [unmixed] red pigments are cinnebar and dragon's blood, which are made from the blood of animals; red is also made from the mixture [laking] of talc and purple, but this is much inferior to the natural colors. Natural green and violet are chrysocolla [malachite?] and tyrian purple, the one made from blood and the other from sea creatures. But the artificial [mixed] colors cannot match them: green can indeed be made [mixed] from blue and yellow, and violet from blue and red, for the contrasting energies of blue and yellow make green, but those of blue and red, violet; but in these cases the artificial colors are far inferior to the natural. ... That red is closer to white than to green and violet is evident from their origin. For red is made with [laked onto] talc, which is white, but green from ochre, which is a weaker [darker] white.

I've quoted these passages at length because they are the earliest descriptions of color change and color mixture. Yet they include several concepts that have been carried into modern color science. The quantity of light or luminance is the fundamental color

attribute. Color must be explained as a balance between the light (reflectance or transmittance) and dark (the absorptance) of substances. The proportions of light and dark produce the visible range of hue and hue purity. There are two types of color mixture — light interacting with materials or the atmosphere, and the blending of substances. Color should be studied only in the behavior of light. The blending of substances is a separate color change process; subtractive mixtures of green and violet were known to the ancients. These blended colors are inferior (dulled, polluted, lower in saturation) than colors in their "natural" form. Rules of color change must be deduced from the behavior of light in materials or the atmosphere; the color change in blended pigments and dyes can violate these rules.

The content of this section, but not the conclusions, relies on John Gage, Color and Culture: Practice and Meaning from Antiquity to Abstraction (University of California, 1993).

The ancient texts were penned by scholars in leisure, not by working artists. We do not have testimony about color from artists until the early Renaissance, when writings by painters about painting methods first appear.

The earliest of these artisan texts is by Cennino Cennini, who published circa 1390 a description of how a painter's work, especially in tempera, got done. His assumptions about color are apparent in his color inventory:

There are seven natural colors, or rather four which are actually mineral in character — namely black, red, yellow and green — and three natural colors which need to be developed artificially — lime white, the blues ultramarine [lapis lazuli] and azurite, and yellow.

Cennini's list of color names obviously refers to pigment colors, and divides them into "mineral" or "artificial" depending on the method of manufacture — the "mineral" yellow is probably ochre (iron oxide) and the

the painter's primaries

"artificial" yellow a laked organic pigment. He says nothing about rainbows, Aristotle, or "primary" colors. For painters, a primary color was a pigment color. But color blending is no longer disparaged. Cennini describes a method devised to model forms that curve from light into shadow (right). This approach uses variations in black or white to model illumination intensity across the same hue. The pigment (the hue) only appears in its pure (darkest and most saturated) form next to the shadow terminator; the terminator is pigment grayed by the underpainting color (a pale green or brown).

Philosophical texts written in the 16th century paralleled this change in approach: the Italians Simon Portius and Girolamo Cardano advanced the idea of an inherent luminosity to characterize each pigment color at its most saturated preparation: yellow is a "white" or light valued color while blue or red is a "black" or dark valued color. Colors ranked in this way retained the ancient light/dark ordering of "natural" hues, so the ancient texts were not contradicted. However "broken colors" — pigment mixed with white or black — created the color scale or tonal gradation needed by painters. The blending of pigments, which the ancient and medieval artists disliked because it obscured decorative (and often expensive) "pure" color, was justified as a method of representation.

As the Greek texts show, awareness and use of subtractive primary mixtures based on red (scarlet or carmine), yellow and blue colorants was already well known to ancient painters and dyers. Yet this longstanding painter's knowledge was not the painter's common practice. The primary triad was an unsatisfactory method for mixing colors because traditional pigments were not saturated and light valued enough to span wide differences in hue effectively. If painters wanted a dull scarlet color, they did not mix carmine and yellow lake: they started with a bright iron oxide or vermilion, then "broke" it with white or black.

Nor were the primaries useful to figure out complex or near neutral mixtures: painters

cennini's rendering ofillumination and shadow

C = pure color, W = white, Bk = black, U = underpainting;

after Kemp (2000)

instead relied on their experience with conventional methods. To create a flesh tone, medieval painters began with an thin underpainting of green terre verte, then glazed it with carmine. The exceptional colors that might be created by paint mixture were (and still are) greens and purples, for which there were only dull or hopelessly impermanent pigments. These colors are furnished as convenience mixtures even today.

Thus, the common practice of painters (and presumably also dyers) from ancient times through the Baroque reflects a completely different understanding of colors and color mixtures. There is no historical source prior to the 18th century that starts with three "primary" or "primitive" colors and explains how to mix all other colors from them. Mention by Alberti or Leonardo of the "artists' primaries" (red, yellow, green and blue) is not applied to explain paint mixing. When mixing techniques are described, focus is on specific color effects that are possible with specific preparations of pigments or grounds.

As a scholar personally acquainted with Rubens, D'Aguilon adopted red, yellow and blue, the subtractive primary triad familiar to painters and dyers of the time, as the fundamental sequence of colors produced by ratios of white and black. But again, these primaries are not recommended for color mixture but are used to anchor the ratios that produce orange, green and violet. D'Aguilon uses the Aristotelian framework to systematize facts, a characteristic tactic of 17th century intellectual culture, but by doing so he discards Aristotle's concern for the causes of color as displayed in light mixtures.

These changes are consistent with color materialism: the natural and obvious interpretation of color as something fixed, unchanging and inherent in physical substances or objects. This is the universal experience of color in the human species because it is the organizing principle of our color vision. Material colors and paint mixtures are now identified as "real" colors; all other colors, including reflections, shadows and Aristotle's beloved rainbows, are only

"apparent" or "accidental" — colors that are not material and that change inexplicably, like a peacock's tail, with point of view or angle of light. Abstract explanations of light and dark are displaced by practical explanations of pigment mixtures. D'Aguilon's account reflects these accumulated practical revisions to the ancient color theory.

Why then did the painters' primary colors become prominent? The broad answer is that the Scientific Revolution of the 17th century and the Enlightenment of the 18th century shifted the European understanding of "theory" away from airy concepts and logic and toward observable consequences and practical applications. By 1664, for example, early chemists were studying dyes and pigments in order to improve them, efforts motivated by the huge commercial importance of textile manufacture. This stimulated a a practical and scientific focus on artistic practice. Thus the Irish chemist Robert Boyle wrote in 1664 that the painter's "simple and primary colors" were black, white, red, yellow and blue, which could "imitate the hues (though not always the splendor) of those almost numberless differing colors" found in nature.

The Baroque's abstract and muddled "color theory" was overturned in the late 17th century by the widely discussed researches of Isaac Newton (1642-1726), first made public in his lectures at Cambridge University in the 1670's and finally published in his Opticks of 1704.

Newton's many innovations are described on another page, but a few key points are important here. He anchored the explanation of color not in substances but in the "refrangibility" (refraction) of light as it is spread apart by a prism or lens. He concluded that spectral "orange" or "violet" light is just as primitive or basic as "red" or "yellow" light, because none of these spectral hues can be broken down into a more basic color. However, they can be mixed in any combination to make all the colors of nature, including white and black and colors (such as

newtonian color confusions

magenta) not found in the spectrum. He concluded that the color of paints or surfaces arises from the selective absorption of some spectral hues and the reflection of others. Based on these facts, Newton rejected both the ancient Greek theory that colors arise from mixtures of light and dark, and the painter's theory that there were just three primary colors — red, yellow and blue.

Newton's work stimulated further color research, yet his observations and conclusions were often misunderstood and at times vehemently attacked, especially on the Continent. These confusions and controversies extend throughout the 18th and early 19th century color literature, and were the source of many color misconceptions adopted by artistic "color theory" developed during the 18th century.

1. Newton endorsed the idea of "primary" colors, because the solar spectrum seems to divide into a handful of homogenous hue bands, in contradiction to the continuous gradations observed in a prism spectrum and despite Newton's assertion that no spectral hue was more or less important than any other.

2. With the help of a sharp eyed assistant, Newton identified seven primary colors in the spectrum, apparently to fit colors to the seven notes of a musical scale; in doing so he rejected the three primaries useful to painters and dyers — red, yellow and blue.

3. Newton incorrectly asserted that the color of a paint was equivalent to the "color" of light it reflected — yellow paints reflected yellow light, blue paints reflected blue light, etc. (This 18th century falsehood is still taught today.)

4. Newton explicitly mentioned, but did not clearly explain, the difference between additive and subtractive color mixing — for example when he used three or four colored pigments and matching colors of light to make a "white" (gray) powdered mixture.

5. Therefore, Newton seemed to imply, especially in his pigment mixing examples,

there must be seven primary colors of paint which would mix in the same way as his seven primary colors of light. (The earliest known artists' color wheel explicitly adopts this assumption.) 6. Finally, Newton aroused intense intellectual animosity. He confounded the conjecture mongering Aristotelian scholars of the time by his empirical demonstration that "white" light is not homogeneous but compounded of various hues; he was attacked by English partisans of a "wave" theory of light for seeming to endorse the competing theory of light particles; in his earlier masterpiece Principia Mathematica (1686) he completely gutted the "vorticist" physical theory of René Descartes, inflaming the Cartesian scholars of France and Italy; and his prism experiments were difficult to replicate (especially by Continental naturalists) and in fact were not adequately verified until the 19th century. These partisans seized on any apparent falsehood or contradiction in Newton's theories as weapons to repudiate him.

So the 18th century public debate came down to this: Newton's hue circle was based on seven spectral "primary" lights, and made very specific predictions about the color that would result from any light mixture. For example, according to his hue circle, a mixture of "orange" light and "green" light would create the color yellow. Yet these prismatic mixtures were not easily verified by other naturalists, and it was quickly demonstrated that Newton's mixtures did not apply to paints, where orange and green make a cadaverous gray. Not realizing the difference between paint and light mixtures, and inflamed by partisan rivalries, many of Newton's adversaries used paint mixtures and the painter's primaries as proof that Newton's primaries (and hence his other color ideas) must be wrong. This wrangle went on for more than a century.

Yet Newton's scientific authority, and the potential usefulness of his analytical hue circle, were too attractive to reject completely. So artists found the

material trichromacy

practical compromise, and inserted pigment primary colors into Newton's hue circle. Even though Newton had shown that all hues were equally "primary," Newton's theory (like the ancient Greek theory) was revised to fit experience with paint and dye mixtures.

This revision occurred early, in an appendix to the Traité de la Peinture en mignature (Treatise on Minature Painting) by the artist "C.B." which was published in The Hague in 1708. This anonymous artist divided the color circle into seven hues in direct imitation of Newton's scheme, at the same time claiming that:

There are properly speaking only three Primitive Colors, which cannot be mixed from other colors but from which all other colors can be mixed. These three colors are Yellow, Red & Blue; as for White & Black, they are not colors properly speaking, White being no more than the perception of light, and Black the lack of this same light.

Here we encounter the conventional wisdom of artists and dyers stated in the formulaic brevity and specificity of an established theory. Color materialism is stated in terms of material trichromacy that has survived from the 18th century to present day. Its key principles: (1) the three primary colors are red, yellow and blue, (2) the primaries exist as three material substances (often identified with specific pigments), (3) the primaries cannot be mixed from other colors, but can mix all other colors. The contradictory fact that the three primaries cannot mix all other colors (as explicitly noted by Robert Boyle, quoted above) is simply ignored.

A second application of Newton's hue circle appears in "A New Theory for Mixing of Colours, taken from Sir Isaak Newton's Opticks," published in 1719 as an appendix to the New Principles of Linear Perspective by England's greatest perspective theorist, Brook Taylor (1685-1731). Taylor, himself an accomplished watercolorist, adapted Newton's hue circle whole cloth, replacing the spectral hues with matching colors of paint (including carmine, orpiment, "pink" or yellow lake, smalt and natural ultramarine). He carefully explained Newton's geometric method as a

convenience to guide paint mixing and to anticipate saturation costs. Although he warned that paint mixtures behave unpredictably and often very differently from light mixtures, Taylor did not seem to grasp the many fallacies assumed when using a color wheel to predict subtractive color mixtures. For example, he did not explain that mixture proportions must be adjusted to compensate for unequal paint tinting strengths. Many of these practical problems were solved in the third statement of material trichromacy, by the entrepreneurial German printer Jakob Christoffel Le Blon (1667-1741), in his Coloritto: or the Harmony of Coloring in Painting Reduced to Mechanical Practice (1725).

Le Blon is one of those many fascinating 18th century characters who focused a deep intellectual curiosity on an unexplored capitalist opportunity. He was an artisan who had read and actually understood Newton's Opticks, and credited Newton for the idea of describing color mixtures as a circle. A decade before, while in Holland, Le Blon innovated a system for using three separate printing plates, each inked with one of the painter's primary colors red, yellow or blue (and sometimes a fourth plate inked with black) to create full color mezzotint prints (right) — the practical basis for today's multicolor process printing. But his key innovation was to join Newton's hue circle with the three primaries of material trichromacy — red, yellow, and blue. He was also among the first color writers to state explicitly the difference between additive and subtractive color mixing:

Painting can represent all visible Objects with three Colours, Yellow, Red and Blue; for all other Colours can be compos'd of these Three, which I call Primitive. ... And a mixture of those Three original Colours makes a Black, and all other Colours whatsoever. ... I am only speaking of Material Colours, or those used by Painters; for a mixture of all the primitive impalpable Colours [of light], that cannot be felt, will not produce Black, but the very Contrary, White, as the great Sir Isaac Newton has demonstrated in his Opticks. White, is a Concentration, or an Excess of Lights. Black is

the second and final stagesin Le Blon's four color

printing method (c.1720)

a deep Hiding, or Privation of Lights.

Unfortunately his business venture to provide "printed paintings" ultimately failed, but Le Blon established the circular arrangement of painters' primaries as the definitive representation of color behavior, and his system inspired many imitators.

Among these, the English entomologist Moses Harris (1731-1785) published an especially elegant color wheel in his slim Natural System of Colours (1766), dedicated to the Royal Academy's Sir Joshua Reynolds (and reprinted in 1811 with a dedication to Benjamin West).

the color wheels of moses harris (1766) a 20th century reconstruction of (left) the Harris color wheel of mixtures between two "primitive" colors red,

yellow and blue; (right) the Harris color wheel of mixtures between two "compound" colors orange, green

and purple; note the imbalanced color distributions caused by the weak tinting strength of the blue pigment

Harris's book briefly summarizes the established dogma of material trichromacy as a kind of commentary to his color wheels, presented as full page, hand tinted engravings. Harris is notable for his explicit recommendation of complementary color contrast, which was a subject of keen interest to late 18th century color theorists:

"If a contrast is wanting to any colour or teint, look for the colour or teint in the system [wheel], and directly opposite you will find the contrast wanted. Suppose it is required what colour is most opposite, or contrary in hue to red, look directly opposite to that colour in the system and it will be found to be green, the most contrary to blue is orange, and opposite

to yellow is purple."

The Harris wheel became quite influential — it was studied and used by many 19th century English painters, including Joseph Turner — and it spawned many related color wheel systems: by English naturalist James Sowerby in 1809, colormaker George Field in 1817, and artist Charles Hayter in 1826. Throughout the 18th century, the politics of science were an important factor. As a rallying point for adversaries of experimental science, Aristotelian theory died very hard, and the painters' "primary" colors was one of its most durable defenses. The painter's color wheel, originally devised as a help to paint mixing, became something of an icon among Newton's detractors because it justified the subtractive RYB "primary" system that seemed to refute Newton's observations.

The French Jesuit mathematician Louis Bertrand Castel (1688-1757) — who famously claimed that "Newton has reduced man to using only his eyes" — strongly opposed Newton's experimental approach to science in favor of the "deduction from first principles" method used by mathematicians and geometricians such as René Descartes. In 1739 Castel advocated a trichromatic color spiral, in imitation of the musical circle of fifths, accompanied by a prism diagram labeled Vrai ("Truth", right), to demonstrate that all colors, including the spectral series, could be explained by overlapping mixtures of red, yellow and blue light. Castel's color wheel was adopted by the Viennese entomologist Ignaz Schiffermüller in 1771, who attempted to expand it into a color system.

Well into the 19th century, color researchers such as the German poet and bureaucrat J.W. von Goethe (1749-1832, diagram right) or the English color chemist George Field (1777-1854) were still espousing the ancient epic poetry of light and dark, and rejecting Newton, in essentially the same terms as Castel had decades earlier. The Scottish physicist David Brewster (1781-1868) was an especially pugnacious holdout, arguing as late as the 1840's that all spectral hues could be explained by red, yellow and blue fundamental colors of light, which Brewster

castel's color theory

hue circle and explanation of prismatic hues from

overlapping light and dark, color added for emphasis

after Kemp (1990)

equated with three colored filters or transmittance curves that could reproduce the entire spectrum (bottom diagram, right). Brewster's theory was dislodged only after Hermann von Helmholtz experimentally demonstrated that mixtures of "yellow" and "blue" light do not make a green mixture: the color is always either a reddish or yellowish gray. Artists focused on the practical guidance provided by the color wheel while ignoring the scientific debate. Perhaps the last artist to subscribe to the antinewtonian theory was the Romantic painter J.M.W. Turner (1775-1851) who, following Goethe, used yellow and blue in his paintings as symbols of the spiritual nature of light and dark. It wasn't until Turner's death, and the publication a year later of Helmholtz's early color researches, that the Aristotelian theory and its classical poetics lost its grip on artistic thinking.

So what became of the ancients' light and dark? Newton's hue circle dealt with changes in hue and saturation only, and left the paint wheel designers with little guidance as to how to represent changes in the brightness or lightness of colors. All the 18th century color wheel authors resolved this issue in terms of tonal gradation, placing either pure black or white paint at the center of the color wheel, mixtures of the primary colors around the circumference, and steps from the primary mixtures toward the center as increasing quantities of white or black paint.

Unfortunately these different mixtures have different effects on a paint's saturation or lightness. Mixing with white changes both saturation and lightness; mixing with black affects lightness only. And, as Newton showed, mixing two different hues of paint also reduces saturation and typically makes a paint mixture darker valued as well. As a result, the 18th century artists' color wheels prolonged confusion about the difference between lightness and saturation, a confusion that is still unresolved in the color hemisphere proposed by Michel-Eugène Chevreul in 1839.

J.B. Mollon's chapter "The Origins of Color Science" in The Science of Color (2nd ed.) (Elsevier, 2005)

19th century color theories that rejected Newton's

Opticks

(top) J.W. Goethe's Aristotelian theory of prism colors as

overlapping light and dark (1810); (bottom) George Brewster's three primary

explanation of spectral hues as overlapping red, yellow and

blue light (1831)

provides a fine account of color science since Newton, and distinguishes between physical and physiological trichromacy. Martin Kemp, The Science of Art: Optical Themes in Western Art from Brunelleschi to Seurat (Yale, 1990) is an astonishingly detailed review of the relationship between science and art, focusing on linear perspective but with three chapters on color theory.

During the same period in which the "primary" color wheel was becoming entrenched in painters' lore, and scientific factions were wrangling over the fundamental causes of color, a few 18th century color enthusiasts focused on a specific practical problem: how to define and represent all possible colors as a single color order system. These early color models were motivated by a scientific interest in summarizing color perception, by the need for a standardized system of color identification for use in science and industry, and by an artist's mystical enthusiasm for color.

All color models must grapple with four design requirements: (1) a color specification that defines all possible colors as a mixture of fundamental attributes, such as "primary" colors; (2) a geometrical framework that locates all colors in relation to each other and to the fundamental attributes; (3) a standardized system of unique color labels; and (4) pigment mixture recipes or physical color exemplars that can be used to match the abstract color specification to natural or manufactured objects. Color models in the 18th century proposed different solutions to these four requirements.

The earliest color system to contain all four components was apparently a set of color scales described in a Latin medical text published in 1677 by the English physician Francis Glisson (c.1597-1677). Glisson's scales are one of the earliest examples of psychophysics, or the quantitative measurement of color sensations in terms of physical color stimuli.

Glisson proposed his scales for the practical purpose of making diagnostically reliable

comprehensive color models

judgments of patient attributes (the color of hair, skin, urine, sores, etc.) and of natural objects. The geometrical framework for these scales, for example Glisson's scala nigredinis or gray scale, is a one dimensional ruler; the color specification consisted of 24 perceptually equal mixing steps between a pure pigment and black or white; the color labels were made by numbering the steps sequentially, from 1 to 23; and precise pigment recipes were provided to create the physical color exemplars. Thus, middle gray was halfway between black and white on the color ruler, contained 600 out of a possible 1200 parts of primary whiteness, was labeled gradus 12us, and was made with 5 measures of lead white and 1/10 measure of lamp black. (I've found similar mixture recipes to be useful in my own painting.) Glisson's scales extend the approach of Portius and Cardano, and they indicate that late 17th century English scientists were looking for an empirical method to match perceptually defined colors with exact mixtures of physical pigments. During the same decade, Newton proposed a similar quantitative approach, on the geometry of a circle rather than a ruler, to analyze the colors that result from light mixtures.

The Göttingen mathematician and astronomer Tobias Mayer (1723-1762), in a university lecture given in 1758, proposed the first comprehensive color order system. Mayer's color specification was based on the painters' three primaries, but Mayer claimed that the system could be applied equally to pigments or spectral lights. The example below, hand painted by Mayer and published in 1775, was obviously limited to paints.

tobias mayer's trichromatic mixing triangle (1758)

as published by G.C. Lichtenberg in 1775; Mayer's original concept was based on twelve color steps

between each primary color (red, yellow, and blue); the white dot indicates the color sample closest to a pure

gray

Mayer's geometrical framework was the equilateral triangle, with the three primaries at each of the corners (above). Color increments along the edges of the triangle between two primaries were defined by an eleven step mixing scale — notated with primary mixture proportions that always summed to 12 and were subscripted like a chemical notation (r11g1, r10g2, etc. to r1g11; — where r stands

for Röte or red, g for Gelb or yellow, and b for Blau or blue). These mixture codes served as the color labels. Mayer chose twelve color steps from one primary to another because his own investigations of human visual acuity indicated that more than 12 color gradations were not perceptually useful. Color mixtures inside the triangle were specified by a three color formula, for example r4g3b5 (again,

the proportions sum to 12), indicating the quantities of the three primaries necessary to mix that color. This defined 91 color samples in the pure pigment triangle. Finally, Mayer made the triangle into a multilevel color solid by mixing the color locations with either white or black paint to produce compounds of four primaries, for example, r3g2b4w3 or r6g1b3k2. (He did not

require mixtures of both white and black, as gray is obtained at alternate levels by equal mixture of the three primaries.) Because the proportions still add up to 12, each added increment of white or black reduces the number of combinations remaining for the three colored primaries and therefore reduces the edge dimensions of the mixture triangles. By stacking these triangles in tonal order above or below the middle, pure hue triangle, Mayer created a dark to light color hexahedron comprising 819 unique color mixtures (right). Using this system he described the color location of several common pigments — the first instance of a pigment color analysis using an abstract color system.

The breakthrough in Mayer's concept is the

tobias mayer'shexahedric color solid

after Grusser (1989)

equivalence between the primary color mixtures, the geometrical framework, and the color notation system. Any color can be analyzed into some mixture of the three primaries plus white or black. This "chemical" color analysis, which exactly anticipates the modern system of tristimulus values, also serves as the color's name; the name is the color's location within the easily visualized color solid. This was a great advance over Le Blon's industrial color mixing system because Le Blon left mixture proportions to the relative ink densities on the handmade mezzotint plates used to print them. Mayer embraced all visible colors in a single abstract measurement framework that (in principle) would apply equally to the natural colors of flowers or stars or the manufactured colors of pigments or dyes.

Unfortunately, Mayer stumbled over four practical problems: (1) Any set of three "primary" paints or lights cannot mix all possible colors, so his system is incomplete. (2) Mixtures of lights or pigments, notated the same way in his system, can produce very different colors — r0g6b6 is approximately a

"white" light mixture but a green paint mixture — so his system is not applicable to both colored lights and paints. (3) The geometry does not clearly represent the three colormaking attributes; there is no continuous white to black grayscale, or an explicit dimension of saturation, so color differences in his system are difficult to interpret. (4) Finally, Mayer did not solve the practical problem of translating his abstract colors into physical color exemplars: in particular, the tinting strengths of his primary pigments or lights must be exactly equated to produce balanced color mixtures. Failing that, the "gray" exemplar in his handpainted color triangle (marked by a dot, above) is not at the center but is next to pure blue, because the red pigment used had an overwhelming tinting strength.

These practical problems seem to have especially occupied the Prussian astronomer and perspective theorist Johann Heinrich Lambert (1728-1777), who published an account of his Farbenpyramide (Color Pyramid) in 1772. Lambert knew of Mayer's system and adopted its triangular geometry,

but limited to 7 step mixing scales between the pure primary colors. Lambert only expanded colors by mixtures with white, stating that black and gradations of gray could be found at the center of each primary mixture triangle. He tasked a Prussian court painter with transforming his conceptual color pyramid into encaustic color exemplars (wax providing both durability and the most brilliant colors), and he discussed at length the procedures necessary to equate the tinting strengths of his primary colors (carmine, gamboge and iron blue). Despite this, his gray sample, like Mayer's, is pushed too far towards the blue primary. Lambert offered his color model as a way for tradesmen (dyers, clothiers) and their customers to reliably identify and compare colors, and perhaps for this reason he rejected Mayer's intuitive but abstract notational scheme for a horridly hopscotch numbering system — from top to bottom down each diagonal, from the left triangle side to the bottom right corner — supplemented by compound color names ("chestnut red brown," "bluish reddish blue") that were better suited to the tradesman's inventory system and fashion patter. Lambert's model again treats hue, saturation and lightness unequally: the most unsatisfactory element in all 18th century color models is the color geometry. But a truly modern representation of colors, all correctly ordered around the three colormaking attributes was first achieved in the Farbenkugel or "Color Sphere", published in 1810 by the German Romantic painter and color mystic Philipp Otto Runge.

As his color specification, Runge derived all colors from mixtures of the primaries red, yellow and blue, plus white and black. But by interpreting Newton's hue circle as representing a slice through a sphere, Runge hit on the geometrical framework that is common to all modern color order systems. Lightness is measured by the polar axis (or latitude of the sphere), hue is represented by longitude around the equator, and saturation by the distance from center to surface. In his model, as he proudly (and correctly) announced, "Every color is placed in its proper relation to all pure elements as well as all mixtures." Unfortunately, the Color Sphere

lacked a color notation system or exemplification; and Runge died before he could define a system of color labels or develop physical color exemplars. But his hand tinted engravings of the model's exterior surface and interior sections showed that a physical model was entirely feasible.

The color systems of Mayer, Lambert and Runge show that 18th century color theorists grappled with the problems of color models piecemeal and from different perspectives, without achieving a comprehensive approach that unified color specification, color labeling and color exemplification within a geometrical framework consistent with the three colormaking attributes. (This story is continued in the page modern color models.)

Let's now turn to the perceptual side of the Enlightenment march of theory. Newton's proof that colors were not in the light forced the conclusion that they must be in the eye. However, the proposal that color sensations might arise from three different "particles" or "membranes" in the retina (the trichromatic theory of color vision) emerged only after the usage of three primary colors had been evangelized by 18th century painting and printing treatises and in the color models just described.

perceptual trichromacy

The Trichromatic Theory. A trichromatic theory was suggested several times in the century after Newton's Opticks appeared — by Mikhail Lomonosov in 1757, George Palmer in 1777, and the English physicist Thomas Young (1773-1829) in 1802 — but 18th century scientists lacked the optical tools to pursue the idea in depth. The hypothesis was revived, definitively stated and demonstrated by the renowned German physicist and physiologist Hermann von Helmholtz (1821-1894) in his On the Theory of Compound Colors (1850) and Handbook of Physiological Optics (1856). Helmholtz argued that just three types of "nervous fibers" or receptors were sufficient to produce the fundamental sensations of color, and he proposed three stretched out and overlapping sensitivity

three receptor sensitivity curves

proposed by Helmholtz in 1856

letters indicate spectral colors; diagram reversed to match

modern convention for spectral

diagrams

functions (right) to describe the response of these light receptors to different wavelengths of light. This is the core of what is now called the Young-Helmholtz three component theory.

Young is famous for stating and experimentally confirming the wave theory of light, based on his observation of interference bands created when a single beam of light is passed through two very narrow, closely parallel slits. His ideas were verified and extended by the French civil servant and amateur physicist Augustin Fresnel and the German optics manufacturer Joseph von Fraunhofer in the early 1820's. These wave experiments affirmed Newton's conjecture that each spectral color had a unique physical attribute (its wavelength or frequency) that determined the perceptual response of the eye's color receptors.

The logical crux of the trichromatic theory, nicely stated by Young, is that the almost infinite number of perceived colors could not possibly arise from an almost infinite number of different wavelength specific receptors in the eye: they couldn't all fit on the retina. So color perception must originate a small number of primary receptor cells, each tuned to a different part of the spectrum and present in every part of the retina. The blending of these different receptor outputs would create the perceived color variety. The painter's trick suggested this small number was three, tuned to colors that Young first suggested were red, yellow and blue (as propoosed by earlier authors, such as Palmer). By 1807, however, Young had changed his primaries to red, green and blue violet.

Nearly a century of research was necessary to confirm the existence of these color receptors in the retina — by microscopic dissection of retinas in 1828, the isolation of rod photopigment ("visual purple") in 1877, and exhaustive color matching experiments in the late 19th and early 20th centuries. These confirmed the essentials of Helmholtz's theory and Young's hypothesis that additive mixtures are best modeled by the additive primary lights red, green and violet (although it turned out that the human light receptors are actually most sensitive to yellow green, green and

violet wavelengths). Maxwell's Trichromatic Measurements. The Young-Helmholtz primaries were used in the first precise, quantitative color matching experiments, conducted in the 1850's by both Helmholtz and the brilliant Scottish physicist James Clerk Maxwell (1831-1879, right). Maxwell created additive color mixtures in two ways: by mixing colored lights through a system of prisms, mirrors and neutral filters enclosed in a long, flat box (a Maxwell box, the first modern colorimeter), or — the method he found more practical and accurate — by visually mixing circular wedges of colored papers on a rapidly spinning disk (a color top or Maxwell disk, shown at right). He demonstrated that any color of light could be matched by a specific combination of just three primaries, which he represented on his color top with the pigments vermilion (scarlet, PR106), emerald green (bluish green, PR21), and ultramarine blue (blue violet, PB29), and in his prism box by the wavelengths 650 nm ("scarlet"), 510 nm ("green") and 480 nm ("blue"). His colorimeter became the most widely used apparatus in modern color research.

In the original version of Maxwell's color matching experiments, the viewer looked through a small lens or eyepiece to see a round patch of illumination surrounded by a darkened field (right). This patch was divided into matching semicircles. The upper half contained a constant target color of "white" light. This was the color to be matched. (Maxwell found that "white" light was a convenient color target because it minimized the errors introduced by chromatic adaptation and the Helmholtz-Kohlrausch effect; and it allowed easy identification of the missing primary in colorblindness.) The lower half of the field contained the additive mixture of two monochromatic "primary" lights (R, G or B) and the test light (T), the light whose chromaticity he wanted to measure. The viewer was asked to turn a small knob to adjust a neutral density wedge filter, placed across the beam of each "primary" light, until their mixture, with the target light, produced a color match to the "white" upper half.

Maxwell's method depends on the fact that a

the young James Clerk Maxwell

holding his color top (c.1860)

Maxwell method of color matching

the intensities of two monochromatic primary lights are adjusted in mixture with a monochromatic test light (T) until the mixture matches the

"white" target field

"white" light mixture can always be produced by the mixture of any spectral color with two of the three additive primaries. (Which two depends on the hue of the target color: G and B must be used with "yellow" to "red" wavelengths, R and B with "green" wavelengths, and R and G with "blue" wavelengths.) First, the brightnesses of the three primaries are adjusted until they match the white standard: this identifies their relative proportions in a white mixture. Then one of the three primary lights is replaced by the test color, such as an orange light or colored paper disk, and the matching is repeated. By subtracting and renormalizing the contribution of the two primaries in the second white mixture from their contribution in the three primary mixture, Maxwell was able to define the test color in terms of the quantity of three primary values it replaced.

Maxwell organized his results as a "diagram of colors" — an equilateral triangle now more often called a Maxwell triangle. Any color can be specified in this triangle as the relative proportions of the scarlet, emerald green and blue violet primaries necessary to match it. The red color represented by the pure scarlet primary is located at the red corner of the triangle; the yellow color matched by equal mixtures of the scarlet and green primaries is located midway between the red and green corners; and the white color matched by an equal mixture of all three colors is located at the center — but only if the primaries have been adjusted to have equal luminance or tinting strength.

james clerk maxwell's "diagram of colors"

after Maxwell (1857); the proportions of the additive primaries red, green, and blue violet (exemplified by

the pigments vermilion, emerald green, and ultramarine blue) always add up to 1; the approximate location of

cerulean blue is shown as an example

Maxwell's Imaginary Primaries. But there was a catch. Maxwell used his color triangle to analyze the primary color composition of many common artists' pigments, only to discover that some pigments were more saturated than any mixtures of his three primaries could match. Thus, the artists' pigment natural gamboge (NY24) was a more intense yellow than any additive mixture of vermilion and emerald green on his color top.

Rather than add a fourth, (yellow) primary to his system, Maxwell chose to subtract chroma from the gamboge. He did this by visually mixing it either with a gray of equal lightness or with a desaturating quantity of the complementary blue violet primary. This shifted the gamboge color toward gray and brought the color back within the triangle, where it could be matched by a mixture of the remaining two primary colors. The amount of desaturating color required to make this match was used to estimate how far the chroma of the gamboge exceeded the gamut of the three primary mixing triangle. This method was extended and carefully explained by the American physicist Ogden Rood, who showed that this "subtractive" method permitted accurate measurements of pigment chroma even if the color was more intense than the visual primaries used in the analysis.

ogden rood's analysis of pigment chroma showing the location of pigments more saturated than any visual mixture of the three primary colors; adapted from Modern Chromatics (1879) with numerical values

omitted and pigment names modernized

In effect, Maxwell defined "primary colors" as mathematical or imaginary concepts, because the true primaries that could match the undiluted color of gamboge yellow would have to be much more saturated than the actual paint primaries used to match the dulled gamboge yellow on a color top!

This was a crucial step in the development of color science, because primary colors no longer had to be real colors, that is, paints you can actually spin on a color top or lights you can actually extract from the spectrum. Even though this seems to make no physical or perceptual sense, it reflects the fact that the mind never sees the cone outputs and therefore our visual primaries are imaginary colors to begin with. Maxwell's system of imaginary, mathematically defined primaries is so useful that it has become the standard method for specifying the appearance and mixtures of all colors.

the dudeen subtractive color mixing triangle

from John Sloan's The Gist of Art (1939); the primaries are cadmium lemon, alizarin crimson, and

phthalocyanine blue [winsor blue]

Rood's work was imitated in many subsequent pigment plot color triangles and color wheels, and for several decades of the early

1900's the triangle replaced the wheel as the trendy representation of artists' color mixing. The Dudeen color triangle, introduced around 1910 by the American artist Charles Winter (1869-1942), exports Rood's plot of isolated pigment colors into subtractive color mixing by replacing Maxwell's green primary with a yellow paint. Unfortunately, the triangle does not accurately represent paint chroma or saturation because Winter adhered to the 18th century artists' dogma that all colors can be mixed from three "primary" paints. For example, cadmium red light is more saturated than any mixture of cadmium lemon and alizarin crimson, yet the color is shown inside the triangle, meaning it is a color that can be mixed directly by those two primaries. Winter's triangle also ignores the many differences between light mixing on a hue circle and paint mixing on a color wheel (the "color wheel fallacy" caused by substance uncertainty), which set the precedent for today's mixing color wheels that reduce pigment measurements to the 18th century color wheel format.

Sources of Color Science edited by David L. MacAdam (Cambridge: MIT Press, 1970) conveniently gathers the important original writings of Grassmann, Palmer, Young, Helmholtz, Maxwell and others in a single volume.

But faulty artists' ideas were only a sideshow in the history of primary colors. Maxwell's color measurement techniques and approach to color specification, as presented to the Royal Society in the 1860's, are among the founding documents of modern colorimetry, the final step in our pursuit of "primary" colors.

At the outset, colorimetry was essentially the description of color matching experiments using three "primary" lights. That is, colorimetry was concerned with two tasks:

• develop a method to summarize any complex spectrophotometric curve as a trichromatic mixture of three "primary" colored lights; and

• using only the "primary" color mixtures,

colorimetry

predict whether two different lights or surfaces will visually match or appear to be the same color to a normal viewer.

Eventually, colorimetry evolved into the foundation of modern color models that aspire to explain all major color appearance phenomena under most any viewing conditions. But it also makes explicit what "primary" colors really are, and how they are used to explain color vision. The Metameric Foundation. Colorimetry is built on the principle of additive metameric colors. As mentioned earlier, metamers are any two different spectral emittance, transmittance or reflectance curves that appear to be the same color — that is, different spectral profiles that produce exactly the same relative stimulation to the L, M and S cones (assuming that differences in luminance can be adjusted away). Metamers arise in three situations:

• light metamers, different spectral emittance curves perceived as the same color

• material metamers, two different surface reflectance curves or filter transmittance curves perceived as the same color when each is viewed with the same light source (right)

• observer metamers, different spectral profiles perceived as the same color due to limitations in the viewer's visual responses (colorblindness or dark adapted vision).

Light metamers are extremely common, for two reasons: (1) lights may comprise any combination of wavelengths, from monochromatic to full spectrum; and (2) all lights are summarized by the eye as just three cone outputs. There is great flexibility in mixing lights, and great limitation in perceiving lights, so that the same color sensation can be produced in many very different ways.

The basis for color matching through the additive mixture of three "primary" lights is that light metamers can be generated by a specific combination of a small number of monochromatic lights. This is summarized as the additive metameric generalization:

reflectance profiles for three metameric grays

these appear to be identical middle gray surfaces when viewed under illuminant C

after Wyszecki & Stiles (1982)

provided they are arranged correctly, three "primary" lights can always produce a metameric color match to any color of light — provided that none of the primary lights can be matched by a mixture of the other two, and the luminance (brightness) of the lights can be freely adjusted.

The primary lights provide a common currency in which any spectral profile can be summarized as the relative power or luminance of just three monochromatic lights. This means, in turn, that two spectral profiles can be said to produce a visual color match if their trichromatic metamers are exactly the same. In this way, metameric color matching provides a procedure by which any color can be objectively compared with any other color — the foundation of the colorimetric framework.

the colorimetric framework two spectral profiles form a colorimetric match if they

are metamers for the same trichromatic mixture

Grassmann's Laws. The usefulness of these "primary" color matches might be trivial — if they only applied in situations that were "arranged correctly". But a few principles known as Grassmann's Laws greatly increase the importance of additive metameric matches by greatly expanding the range of circumstances in which the test light and its equivalent "primary" mixture will appear to be the same color. In modern colorimetry, Grassmann's original statements are summarized as three algebraic principles:

• Additivity: if a third light is mixed in equal

amounts with both the test light and the metameric mixture of three "primary" lights, the color match (metamerism) remains unchanged. (In algebra: if x = y [the colors match], then x+z = y+z [the match is unchanged].)

• Proportionality: if the luminance of both the test light and the three "primary" lights in the matching mixture are increased or decreased by an equal proportional amount (such as 10%), the color match remains unchanged. (If x = y then x*z = y*z or x/z = y/z.);

• Transitivity: If either the test light or the "primary" mixture is metameric with any third light or mixture, then either (a) the test light or (b) the "primary" mixture can be replaced by this third light, and both the additivity and proportionality laws will still govern the new color match. (If x = y and x = a, then a = y; and if also y = b, then x = b and a = b.)

Grassmann's Laws mean that a color match persists despite a change in color appearance. The test light and its matching primary mixture can be made dimmer or brighter, or mixed equally with another color of light, or replaced by a third matching light, and the two lights still appear to match, even though the color or brightness of the lights has visibly changed.

The last point means that all the color matches produced by mixing monochromatic (single wavelength) primary lights can be duplicated by passing "white" light through narrowpass (multiple wavelength) color filters, or even by changing the color of the "primary" lights themselves: one choice of "primary" lights can be replaced by another. Colorimetry builds on the fact that additive color mixing is both promiscuous and precise.

As an aside: it turns out that Grassmann's Laws are not true for many additive mixtures, most famously in the Helmholtz-Kohlrausch effect, and do not hold across changes in luminance adaptation, but they are true enough often enough so that color matches by themselves can unlock the basic perceptual structure of color.

Color Matching Experiments. We can motivate an explanation of the colorimetric system by looking at the specific problems that must be solved to measure the chromaticity of the spectrum locus — the single wavelength lights or monochromatic lights that define the physical limits of color vision — using the colorimetric method of trichromatic color matching.

First, it was discovered that Maxwell's color matching method, in which a trichromatic mixture is adjusted to match a "white" standard, tends to produce errors in the trichromatic specification of highly saturated colors such as monochromatic lights. So an alternative method of matching colors with a mixture of three "primaries," known as the maximum saturation method (right), was used instead.

The target color in the match is no longer white, as in Maxwell's method, but any single wavelength or complex (broadband) light mixture we choose. The viewer attempts to match this target color by a mixture of three real (visible) RGB "primaries" of monochromatic light, typically at wavelengths around 645 nm (R), 526 nm (G) and 444 nm (B). For all moderately saturated and near white colors, this arrangement leads to a direct color match; for all wavelengths above "yellow" (~570 nm), only the R and G monochromatic primaries are needed to match a spectral hue.

However, as Maxwell discovered, there are many colors, including many monochromatic lights, that are more saturated than can be matched by any mixture of three standard primary lights. In the conventional choice of RGB primaries, these hues include "green", "cyan", "blue" and "violet" lights on or near the spectrum locus, and highly saturated extraspectral "magenta" and "purple" mixtures. In these cases, the third primary is mixed with the out of gamut target color (shown in the diagram as R added to a "blue green" monochromatic light in the upper semicircular field), to desaturate the target color — move it toward "white" — until it can be matched by a mixture of the remaining two primaries (shown in the diagram as G and B mixed in the lower semicircular field).

maximum saturation method

of color matching

the intensity of a desaturating primary is adjusted until its

mixture with an out of gamut target color matches a mixture

possible with the remaining two primaries

The diagram (right) shows this solution in a generic chromaticity diagram. The RGB lights, located on the spectrum locus, define a triangular "real" gamut that contains all light colors that can be matched by a direct mixture of the RGB lights. The "out of gamut" colors that are within the chromaticity diagram but outside the RGB mixing triangle (shown as squares) must be matched by mixing them with one of the RGB primaries, to desaturate them. The quantity of the added primary, as shown by the arrows, measures how far the color's chroma exceeds the gamut of the RGB mixing triangle. Thus the RGB primaries are made to match the color — even though they can't match the color!

All colors that must be desaturated in this way are "out of gamut" or unmixable colors. They arise because of the asymmetrical curved or horseshoe shape of the chromaticity space. That is, the desaturating measurement technique is a way to get past a physiological obstacle to the measurement of color vision: the overlap between the L, M and S cone fundamentals.

Individual Differences. After color matching mixtures were defined by several viewers for all the spectral hues, large individual differences were discovered in the results. These were determined to arise from (1) the prereceptoral filtering of "blue" and "violet" light by the lens and macular pigment, and from (2) individual differences in the cone sensitivity curves, caused by genetic differences in the cone photopigments and in the proportional numbers of L, M and S cones in the retina. These individual differences constitute a physiological complication in the measurement of color vision.

In the late 1920's W.D. Wright realized that most of these individual differences or "errors" could be eliminated mathematically. The saving resource had been described by Newton: passing a monochromatic light through a colored filter does not change the color of the light, it only makes it dimmer. So the logical fix to the "yellow" filtering of light was to eliminate differences in the perceived brightness and tinting strength of the monochromatic RGB primary lights.

real (RGB) and imaginary (XYZ) primaries in relation to a chromaticity diagram

wright's WDW chromaticity coefficients his rescaling of the Stiles-Burch 1959 color matching

data (adapted from Wyszecki & Stiles, 1982)

Wright's adjustment involves two steps: (1) mathematically rescale the relative luminances of the three primaries for each viewer so that the R and G proportions are exactly equal at 580 nm ("yellow") and the G and B proportions are equal at 488 nm ("green blue") (equal tinting strength); then (2) normalize the luminances across all viewers so that the maximum value of each pure primary hue is 1.0 (equal brightness). This eliminates nearly all of the color matching discrepancies between observers, as shown above in the WDW diagram of mixture curves for 50 subjects with normal color vision.

The White Point. In order to revert these WDW corrected color matching proportions back to the relative proportions of monochromatic light required in the original metameric mixtures, or equate the colormatching results from different colored "primary" lights, the proportional radiance (radiant power) or luminance of the three lights must also be specified.

Either choice determines a fourth primary color, the pure white that results when the three monochromatic lights are mixed. The

location of this mixture in a chromaticity diagram is called the white point — the only color with exactly zero chroma. Thus, all trichromatic systems are defined by four primary lights — referred to as the cardinal stimuli. The abstract white standard is the equal energy illuminant (E), defined as a perfectly flat spectral power distribution. It is often used as a psychophysical standard because it produces exactly equal outputs from equal area cone fundamentals. This white balance requires radiant power ratios between the three "primary" lights of roughly 72.1 : 1.4 : 1.0 (R:G:B), which produce relative luminances of about 10 : 46 : 1 (diagram, right).

Despite the fact that short wavelength "primary" light is both visually dim and radiantly weak, it is able to counterbalance the high saturation (tinting strength) of the L cones and the high luminance of the M cones and the L+M mixtures. If we apply Newton's method of geometrical weighting to the luminances alone, then the centroid (C) is located substantially toward the G primary to give the S cones a compensating leverage. (Note the locations of the white point in this chromaticity diagram, which shows the relative contribution of foveal and wide field cones to a "white" color sensation.) This is the sense in which the S cone outputs are heavily weighted in color perception.

The equal energy illuminant is usually not used to define the white point in practical colormatching tasks, such as industrial color control; compared with natural daylight, the E illuminant has a faint magenta tint. Illuminants that approximate the chromaticity of artificial or natural radiant power distributions, especially CIE D65, D50 or A, are used instead.

Real Color Matching Functions. The WDW averaging of color matching curves and the luminance adjustments to a standard white result in the RGB color matching functions of three real, monochromatic primary lights. The r(λ) curve is more than 3 times higher than the others because "red" wavelength primary has a low luminance and moderate

the fourth primary

circle areas are proportional to the

luminance or radiance of the trichromatic "primaries" that

match an equal energy illuminant

(E); the centroid of the luminances is at C

tinting strength, so more of the R primary must be used to match the high luminance of the G primary and the high tinting strength of the B primary.

RGB color matching functions Stiles-Burch 10° color matching functions averaged

across 37 observers (adapted from Wyszecki & Stiles, 1982)

These are not the spectral emittance curves for the RGB primary lights used in the color matching. They trace the tristimulus values or proportional quantities of each R, G or B primary light in the mixture that matches the spectral hue at each wavelength. The negative tristimulus values indicate that the primary must be mixed with the target light — primarily R with "blue green" and most "blue" spectral hues and G with extreme "violet" hues. Each pair of curves intersects the zero line at the location of the third primary.

The tristimulus values are stimulus quantities determined by the physical properties of the "primary" lights. As a result, the curves are specific to the actual choice of primaries used: different primary lights result in different color matching proportions, which produce different tristimulus values. To avoid confusion, the primary lights are denoted with a capital R, and the tristimulus value of the light, the relative quantity

required in a color match at each wavelength, with a lowercase r(λ). Thus, in the example (right), 2.8 parts of the R primary light (read from the r(λ) curve), 0.6 parts of the G primary light (read from the g(λ) curve) and zero parts of the B primary light (read from the b(λ) curve) will produce an exact color match for a "yellow" spectral hue.

If the light is actually a mixture of many different wavelengths, then the tristimulus values for each wavelength are multiplied by the intensity of light at that wavelength, and the products are summed across all wavelengths to get the three tristimulus values. (The color of the white point light is simply the sum of all three curves across all wavelengths.)

Size of Color Stimulus. Now color researchers encountered yet another physiological complication to the measurement of color vision. Because the cones are unequally distributed across the retina, it matters how large and where the color stimulus appears in the visual field — that is, how it is imaged on the retina. This motivated the development of two different standards for color matching:

• The earliest color matching curves (circa 1890 to 1930) were based on a 2° or foveal presentation of color stimuli. (A 2° visual field is about the size of 1 inch viewed from a distance of 29 inches, or 10 cm viewed from 2.9 meters.) This was done because it was not then technically feasible to produce bright and homogeneous color stimuli across large visual areas, and because it minimized rod intrusion, or the mixture of rod and cone responses, in color matching of dim lights. As a result, the 2° mixtures are more robust across moderate ("reading light") to bright (noon daylight) levels of illumination. These curves are denoted by the date they were adopted (1931) or the field size (2°). Unfortunately, these early studies combined data using different primary lights (including filtered "white" lights), and estimated the relative luminances of the primary lights from the 1924 luminous efficiency function, which was later found to underestimate the luminance of short wavelengths. Judgmental revisions were imposed in 1951 to correct for

rgb color matching functions

CIE 1964 color matching functions

for the 10° standard observer and

the real (RGB) primaries

this, but the uncorrected curves are still occasionally used.

• Later (circa 1960), color matching curves were measured in a 10° or wide field presentation of color areas that extended well outside the fovea and filtering by the macular pigment. (A 10° visual field is about the size of 1 inch viewed from 5 3/4 inches, or 10 cm viewed from 57 cm.) These curves are based on two large, carefully screened samples of subjects who viewed monochromatic "primary" light mixtures at radiances well above rod saturation (except for extreme "red" mixtures, which were corrected for rod intrusion). These curves are also denoted by the publication date (1964) or the field size (10°). I use the wide field data throughout this site because human wide field color discrimination is about 2 to 3 times more accurate than foveal color discrimination, and because the "primary" light radiances were directly measured rather than inferred from a flawed luminous efficiency function; the 10° curves are also preferred for industrial colorimetry. The drawback is that the curves are most accurate at daylight levels of illumination and can succumb to additivity failures under mesopic light levels.

Imaginary Color Matching Functions. But we're still not done. The tristimulus values contain negative (subtracted) r(λ) and g(λ) quantities for the out of gamut wavelengths in the original color matching mixtures. As these negative values conceptually amount to saying that the photoreceptor pigments sometimes emit rather than absorb light, and as they are both an artifact of the maximum saturation method with real primary lights and of the overlap in the L, M and S cone fundamentals, a mathematical manipulation is applied to create three new imaginary XYZ primaries (as shown in the diagram above right).

The new mixture proportions x(λ), y(λ) and z(λ) are found by multiplying the RGB tristimulus values at each wavelength by a transformation matrix to get the XYZ color matching functions:

x10(λ) = 0.341r10(λ) + 0.189g10(λ) +

0.388b10(λ)

y10(λ) = 0.139r10(λ) + 0.837g10(λ) +

0.073b10(λ)

z10(λ) = 0.000r10(λ) + 0.040g10(λ) +

2.026b10(λ)

where as before λ denotes a specific wavelength.

This transformation does not undo the desaturating physiological obstacle to the measurement of color vision — it just turns it on its head as a supersaturated definition of the primary lights! That is, the XYZ primaries are outside the gamut of all real colors and are therefore invisible. No color of light or surface can reproduce them. However, their imaginary mixing triangle completely contains the chromaticity space of all real, visible colors, so all colors can be described as the positive mixture of the XYZ imaginary lights.

So here, at last, are the 10° (wide field) XYZ color matching functions:

1964 XYZ color matching functions CIE 1964 color matching functions for the 10° standard

observer and the imaginary XYZ primaries (from Wyszecki & Stiles, 1982)

All negative values have been removed, and the white point or achromatic standard is still defined by an equal energy illuminant. The XYZ tristimulus values are the fundamental stimulus metric used in colorimetry.

The Chromaticity Diagram. Each of the tristimulus values combines information about chromaticity (radiance in its part of the spectrum) and luminance (its part of the radiance across the whole spectrum). To obtain coordinates for a two dimensional chromaticity diagram, the effect of luminance on the tristimulus values is made constant, which is done by normalizing the values. That is, X and Y (the x

10(λ) and y

10

(λ) values summed across all wavelengths) are divided by the sum of all three tristimulus values:

The normalized z value is redundant, since the normalized weights sum to 1.0, so z can be recovered by subtraction:

z = 1.0 – x – y.

This leaves the normalized x and y values to indicate the chromaticity of the color. The curves are never displayed in the format we have used so far — value as a function of wavelength (right) — because hue (dominant wavelength) is what we want to describe. Instead, the x and y values are displayed as a two dimensional rectangular plot, which creates the CIE 1964 xy chromaticity diagram.

normalized tristimulus values

compare with the WDW diagram above

CIE 1964 xy chromaticity diagram the chromaticity diagram for the 10° standard observer, represented as the imaginary XYZ primaries normalized to give all colors equal brightness; colors are illustrative

only (adapted from Wyszecki & Stiles, 1982)

In this diagram the x,y values at each wavelength define the spectrum locus or the chromaticity of monochromatic light and the perceptual limits of color vision. All additive color mixing can be represented as the geometric mean of all chromaticities in the mixture, and two colors with the same chromaticity (x,y values), viewed in standard display and lighting conditions, will appear identical to normal viewers.

There is one last twist. Thanks to the specific transformation matrix used, the unnormalized Y primary (the y10(λ) color

matching function) is identical to a 10° photopic sensitivity function, so the y10(λ)

values define the apparent brightness of each wavelength. As a result, colors are commonly specified using Y for luminance and x,y for chromaticity.

Here also there is a muddle. The Judd-Vos luminosity function VM(λ), which is in

widespread use, is derived from 2° color matching functions that give unrealistically low

weight to the "blue" and "violet" wavelengths. The recently published Stockman & Sharpe 2° luminosity function V*(λ), which is not in standard use, gives a more accurate weight to the short wavelengths. It is also closer to the CIE 1964 y

10(λ) values.

The CIE Yxy Standard Observer. The WDW corrected XYZ values, in the form of the x,y chromaticity diagram and Y luminous efficiency function, represent the CIE Yxy standard observer — first published from 2° color matching data in 1931 and supplemented by 10° data in 1964. The standard observer is an idealized human retina that does very well at the limited task of predicting additive color mixtures and color matches that are viewed in isolation and at mid mesopic to photopic luminance levels.

Color matching data, repeated and varied across hundreds of different color samples and viewing situations for both normal and color deficient viewers, and archived in the color vision literature with light sensitivity and hue cancellation data, are the foundation texts of color research. They provide a quantitative basis for evaluating theories of color vision, and they stand for all the practical situations in which people say two different color stimuli do or do not create the same color sensation.

In addition, different transformation matrices can be used to convert the XYZ color matching curves into cone sensitivity curves, or to define the L*, u* and v* uniform perceptual dimensions of the CIELUV color model, or to define the L*, a* and b* opponent dimensions of the CIELAB or CIECAM02 color appearance models. Here, for example, are the CIE transformation equations that define the equal area cone fundamentals:

L(λ) = 0.390X(λ)+0.690Y(λ)–0.079Z(λ)

M(λ) =–0.230X(λ)+1.183Y(λ)+0.046Z(λ)

S(λ) = 1.000Z(λ).

Smith & Pokorny devised population weighted curves from the 2° standard observer so that the L and M functions sum to the photopic

sensitivity function V(λ):

L(λ) = 0.15516X(λ)+0.54308Y(λ)–0.03287Z(λ)

M(λ) =–0.15516X(λ)+0.45692Y(λ)+0.03287Z(λ)

S(λ) = 1.000Z(λ).

And here are Stockman, MacLeod & Johnson (1993) 10° cone fundamentals, calculated from the 1964 10° standard observer:

L(λ) = 0.23616X(λ)+0.82643Y(λ)–0.04571Z(λ)

M(λ) =–0.43112X(λ)+1.20692Y(λ)+0.09002Z(λ)

S(λ) = 0.04056X(λ)–0.01968Y(λ)+0.48619Z(λ)

We might pity an observer who, like Lieutenant Kije, exists only in official documents, but he has had an unusually productive career. The XYZ color matching functions enable electronic color measurement in thousands of practical applications. Light intensities are measured through three colored filters or photometric diodes with transmission profiles that match each function, or light intensities are measured at regular (usually 1 nm to 5 nm) intervals across the spectrum, then multiplied by the x10, y10 and z10

weights at each point and summed to get the total XYZ tristimulus values. These estimate the color's brightness and chromaticity as it appears to a "typical" viewer with "normal" color vision.

The chromaticity diagram, and the trichromatic or trilinear system it is based on, have several cool and useful properties — as backround, you may want to refer to the discussion of the trilinear mixing triangle:

• Three Number Color Specification. Every visible color must lie within the chromaticity diagram, which means all possible colors can be defined as a proportional mixture of the XYZ primary lights.

• Illuminant Adaptation. The definition of

the white point in the chromaticity diagram can be adjusted in relation to a second set of XYZ values, which define the brightness and chromaticity of the light source. In this way the standard observer can "adapt" to a wide range of viewing situations and predict illuminant based metamers.

• Luminosity Specification. The Yxy system defines the brightness of a color as its total Y value; its lightness is the ratio between the Y values of the color and a white surface under the same illumination.

• Hue Specification. The dominant wavelength of a color is defined as the point where the spectrum locus intercepts a line drawn from the white point through the color's x,y location in a chromaticity diagram.

• Chroma Specification. The hue purity of a color is approximately defined by its chromaticity distance from the white point. (In the original x,y chromaticity diagram, the relationship between chromaticity distance and chroma varied across hue, a problem largely fixed in CIELAB.)

• Straight Mixing Lines. The mixtures between any two colors of light, defined as points within the chromaticity diagram, are described by a straight line between them. (Beware! Mixtures of colors of paint, because they are surface colors, do not make straight lines in a chromaticity diagram or color space!)

• Visual Complements. The visual complement of any hue is defined by a straight line from that hue through the white point to the opposite side of the diagram. Thus, the visual complement of a "deep yellow" (580 nm) is a "greenish blue" (480 nm).

• Perceived Color Differences. The distance between any two colors on the chromaticity diagram approximates the perceived difference between the colors. Unfortunately, this approximation is very poor in the original x,y chromaticity diagram and Y brightness measure, but was substantially improved in the CIELUV u,v chromaticity diagram (for emitting colors) and in CIELAB and CIECAM

(for reflecting colors).

The intellectual elegance of this colorimetric edifice, built over a century of continuous work, is that all the essential information about an unrelated color — any color seen in isolation, from a single wavelength light to the most complex surface reflectance curve — can be captured, compared and contrasted with other colors through the mechanism of three numbers.

This completes my historical survey of "primary" colors. We began with the rudimentary color concepts of Greek philosophers and ended with the complex color analysis of 20th century colorimetry. I have tried to show how the idea of "primary" colors has evolved from vague abstract notions to specific technical concepts. Now I want to summarize this review as principles for artistic practice.

Two Primary Paradoxes. It is easiest to begin with the modern conception of primary colors and expand the discussion from there. The key conclusions can be stated as "primary" paradoxes.

imaginary or imperfect primaries

The first primary paradox is:

Primary colors are either imaginary, invisible "lights" that can describe all colors, or they are imperfect, real colorants that reproduce only some colors.

This double impossibility — you can't mix all colors with the primary colors you can see, and you can't see the primary colors that can mix all colors — arises from the physiology of color vision, the way the human eye is structured.

The sensitivity curves of the L, M and S cones overlap each other: every monochromatic (single wavelength) hue must stimulate two or even three cones simultaneously. As a result, the boundary of visible colors curves away from the "pure" primary corners of a mixing triangle, creating the horseshoe shaped chromaticity space of visible colors (right).

the first primary paradox

spectral primaries RGB, which are visible, can't mix all colors; mathematical primaries XYZ, which describe all colors, are

invisible

Because of its curved borders, the chromaticity space cannot be completely enclosed by any triangle defined by three monochromatic lights RGB around its border, and therefore all visible primaries cannot mix all possible colors — which makes them imperfect. Any three primary colors XYZ that completely enclose the chromaticity space, and therefore define all visible colors, must located outside the chromaticity space of real colors — which makes them imaginary.

The second primary paradox is:

All choices of imaginary primary colors are arbitrary; they are only measurement units. All choices of "real" primary colors are arbitrary; colorant selections depend on cost, availability, convenience, medium and image quality.

The imaginary primaries used in colorimetry are simply standardized units of measurement, like the meter, joule or yen. Just as the imaginary foot used in distance measurement does not represent a real human foot, the imaginary primaries used in color measurement do not represent real lights. Just as the meter could be longer or shorter and still work just fine as a standard unit of measurement, there is an infinite number of triangles of different sizes or shapes that would completely enclose the chromaticity diagram (right) and therefore would work just fine as a standard color gamut of imaginary primaries.

As with most measurement units, the imaginary XYZ primaries have been adopted in part for reasons of convenience. The transformation matrix used to define the imaginary primaries was chosen to reproduce the luminous efficiency function in the Y primary, but this was an arbitrary decision. All imaginary primary colors are arbitrary.

The material primaries are also arbitrary standards, but of a different sort. There is only one necessary restriction on the "primary" lights used in color matching experiments: they must form a triangle with all three corners inside the chromaticity diagram.

the second primary paradox

all real primary colors RGB, and all mathematical primaries

XYZ, are arbitrary choices

Otherwise, the shape and location of the triangle doesn't really matter. In fact, many different monochromatic lights and "white" lights tinted with color filters have been used color matching experiments: there has never been a standard or "best" set of RGB lights. They were chosen for a variety of operational reasons, then were transformed into the same XYZ system by using different transformation matrices.

The material primaries used in color reproduction (including painting, photography and video) are the outcome of a long and painstaking development of physical colorants (dyes, pigments, phosphors, diodes and lights) in chemistry, physics and engineering over the past three centuries. This development was marked at each step by tradeoffs or compromises. The colorants have not been standardized by laws of nature but by government codes and industrial standards, the envelope of feasible manufacturing costs, consumer expectations of longevity or durability, and accepted practices of color reproduction or existing color technologies. They also accommodate subjective standards of "good" and "bad" color reproduction for a given purpose in a given viewing situation. Compromise always occurs in color reproduction, which means all real primary colors are arbitrary. The diagram (right) shows the location of the subtractive magenta, yellow and cyan primaries, defined as optimal (maximally saturated) colors in the CIELAB a*b* plane. Painters who want to use a primary palette can chose from among the labeled pigments. Yet most painters will chose a hue of "primary" yellow that is too red, a "primary" magenta that is too yellow, and a "primary" cyan that is too red, rather than the optimal hue choices — cadmium lemon (PY35), cobalt teal blue (PG50) and cobalt violet (PV49). Why would they do this? Because the alternative selections are less granulating, more transparent, and mix darker values. They compromise to improve color quality.

Similar tradeoffs have determined the selection of commercial standards for video and photography (shown below on the CIELUV u*v* plane), and for commercial

optimal and actual primary paints

as located on the CIELAB a*b* plane

printing (shown here). Artists' pigments, film dyes and video phosphors can mix only about half the total range of visible colors , but this restriction avoids problems of impermanence (low lightfastness or chemical stability), high manufacturing cost, quality control and visual standards of image acceptability — especially in the imaging of flesh tones.

gamuts used in painting, photography and video

on the CIELUV chromaticity diagram; adapted from

Hunt (2004)

The arbitrary nature of real "primary" color choices appears across history as it does across modern media. Because of advances in chemistry and industrial manufacture, pigment selections have changed considerably over the past three centuries (for a history, see Bright Earth: The Art and Invention of Color by Philip Ball). In the earliest industrial color mixing system devised by Le Blon, the primary colors were a mixture of carmine, madder lake and vermilion (mixed to make red), yellow lake, and prussian blue — the best pigments for the job available in the early 18th century. The artists' color wheel proposed by Moses Harris used vermilion, orpiment and natural ultramarine. Charles Winter's 20th century mixing triangle used alizarin crimson, cadmium lemon and phthalo blue. Contemporary painters would probably

prefer hansa yellow, quinacridone rose, and phthalo blue.

Pigment innovation has even created entirely new primaries and new systems of color mixing. Thus, magenta was not identified as a subtractive primary color until the CMYK system was invented by Alexander Murray in 1934, because suitably lightfast magenta inks were unavailable before then. The CMYK system, in turn, cannot reproduce many saturated oranges, violets, blues and yellow greens, and in specific applications where brighter colors are required, newer printing systems with larger gamuts — Hexachrome™ (six primary colors of ink) or Heptatone™ (seven primary colors) — can be used instead.

What makes these tradeoffs feasible — and often unnoticeable in practice — is the remarkable ability of our color vision to accept different color images as equivalent or identical, provided the gamuts used to reproduce the images retain the relative relationships between all the colors in the image, especially relative lightness and hue. Thus, we can happily watch a Discovery Channel documentary on tropical birds, coastal reefs or erupting volcanos without noticing that the leafy greens, littoral cyans and magma reds are really much duller than they appear in life.

The reason we don't notice the color difference is that color vision treats all colors as arbitrary, in the sense that the accuracy of a color choice depends on the image context, viewing situation and viewer expectations. Video technology reproduces acceptable color relationships in context, so the image as a whole appears accurate even though separate image colors do not match the actual colors of the represented objects. (This topic is explored in the sections on color constancy and gamut mapping.)

Three Artists' Misconceptions. The primary paradoxes were already known in the 18th century, at least in the recognition that paints and dyes could only "imitate the hues (though not always the splendor) of those almost numberless differing colors" of nature, and that different colors (different pigments or dyes) could equally serve as a "primary" red,

yellow or blue.

Unfortunately, the recognition came long before scientific explanations of overlapping photoreceptor sensitivities, additive mixtures and gamut mapping were available. As a result, four misconceptions developed in the 18th century to explain the problems with primary color mixtures ... and many artists repeat them even today.

The first misconception is that "primary" colors must be visible colors, in the sense that an artist can pick a color of sticky paint or a wavelength of visible light and say, "there, that is the primary yellow". But the first primary paradox shows this belief is false. The "primary" colors that describe color vision are imaginary colors — and the mind never has direct experience of the "primary" signals from our three photoreceptors. The choice is not between one shade of color and another but between a visible color and an imaginary color. It is no more possible to find a paint that matches "primary" yellow than it is to find a horse that matches Pegasus.

The second misconception is that "primary" colors must be specific colors, in the sense that an artist can pick one color of primary yellow paint as the "nearest match" to the "true" primary yellow color, or that one primary yellow paint is the "best" primary yellow. (See for example the "color theory" book by Jim Ames.) But, as we have seen, the selection of real colorants is always arbitrary: it has much more to do with perceived image quality than with "objective" color characteristics. Almost any three colors can serve as primary colors, depending on how you want to use them. The only relevant issues are (1) the actual range of mixtures (gamut) you are able make with the colorants, and (2) whether this gamut produces the desired visual effect in the images you want to represent.

The third misconception is that none of the various colors of primary paints are the "true" primary color because all paint colors are "impure" or polluted by added light from the other two primaries. (See for example the justification offered for the split "primary" palette.) This is an especially quaint

anachronism from the 18th century, and it is wrong from several points of view. If a paint really were "pure" and only reflected a single wavelength of light (which is the "purest" possible color stimulus), the paint would have a luminance factor near zero and would appear blacker than the "purest" black paint! And that monochromatic "yellow" light is no more saturated than a mixture of a monochromatic "orange" and "yellow green" light, so light purity is not the cause of hue purity. Finally, even if our primaries were three "pure" colors of light (regardless of their hue), we still couldn't mix all other colors. "Purity" or pollution has absolutely nothing to do with the limitations of primary colors of paints or dyes. All three misconceptions are forms reification — the belief that primary colors are real. But if they are real, what do they consist of? The schematic (right) shows a sequence of physical or perceptual components that are currently used to explain the experience of color. The task for a "color theorist" is to point to a step in the diagram and say, "here is where primary colors are located". Are "primary" colors actually memory colors? Are they specific colorants? Are they produced by subtractive mixture, or additive perception? Are they cone outputs, or opponent codes?

There is no fixed location for a reified concept because it must apply to many different attributes of things in many different situations. The "primary colors" in the retina, in consciousness, in colorimetry, in color printing or in color television have nothing in common, either. All "primary colors" are a figure of speech, a fiction treated as a reality, not a feature of the world. If "color theorists" want to claim that primary colors are real, they have some fast talking to do!

These intellectual issues are inconsequential, however, because talk has little to do with procedure. From the Greeks through the Baroque, painters simply did what they did without an intellectual color theory to rely on. If they talked about "primary" colors, they meant the term to refer to types of colorants, not to recipes of light and dark, or yellow and green. Abstractions were used by the scholars, the philosophers and naturalists,

not by the artisans who actually worked with color. The same is true today. The "primaries" in color television or color printing evolved by research trial and error, manufacturing limitations and consumer acceptance, not by turning a crank on a "color theory" calculator. Then as now, there is a large gap between theory and experience.

For artists, any attempt to fuse color mixing with paints with an abstract, rigid system of "primary" colors runs up against an additional problem: the system cannot accurately describe actual paint mixtures. It also idealizes color relationships, divorcing them from the visual context of specific objects in space, or pigmented materials on a specific type of ground, as viewed under a specific intensity and color of illumination.

The conclusion of this historical excursion is that "primary" colors are only useful fictions. They are either imaginary variables adopted by mathematical models of color vision, or they are imperfect but economical compromises adopted for specific color mixing purposes with lights, paints, dyes or inks.

Primary colors are sometimes defended as a pedagogical simplification to teach elementary color mixing. But, as I propose elsewhere, there are better frameworks for that purpose, too. "Useful fictions" should be employed only when they are useful.

At bottom, the only justification for primary colors is to minimize the number of components required to mix all colors. This limitation makes biological sense if you are evolving a color sensing eye (and need to minimize the number of photoreceptor cells), mathematical sense if you want to model how that eye works (and want to do it with the fewest variables), economic sense if you are printing a color job (where each color requires a separate printing plate, ink, and pass with the printing press), or technological sense if you are manufacturing color televisions or computer monitors or color film (where each color requires a separate phosphor or dye).

But in every case the choice of primary colors is either arbitrary or imperfect. And if you are not building eyes or modeling color vision

responses or running a printing press or designing a computer monitor, and can inexpensively "expand your gamut" with four colors — or six, or twelve, or twenty — on your palette, then "primary" colors are irrelevant to the task before you.

N E X T : modern color models

Last revised 08.01.2005 • © 2005 Bruce MacEvoy

modern color models

The first six pages have

examined the fundamental aspects of color perception — the trichromatic mechanism, the three colormaking attributes that describe color sensations, the geometry of color (including the hue circle, opponent functions and response compression), the many basic forms of color, and the complex effects of context, contrast & adaptation, and finally the principles of additive & subtractive color mixing. This page describes the development of modern color models and discusses their relationship to these color fundamentals.

A color model represents the logical or perceptual relationships among colors of lights or surfaces. From the modern perspective, a color model must meet the following four requirements:

(1) a color specification that analyzes every light or surface color into a mixture of fundamental attributes (such as "primary" colors, trichromatic cone responses or tristimulus values, or unique hues);

(2) a geometrical framework that locates all the possible colors in relation to each other and to the fundamental attributes;

(3) a unique color identifier or color notation (now usually the numerical value of the three colormaking attributes — brightness/lightness, hue and hue purity) for every possible color; and

(4) a definition of physical exemplars, specific mixtures of lights or paints, that recreate the measured color perception when viewed within a standard surround under standard lighting conditions.

There are two kinds of modern color models. A color order system is based on a geometrical or enumerative framework that provides the color notation. The fundamental attributes used in the color specification are "pure" pigments or ideal colors; exemplars are

colorvision

the evolution ofcolor models

Swedish NaturalColor System

Munsell color system

OSA uniform color scales

CIELUVuniform color space

CIELABuniform color space

CIECAMcolor appearance

model

manufactured as pigment recipes in specific media. These systems are common in manufacturing applications based on visual color comparisons under fixed (standard) viewing conditions.

A color appearance model is based on a geometrical framework whose dimensions can be adjusted to represent the color changes caused by different illuminants, illuminance levels and surround contrasts. The color specification is based on color matching functions measured by spectrophotometer; these measurements produce the color notation and identify matching physical exemplars.

Contemporary artists' color wheels are color order systems that show only the hue/chroma relationships as defined in a more comprehensive color model.

There are many color models currently in use by scientists and designers, but I will describe six, including CIELAB — one of the simplest and most practical from an artist's point of view — and CIECAM02, probably the most complex model in current use.

We are so accustomed to our technologically enhanced, fashion nuanced and market driven color environment — our modern "color culture" — that it is surprising to realize how differently people experienced and thought about color just two centuries ago. There were no modern pigments, dyes or neon signs to dazzle human eyes. Color was a mysterious quality for laypersons and naturalists alike, and it was a difficult task simply to find reliable ways to attach a name to a specific color.

Color Naming. The earliest color labels are embedded in common speech. Every language has words to name colors, though in many primitive cultures only a handful of words are available, and the words make very gross distinctions between light and dark, or warm and cool colors. Thus the Black Sea is not black, but dark blue; its color name has been handed down from a time when the color

the evolution of color models

ideas green, blue, dark and black were denoted by the same word. This doesn't mean that primitive speakers could not see the differences between those colors, just that the differences were not conceptualized as abstract color categories.

As human knowledge and technology developed in areas such as painting, dyeing, weaving, ceramics, cosmetics, medical diagnosis, mineralogy, botany, horticulture, entomology and chemistry, more precise color comparisons across different kinds of materials became useful. This led to the development of color naming systems. The earliest and most obvious approach was to anchor color names on a distinctively colored flower, fruit, mineral or organic compound (dye) — and so we have the colors lemon, primrose, saffron, amber, gold, orange,

vermilion, rose, ruby, burgundy, carmine, violet, sapphire, turquoise, emerald, leaf

green, ochre, sepia, indigo, ivory, ebony and so on. The world itself was a reference book of color. During the 16th and 17th centuries, naturalists and their rich patrons collected samples of sea shells, corals, flowers, gems, minerals, ceramics and insects as a cabinet of curiosities, and these artifacts were sometimes used to identify and preserve unusual color exemplars from the natural world. As a result, dyers, printers and naturalists (especially botanists and entomologists, collectors of plants and insects) were among the most active color researchers during the 18th and early 19th centuries.

However, early color enthusiasts had no assurance that they had sampled the full range of possible colors — they did not understand the physiological limits of color vision, and therefore could not be sure that a new insect, coral, flower or gem might not reveal a hue that had never been seen before.

This uncertainty was swept away in 1704 when Isaac Newton published his Opticks, the first scientific analysis of color. Among the many stunning breakthroughs in this book was Newton's claim to have identified all fundamental colors — and by extension all possible mixed colors. Any color could be

reduced either to a pure spectral hue or to a geometrically defined mixture of spectral hues. Newton symbolized this intellectual closure as a closed circle: his hue circle. So ended doubt about the range of possible colors.

However, the practical problem remained that precise spectral mixtures were difficult to achieve until the mid 19th century, object colors were typically duller and more complex than the colors of mixed spectral lights, and all those complex colors still had to be identified with a name and captured as a physical exemplar. In fact, the last two requirements were the most important and the easiest to fulfill. So naturalists had to derive their color identifications and color labels from a color atlas, a tradition solution that extends from A.G. Werner's Nomenclature of Colors (1774) up to Robert Ridgeway's Color standards and color nomenclature (1912). These provided a series of hand painted colored patches as a visual standard for each color, with the color's name and, in earlier versions, a list of flowers, insects or minerals that exemplified the color in nature. Similar tools are still used today in horticulture, agriculture and food processing.

Color Mixture. If naming the color was incidental to using it, then colors could be reduced to a recipe or proportional mixture of a few standard colorants or "primary" colors. The entrepreneurial printer Jakob Christoffel Le Blon first applied this approach to the industrial task of color printing, by showing that color images could be created from three primary or "primitive" colored inks, usually supplemented by a fourth black ink, one ink printed over another with separate, carefully aligned mezzotint plates (a technique developed earlier in woodblock printing of book illustrations). Multicolor printing systems similar to LeBlon's, though not commercially successful, continued up to the end of the 18th century; the multicolor printing method was revived when chromolithography was invented in the 1860's, which did not become widely used until the 1890's. But from that time until today color printing systems based on standardized ink colors and mixture recipes have been universally used by commercial printers for mass reproduction of color images. Modern color mixing systems include the four

ink process (CMYK) color system (developed in 1934), the 14 ink Pantone™ color system, and the six ink Hexachrome™ color system, to name a few.

The Pantone and other printing systems are based on standardized printed color samples, each color reproducible as a carefully proportioned mixture of a limited number of "primary" inks. These are really "color cook books" tied to specific technologies of color reproduction, and they require the graphic artist to visually select from a limited (though sometimes very large) index of printed color samples. These books provide no way to visualize how all the colors fit together, in the same way that a city phone directory gives you no idea of how the city looks on a map.

Color Models. This need for a geometrical framework or map of color brings us to modern color order systems, which put every color in its place and specify colors as combinations of fundamental color attributes. Arguably the first color order system was proposed by the German astronomer Tobias Mayer as a university lecture in 1758. Mayer offered his system, which was not published until 1775, as a concept, but he described how to analyze all colors as "primary" color mixtures, showed lightness as a completely separate dimension of color from hue, and demonstrated how the system could be used to identify or compare object colors, such as the colors of pigments. Mayer relied on visual color matching to meet the first requirement of a modern color model (stimulus measurement), but he showed how a consistent geometrical framework could provide unique numerical labels for colors. The first color model to adopt the three dimensional framework that has become standard in color science was the Farbenkugel or "Color Sphere" proposed by the German romantic painter Philipp Otto Runge (1777-1810) in 1810 (right). The sphere contains the white to black value scale as its polar axis, and Newton's complete hue circle of pure or maximally intense hues as the equator. Runge's hue circle is also one of the first to divide the hue circle into "primary", secondary and tertiary hues. As Runge proudly claimed:

It will be impossible to think of any nuance produced by a mixture of the five elements

(blue, yellow, red, white and black) and not contained in this framework; nor can the

whole system be represented by any other correct and complete figure. And since each

nuance is given its correct relation to all the pure elements as well as to all mixtures, this

sphere must be considered a universal chart, enabling anybody to orient himself as to the

overall context of all colors.

Michel-Eugène Chevreul followed with his own "color hemisphere" in 1839, and abstract color systems became one of the minor achievements of 19th century European scientists and the artists who studied their works.

Color Model Assumptions. The geometrical framework used in modern color models consists of the three colormaking attributes arranged to define a three dimensional space. The figure below shows how this is done. The vertical black to white dimension is the lightness or value of a color; the circumference of the horizontal disk perpendicular to the lightness dimension is the hue of a color; and the lateral distance or radius on this disk, from the center outward, is the chroma (approximately the saturation) of a color.

the geometry of colormaking attributes in modern color models

Notice that this arrangement allows hues to

one of the first modern color

models: Philipp Otto Runge's

"color sphere" (1810)

top row: exterior views of the

white and

black "poles"; lower row:

horizontal and

vertical slices through the

sphere

change gradually from one to the next, but defines chroma and lightness as rulers or ratio scales starting from a definite zero point — black for lightness, and gray for saturation.

Color models differ in the specific assumptions that are used to define the color geometry and color labels and the specific measurement methods used to link the geometry to color stimuli and color exemplars. My selection of color models is intended to highlight these differences:

• Geometrical Uniformity - The perceptual facts of color are tremendously complex, and many early models emphasized a geometrical or logical framework that summarized color in a simplified way. These systems use visual color matching to measure colors, appeal to the phenomenology or subjective relationships among colors, and emphasize a framework for verbal color communication. The best modern example is the Swedish NCS color model.

• Perceptual Uniformity - Here the goal is to create a color geometry where the units of measurement stand for equal apparent color differences on all the colormaking dimensions. Perceived color differences determine the color geometry and exemplification as physical color samples. The classic modern example is the Munsell Color Order System; very different recent examples include the OSA uniform color scales and the CIE 1976 UCS (uniform chromaticity scales) diagram.

• Trichromatic Colorimetry - Increasingly, modern color models are linked to the electronic measurement of spectral emission or reflectance profiles, expressed as a mixture of three imaginary "primary" lights called the XYZ tristimulus values. This standardizes the "viewing eye" used to compare colors and allows automated color matching. The modern examples of this approach are CIELUV and CIELAB.

• Color Appearance - The earliest color models only described colors that were viewed or compared in a standardized viewing situation. In the past few decades, more ambitious color models have been developed that adjust the color space to represent the effects of the visual context (the illuminant,

surround and background colors) and extreme viewing conditions (small or large color samples, dim or bright illumination). This raises them to the status of color appearance models — color models that predict a wide range of real world color experiences. The current example of this approach is CIECAM02.

An authoritative summary of the development and empirical foundations of modern color models is Rolf G. Kuehni's Color Space and Its Divisions: Color Order from Antiquity to the Present (Wiley Interscience, 2003). For an interactive tutorial on historical color models, see J. Frans Gerritsen's Evolution in Color (Schiffer, 1988).

The best technical overview of modern color order systems, uniform color spaces and the newest color appearance models and prototype image color appearance models (ICAMs) designed for color reproduction technologies is Mark Fairchild's Color Appearance Models (2nd ed.) (Addison Wesley, 2005); see also the updates and information at Fairchild's web site.

There's a delightful menagerie of historical color models, based in part on Gerritsen's book, collected at the Colorcube web site. The most comprehensive historical review of color theories, with ample illustrations of each color model, is provided at the Colorsystem Virtual Color Museum. For an archive of historical color model illustrations, see the page by Dr. Hans Irtel.

Two different European approaches to color emerged by the middle of the 19th century. One relied on a quantitative description of color via the methods of psychophysics, a tradition founded by James Clerk Maxwell and Hermann Helmholtz. This approach originated in the work of Isaac Newton and laid the foundations for the color system of Albert Munsell and the many CIE colorimetric color models.

The alternative approach, which became dominant in European philosophy and visual arts, emphasized the logical description of color experience. Color was idealized as "pure" sensations, organized as verbal or geometrical models of color relationships. The Swedish Natural Color System (NCS), proposed by Tryggve Johansson in the 1930's and

Swedish Natural Color System

eventually realized by Sven Hesselgren and Anders Hård at the Scandinavian Colour Institute in the 1960's, is a modern color model that exemplifies this approach. The NCS is currently a color standard in several Scandinavian and EU countries.

The experimental pedigree of the NCS goes back to Ewald Hering's Das natürliche Farbsystem (1905), which describes colors as the result of opponent color processing and the mixture of four unique hues plus black and white. Hering's was a phenomenological or subjective approach to color: he tried to describe the universal patterns or laws of our color experience without specifying what kind of external stimulus or internal color receptors might produce it. This phenomenological approach can be traced from Hering back to the Romantic German philosophers Arthur Schopenhauer, Georg W.F. Hegel and ultimately to J.W. von Goethe — although those authors and their philosophical concerns were of little practical use to the artists of their time.

Four Components of NCS. This phenomenological or "in the head" approach to color modeling is based on four components.

The first is a single, universal color specification formula:

color = C(u1+u2) + S + W

where C represents the apparent proportion of pure hue (chromaticness) in the color, S (German Schwartz) is the apparent proportion of black in the color, and W (German Weiss) is the apparent proportion of white. The chromatic ingredient consists either of a single unique hue, or more commonly of the mixture of two adjacent unique hues, shown as (u1+u2). Hering called any color

mixed with either white or black (or both) a veiled color, and by these mixtures accounted for all dull, diluted and near neutral colors.

The basic formula has a long pedigree. The Western painting tradition used the technique of broken color to adjust pure pigments

(high chroma) colors by mixture with white and/or black paints, a method described by Cennini, Alberti and Leonardo. The same mixture geometry is used in Michel-Eugène Chevreul's color hemisphere. Hering's color specification was also used by the German chemist and Nobel laureate Wilhelm Ostwald (1853-1932) in his Mathetische Farbenlehre (Quantitative color theory) published in 1917 and exemplified by the Farbkörper (Color Atlas) published in 1919. Ostwald's system was very influential among the artists and designers of De Stijl and the Bauhaus.

The second component of the phenomenological approach to color is a restricted version of the universal color geometry. The four Hering unique hues are arranged to create four cardinal points around the hue circle, as shown in the figure. Following Hering's original concept, the y/b and r/g opponent functions define two dimensions at right angles within the hue circle. Antagonistic unique hues, which are not allowed to mix in Hering's theory, are on opposite ends of the two dimensions. The third opponent dimension defined by white and black is placed perpendicular to the first two.

three color dimensions defined by the hering colors

The third component consists of two color mixing rules:

(1) Only unique hues on different opponent dimensions can be mixed; unique hues at opposite ends of the same dimension cannot be mixed. (That is, we are not allowed to make "yellowish blue" or "reddish green" mixtures.)

(2) White and black can mix with each other,

and with any hue mixture, in any proportions; this provides the full range of shades, tones and tints for any hue.

The fourth and last component is a fixed sum for the color specification:

C(u1+u2) + S + W = 100

in the same way that mixtures in Tobias Mayer's color hexahedron must sum to 1. This forces the color geometry into a triangular (conical, hexahedral) form.

NCS Color Model. These four design components interconnect the six Hering colors as 13 elementary scales — a single gray scale (white to black), and three chromatic scales for each hue (e.g., red to white, red to black, and red to gray) — that measure off mixtures among the six cardinal colors.

The basic mixing formula color = C + S + W = 100 dictates that the model is most conveniently represented as vertical sections, called hue triangles, that include one pure hue or hue mixture, pure white and pure black as the three corners of an equilateral triangle. This is equivalent the geometry of two cones joined at their base that was used in Ostwald's system, as shown below for the 13 elementary scales and a purple (mixed red and blue) hue section.

geometrical framework of the swedish NCS color model

The NCS is exemplified as the NCS color atlas, a large book of standard color

swatches. The atlas contains 40 of these hue triangles at equal intervals around the hue circle — nine steps (increments of 10% mixture) between each pair of adjacent unique hues. The atlas also includes a representation of the complete hue circle at maximum chroma, a lightness scale from white to black, and several "off white" color samples as a help to specifying pastel colors.

Each hue triangle displays a wide selection color samples made from mixtures of the pure hue with black (S) and/or white (W). Lines of equal black mixture are shown as diagonal rows parallel to the top edge of the triangle; blackness increases from the top edge to the bottom corner. Lines of equal whiteness are shown as diagonal rows parallel to the bottom edge; whiteness increases from the bottom edge to the top corner. As a result, gradations in chroma (C) are represented by vertical columns through the triangle, from the left corner (the maximum chroma), which contains no white or black, to the gray scale along the vertical edge. Color samples for the pure hues, white and black are omitted due to the limitations of available pigments, and very dark or near neutral samples are usually omitted to reduce production costs and visual clutter.

a page from the NCS color atlas 96 (standard version)

The NCS notation or color labeling defines the visual appearance of the color and shows how to find it in the NCS color atlas 96 (1996), represented by the sample page above. The tonal mixture is stated before the hue. The first two digits give the percentage of black in the color, followed by the two digit percentage of pure color. (The percentage of white is omitted, as it is equal to the other two percentages subtracted from 100.) Next, hue mixtures are notated with letters for the two unique hues contributing to the mixture, bracketing the percentage of the second hue in the mixture: Y60R represents a red orange mixture of 60% red and (by subtraction) 40% yellow. Pure hues are notated simply R, Y, G or B. Thus, the full notation S 1060-Y60R represents (1) a pure hue that is mixed from 60% red and 40% yellow, and (2) a color that is mixed from 10% black and 60% pure hue (and 30% white). Achromatic (gray) tones are indicated simply with the proportion of black, followed by N for neutral: S 1500-N represents a light gray containing 15% black (and 85% white).

A significant feature of the NCS is that all the pure color standards are imaginary: the point of comparison for a pure white or pure yellow is visualized in the mind, and color mixtures are judged against these ideal standards. (This is why there are no color swatches at the points C, S or W in the sample hue triangle above: no pigment can match these pure, ideal colors.) This was consistent with Hering's original phenomenological color definitions, but it was also validated by experiments that showed people were just as accurate judging color mixtures from ideal (imaginary) color standards as from physical color samples.

Using and Interpreting the NCS. The NCS was created primarily for communicating about color in everyday and design applications, because its simple color geometry and direct relationship to visual color judgments makes color easy to describe. The only "measurement tool" necessary is a person with normal color vision, training in the NCS notation conventions and access to an NCS color atlas to use as a reference. (As with Munsell, viewing conditions must be carefully standardized if color

judgments are to be comparable.)

A designer or architect who wants to communicate a specific color standard simply estimates the mixture of Hering colors that creates it, finds the matching color in the NCS color atlas, and determines the color's NCS color notation. A textile mill or construction company then uses the NCS notation to identify the color sample they should match in fabric or wall paint. The major drawback to this method is that most people find it very difficult to identify dull or dark colors (browns, tans or maroons in particular) in terms of saturated unique hue mixtures. The geometrical simplicity of the NCS introduces some significant distortions or complications into the perceptual color space. Because the four Hering colors are not equally spaced around a perceptual color circle (as shown for example on the CIECAM acbc plane), the hue differences around the

NCS color circle are not perceptually equal, either. Differences between the yellow green hue triangles are perceptually very small, while hue differences between the blue green and purple hue triangles are quite large. This means fine color discriminations are possible for yellow green colors, while the blue green and purple colors require some guesswork. In addition, the chroma spacing is unequal from one hue to the next, and from neutral to intense colors within any hue (right).

In addition, for most parts of the color circle, opposite colors are not "mix to gray" visual complements, because the unique hues themselves are not visual complements. The visual complement of unique red is not unique green, but a blue green located at roughly G40B; the visual complement of unique blue is not unique yellow, but a deep yellow at roughly Y30R. Finally, the artist's mixing complements are also different from the NCS complements. And while the NCS establishes new complementary relationships, there is no evidence that these are more (or less) pleasing or effective than the complementaries defined in other ways.

Most perplexing, the "pure" hues at maximum chroma vary significantly in lightness around the color circle: an intense yellow is

lines of constant NCS hue and

chroma plotted on theCIELAB a*b* plane

after Kuehni (2003)

much lighter than an intense blue, but in NCS they are all notated as containing no black and no white, and are placed at the same halfway point on the vertical white/black dimension. This means that the white/black mixture does not consistently describe the actual lightness of colors, and all the mixture intervals (columns and diagonal rows in the hue triangle) do not define comparable steps across different hues. For a light valued yellow hue, the 10 gradations in W (between yellow and white) are perceptually quite small, while the 10 gradations in S (between yellow and black) are quite large. For a dark valued blue violet, the reverse is true. This is entirely consistent with the Hering definition of black as a color rather than as the absence of light, but it makes the NCS noncomparable with other color systems based on lightness.

The benefit of this apparently arbitrary relationship is that different hues at the same location within their respective hue triangles — that is, hues identified with the same whiteness and blackness numbers (S1060 for the orange in the illustration above) — have the same nuance, and nuance is an effective way to equate colors, as described in the page on color harmonies.

Most color order systems that build on a simple subjective or geometrical framework have similar drawbacks. These are not serious as long as the models are used only as a way to label and communicate about individual color samples, but the NCS must not be used to model perceived color differences. And these drawbacks may even be an advantage in color design, for example when equating the apparent whiteness of various hues in pastel color schemes.

In general, however, the phenomenological and geometrical approach did not generate much interest among American and British research psychologists, who turned instead to psychophysical methods of color scaling.

For more information about the NCS and related color products, see the NCS web site.

Munsell Color System

The Munsell Color System is arguably the first modern color order system — based on the three colormaking attributes, and implemented through careful color measurement. Conceived in the 1890's by the American artist and educator Albert H. Munsell (1858-1918), it was described as a theoretical color model in 1905 and exemplified as a 15 page atlas of color samples in 1915. (This was extensively revised and republished in 1929 as the Munsell Book of Color, comprising 20 hue pages that each contain about 20 color samples.) The Munsell system was extensively revised or "renotated" in the early 1940's, when it was adopted as the standard color reference system in the USA. It remains one of the most popular and widely used color order systems.

Munsell originally conceived of his system as a method to describe color for artists and teach color to children. He was aware of the European, geometrically regular color models of Chevreul, Wundt and others, and at first conceived (and patented) his system as a color sphere. But with a typically American empiricism, he convinced himself through analysis of paint samples that color space was not geometrically regular. Instead, Munsell sought to build his model on equal perceived color differences on each colormaking attribute, linked in some cases to measurable changes in color stimulus composition, in a freely branching geometry called a color tree.

Munsell was inspired by and heavily relied on the expertise of the American physicist and color researcher Ogden Rood, who showed Munsell how to use a color top to analyze complex colors into additive color mixtures of "primary" colors, and to develop gray scales based on proportional mixtures of black and white. With this method Munsell was able to simulate incremental steps in chroma (proportional mixtures with gray) or hue (by proportional mixtures of "primary" colors, or analogous colors such as red and yellow), and to identify visual complementary colors (saturated hues that additively mix to a pure gray). Over a decade of patient, incremental work, Munsell analyzed reflective or surface colors into their component lightness, hue and chroma, published in his atlas as equal apparent differences on each of these

colormaking attributes.

Geometry of the Munsell System. The backbone of the Munsell system, the "trunk" of the color tree, is a vertical dimension of lightness or value, which was developed through human perceptual judgments of equal differences in lightness across visual (color top) mixtures of white and black paints. The Munsell value scale ranges from pure black (0) to pure white (10); each step is divided into decimal increments, resulting in a 100 step lightness scale. At the middle value level is a hue circle defined by five equally spaced hue dimensions — red (R), yellow (Y), green (G), blue (B) and purple (P) in clockwise order (yellow at the top, red on the left). These principal colors are separated by five mixture hues between them — yellow red (YR), green yellow (GY), blue green (BG), purple blue (PB), and red purple (RP) — each the visual complementary color of the principal hue directly opposite it. These principal and mixture hues divide the hue circle into ten equal hue segments, and each hue segment is again divided by ten (counted in the clockwise direction), resulting in a 100 step hue circle. The "standard" or central example of each color segment is located at step 5 (diagram, right).

Finally, each hue was calibrated in equal chroma steps from zero (pure gray) to the maximum color intensity in the paints or inks used for each hue; in the idealized (aim) colors, chroma intervals are calculated out to the optimal color limits.

The approximately cylindrical framework of the Munsell system (below), which includes a value scale limited by the luminance factor of surfaces and chroma steps bounded by the optimal color limits for each hue. The dimensions are not otherwise connected, which corresponds to the separate perceptual measurement procedures used to define them.

the 40 standard munsellhue circle divisions

conceptual framework of the munsell color order system (1905)

Colors are "named" through the standard notation sequence hue value/chroma. Thus, the pigment vermilion would be notated as 8.5R 5.5/12 — a hue of 8.5 in the R segment, at value 5.5 and chroma 12. Any physically realizable surface color (paint, ink or dye) can be located within the Munsell framework by using decimal increments on the hue, value and chroma dimensions. (Munsell apparently adapted his color terms from the French valeur and chromatisme, which he picked up while studying art in Paris in the 1880's.)

So how does one measure color with the Munsell system? At first (and commonly today) through human color judgments. The Munsell colors are standardized as carefully prepared color samples or paint chips, presented on separate pages of a reference catalog, the Munsell Book of Color. Each page contains color samples of a single hue, arranged in a two dimensional grid defined by value and chroma. Colors are identified by placing them next to the atlas samples until the nearest color match is found. Decimal color values are inferred by locating a sample color between two existing Munsell chips. These visual judgments are accurate only if the comparison color sample is as large as the atlas samples, and all colors are viewed on a gray background under the same daylight or incandescent illumination (usually, illuminant C).

The Munsell Renotations. In the 1920's

some of the 1915 Munsell samples were first measured with a spectrophotometer, and these were mapped into the CIE 2° Yxy color space shortly after it was developed in 1931.

The early measurements were made by the USA National Bureau of Standards, which took an interest in developing the Munsell system as a color standard. In the 1930's the Optical Society of America also began a technical study of the system. The entire 1929 Book of Color was measured spectrophotometrically in 1935 and published as Yxy values in 1940. These revealed major discrepancies between the 1915 and 1929 color samples, and major irregularities in the spacing of color samples on the Yxy chromaticity diagram, particularly in the chroma intervals but also in the lines of equal hue.

The OSA committee primarily focused on defining the Munsell value scale as a mathematical formula, based on visual judgments of gray samples by a large sample of viewers, and on judgmentally adjusting or "smoothing" the contours of Munsell hue and chroma on 1931 xy chromaticity diagrams. These calculations were used to revise the value scale, to equalize the hue and chroma intervals, to extend chroma intervals out to the optimal color limits, and to redefine material color specifications. This renotated system was published in 1943 as specific Yxy values for 2700 unique color locations, as a mathematical formula to calculate Munsell value from XYZ tristimulus values, and as several 1931 xy chromaticity charts used for the visual estimation of Munsell hue and chroma values from xy values. Subsequent editions of the Book of Color are blended to match these 1943 targets. The renotated system is the standard specification of Munsell colors used today.

Subsequently, the OSA committee working on uniform color scales (discussed below) revisited the renotation data, generally to examine the effects of imposing a genuinely three dimensional definition of color differences, but particularly to examine the effects of response compression on the chroma of different hues. The data for this re-renotation system were published in 1967 for more than 2900 color samples, and

represent a major revision to the Munsell standards. It is not in general use.

Today all the Munsell colors are available as idealized tristimulus values or aim colors, and Yxy color locations or color spectrophotometric data can be translated into the Munsell notation entirely by computer software. Thus the color system designed for teaching color to children has ascended to the realm of digital exemplification and industrial color standards.

The Asymmetry of Color Space. Munsell and his successors worked hard to produce color samples that were perceptually equidistant or equally different from neighboring colors on the individual dimensions of value, chroma and hue. Thus, the difference between a chroma of 2 and a chroma of 4 is intended to appear to the viewer as large as the chroma difference between 12 and 14. However, these measurement units are not comparable across dimensions; the principle of equal perceived distance applies within each dimension of the model separately, not between any combination of color attributes. This is obvious from the fact that 10 units encompass the entire range of values (from black to white), but only 10% of the total range of hues (for example, from yellow to orange) and, for most hues, only half the total range of chroma.

However, the empirical measurements that have been at the heart of the Munsell system from the beginning compelled Munsell to an important realization: the natural color space is highly irregular when it is represented without geometrical preconceptions. Thus, Munsell always conceived of his color model as a sphere, but allowed for unequal dimensions of chroma at different levels of lightness and across different hues. Two "pages" from the Munsell system at the complementary hues 5Y and 5PB show this clearly.

two pages from the munsell book of color (1929)

These hues are directly opposite each other on the Munsell hue circle, so they show a vertical "slice" through the Munsell color solid (sometimes called a color tree). This shows what is obvious when you think about it: yellow at its highest chroma has a much lighter value than does blue at its highest chroma. These lopsided relationships between value and chroma affect nearly all hues around the color circle. As a result, no simple geometrical form accurately represents perceptual color space. All color models based on triangles, circles, squares, pyramids, cones, spheres, cubes or cylinders must (and do) grossly distort perceived color relationships. Munsell was the first researcher to document this basic color fact as a color model.

In addition, Munsell's color studies and the subsequent renotation research revealed that the background or surround color significantly affects the response compression (contrast) in lightness or chroma; in effect, lightness and chroma are contrast perceptions of brightness and colorfulness. In addition, the Munsell workers documented poor chroma or lightness discrimination in very intense or very light valued colors, and uneven perception of hue differences, especially as hue differences become very large. By its focus on perceptual uniformity in the spacing of material color samples, the Munsell research uncovered the

many geometrical complexities in color space.

The Limited Gamut of Color Atlases. The continued use of human color judgment with the Munsell or NCS color atlases may create the impression that all surface colors are contained in these references. This is false, and leads to the issue of color gamut is as it applies to any hardcopy (printed or painted) or softcopy (computer monitor) displays of a color space. The range of colors represented in a Munsell atlas is limited by the gamut of paints or inks used to create the color samples. In fact, two different versions of Munsell color samples, in "glossy" and "matte" preparations, are available. The glossy colors have a slightly larger gamut or range of chroma.

But even the glossy colors are incomplete. The figure at right shows the range of surface colors represented by the Munsell color solid as irregular colored shapes, enclosed within a white envelope that represents the optimal color stimuli or maximum chroma for surface colors of each hue. (Colors with a higher color intensity than the white boundary will appear fluorescent or self luminous.) The Munsell system represents the range of colors that can be achieved by high quality acrylic paints, or inks printed on highly reflective white paper; the range of colors possible with watercolor pigments is significantly smaller.

Comparison of the Munsell color range with the optimal color envelope shows that the yellow and red pigments do a good job of filling out the potential color space, while modern lightfast magenta (RP), purple (P), blue (B), blue green (BG) and green (G) pigments reach less than half the chroma potential for their hues. Thus, the Munsell color atlas, and in fact any color atlas in any color system, exemplifies an incomplete and skewed subset of the total asymmetrical color space. Note, for example, that the G dimension of the Munsell atlas is smaller than the RP dimension, although in the perceptual surface color space just the reverse is true.

OSA uniform color scales

maximum chroma ofmunsell color samples

compared to the limits of

surface color chroma; after

Kuehni (2003) and

Perales, Mora et al. (2004)

As we've seen, the Munsell system contains two significant problems: (1) a variety of discrepancies were found in the perceptual spacing of colors, depending on their location in the color space, and (2) the quantitative difference between colors could only be defined on a single color attribute (lightness, chroma or hue) at a time. These problems were not resolved in the Munsell renotation, and the Munsell system remained an inconvenient and uncertain basis for quantifying perceived color differences on all three colormaking attributes.

The subsequent development of the colorimetric system did not resolve matters, as the standard chromaticity diagram also badly distorted perceived color differences — the chromaticity differences between greens are much too large, and differences between blues are much too small.

Methods to quantify perceived color differences were very important in the implementation of color measurement, for purposes as diverse as photographic dye patents and governmental standards, and for manufacturing color control in industries as dissimilar as textiles and automotives. These requirements stimulated an effort to develop a truly uniform color space, from the ground up, as a set of uniform color scales across the central area of moderately saturated colors. This task was taken up by a committee under the auspices of the Optical Society of America (OSA), in collaboration with the USA National Bureau of Standards, and led by Deane Judd and David MacAdam. The final UCS aim color tristimulus values, color scales, recommendations for their use and conclusions regarding the human color space, were published in the 1970's as the Optical Society of America's Uniform Color Scales (UCS).

Rhombohedral Lattice. The first issue was the specification of the color geometry. The decision was made to shift from the "wheel and spoke" arrangement of Munsell to a cartesian or three dimensional set of dimensions, as in the CIE Yxy color space.

The color geometry should also support

measurement of perceived color differences in all directions, unlike Munsell where intervals of chroma are not perceptually equal to intervals of value or hue. To assess perceived color differences in all directions of the color space using identical psychometric tasks, it is desirable to have diagonal dimensions added to the cartesian space.

The OSA committee found the solution to both problems in a rhombohedral lattice as the basic color geometry — the same geometry found in a carbon crystal (diamond or graphite). It is difficult to represent as a single image, but the logic behind it is straightforward.

rhombohedral lattice structure of OSA UCS

(left) a triangle of three spheres fitted into a hexagon of seven spheres, with three more spheres fitted from

below; (right) the cubo-octahedron with edges of equal length (black), linked by six scales passing through a

central color; (bottom) six sets of parallel scales, keyed by color

The densest possible stacking of spheres in three dimensions is pyramidal: seven spheres in a plane with three spheres stacked in the gaps between them, as oranges are stacked in a grocery bin. The rhombohedral lattice continues this stacking in all directions out to the perceptual limits of the color space. The entire color space can be "filled" with spheres in this stacking arrangement, starting from a single sphere that marks a neutral, mid valued

gray.

The stacking aligns the spheres as sets of parallel color groupings (above): seven cleavage planes, and six perceptual scales defined by the intersections between any two sets of cleavage planes. These create a rigid measurement framework within a three dimensional (Euclidean) color space, intended to reveal for color scientists any irregularities in the color space as discrepancies in color distances calculated across the different scales or cleavage planes. Set aside the emphasis on rigor, and the various color scales were offered to artists as dimensions of harmonious color variation.

The lattice naturally suggests two measurement benchmarks: (1) the interval between any two adjacent color samples represents a just noticeable difference between the colors; and (2) the smallest intervals or steps between colors must be perceptually equal in all directions of the color space. The perceptual error or uncertainty in identifying a specific color approximately forms a sphere around it, and the spheres around all colors will be the same size — not the ellipses of different sizes and shapes that appear in the CIE chromaticity diagram. In fact, the OSA UCS system was based on judgments of colors spaced by about 20 jnd's, but in theory this only changes the perceived distance between color samples, not the geometrical regularity of the color scales. The OSA Uniform Color Space. The UCS exemplification projects the rhombohedral lattice into the color space so that a cleavage plane of square stacking defines the hue/chroma planes at constant lightness; each square defines a measurement interval of two units. These planes are staggered or shifted in relation to each other, so that chromaticity coordinates are even or odd numbered on alternating lightness levels. The lightness dimension is perpendicular to these planes.

The three perpendicular dimensions of the uniform color space are the lightness dimension L and two chromatic dimensions, j (for jaune, approximately a y/b opponent dimension) and g (for green, approximately a g/r opponent dimension). The mid valued gray

staggered square tiling ofhue planes in OSA UCS

two adjacent lightness levels

shown

on the CIECAM ab plane,

with numbering of j+ samples

that is the anchor of the system has a value of 0 on all dimensions; colors with negative values are darker, bluer or redder.

the OSA UCS color solid conceptual side view of the OSA UCS whole step aim colors, with the vertical L scale expanded for visual

clarity; adapted from Yxy tristimulus values in Table I(6.6.4) of Wyszecki & Stiles (1982), which reverse the

orientation of the g dimension

The development of the OSA UCS sprawled across two decades and many color scaling experiments, drew on dozens of previous color scaling studies, as well as data from the Munsell renotation and the CIE Yxy system, and began with psychophysical studies of limited color judgment tasks, such as equal hue spacing at constant lightness and chroma, or equal chroma spacing at constant lightness and hue. In effect it was a conceptual integration of the best color research up to that time, with empirical testing of the major conclusions and solutions.

These studies led to a selection of 43 hexagonally arranged, perceptually equally spaced color samples at a constant Munsell value of 6. I reproduce below the 48 OSA aim colors for L=1 as approximate equivalents to

these color stimuli. The range of colors is relatively muted: the most intense color sample (the orange at top right) has a CIELAB chroma of 74.

OSA UCS constant lightness plane OSA UCS aim colors for L = 1 (CIELAB L* = 63 to 68) under equal energy illuminant; j = 9 to -5 and g = -9 to 5, with neutral indicated by white dot; data from

Wyszecki & Stiles (1982)

Several groups of viewers examined two pairs of colors sampled at random from this set, and were asked to choose the pair that showed the larger color difference; by statistically combining these color judgments across all viewers, the perceived differences between all colors could be given an average numerical value. These values were then used to check formulas proposed to estimate perceived color differences, based on the Ljg values of two colors. Subsequent studies using revised or limited color samples were done to extend the results to different values and to adjust for the Helmholtz-Kohlrausch effect. The final rhombohedral model of 500 color samples and 58 pastel samples was built on these foundations. The diagram (right) shows the 500 OSA UCS "full step" aim colors projected into the CIELAB color space. The average distance

between aim colors on the CIELAB L, a* or b* dimensions is about ∆Eab = 12 — that is,

about 12 jnd's. The image shows the sampling is fairly complete (when compared for example to a similar representation of watercolor pigments) and is generally regular, with a tendency for CIELAB chroma spacing to grow larger in yellow and green colors. (The slight downward bowing visible in the color rows is a compensation for the Helmholtz-Kohlrausch effect.)

The various diagonal scales or cleavage planes through the color space were intended to identify palettes of complex color change that might be useful to graphic artists and color designers. They turned out to be wildly unpopular for that purpose. The legacy of the OSA UCS is as a research landmark and a uniform tiling of the color space that is useful to assess color models or imaging systems.

Color Space Is Noneuclidean. Despite the extensive and patient research program and the elegant color model it produced, the OSA committee had already in 1967 come to a dispiriting conclusion:

We will affirm to the world that no regular

rhombohedral lattice sampling of color space, with a fixed background, can exist; we will

produce the best approximation to such a lattice for a neutral value 6 background that

we can design.

In plain language: it is impossible to represent uniform color differences as a three dimensional color model. The human color space is noneuclidean, which means a three dimensional framework cannot describe it. Any color difference formula or color model that represents color in only three dimensions (such as lightness, hue and hue purity) gives a distorted picture of color differences and color relationships.

The first and perhaps most important reason why this is so was identified by Deane Judd in 1968 as hue superimportance; the effect might better be described as chroma compression. It appears as a fundamental discrepancy between measures of just noticeable difference in chroma and in hue. The diameter of any hue circle at constant

OSA UCS aim colors in theCIELAB color space

under illuminant D65; layer

OSA L = 1 shown in magenta;

the g dimension is reversed in

all CIE color models

chroma is always perceptually shorter than the circumference, measured across all hues. This discrepancy is quite large: if the ratio of the circumference to the diameter of a euclidean circle is roughly 3.14 to 1, the same ratio in a hue circle is greater than 6 to 1. Judd represented this fact as a "pleated disk" (right): chroma is measured outward along the folds in the pleats, while hue is measured zigzag along the edge of the fan, which has roughly double the length of a flat circumference. Alternately, if the relationship is forced into two dimensions, the chroma distances must be elongated, producing elliptical discrimination ellipses, and the ellipses become larger (chroma discrimination becomes weaker) at higher chroma values (right). The OSA committee concluded that both lightness and chroma had to be adjusted by a cube root or exponential compression to correct for this discrepancy.

The second problem involves chromatic contrast, in particular crispening, which makes small color differences, or differences judged against a similar background, appear relatively larger. Most of us are familiar with the "reading magnifiers" that enlarge words when rested on a printed page. Crispening acts like a magnifying bubble inside the color space, enlarging the apparent contrast between similar colors on lightness, chroma and hue. As a result, all small color differences are magnified in comparison to large color differences, and "small distance" color difference formulas tend to overestimate the perceived color difference between colors that are very different.

Just as a reading magnifier can be shifted around a page, the crispening locus can migrate around the color space, depending on the color and lightness of the background (surround) used to judge colors, the chromaticity of the illuminant. To control this, color vision experiments and color atlas viewing standards use a mid valued gray surround in color presentations, so that crispening occurs as an increased chroma sensitivity around near neutral colors.

The third problem is that hue superimportance is not equal in all directions: chroma

the hue circle as a pleated disk

the circumference is more

than

six times the length of the

diameter

after Judd (1968)

hue/chroma discriminationellipses in CIELAB

from Kuehni (2003)

compression is strongest in yellow and green hues and weakest in red and blue hues. It also changes across different values, becoming more extreme in lighter valued (more luminous) colors.

The final problem, related to the previous one, is the unequal spacing of hues, which is explored on a previous page. Some hues produce a greater number of perceptible color gradations than others; in particular, color discriminations are much more acute for warm hues than for green hues. The two fundamental problems in color models uncovered by the OSA UCS research strangely parallel the two primary color paradoxes:

• The first is that all color models we can see cannot represent colors relationships

accurately, and color models that represent color relationships accurately cannot be seen (physically constructed or represented as an image).

• The second is that all color difference formulas are arbitrary, in the sense that they must include many judgmental corrections for specific discrepancies, can only provide difference estimates that are approximately correct for small (or large) color differences, and provide difference estimates whose accuracy depends on where in the color space the color difference is calculated.

The primary color paradoxes can be explained as resulting from the overlap in three cone sensitivity curves. The color model paradoxes can be generally explained by the fact that the perceptual color space changes continually under the influence of many contextual factors. It's not that change cannot be expressed as a static euclidean model. It's that the perceptual space adapts to different color stimuli, color differences, contrast backgrounds and light sources in different ways, depending on which specific combination of color stimuli is being used to measure it.

The previous section described the

CIELUV uniform color space

efforts by the Optical Society of America to build a truly uniform color space in three dimensions based on rigorous psychometric and geometrical foundations, and the discovery that such a goal is fundamentally impossible. Now we turn to a second strand of color research, which had a more limited aim in view: to discover a uniform color difference formula that could be used in specific practical applications.

Color Matching and Color Differences. Since the early 1920's, a major goal of colorimetry was the prediction of an unrelated color response through the photometric measurement of a physical color stimulus. The approach that seemed most efficient was to measure the spectral power distribution of the light emitted or reflected by the color stimulus, translate this into photometric units by means of a luminous efficiency function or a standard set of color matching functions, then use these quantities to estimate the subjective brightness or chromaticity of the stimulus when it is viewed as an isolated patch of color.

However, the XYZ tristimulus values that came out of color matching tasks literally only predict color identity, that is, whether two colors will appear the same. The whole problem of how much two colors will appear different was left undetermined. The CIE xy chromaticity diagram does represent the relative difference between two colors — that one color sensation is redder, or brighter, or duller than another, if both colors are measured in the same way. But the desired next step was to subtract one set of XYZ tristimulus values from another, and use the numerical difference to predict the perceived color difference between them.

This estimation procedure did not work well. A major problem was that the CIE xy chromaticity diagram is not a uniform chromaticity scales diagram or UCS. In a true UCS an equal chromaticity distance is an equal perceptual difference, no matter which color attributes are measured. But two colors separated by an equal Yxy (or XYZ) difference can appear nearly identical (if the colors are green or light valued) or very different (if the colors are violet or dark

valued). They cannot consistently predict whether a color difference will be unnoticeable or obvious to an average viewer. This was a major obstacle to using colorimetry in the industrial control of dyes (textiles and photography), inks (printing and packaging) and paints (automotive and architectural colors) — especially after inexpensive and reliable spectrophotometers became available in the 1950's. As the measurement standards were already in place, the easiest solution was a hack. The original chromaticity diagram could be mathematically stretched or compressed until the numerical difference between the tristimulus values of two colors approximated the perceived difference between the colors. (These differences would be applied only to similar colors: large color differences were not important to quality control problems.) These mathematical distortions are called projective transformations, and they are identical to the warping or "keystoning" that occurs when a slide is projected onto a curved surface or onto a wall at an oblique angle (right). These transforms don't change any of the foundation procedures of colorimetry or the "straight line" color mixing relationships of the chromaticity diagram, just the color differences calculated from them.

Projective transformations were proposed independently by Deane Judd and David MacAdam in the 1930's; Judd's version is shown below. It radically compresses the "green" part of the chromaticity space while expanding the "blue" and "red". The white point is located close to the R–G mixing line, because the L and M cones dominate the perception of whiteness (compare with my cone chromaticity diagrams).

"keystoning" as an example of a projective

transformation

an early projective transformation the CIE 1931 chromaticity diagram within a Maxwell

triangle defined by three imaginary primary lights that produce an approximately uniform color space (after

Judd, 1935)

Projective transformations were only one of several solutions to the color difference problem. By the 1960's anywhere from 13 to 20 different formulas were being used for different applications in England and the USA. To corral this diversity, the Commission Internationale de l'Éclairage (CIE), an international clearinghouse for color research at universities and research laboratories, adopted in 1976 two color difference formulas that seemed most promising for further work: CIELUV, described here, and CIELAB.

The CIELUV Dimensions. CIELUV is a much revised and expanded version of the projective transformation proposed by David MacAdam in 1937 and adapted as a color difference space by Günter Wyszecki in 1964. It builds on two uniform chromaticity scales (UCS), denoted u' and v', derived from the standard XYZ tristimulus values.

Recall that a basic problem in colorimetry is devising a measure of chromaticity (hue and hue purity) that is not affected by changes in the luminance (brightness or lightness) of the color. The CIE xy chromaticity diagram accomplishes this by normalizing the XYZ values, or dividing each score by the sum of XYZ values:

x = X / (X + Y + Z) y = Y / (X + Y + Z)

The CIE UCS adopts the same normalizing strategy for the color's tristimulus values, but with a specific reweighting of the Xc, Yc and

Zc scores that changes the shape and

orientation of the chromaticity diagram, and the location of the white point inside it:

u'c = 4Xc / (Xc + 15Yc + 3Zc)

v'c = 9Yc / (Xc + 15Yc + 3Zc)

The u' and v' scales alter the dimensions of the chromaticity space but preserve the trichromatic color geometry. That is, in the CIE UCS and CIELUV, Grassman's Laws of color mixture are still valid: all colors are defined by additive mixtures of three imaginary "primary" lights, and therefore color mixtures are described by straight mixing lines.

The next problem is representing the luminance or intensity of the illumination and chromatic adaptation to its color. To incorporate these effects, the luminance factor Yc is used to expand the dimensions of the

u'cv'c diagram to approximate the increase in

colorfulness that occurs with increased illuminance, and to shift the location of the white point to center it on the chromaticity of the light source, defined by a second set of tristimulus values (XwYwZw). This yields the

relative brightness dimension L* and the relative chromaticity dimensions u* and v* (u'w and v'w are computed from XwYwZw as

shown above):

L* = 116*(Yc/Yw)1/3 – 16

u* = 13L*(u'c – u'w)

v* = 13L*(v'c – v'w)

These adjustments center the u* and v* dimensions on the achromatic point at the origin of a u*v* cartesian plot, insert a cube root compression into the brightness contrast, and (by the factor 13L) mimic the Hunt effect which causes colors to increase in colorfulness as their luminance increases. These calculations apply to colors perceived as lights, so extremely dark colors — with luminance ratios (Yc/Yw) less than 0.01 — are

out of bounds.

At last we get a definition of chroma across different levels of brightness as the euclidean chromaticity distance between the color and the white point:

Cuv = [u*2 + v*2]1/2

... we get a simple numerical definition of hue as the hue angle measured from the white point in relation to the u* dimension:

huv = arctan[v*/u*]

... and we end up with a version of the color difference score that was the origin of the model, ∆Euv, as the euclidean distance

between the L*, u* and v* values of two similar colors:

∆Euv = [(L*1–L*2)2+(u*1–u*2)

2+(v*1–

v*2)2]1/2

where "similar" means colors that are separated by a ∆Euv value of 10 or less.

The Uniform Color Space. The result is the 1976 CIE L*u*v* uniform color space or CIELUV, in which the brightness and chromaticity difference between two colors is proportional to their perceived difference when viewed side by side in a gray field at moderate brightness.

CIELUV provides the same chromaticity dimensions as the u'v' uniform chromaticity scales diagram (the CIE 1976 UCS), shown below. This represents equal chromaticity differences between lights of equal (unspecified) luminance as approximately equal euclidean distances on the chromaticity plane.

CIE 1976 UCS diagram computed from 10° XYZ values under an equal energy illuminant; the diagram shows all possible colors as they appear in lights, bounded by the pure spectral hues; colors within the diagram only symbolize the

approximate location of colors

The top edge of the color surface spans the hues of monochromatic or single wavelength light measured from 750 (700) to 520 nm; the left diagonal edge completes the spectrum from 520 nm to the short wavelength visual limit at around 380 nm. The right diagonal edge (called the purple line) represents the extraspectral crimson, magenta and purple hues that are mixtures of "red" and "violet" light.

The diagram below shows the effect of the u'v' scaling on equal chromaticity differences measured in different directions around the chromaticity surface. The equalizing effect is especially noticeable by comparing the color differences around the spectrum locus, and the color distances from "blue" toward "green" and "blue" toward "red".

comparison of equal perceptual distances equal perceptual distances, drawn at 10 times actual size, in CIE xy and u'v' chromaticity diagrams; after

Wright (1969) and Hunt (2003)

Throughout the 20th century, the Munsell system figured prominently in efforts to identify color scaling problems or confirm that a color difference formula accurately described color differences. The diagram below shows the relative improvement in the spacing of Munsell lines of equal hue and chroma for surface colors of value 6.

comparison of munsell hue and chroma lines of equal Munsell chroma (steps of 2) and hue

(steps of 5) at value 6 in CIE xy and u'v' chromaticity

diagrams; after Wyszecki & Stiles (1982) and Kuehni (2003). Note that all CIE systems reverse the

ordering of Munsell hues.

The improvement is especially noticeable in the more circular shape of the chroma contours around the white point, in the more equal spacing of green hues, and in the balanced chroma intervals around the green, blue and purple sides of the chromaticity space. However, significant discrepancies (chroma compression or expansion) appear in the yellow green to red parts of the diagram.

Current Use of CIELUV. The CIE 1976 u'v' diagram is the "least wrong" chromaticity diagram in general use, and is a huge improvement over the distorted 1931 or 1964 diagrams which still lurch through the color literature. It gets the relative sizes of the green, blue and red areas of color space about right, as well as the perceived hue purity of colors, including spectral hues, as the distance from the white point. It should always be used to display basic chromaticity data.

CIELUV has been a popular color space for lighting, video and photographic applications which require measurement of lights, light filters or optical systems, because CIELUV represents the additive mixture of two lights as a straight line across the color space. (R.W.G Hunt's authoritative 2004 text, The Reproduction of Color, 6th edition, consistently relies on it.) CIELUV is quite useful to predict the appearance or mixture of colors produced by luminous displays — such as computer monitors, television screens, or transparencies projected onto a uniformly reflecting surface — where the brightness of colors is a constant proportion of the luminance of the source illumination (there is no "external" light source), although CIELUV is also used to specify the color of gems or optical glasses illuminated by a standard "white" light source, and the color of photographic dyes and filters.

Considered in terms of the four requirements of a modern color model, CIELUV (and the Yxy standard observer system on which it is based) represent a major departure. This isn't that the color specification is exclusively in terms of

continuous numerical values, because that was innovated centuries ago by Isaac Newton and Tobias Mayer. The innovation is that there is no color exemplification. All color measurements are made electronically, using a spectrophotometer that measures the separate XYZ values directly and then calculates the coordinate values for any standard color system. The exemplification is implicit in all physical color stimuli, whether lights or surfaces, that have identical or similar color coordinates. However, CIELUV suffers from a major drawback: the ∆Eu*v* color difference formula

yields a poor prediction of color differences, especially for surface colors. In fact, when a variety of color models are tested for their ability to predict surface color differences, CIELUV is almost always at the bottom of the heap.

CIELUV does even worse at predicting corresponding colors, or colors that match under different colors of illumination (illuminants). The problem is that CIELUV represents relative color differences in relation to the white point as a difference or simple subtraction (e.g., u'c – u'w), rather than as a

ratio or proportion. This means that if the white point (the illuminant) is changed, or is strongly chromatic, all colors are shifted in a parallel direction by a constant amount (as if printed on a moveable transparency), regardless of where they are located in the chromaticity space.

If colors are shifted from yellow toward blue, the compressed chroma intervals in the yellow green to orange part of the u*v* chromaticity diagram do not change, so CIELUV grossly overestimates chroma differences wherever these boundaries are relocated. If colors are shifted from blue to yellow (for example, the color of a gem viewed under tungsten rather than halogen light), CIELUV thrusts the predicted color locations completely outside the spectrum locus, which is perceptually impossible.

As corresponding color predictions are a minimal requirement for modern color appearance models, CIELUV has been

discarded as the basis for further work.

The second color difference formula adopted by the CIE in 1976 (along with CIELUV) was the CIE L*a*b* uniform color space or CIELAB. CIELAB is based on a color difference formula developed by E.Q. Adams and D. Nickerson in the 1930's to measure color fading in textiles. Like CIELUV, it is an attempt to hack the XYZ tristimulus values to produce a reliable method for calculating color difference scores. However, CIELAB is based on a very different transformation strategy.

The CIELAB Dimensions. The CIELAB formula comprises four transformation steps, which are intuitive when examined separately.

Recall that the color geometry common to all modern color models consists of a brightness/lightness dimension that is perpendicular to (separate from) the chromaticity plane or hue circle. This geometry is implicit in the XYZ tristimulus values: the Y value represents the photopic luminosity function of the specified color. We start with the color's Y tristimulus value (Yc) as the measure of its luminance or

luminance factor (labeled L, as in CIELUV), and use the Xc and Zc values as measures of

chromaticity (hue and hue purity).

The X value increases primarily as the L cone response to a color becomes relatively large, so it is the "red" anchor for an r/g dimension (labeled a); the Z value increases with S cone response, so it is given a negative sign to represent the complementary "yellow" of a y/b (b) dimension:

L = Yc

a = Xc

b = –Zc.

The first transformation step is an adjustment of the tristimulus values to represent a chromatic adaptation to the illuminant (color of illumination). The correct method (a

CIELAB uniform color space

von Kries transform) divides the cone excitations produced by the color area by the cone excitations produced by the illuminant. CIELAB instead uses the "wrong" ratio between the tristimulus values XwYwZw of the

illumination. These are a standard both for the luminance upper limit represented by a perfectly reflecting "white" surface (Yw is

always equal to 100) and for the chromaticity inherent in the light itself (in the values of Xw

and Zw relative to 100).

L = Yc/Yw

a = Xc/Xw

b = –Zc/Zw.

The tristimulus values of a perfectly white or equal energy illuminant are defined as Xw

= Yw = Zw = 100. An illuminant with a

perceptible "warm" (yellow or red) chromaticity has values of Xw greater than

100 and values of Zw less than 100; "cool" or

blue illuminants have low Xw and high Zw.

The adaptation ratios reduce or increase the values of Xc and Zc in proportion.

In the second step, CIELAB applies an exponential compression to all three adaptation ratios. This inflates the perceived chromaticity and lightness differences among dark colors, and inflates the chromaticity of yellows relative to blues. At the time CIELAB was published, different compression fractions had been tried in color difference formulas, and the cube root seemed to perform about as well as any:

L = (Yc/Yw)1/3

a = (Xc/Xw)1/3

b = (Yc/Yw)1/3.

Although the Y tristimulus value represents the luminance of the color area, all three tristimulus values contain similar luminance information, because the XYZ values all get larger as the surface reflectance increases from dark to light. As a result, the XYZ values are highly correlated in actual color

measurements, from 0.52 [Y and Z] or 0.56 [X and Z] to 0.88 [X and Y]. At the same time, the Y tristimulus value contains unique chromaticity information, because the XYZ curves all peak at different parts of the spectrum. So the third transformation step separates the chromaticity information from the luminance information contained in all three values. CIELUV does this by normalizing the luminance information (dividing all values by the XYZ sum). CIELAB does it by subtracting one value from another:

L = (Yc/Yw)1/3

a = (Xc/Xw)1/3 – (Yc/Yw)

1/3

b = (Yc/Yw)1/3 – (Zc/Zw)

1/3.

This creates two undulating curves for the difference values of spectral hues (diagram, right).

An explanation: when applied to quantities of the same thing, such as dollars or gallons, subtraction just identifies the quantity of the difference. When applied to quantities of dissimilar things measured within a similar range of values, subtraction purges any information the two measures have in common (in this case, information about the luminance) and leaves as a single number all the unique information in both (the combined information about hue and hue purity). As the XcYcZc values are already standardized on the

white point (by the adaptation transform), the subtraction also centers the values of a and b at zero for a surface color that exactly matches the chromaticity of the illuminant: a pale yellow surface under a pale yellow light will appear to be a "pure" white.

Finally, the L, a and b dimensions are expanded by different factors so that a unit scale value on any combination of CIELAB dimensions represents an approximately equal and just noticeable perceptual difference. As the Y–Z curve (b dimension) has a larger amplitude than the X–Y curve (a dimension, diagram above right), it is multiplied by a smaller amount. The slope and intercept of the L function is also adjusted to match the units

opponent functions defined by tristimulus differences

X-Y and Y-Z

of Munsell value:

L* = 116*(Yc / Yw)1/3 – 16

a* = 500*[(Xc / Xw)1/3 – (Yc / Yw)

1/3]

b* = 200*[(Yc / Yw)1/3 – (Zc / Zw)

1/3].

These formulas take an alternate form, not shown here, for extremely dark colors (where any adaptation ratio is less than 0.009). For details see the references at the end of this section.

CIELAB yields a reliable correlate (relative measurement) of chroma as the euclidean distance between the chromaticity of the color and the achromatic point:

Cab = [a*2 + b*2]1/2

... and a numerical definition of hue as the hue angle:

hab = arctan[b*/a*]

... and its own color difference score ∆Eab,

obtained as the euclidean distance between the L*, a* and b* values of two similar colors:

∆Eab = [(L*1–L*2)2+(a*1–a*2)

2+(b*1–

b*2)2]1/2

where "similar" means colors that are separated by a ∆Eab value of around 10 or

less. As a rule of thumb, 10 units of CIELAB lightness exactly matches 1 unit of Munsell value, and 10 units of CIELAB chroma approximately matches 2 units of Munsell chroma. The average ∆Eab for the first

chroma step in Munsell aim colors across all hues and values is about 5.8. Note that ∆Eab

is approximately in units of just noticeable difference, so color differences at or below 1 are generally not visible.

The Uniform Color Space. The CIELAB transformations yield approximately perpendicular dimensions that are often represented as a cylindrical geometry. That

is, the L* dimension is the axis of the cylinder, through the achromatic point; hab represents

the hue angle or circumferential direction of the color, and Cab the distance of the color

from the cylinder axis.

geometry of the CIELAB color model

The diagram is somewhat misleading. In practice, the color difference (euclidean distance) score is based on the cartesian (a*b*) coordinates and not cylindrical radians or degrees; and the distribution of surface colors in CIELAB tapers toward the achromatic center at very high or low lightness.

The point is that CIELAB color relationships are not distorted by forcing them into a conceptual geometry, such as the ipsative hue triangles of NCS. Color measurements are limited vertically by the luminance factor of surfaces, and the chroma extent is limited by the domain of real surface colors or lights, but these are boundaries imposed by color perception, not arbitrary geometry or logic.

The illustration below shows the location of 700 commercial watercolor paints in the CIELAB space, with color icons grouped onto separate lightness planes for clarity. These define a roughly ellipsoidal or "football shaped" color domain inside the CIELAB color space.

700 watercolor paints in the CIELAB color space

based on spectrophotometric measurements reported in the guide to watercolor pigments; red (a+) placed

on left to correspond to artist's color wheels

Note the similarity in the side view of the pigment distribution (at left) and the chroma limits of the yellow/blue color samples in the Munsell color pages discussed above. Compare also to the outline of OSA UCS aim colors projected into the CIELAB space. (For a "top down" view of pigment locations, see the CIELAB a*b* plane.)

How closely does CIELAB approximate a uniform color space? If we set aside the small problem that a UCS in three dimensions is impossible, then CIELAB does remarkably well, given its origins as a hack. A standard basis for comparison — the distribution of Munsell aim colors at Munsell values 4, 6 and 8, out to the limits of surface color chroma — is shown below.

munsell aim colors on the CIELAB a*b* plane

under illuminant D65; aim colors at 2.5 hue intervals and /2 chroma intervals for values 4, 6 and 8 out to the optimal color limits; constant CIELAB chroma indicated by gray circles. Note that all CIE systems reverse the

ordering of Munsell hues.

Ideally, this diagram would look like radial spokes within concentric circles. (The "wedge" shaped outline results from the optimal color limits — see, for example, this diagram — and is not a fault per se.) The exaggerated spacing of Munsell chroma into the yellow and yellow green hues, the displacement in the lines of constant hue as lightness increases (especially in the blue greens), the curving lines of constant violet and green hue, and the wide gaps in the hue spacing of green colors, are all primarily or partly due to irregularities in CIELAB (although some are actually problems in Munsell). The distribution of OSA aim colors makes a much more favorable impression of uniformity. CIELAB should always be used to represent surface colors, and not CIELUV.

Because CIELAB includes an adjustment for chromatic adaptation, the location of colors will shift, depending on the chromaticity and luminance specified for the achromatic point, as shown below.

corresponding colors in CIELAB Munsell aim colors at value V = 6 represented under

"daylight" illuminant D65 (with a correlated color temperature of 6500°K, left) or "incandescent"

illuminant A (4000°K, right)

These illuminant shifted color locations or corresponding colors are not very accurate. Nearly all the change is produced along the b dimension. The overall color predictions — for example, under illuminant A deep blue of chroma /14 will appear gray, and the gray will appear a deep yellow of chroma /8 — are approximately right, though much better results are possible by using a different adaptation to the illuminant.

CIELAB can justifiably be called an opponent color space, because its chromatic dimensions are defined as the contrast between specific opposing hues, analogous of the opponent processes hypothesized by Hering. In fact, the X–Y and Y–Z contrast dimensions have a very similar shape and peak wavelengths to the Hurvich and Jameson opponent functions. On these grounds, the dimensions are usually interpreted as:

L* = white (L+) vs. black (L=0) a* = red (a+) vs. green (a–) b* = yellow (b+) vs. blue (b–)

This interpretation requires three qualifications. First, the lightness dimension L* does not represent black as a distinct color sensation, as conceived by Hering and observed in lightness induction, but as the absence of light (surface reflectance).

Second, the connection between the a*b* dimensions and hue depends on how the connection is defined: the opponent contrasts

do not consistently identify four hues as the contrast anchors:

• The physiological contrast defined by the a or b dimensions is found in the dominant wavelength or peak of the positive and negative sections of the X–Y and Y–Z curves (above), interpreted as cone sensitivity curves or transmittance profiles. These identify the contrast hues as magenta (a+, a mixture of orange and violet), middle green (a–), middle yellow (b+) and violet (b–).

• The a and b dimensions are correlated around –0.35. Substantively, this means that the most intense yellow colors (b+) tend to be greenish (a–), and the most intense violet colors (b–) tend to be reddish (a+). Statistically, it means that the anchor colors are not perpendicular to each other, although this is how they are always defined.

• The hue of surface colors located at the ends of perpendicular a* and b* dimensions, as shown here, are magenta (a+), blue green (a–), light yellow (b+) and cobalt blue (b–).

• Finally, the Hering unique hues are displaced from the ends of the perpendicular a*b* dimensions by a large amount, as shown here. Unique red and unique green are both shifted about 20° toward yellow, and the separation between unique red and unique blue is more than one third (130°) of the hue circumference. Third, the cube root compression applied to the tristimulus values creates a nasty kink in the a* chromatic dimension (right), which significantly departs from the undulating profile of empirically measured opponent functions. This especially stretches out the distance between blue hues with "green" content, and causes the a+ red to contain too much blue, compressing the distance between yellow and red colors.

Because they are based on difference scores, CIELAB chromaticity dimensions do not redistribute or normalize the luminance information across the chromaticity coordinates: they expunge it. As a result, the CIELAB color metrics cannot be expressed directly as the additive mixture of three

"primary" colors of real or imaginary lights. When narrowband optimal colors are represented in this cone opponent space, they produce an erratic, double lobed circuit, with the spectrum ends diving toward the achromatic origin (right). This is recognizably an upside down image of the cone excitation space, pinched and skewed by the cube root transformation. Note also the exaggerated spacing of the blue hues.

CIELAB measures chroma, the chromatic content of a color independent of its luminance; the a*b* plane does not represent saturation. Unlike the straight line, additive mixture between any two colors of light in the CIE UCS (or any chromaticity diagram), color mixtures can take curving or unpredictable paths on the CIELAB a*b* plane. This is not a result of the subtractive mixture of the two physical colorants (paints or dyes) but is basic to the CIELAB space.

Current Use of CIELAB. Like CIELUV, color specification in CIELAB is tied entirely to spectrophotometric measurements of color; it can't be used routinely without a color measurement device, and there is no standard CIELAB color atlas available. However, the wide use and practicality of the CIELAB system have spawned a number of proprietary color order systems or color atlases based in whole or part on the CIELAB geometry, including the American Colorcurve System, the German RAL Design System and the English Eurocolor Atlas.

Fairchild (2005) reports validation studies that pit several color appearance models against each other, using datasets that measured color matching under illuminant adaptation (corresponding colors) or preferred contrast and chroma in color image reproductions viewed at different luminance levels. Overall, these studies showed that different models performed well in predicting some types of color judgments but not others. In every case, however, CIELAB typically performed well against more complex models and occasionally was as good as the best; CIELUV was often the worst.

A major problem is that CIELAB uses what is called a wrong von Kries transform to

opponent geometry of CIELAB

(top) opponent functions a and

b; (bottom) trace of optimal

color stimuli on the a*b*

plane;

both displays under equal

energy illuminant

model chromatic adaptation. This computes the contrast ratio between a color and the white standard or illuminant directly on the XYZ tristimulus values, rather than on cone fundamentals. In addition, the cube root compression is not optimal when applied to the tristimulus values, and results in chroma intervals that can be misplaced in some parts of the hue plane: in particular, yellow chroma is not compressed enough, and blue chroma is compressed too much.

These failings aside, from the same standing start as CIELUV, CIELAB has become the standard colorimetric space worldwide. CIELAB remains the most practical and widely implemented color model available. Indeed, several extensions of or revisions to the basic CIELAB framework, including S-CIELAB and RLAB, have been published to improve its performance and suitability for a wider range of color modeling problems. Colors are not forced into an arbitrary geometric shape that distorts perceived color relationships. These extensions are possible because the CIELAB geometry does not impose an arbitrary symmetry on chroma, hue or lightness. The calculation from XYZ values to Lab values is simple and easily inverted (from Lab values back into XYZ), and can be replaced by a variety of chromatic adaptation transforms.

The original or revised CIELAB color difference formulas are widely used for automated color quality control in areas such as textiles, plastics, architectural and automotive coatings, printing, imaging and art materials, and in ASTM documents. Color samples from any other color model, including Munsell and NCS, can be conveniently located and compared in the CIELAB space, so it has become a convenient representation space for the evaluation of color models in general.

CIELAB is a useful color framework for painters who want to understand color perception and color mixing problems in paints, not least because its lightness and chroma metrics are, on average, ten times the same attributes in the Munsell color space. In 1996 I used CIELAB pigment locations as the foundation of my original artist's color wheel. However some of the "bad" hue and chroma spacing problems, which I had

corrected by hand using the Munsell renotation data, later decided me in favor of the CIECAM02 color relationships for the current (2006) version of the color wheel.

My principal source for information about CIELAB and CIECAM is Mark Fairchild's Color Appearance Models (2nd ed.) (Addison Wesley, 2005); see also the updates and information at Fairchild's web site.

Artists may be interested in the average location of watercolor pigments on the CIELAB a*b* plane, also available as a PDF file.

The Adobe Technical Guides have a good overview of color models in general, the CIE series, and the groundbreaking Munsell color system.

Daniel Smith has republished their Watercolor Paint Guide, which includes a map of their watercolor paint colors on the CIELAB a*b* plane, as "The Study of Color", available online at their InkSpot archive and reprinted occasionally in their catalog.

Because they are limited to the trichromatic outputs from the L, M and S cones, both CIELUV and CIELAB only model the color information generated by the photoreceptor response to small and isolated color samples. They cannot model many of the contextual effects of color perception, including luminance adaptation (surround illuminance levels), chromatic contrast or chromatic assimilation that arise in real world viewing conditions with heterogeneous, strongly contrasted, or three dimensional color stimuli.

In the three decades since CIELAB was published, several models have been proposed to represent these more complex color phenomena. The most recent is CIECAM02 (CIE Color Appearance Model 2002, based on CIECAM97s), developed through the research and committee products of Robert Hunt, Yoshinobu Nayatani, Mark Fairchild, Nathan Moroney and others. CIECAM represents a culmination and also an end point in the development of color appearance models.

Detailed instructions for computing and using the latest CIE models are available in the texts by Fairchild and Hunt (cited below). My goal is

CIECAM color appearance model

to explain how the input information and calculations affect the final color space. All diagrams were generated from Fairchild's spreadsheet version of the CIECAM formulas, cited below.

The CIECAM02 Dimensions. The CIECAM calculations are quite complex when compared to CIELAB. CIECAM also requires more starting information (refer to graphic at right): • Colorimetric information: the XYZ tristimulus values for the color area being modeled, the XwYwZw tristimulus values for the white

standard or illuminant, and the adaptation luminance Yb of the adjacent color

background, equivalent to the standardized (XYZ) luminance (where Y = 2 for a Munsell value of 1 [near black], Y = 20 for a value of 5 [middle gray], and Y = 90 for the Munsell white).

• Photometric information: the average luminance of the visual environment or

surround La, in nits (cd/m2).

• Context parameters: (1) contrast factors F and Nc, which both have values of 1.0 when

the luminance (reflected illuminance) in the surround matches the illuminance on the color area (documents or prints under workplace lighting), 0.9 when the surround illuminance is dimmed compared to the image (computer displays or overhead transparencies), and 0.8 when the surround illuminance is dark compared to the luminance of the image (cinema, slide or video images); and (2) an exponent c that modulates the response compression in image lightness, brightness and chroma caused by background lightness (the Bartleson Breneman effect), empirically set at values of 0.69, 0.59 or 0.525 for the same viewing contexts. These parameters are not measured in the scene, but are determined by visual judgment and then read from a graph.

• Response Compression Factors: (1) a luminance adaptation factor D, which increases toward a limit value of 1 as the color area appears reflective rather than emitting (that is, the surround luminance La increases,

graphical summary of CIECAM

input values and parameters

and/or F increases — the luminance of the surround matches the luminance of the image); (2) a power function FL that models

the increase in brightness and colorfulness caused by brighter viewing environments (higher levels of surround luminance La); (3)

chromatic contrast factors Nbb and Ncb,

derived from the ratio Yb/Yw, that are used

to calculate the increase in chroma, lightness and brightness caused by darker backgrounds; and (4) exponents z and n, also derived from Yb/Yw, that define the response compression

on lightness and chroma caused by background lightness.

Note that the color area may be part of a larger image, but all adaptation or contrast factors operate on the color area in isolation. CIECAM only represents shifts due to lightness contrast with the background or the effects of illuminance levels or luminance adaptation. It does not model chromatic contrast, chromatic assimilation or effects of spatial frequency between components of an image.

Chromatic Adaptation. Much of the development work leading up to CIECAM involved the choice of chromatic adaptation calculations that gave accurate and invertible results.

The equal area XYZ tristimulus values remain the standard color specification only by virtue of their broad implementation. They give bad results if used directly to calculate chromatic adaptation (as is done in CIELAB), and equal area cone fundamentals must be used instead. In addition, different response functions must be used to model the effects of chromatic adaptation and luminance adaptation. These tasks are combined through an intricate sequence of hacks: • The tristimulus values of the color area (XcYcZc) and the illuminant (XwYwZw) are

converted into "sharpened" color matching functions (which include negative values), resulting in preadaptation values for the color area (RGB) and the illuminant (RwGwBw), as

shown in the diagram below. These equalize the relative contribution of the R and G (X and Y) values and create negative

(supersaturated) values in the G curve.

• Adjustments for luminance adaptation (D) are made on the color and illuminant RGB values, resulting in post adaptation values for the color area (RcGcBc) and the illuminant.

This is the point where the illuminant tristimulus values are used to perform a von Kries transform for chromatic adaptation, shown below for the R value:

Rc = [(100D/Rw)+1–D]R

The same adjustment is performed on the Gc

and Bc values. This step corresponds to the

adaptation ratios in CIELAB, which are done on the tristimulus values directly and are therefore wrong von Kries transforms. The CIECAM formula has zero effect (Rc = R) in

cases where (1) colors are viewed under an equal energy illuminant (the RwGwBw

values are all 100), and (2) there is complete adaptation to the illuminant (D = 1). Otherwise this transform decreases or increases the cone output to match the chromaticity of the illuminant, in proportion to the degree that adaptation only partly occurs — that is, D < 1 when the surround is darker than the image, and the difference between image and surround luminance prevents complete adaptation. This becomes especially significant when the surround luminance is

below 300 cd/m2.

• The post adaptation RcGcBc values are

converted back into XYZ tristimulus values. Parallel transformations are done to retrieve the illuminant XYZ values.

• The post adaptation XYZ values are converted into a specific type of equal area cone fundamentals (Hunt Pointer Estevez fundamentals), denoted R'G'B'. • Finally, a response compression is applied to the R'G'B' cone fundamentals. This compression is approximately hyperbolic with a minimum value near zero and an upward slope that changes in relation to the level of surround luminance La, expressed as the

response compression factor FL (right). The

calculation is shown below for the R' value:

The same adjustment is made to the illuminant R'wG'wB'w values. This

transformation has the double effect of amplifying cone response differences (contrast) at very low tristimulus values (the curve has a much steeper slope at low R' values), and increasing the overall response contrast in brightness and chroma as luminance increases (the maximum value of R'a and the overall slope increases). Because

wavelengths at the tails of a cone fundamental produce a much lower response (tristimulus value) than wavelengths near the peak, and the transformation increases relative response at low tristimulus values, the transformed cone fundamentals have substantially raised tails and broad, rounded shoulders around the peaks (see diagram below). These calculations yield post adaptation, response compressed cone fundamentals denoted R'aG'aB'a and R'awG'awB'aw.

These circuitous calculations result in a "correct" von Kries transform for chromatic adaptation, adjusted in relation to the degree of chromatic adaptation, and a response compression scaled to surround luminance (luminance adaptation).

Lightness/Brightness. Correlates of lightness (J) and brightness (Q) are computed from the post adaptation, response compressed cone fundamentals R'aG'aB'a, the

background contrast factor Nbb, and the

surround luminance compression factor FL, as

follows:

Aw is computed from the illuminant

R'awG'awB'aw values. A is essentially a

luminosity function with rounded peak and raised tails that is adjusted by the contrast factors c, z and FL to represent compression

luminance dependent response

compression from R' to R'a

effects caused by background contrast and surround luminance.

Opponent Dimensions. A set of preliminary opponent dimensions are calculated as:

a = [R'a+(B'a/11)]–(12G'a/11)

b = (R'a+G'a–2B'a)/9

Note the similarity between these opponent dimensions and the fundamental dimensions of a cone excitation diagram, for example the dimensions L–M and L+M–S of a trilinear mixing triangle. The main differences are in the small amount of S (B'a) output added to

the L (R'a) cone output in the a contrast, and

in the better relative weighting of the cone outputs.

These preliminary ab dimensions are used to derive the color's hue angle (h), which in turn is used to derive an eccentricity factor e that adjusts the scaling of the a and b dimensions to represent the differences in chroma compression that occur around the hue circle.

Hue Purity Correlates. Next, chroma (C) is computed as the euclidean distance from the origin on the response compressed ab dimensions. I present the formula to show how intricate it is:

The formula can be parsed as follows: (1) the basic chromaticity distance is defined as the euclidean distance on a and b between the color and the achromatic point; (2) the chromaticity is multiplied by the eccentricity factor e, which produces a different chroma scaling along each hue angle of the ab chromaticity plane; (3) the rescaled chroma is multiplied by the chromatic induction factors Nbb and Ncb, which increase chroma as the

background becomes darker; (4) the contrast scaled chroma values are normalized on the sum of response compressed cone outputs (R'aG'aB'a); and (5) the normalized chroma

values are adjusted to compensate for the color's lightness (J) and the background contrast exponent (n).

Modern chroma metrics in CIECAM and other color models are highly complex, but this is necessary to achieve equal chroma spacing around the hue circle, appropriately normalize the luminance information across an equal chromaticity plane, and fit the correct response compression in relation to background contrast, scene luminance and color lightness. The cylindrical coordinates of lightness/brightness, hue angle and chroma are the final form of the CIECAM system.

The cylindrical coordinates are used to compute the remaining appearance attributes saturation (s) and colorfulness (M). Trigonometric functions are then used to transform the color space into cartesian coordinates Jab, whose chromaticity units are in terms of chroma, saturation or colorfulness.

Finally, there is no color difference formula optimized for the CIECAM model: the sequence of color models that began in color difference formulas ended in a model without one. However, very good results have been obtained by using the standard euclidean distance between similar colors:

∆E02 = [(L1–L2)2+(aC1–aC2)

2+(bC1–bC2)2]1/2

where "similar" means colors that are separated by a ∆E02 value of around 10 or

less. The average CIECAM ∆E02 for the first

chroma step in Munsell aim colors across all hues and values is about 7.7, slightly larger than in CIELAB. Note that the ∆E02 is

approximately in units of just noticeable difference, so color differences at or below 1 are generally not visible.

Graphical Analysis of CIECAM. It is hardly possible to understand a color model as complex as CIECAM from the calculation stream alone. The effect of the calculations (and parameter values) on color specifications must always be examined graphically.

Response Compression. Probably the single most significant feature of CIECAM in comparison to CIELAB and all previous color models is the pervasive use of exponential

functions to model response compression. CIECAM contains four variables — c, z, FL and

D — used exclusively as exponents or as nonlinear scaling factors. A graphical example of the compressive, "bending" effect of these power transforms is shown in the explanation of the R'aG'aB'a cone fundamentals, above.

Response compression is necessary both to model the basic psychophysical functions of lightness, brightness, colorfulness, chroma, saturation and hue, and to model the nonlinear changes in these functions caused by changes in the color context (background contrast, surround luminance, chromatic and luminance adaptation). Overall, including the use of trigonometric functions to compute hue angle h and the eccentricity factor e, nonlinear transforms are used in fourteen of the 22 CIECAM calculation steps. In this regard CIECAM testifies to the importance of response compression in all aspects of color perception.

Chromatic Adaptation Transforms. All the CIECAM calculations are made with equal area cone fundamentals, which correspond to the equal area XYZ color matching functions. However they are typically shown in color vision texts as normalized cone fundamentals to facilitate visual comparison of the curve shapes, especially in the tails where the adaptation adjustments have the greatest effect.

The diagram shows the pre adaptation, "sharpened" color matching functions RGB and the post adaptation, response compressed R'aG'aB'a cone fundamentals.

chromatic adaptation functions in CIECAM under illuminant D65; (left) CAT02 RGB system of pre

adaptation, "sharpened" color matching functions; (right) post adaptation, response compressed cone

fundamentals R'aG'aB'a

The key features of each set of curves are visually obvious when compared both to the XYZ color matching functions and to normalized LMS cone fundamentals, linked above.

The RGB color matching set introduces negative values in the R and G curves, which makes them resemble the original RGB color matching functions, except that the "out of gamut" hue is not blue green but blue violet. This defines the B "primary" as supersaturated and increases the chromaticity distance between the B and G "primaries".

The R'aG'aB'a cone fundamentals resemble

the logarithmic cone fundamentals, because these curves were transformed using a power function. In fact the curves have a roughly triangular shape that opens up hue differences in the tails and significantly improves on the cube root transform used in CIELAB. The separation between R'a and G'a

is also reduced so far that hue discrimination (spacing) is more specifically affected by changes in R'a outputs for hues at

wavelengths above 580 nm, and by changes in B'a outputs for all hues below 580 nm.

Opponent Geometry. The final chroma based (luminance independent) opponent dimensions in CIECAM, aC and bC (right, top) closely

resemble the Hurvich and Jameson opponent functions and the X–Y and Y–Z dimensions of CIELAB before the cube root compression is applied (above).

The more intricate chromaticity calculations in CIECAM remove the kink found around 500 nm in the CIELAB a* dimension (see above), and produce a less angular, more evenly spaced involute of optimal colors, especially from cyan to violet (right, bottom). This is one of the most important differences between CIELAB and CIECAM. The correlation between the dimensions is also substantially

reduced, to –0.14 from the –0.35 in CIELAB — a deviation from perpendicular of about 8°.

The historical XYZ tristimulus values produce some sawtoothing in the b curve across yellow green hues, the result of amplifying (via the chromatic adaptation transformations) some coarsely interpolated Z values where the S cone response is near zero. The sawtoothing is amplified to a significant degree under "yellow" illuminants (such as illuminant A), and will introduce discontinuities in the placement of saturated yellow greens. A new Z function derived from the recent Stockman & Sharpe estimates of S cone sensitivity would eliminate the problem.

Chromaticity differences scaled on chroma (aC

and bC) are independent of changes in

surround luminance La or background contrast

(Yb/Yw). The dimensions scaled on

colorfulness, aM and bM, expand as scene

luminance La increases, to model the Hunt

effect, and as brightness induction increases (low values of Yb). CIECAM also provides

dimensions scaled on saturation, as and bs,

which contract under increases in scene luminance or brightness induction; the saturation metric also produces a large "donut hole" gap between the achromatic center and the first Munsell value step, consistent with the crispening effect.

Chroma Scaling. As I explain in the discussion of hue purity, measures of hue purity (chroma or saturation) have been the most troublesome, imprecise and complex features of modern color models. No exception, the most intricate aspects of CIECAM concern the scaling of colorfulness, chroma and saturation.

opponent geometry of CIECAM

(top) opponent functions ac

and bc based on chroma

scaling;

(bottom) trace of

monochromatic color stimuli

on the acbc plane;

both displays under equal

energy illuminant

The diagram below shows the final chroma scaling in CIECAM in comparison to the preliminary CIECAM dimensions and to the chroma scaling in CIELAB. The two diagrams (right) show the distribution of optimal colors on the CIECAM acbc (chroma) and

asbs (saturation) planes. CIECAM achieves

good consistency in the scaling of both quantities, and the resulting roughly circular volumes (especially in the saturation metric)

indicate that CIECAM chroma and saturation are approximately relative measure of hue purity, in which optimal colors provide the perceptual standard for maximum chromatic intensity.

chroma scaling in CIECAM02 (left) Munsell aim colors for V = 5 in CIELAB; (right) the Munsell aim colors in CIECAM02, showing the chromaticity locations on the preliminary opponent

dimensions ab (gray) and on the eccentricity corrected dimensions (blue); because the dimensions before and after adjustment are measured on different scales, the two views are standardized to have equal chroma at C

= 8.

In comparison to CIELAB, the final CIECAM chroma values produce a very large contraction in all highly saturated colors, including colors near the optimal color limits that are not usually found in material colors, and an expansion in the chroma of near neutral or desaturated colors. In comparison to the preliminary ab dimensions, the final CIECAM chroma values produce the largest relative contraction in colors from middle blue through magenta to orange.

During work on the OSA uniform color scales in the 1950's it was found that the chromaticities of any opponent dimensions color model must be scaled differently for each hue quadrant of the color space. In CIECAM this is achieved (not very satisfactorily) through the eccentricity factor e, which shifts a circle of constant chroma by about 0.2 toward middle blue (hue angle 245). This most strongly contracts the chroma of deep yellow hues and expands the chroma of blue hues, with no effect on the chroma of greens and purples.

optimal color boundaries on

the CIECAM ab plane

(top) chroma metric,

(bottom) saturation metric;

under EE illuminant, 20%

background reflectance, white

surface

luminance 318 cd/m2

This eccentricity scaling is easiest to see by comparing the CIELAB and CIECAM chroma of dull to moderately saturated Munsell aim colors, as shown below. The increase in blue chroma at around hue angle 245, and the depression of chroma at around hue angle 65 are clearly visible. The adjustments also introduce more variation in chroma values across different lightness levels in yellow, red and purple hues.

chroma adjustments by hue angle in CIECAM02

measured chroma of Munsell aim colors for value V = 4 to 8 and chroma C = 2 to 12, in CIELAB and CIECAM02;

illuminant D65

Note that, in a color space based on perfectly accurate color samples and a "true" measure of perceived chroma, the lines of points would be perfectly straight and horizontal.

Hue Scaling. Chroma spacing also significantly affects hue spacing. The CIECAM calculations produce a much better spacing and straightness in lines of constant hue. The diagram below shows the location of radial colors, defined in the OSA color space to avoid the flaws in the spacing of Munsell hues, in CIELAB and CIECAM. The CIELAB lines show unequal spacing around the hue circle and strongly curving hue lines in purple hues. The CIECAM values lines are almost exactly equally spaced, the lines of constant hue are much more linear, and the overall distribution

is much closer to circular.

lines of constant hue in CIELAB and CIECAM02

radial sample of OSA UCS color space for three lightness values L = –2.3, –0.5 and 1.8, under

illuminant D65 (aim color data from Moroney, 2003)

Brightness/Lightness. The effects of surround luminance and background contrast on both lightness and brightness are fairly straightforward.

First, consider situations in which the scene parameters Nc, F and c are held constant at

"normal" values that represent the viewing of papers or prints under the same illumination as the surround (La).

In this basic context the environmental illumination can be varied from dim office lighting of about 100 lux (La = 30) to

afternoon daylight illumination of about 10000 lux (La = 3000), and the documents or prints

can be viewed against a background that is either dark gray (Yb = 5), middle gray (Yb =

20) or white (Yb = 90). The diagram below

shows the effect of these variations on lightness (J) and brightness (Q).

lightness and brightness in CIECAM02 (left) lightness values J at three levels of background

standardized luminance, Yb; (right) brightness values Q

at three levels of surround luminance La and three

levels of background standardized luminance; averaged values across 2800 Munsell colors, equal energy

illuminant.

The curves for lightness J (diagram, left) show the effect of background contrast on the spacing of a gray scale. A white background minimizes the response compression and produces a relatively linear spacing gray values in relation to the color's luminance (Yc). A dark gray background increases the

overall response compression, producing more contrast among dark valued colors and less contrast among light valued colors. This is the Bartleson-Breneman effect. These changes in the lightness curve are identical across all levels of surround luminance (La), because

relative lightness remains constant across the normal range of illumination.

The curves for brightness Q (diagram above, right) show the expected effect of increasing surround luminance: as La goes up, so too

does the brightness of all colors and the perceived amount of contrast between dark and light colors (the Stevens effect). However, background contrast also increases apparent brightness through brightness induction — dark backgrounds make colors appear more luminous (brighter and more colorful). And this "color amplifying" effect of darker backgrounds becomes greater at higher levels of surround luminance.

In a similar way, changes in surround

luminance La have no effect on chroma but

increase relative colorfulness. Changes in background contrast Yb have a small effect on

chroma: in the range shown, from 5 to 90, the chroma increases by about 1.5 Munsell steps (as shown below), and produce an even smaller increase in colorfulness.

chroma and background contrast in CIECAM02

(left) Munsell aim colors for V = 5 in CIELAB; (right) the Munsell aim colors in CIECAM02, showing the

chromaticity locations on the initial opponent dimensions (gray) and on the eccentricity corrected

dimensions (blue); because the dimensions before and after adjustment are measured on different scales, the two views are standardized to have equal chroma at C

= 8.

Surround Contrast. The effect of changing the surround contrast parameters c, Nc and F,

which model the difference in color appearance between reflective documents viewed in bright environments and projected or emitting images viewed in dark environments, is small and uniform within a realistic range of values for the surround luminance (La).

Changing the luminance value of the surround, La by itself has no effect on the chroma or hue

of colors. However it does affect both lightness and brightness and, through brightness, relative colorfulness as well.

context and lightness/brightness in CIECAM02

(left) lightness values J under normal scene contrast (Nc = 1.0, F = 1.0, c = 0.69) and dark scene contrast

(Nc = 0.8, F = 0.8, c = 0.525); (right) brightness

values Q at two levels of surround luminance La and

two levels of surround contrast; averaged values across 2800 Munsell colors, equal energy illuminant.

The diagram for lightness (left) shows that dark viewing environments decrease somewhat the contrast in light values and increase the contrast in very dark values. Increasing the scene luminance improves the discrimination of light values and reduces contrast in dark values.

The effects on brightness (and by extension on colorfulness) are similar but much larger. Viewing a video display in a dark environment (La = 30) produces greater brightness than

the same display in a well lit environment (La

= 300), but this is offset by the shape of the brightness function, which becomes flatter and more sharply bent as surround luminance gets darker, a compression that can be only partly offset by increasing the contrast (gamma) of the display. In fact, an optimal video image appearance usually requires only a slightly dimmed room illumination, provided that the lights do not reflect off the television screen. The newest liquid crystal and plasma displays provide excellent contrast at near normal levels of indoor illumination.

Unfortunately the best balance between image luminance and surround luminance is not easily derived from CIECAM, because the

image luminance values are standardized (limited to a maximum value of 100) by the tristimulus values. Despite the worked examples in the CIE technical reports and current color texts, this aspect of the model remains a judgmental art.

Illuminant Adaptation. Finally, like both CIELUV and CIELAB, CIECAM can shift the achromatic point of the color space to match changes in the illuminant, which allows prediction of corresponding colors under a new illuminant.

corresponding colors in CIECAM02 Munsell aim colors at value V = 6 represented under

illuminants with a correlated color temperature of 6500°K (daylight D65, left) or 4000°K (incandescent A, right)

The shifts shown here indicate that the Munsell neutral color sample will appear to be a moderately saturated blue in daylight, and a Munsell orange at chroma 8 will appear closest to a neutral gray. Note the improved spacing of colors as the illuminant changes, compared to the stretched out corresponding colors predicted by CIELAB. The CIECAM Color Space. Is CIECAM02 worth the trouble? All available research suggests it is, but much depends on how the evaluation is made.

A comparison of the locations of the Optical Society of America's Uniform Color Scales (OSA-UCS) in CIECAM02 (right) and in CIELAB (shown here) shows many small differences, particularly in the chroma spacing of colors around the hue plane, the downward shift in lightness values, and the more equal chroma spacing across different lightness levels.

Cumulatively these amount to significant alterations in the color appearance predictions.

A much sharper contrast is visible in the placement of Munsell aim colors in CIECAM (below), compared to CIELAB (shown here). The strongly curved lines of constant hue in blue violet and purple hues are completely remedied, and there is generally a more stable alignment of hue angles across different lightness levels. The gap in the spacing of green colors (in the upper left quadrant) is a fault in Munsell, not in CIECAM, but I am unsure about the similar gap that appears in blue violet (b–) hues.

munsell aim colors on the CIECAM02 acbc

plane under illuminant D65; aim colors at 2.5 hue intervals

and /2 chroma intervals for values 4, 6 and 8 out to the optimal color limits; constant CIECAM chroma indicated by gray circles. Note that all CIE systems reverse the

ordering of Munsell hues.

A specific quirk I uncovered in my technical review is that CIECAM chroma spacing is strongly compressed for colors approaching the optimal limits, which is visible in dark valued violet and blue green hues (above). In contrast, CIELAB maintains a perfectly regular spacing out to the chroma limits. It may be that the optimal limits, which are materially

OSA UCS aim colors in theCIECAM02 color space

under illuminant D65; layer

OSA L = 1 shown in magenta;

the g dimension is reversed in

all CIE color models

not possible in surface colors without a contrived boost in luminance contrast, are simply outside normal visual experience and therefore irrelevant to the correct spacing of perceptual attributes.

Future Prospects. As CIECAM is only a few years old, there is currently no spectrophotometric implementation and no software available, apart from spreadsheets and MATLAB algorithms.

Unlike CIELAB, which can be defined completely and automatically with a spectrophotometer, CIECAM requires the manual (judgmental) specification of parameters for surround luminance, background contrast, and viewing context. These can be set to default values and CIECAM used in the same way as CIELAB, but the potential of the model depends on automating these values.

Fairchild (2005) does not include tests of CIECAM02 per se, but the many development studies of CIECAM, and of related models such as the one developed by Hunt and Luo, indicate that there is no further improvement possible within the current conception of the viewing context. Looking ahead, Fairchild strikes a dour note:

It appears that the time between CIECAM02 and the next CIE color appearance model will

be significantly longer than six years. One

reason for this is that this type of model seems to be predicting the available visual

data to within experimental uncertainty. ... The cost and difficulty of collecting such data

as well as inherent inter-observer variability make it unlikely that significant improvements

in the available data will be obtained in the foreseeable future. (p.277)

He adds that it might be worthwhile just to "start over from scratch" and rebuild colorimetry on more advanced principles based on more recent data.

In fact, there is much more vigorous activity than this view implies. Current work is focused on ICAMs — image color appearance models — that can account for differences in the size of color areas, chromatic contrast, crispening,

spreading, and differences in the quality or processing of images. And targeted revisions of color models, like those made on CIELAB, can produce a large number of separate modules or patches that can be swapped in and out of existing color models for specific applications or viewing situations. Future work is likely to be as creatively disorganized as it has been in the past.

My summary of CIECAM97s and CIECAM02 is based on Mark Fairchild's Color Appearance Models (2nd ed.) (Wiley: 2005) and R.W.G. Hunt's Color Reproduction (Wiley: 2004). An overview of CIECAM02 is available as a color appearance lecture and as a spreadsheet of worked examples from the Imaging Science Lab at Rochester Institute of Technology. Fairchild also provides an overview of ICAMs.

Artists may be interested in the average location of watercolor pigments on the CIECAM aCbC plane, also

available as a PDF file.

N E X T : the structure of vision (i)

Last revised 08.01.2005 • © 2005 Bruce MacEvoy

the structure of vision (i)

This page and the next

explore the visual processes that transform our binocular, retinal images into a flowing, rich, three dimensional experience of the

world.

We won't completely ignore the topic of color, because the perception form and space affects our color perceptions. However, our main interest is to clarify or even discover artistic strategies or resources in the way vision works.

I explain the basic visual processes and the evidence for their importance to vision, then review the artistic implications of these processes for artistic representations. I especially try to clarify the relationships among the many aspects of color vision. By alternating between science and art, I hope to keep the discussion focused and useful.

This page and the next are technical, but include much information relevant to the principles of composition and design.

A common idea is that vision constructs and interprets what we see. This is usually said to assert that the influence of experience and culture is closely intertwined with our biological or cognitive capabilities. But it more accurately means that one visual capability builds on or flows out of another, regardless of how much that capability depends on experience, and in ways that are most often unconscious and far below the complexity of attitudes or beliefs.

How can we describe this process? The metaphor that seems to apply everywhere is the weaving of contrasting sources of information. This process begins in the retina, with the network of retinal interconnections among receptor cones and rods, and expands until literally most of the

the weave of vision

colorvision

the weave of vision

center/surroundreceptor fields

edge & region detection

texture & surface analysis

cortex contributes to visual experience. At each step in this process, there is a competitive separation or combination of related sensory signals: differences are accentuated and similarities smoothed together.

This weaving occurs across a sequence of visual tasks, each task building on and partly influencing the outcomes of preceding tasks. A highly simplified description of this sequence is shown below.

the major stages of visual processing after Stephen Palmer (1999)

In the first stage, the eye forms the basic retinal image from the response of the millions of separate cones or rods to the optical image projected onto the back inner surface of the eye, as discussed in the page on light and the eye. Each of these cones independently codes a very tiny area of the total optical image, like a single pixel in a computer image. At the same time, these autonomous cones are linked together through a network of other retinal cells, so that the output from neighboring cells can be combined into center/surround receptive fields. This retinal network creates the opponent coding of color, sharpens edge contrast, and performs a basic frequency analysis of the retinal image.

The next step involves the construction of a primal sketch. The retinal image is "filtered"

to eliminate noise and increase contrast through the complex cells in the visual cortex, which also perform edge & region detection that simplifies the two dimensional image into a "line drawing" of edges enclosing continuous areas. Simple principles of two dimensional geometry are used to connect broken or interrupted edges across the entire image. This primal sketch is created using the retinal location as the basic framework, and by aligning and merging the retinal images from both eyes, which results in a rendering of the visual image that we can think of as a moderately detailed line drawing.

The third stage shown in the diagram elaborates the primal sketch into textures and surfaces. The resulting surface layout identifies separate surfaces through movement, luminosity, reflectivity, texture and color, approximately determines the slant or curvature of these surfaces through perspective gradients and illuminant shading, and uses a variety of depth or distance cues (binocular disparity, motion parallax, retinal image location, occlusion, visual fusion, etc.) to locate the surfaces as near or far from the viewer in three dimensional space. This analysis also guides and clarifies the edge and region detection that preceded it. The result is a 2.5 dimensional sketch, with shows the tilt, slant and distance of visible surfaces in relation to the viewer's location and orientation in space. We can think of this rendering as a bas relief image of the world.

The next, object representation stage completes the 2.5 dimensional sketch in three dimensions by identifying discrete objects or continuous surfaces in space. This depth and volume analysis uses basic knowledge of three dimensional geometry and object grouping heuristics (such as common movement, connectedness or visual similarity) to join together surfaces interrupted or hidden from view behind closer objects; infer the unseen, back sides of objects; and conceptualize three dimensional forms having volume and shape. Again, this object representation guides the surface layout analyses that come before it, is highly dependent on our experience with things, and begins to transform the visual image into

intellectual or conceptual content.

In the penultimate or categorical representation, objects are recognized or categorized in terms of their physical properties or the functional possibilities (or affordances) that were encountered in similar objects in past experience. That is, the purely surface and volumetric characteristics of objects are merged with abstract ideas of color, form, hardness, weight, stability, temperature, function and origin derived from past experience. At this point even unseen features (such as teeth inside a dog's mouth), anticipated outcomes (the fear of falling when looking down from a high balcony) or even false perceptions (an open doorway that is actually a closed glass sliding door) are "seen" as real.

Only after all these tasks are completed does the weave of vision enter consciousness and become visual experience. At this level the physical scene is already joined to our awareness of our own body; we have emotional reactions to what we see, assign words or labels to things, direct our gaze to explore specific aspects of the scene, and use what we see to guide our behavior. Two cautions. First, although described as separate steps in visual perception, these various tasks are highly interdependent. Second, the separation into tasks and their description depends heavily For example, color perception appears to require contributions from the retina, the lateral geniculate nucleus, the primary visual cortex, and several secondary regions of the visual and language cortex. The essential property of vision is that it forms a continuous weave: no part can be separated from any other without damaging or destroying the whole.

The problem with much of the art design literature is that it assumes our visual capabilities work in a fixed or mechanical way, and therefore can be translated into simple design principles. In fact, our visual capabilities mutually influence or compete with one another, yielding or asserting their contribution to our visual experience depending on the relative importance of the others. These dynamic

design principles are much less well understood, but they are probably the most important considerations in a visual design. Images determine the balance of visual interpretation by how much perceptual material they offer to arouse these interacting visual capabilities.

Our understanding of human vision relies on four types of evidence: (1) detailed anatomical knowledge of how nerves and regions of the human eye and brain interconnect; (2) measurements of the response of single cells to simple visual stimuli in the visual pathways of small mammals (cats and monkeys); (3) extensive experimental study of human visual performance, including susceptibility to visual illusions; and (4) practical experience in building electronic sensors and programming computer neural networks to perform equivalent visual analysis tasks. The resulting picture of human vision is plausible, though it is also largely speculative — habitual scientific explanations applied to ambiguous facts.

An excellent overview of the most recent research and concepts in vision science is Stephen Palmer's Vision Science: Photons to Phenomenology (MIT Press, 1999), in text hardback. A much shorter, somewhat older but thoughtful survey is Richard Gregory's Eye and Brain: The Psychology of Seeing (Princeton University Press, 1997), currently in its 5th paperback edition.

center/surround receptive fields

Center/surround organization of visual fields, opponent organization.

Competition is an essential component of visual processing: it sharpens, or provides contrast enhancement, in a neural representation, adjusts the network's total activity to a constant overall level of stimulation, and prevents cells from becoming saturated in response to variable inputs.

In pursuit of competition, the cones and rods of the retina are systematically interconnected as groups that can signal when some but not all of them are stimulated by light — that is, when a contrasty edge falls across them. These clusters are themselves clustered, and those clusters clustered, to create a spatial

frequency interpretation of the visual image. Center/Surround Design. Schematically, the process works as follows. A spatial array or row of receptor cells responds to a sharply defined light stimulus (diagram at right, top). This produces both direct (stimulating) outputs to the nearest bipolar cell, and indirect (inhibiting) outputs to nearby horizontal cells (middle). As these separate outputs are averaged in deeper layers of vision, edges become accented by increasing the light and dark contrast at the edge location (bottom). These edge contrasts are very easy to induce — on lightness, chroma or hue — in what are called Mach bands.

Through the appropriate neural network these contrasts can occur across different retinal distances (visual angles), different orientations or shapes, even different patterns of movement, which basically transforms the retinal image into a spatial frequency analysis (diagram at right), which can block out large areas of value or provide a detailed outline of form (illustration at right). The very broad utility of our pattern and spatial perception capabilities is suggested by the fact that they underlie many of our most civilized capabilities, from reading text to catching a fly ball. They are also intimately connected to, and strongly influence, our perception of color.

responses of an "off center/on surround" receptive field to different patterns of

light and dark

These response fields are in turn sensitive to changes in the light stimulus, producing a visual fusion across time, or motion blurring in quickly moving objects, regardless of their size. This boundary is defined by the number of responses the cell can omit across time,

design of an "on center/offsurround" retinal receptive

field

how quickly the cell changes its responses over time, and the synchronization of the changes. Center/Surround Contrasts. If the retinal receptors are joined into these larger center/surround fields, how do individual cones convey color or luminosity information? The answer seems to be that individual cones contribute to multiple fields, and the fields themselves are combined to produce the opponent contrasts.

We've seen that there are three basic opponent contrasts — w/k, y/b and r/g — but these can be represented in two ways, resulting in six types of center/surround fields:

As there appears to be about 1.25 million ganglion cells in the human retina, but there are about 6 million cones, at least 5 cones, on average, must feed into each ganglion cell, though this ratio is probably much lower in the fovea and much higher in the periphery. In fact, as many as 25 different types of ganglion cell exist in human retinas, with different cell body sizes and different connection patterns to other cells. (The dendritic connections are smallest in the fovea and may be as much as 10 times larger toward the periphery of the retina.).

In the human retina, the three commonest ganglion cell types are the large parasol, small parasol and the midget ganglion cells, which connect to separate layers of the lateral geniculate nucleus (LGN) between the eyes and the brain. These connections have not been measured in humans, but in monkeys with demonstrably equivalent visual responses, by measuring the rate of synaptic impulses (cell firing rate) in single LGN or visual cortex cells receiving information from a single center/surround field.

w/k contrast: +W-K (white) +K-W

(black)

r/g contrast: +R-G (red) +G-R (green)

y/b contrast: +Y-B (yellow) +B-Y (blue)

response curves of six center/surround LGN color cells

changes in firing rate of center/surround cell with changes in monochromatic wavelength shining on its receptive field in the retina; horizontal lines show baseline firing rates (primate visual cortex, from De

Valois & De Valois, 1997)

If there is a fundamental harmonic or mathematical structure to color vision, I think it would closely resemble these curves. Because the retinal cells are always producing a baserate neural signal, each of the contrast fields has a resting or adapted value shown by the horizontal lines; these appear to be different for each type of contrast, not unlike the different fundamental frequencies of musical tones.

The colored curves show a number of peaks and crossings that do not correspond to the cone sensitivity peaks or the hue cancellation curves, but do identify significant color landmarks of their own. The +Y-B peak, at the crossing of the +R-G and +G-R curves, is very close to the warmest red orange hue, while the complementary +G-R peak above the crossing of the +B-Y and +Y-B curves is close to the coolest blue green hue. Unfortunately, we lack a clear picture of these contrasts in human subjects, and a clear understanding of how they are combined and transformed to produce conscious color experience.

To make things even more complicated, response fields react somewhat differently to patterns of color differences as opposed to patterns of luminance or brightness differences.

center/surround visual fields respond differently to color or luminance

As this diagram shows, a typical +R-G center/surround can code either for color (at

left) or for luminosity (at right), depending on the specific size, color and movement of the visual stimulus. In addition, the color response has a lower resolution than the luminosity contrast, and somewhat lags in time the luminosity response. Color is a fuzzier and slightly tardy arrival in visual experience, while luminosity contrast is prompt and crisp.

Although the center/surround organization of the retina has not been demonstrated by explicitly tracing retinal nerve connections, it does explain a large range of visual phenomena, including visual illusions that are hard to explain in any other way. One of the most popular is the Hermann grid.

a hermann grid and a scintillating grid the lower diagram shows that an "on center/off

surround" receptor field receives greater inhibition at line intersections, and therefore reports a darker color

Direct your gaze at any intersection of horizontal and vertical lines in the grid on the left. You may notice the appearance of diffuse, faint dots in the intersections around it — but if you look directly at them, they disappear, only to reappear that the intersection you were just looking at.

The schematic underneath shows the center/surround explanation for this effect. The dots disappear at the center of attention because the center/surround fields there are extremely small, and so report all the edges accurately. However the peripheral

intersections fall on peripheral center/surround fields which are on average of a larger diameter. Some of these have a diameter roughly twice the thickness of the lines in the grid, which causes an "on center/off surround" field to be more inhibited at the intersections than elsewhere: this inhibition produces the appearance of a darker, fuzzy dot.

You will notice that the red colored half of the grid produces pinkish colored dots, although these may appear slightly fainter than the dots in the black and white half.

A striking variant is the scintillating grid (above, at right), in which the illusory darkening of the gray line intersections competes with white dots placed at the same locations. Fixating directly on any single dot shows it to be white, but dots in the parafoveal field appear to be filled with gray dots, while dots in the peripheral field seem to be replaced by black dots. This makes the illusory nature of the dots even more obvious: some say that this grid is actually the Bush administration's secret map showing the location of Saddam's weapons of mass destruction!

Spatial Frequency Analysis. So far the retinal center/response fields have been described in terms of simple, center vs. surround contrasts of luminosity or color. By the time these responses reach the visual cortex, however, the fundamental emphasis has been radically altered. This brings us to the next major stage of vision, the image frequency analysis. Let's look first at what a frequency analysis does, then look at how this is probably performed by our visual system.

We start by inspecting the perception of spatial frequencies in our conscious visual experience. This is commonly done with a contrast sensitivity plane, similar to the one pictured below. (Unfortunately, a computer monitor is limited by its pixel spacing and contrast settings; the best contrast stimuli are printed on very fine grain, high contrast photographic papers.)

a contrast sensitivity stimulus the number of vertical stripes in a constant horizontal visual angle (spatial frequency) increases left to right, and lightness contrast (luminance amplitude) increases

from top to bottom

This contrast sensitivity stimulus shows

alternating black and white sinusoidal waves that change visually in two ways: the spacing between the waves decreases from left to

right, and the contrast or lightness difference between the peaks and troughs of the waves decreases from bottom to top. Eventually the contrast between light and dark becomes so subtle, or the spacing between the bands so narrow or so wide, that the stripes seem to

disappear altogether.

This is most evident at the top left and top right corners of the stimulus. The boundary where the waves disappear shows (1) the minimum contrast sensitivity (minimum amount of contrast) necessary to perceive alternating bands at each spatial frequency. This frequency/contrast relationship becomes more obvious if you view this image from a distance of 1, 3, 6 and 12 feet (your room or cubicle allowing): the stripes at far right will disappear and the stripes at center will become shorter, because the visual frequency of the bands increases with distance.

The boundary where the bands dissolve into continuous gray defines a characteristic contrast sensitivity function (right): contrast sensitivity is greatest (extends to the most subtle lightness differences) at around 4 to 5 cycles (black stripes) per visual degree.

the contrast sensitivity function

from Palmer (1999)

(A visual degree is roughly the apparent size of your thumbnail viewed at arm's length.) At higher spatial frequencies, greater contrast is necessary to see the bands until, at around 60 cycles per degree, even pure black and white stripes become invisible: visual fusion occurs for all textures.

The contrast sensitivity function is actually made up of separate, narrow frequency functions corresponding to complex cell wavelet fields of different spatial frequency. Each wavelet contributes a narrow sensitivity to a specific spatial frequency, but the combined fields overlap to produce the continuous contrast sensitivity function. (Note that the contrast stimulus is designed with vertical stripes; different groups of complex cells provide contrast sensitivity tuned to other orientations or direction of movement.) And, as we've seen demonstrated with the scintillating grid, the highest visual resolutions (the smallest response fields) are only available in fovea, while the coarsest resolutions span a broad area of the retina and are limited to peripheral vision. Two images of Groucho Marx, at low and high spatial frequencies (right), show how the highest frequencies are important to identify detailed textures, edges and rapid changes of contrast, while low frequencies make broad contrasts between areas of different lightness or color.

This is a radical difference between human (mammalian) vision and, say, a digital camera. The camera records a scene as a constant matrix of equal sized pixels, equally spaced across the whole image: resolution is consistent across the whole image. The eye records a scene as many layers of overlapping visual frequencies, with the highest frequencies concentrated at the center of view (the foveal field): resolution depends on what we look at.

Wavelets, Orientation & Motion. The visual cells of the cortex, first investigated by Hubel and Weisel in 1964, respond primarily to the spacing, orientation and movement of edges or isolated dots or lines.

the face of groucho marx aslow and high spatial

frequenciesfrom Palmer (1999)

The diagram at right suggests how this is

done. Separate but overlapping center/surround fields in the retina produce a series of peaks and valleys along the axis of their grouping, producing a wave function in visual sensitivity. These fields map directly to relay cells in the lateral geniculate nucleus (LGN), which in turn feed to a single complex cell in the visual cortex. However, the inputs from the LGN are themselves arranged in a center/surround pattern, which unites the separate retinal fields into a single waveform receptive field or Gabor wavelet. This is shown in cross section as a tapering wave function, and in two dimensions as a retinal pattern of excitation and inhibition (light and dark).

What good is this? Well, this type of field would be maximally stimulated or maximally inhibited by a pattern of light and dark lines that exactly matches the spacing of excitation and inhibition. Other spacings would produce a smaller response, while very discrepant spacings would produce no response at all.

Also, spaced lines will stimulate this wavelet only if they are close to parallel to the waveform orientation — in this case, the lines would have to be vertical. Horizontal lines, whatever their spacing, would cross all the fields equally, and produce no response.

Finally, the firing of LGN cells comes in spikes rather than the continuous signal of the cones, and these spikes importantly define a pattern across time. If the complex cell is tuned to a particular temporal pattern, then the movement of a single line along the waveform axis would produce a series of spikes to the complex cell depending on the speed of the line. It also appears that the complex cells are tuned to different frequencies in time, which have been studied using flicker stimuli of flashing, stationary lights.

These wavelet structures are actually embedded in the large structure of the cortex itself. Each region of the retina feeds into a large population of complex cells, organized into compact columns about 2mm wide and 10mm deep. Within each column, complex cells are organized around the circumference like the points on a compass, to respond to different spatial orientations or directions of

overlapping retinal/LGN receptive

fields summed in a wavelet filter cell

in the visual cortex

a single foveal cone (blue) contributing to different center/surround clusters

movement; from top to bottom within the column, the cells are tuned respond to different visual spacings or visual frequencies. Columns from the two eyes are layered side by side in matching areas of the binocular field, and the columns are arranged across the cortex according to their overall location in the retina.

Neural organization that precise and extensive implies processing tasks of incredible importance to visual experience.

It is not clear how color is involved in these contrasts, but one account is that the entire visual scene is first "outlined" using luminosity information alone, then "painted" with the color information brought through separate pathways.

the gradation of visual information

I described earlier the importance of the primate visual design for life among the trees, and in that context the emphasis on motion and spatial frequency information makes sense in the resolution of distance and body movement information. The superficial resemblance between the contrast sensitivity diagram and the inescapable perspective gradient suggests the usefulness of spatial frequency analysis for distance perception, especially via the systematic changes in spatial frequency that characterize an approaching object. The fact that spatial frequency analysis is so powerful and flexible in the definition of edges and textures indicates it is truly the foundation of visual perception.

edge & region detection Now edges and regions.

Partitive Mixing. These boundaries on visual frequency mean that human vision divides roughly into three categories: colors, textures and object surfaces. Each is determined by the visual fusion for the available visual size and contrast.

The human contrast sensitivity curve shows that any contrasting elements smaller than about 1 pixel (roughly 1/80th an inch) viewed from about 48 inches will appear to be a single color. However, a variety of effects appear in vision depending on the exact spacing of the elements and their contrasting hues or values, as the next example shows.

color shifts caused by differences in spatial frequency

At relatively large visual sizes (left), the gray color interacts with the intense orange background according to the principles of simultaneous color contrast: the color shifts toward the complement of bright orange (dull blue) and appears darker and cooler.

At moderately small sizes (center), the spreading effect causes the gray to retain its identity, but now the shift is toward (rather than away from) the surrounding color, making the gray appear lighter and warmer. At extremely small sizes (right), as in the tiny dots in one of Seurat's Neo-Impressionist paintings or modern halftone color reproductions, partitive mixing (also called visual fusion) occurs, and we see the additive mixture of the orange and gray light to produce a grayed maroon. Visual fusion was

exploited particularly by the Neo-Impressionists to create color mixtures through partitive mixing or optical color mixing, though exmaples of the technique can be readily found in the paintings of Delacroix, Watteau and Rubens. More dramatic effects due to spatial frequency have been exploited by Op Art painters such as Bridget Riley.

It's difficult to demonstrate here, but temporal frequency also has an effect on color, though the principal demonstration is commonly that a completely black and white pattern, if rotated rapidly under an intense light, can produce phantom reds, greens and blues.

Anyone who has put together jigsaw puzzles knows the strategy of finding and fitting together the edge pieces first. The edge shapes are easy to recognize, their connections are limited to two sides only, and they determine the location of shapes inside the puzzle. Our visual system seems to work along similar lines: identify the obvious edges, then use these to define shapes or regions in the image. Edge Contrast Effects. Various mechanisms are active to sharpen edges by increase the color difference between the two areas on either side.

the relationship between area and texture

And so.

There are various ways to characterize the complexity of edges and forms.

mach bandsa gradation from light to dark

appears bordered by light and dark bands, which become

more prominent as the gradation

becomes steeper

The first method is by the number of edge crossings by a straight line between two randomly or regularly selected points. The simplest area colors have few or no edge crossings between two points inside the form, and only one edge crossing between a point inside and a point outside the form. Most texture colors have a large number of edge crossings, as shown in the examples.

high crossing and low crossing areas and borders

A second method is by grid scaling. A square grid of fixed spacing is placed over the surface of a pattern or texture, and the number of squares that contain an element are counted. The spacing is changed, the grid is placed at random on the texture, and the process is repeated. After several counts the number of texture containing squares N is divided by the width of the squares, W, to yield the ratio, W/N. In natural textures and forms, such as gravel, coastlines and lightning, this ratio is about 1.3.

First of all, contrast is most enhanced along an edge, especially between areas that differ slightly in lightness, chroma or hue. This makes the edge easier to see. The first example involves Mach bands (first described by Ernst Mach in 1866) appearing clearly in areas that increase slightly in lightness across the page.

center/surround response to a Mach band

Within each band, the edge against a darker band (on the left) appears lighter, and the edge against a lighter band (on the right) appears darker. The lightness shift increases as we near the edge on either side, which gives the appearance of scalloped grooves, such as the fluting on an Ionian column.

chevreul illusion for small changes in lightness (top), chroma (middle) or hue

(bottom)

The second example shows a chroma transition for a constant hue and lightness of red, and the third a hue transition from yellow green to red at a constant lightness saturation of 70%, (which makes the yellow appear dull green). There is a weaker Mach effect for

chroma and a very weak effect for hue — as we would expect, because hue is a weaker contrast stimulus than lightness or chroma. Within each chroma band the edge against a more intense color (on the right) shifts toward gray (less intense) and the edge against a less intense color appears more intense; in the hue demonstration the edge against a redder hue (on the right) shifts toward green (cooler) and the edge against a cooler color shifts toward red or yellow (warmer).

Notice that the Mach effect is more apparent in some of the chroma or hue bands than in others, while the effect across value gradations appears equal. Because value structure is essential to our perception of three dimensional form, the eye has adapted to discriminate equally even slight differences in edge lightness across a wide range of tonal values.

This induced shift in the quality of color along an edge was also described by Michel-Eugène Chevreul, who influenced a few contemporary artists to use it as an artificial accenting device — for example, as Georges Seurat did extensively in his pointillist Un Dimanche après-midi à Ile de Grande Jatte (1884). But the trick is in fact old, and easily found in works by Rembrandt or Tintoretto.

Area Filling. Perhaps the simplest and most pervasive of these illusions, which is related to the "filling in" responsible for the spreading effect, is the Craik-O'Brian effect, crudely illustrated in the figure below.

the craik-o'brian (cornsweet) effect

The subtle gradation in value necessary to make the illusion more dramatic can't be fully achieved in a browser digital image, but the gist is easy to explain. The mind relies on the difference in lightness at the edges of forms or surfaces in order to determine the visual appearance of the areas bounded by (inside or outside) the edges. In this case, the center of the dark circle, and the outside edge of the surrounding ring, are exactly the same lightness, but they appear to be very different values because the mind adjusts them to correspond to the strong light/dark contrast at their common edge.

Borders improve y/b discrimination, degrade w/k discrimination, and have no effect on r/g discrimination.

Pattern or Border Effects. Many complementary color effects were first systematically described in On the Law of Simultaneous Contrast of Colors (1839) by Michel-Eugène Chevreul, for many years the chief scientist at the Gobelins (Paris) textile and weaving factory. The next illustration goes back to the earliest modern color studies, which studied of color effects induced by changing the colored threads within the same textile pattern.

spreading effects in complex patterns

These color shifts are called the spreading effect, which is produced by changes in a single color within a larger pattern of interlocking colors. In the top pattern, the background reddish brown and the blue scrolling pattern seem to change hue and value when a black border or a white border is added between them. In the bottom pattern, the blue seems lighter when combined with white than with dark brown, and darkest when the brown is the background rather than the tracery.

These illusions seems to contradict the "center of gravity" contrast principle, but in fact they define its limits. Seen in the metaphor of a computer, the mind must perform a series of complex analysis tasks in order to understand a visual image. One of these is the identification of edges, which we've seen leads to edge contrast effects such as Mach bands.

//

Roger Hanlon, a marine biologist at Woods Hole, Massachusetts who studies the camouflage skills of the cuttlefish and octopus, has found natural camouflage systems correspond to three disguise templates: uniform color, random patterns within a single color variation, and disruptive patterning that disguises the body outlines. These correspond to color, texture and outline as the three most important perceptual mechanisms for object perception. The first two mechanisms degrade the color and texture cues for outline, and the last degrades the cues for object recognition from perceptible outline.

//

Equally important is the identification of surfaces, because these define solid planes and three dimensional forms. Surface recognition occurs in part through textures, patterns or gradients appearing on the surfaces. This is how the "spreading effect" seems to arise, because it is strongest when the eye interprets a pattern as lying on a single surface. The surface is made more consistent or unified by bringing its various colors toward the average color.

texture & surface analysis

The next step in visual analysis is believed to involve resolution of the edge and region analysis into depth and volume. An important bridge in this transformation is resolution of surface texture.

Surface texture is important for three reasons: it provides important visual clues to the slope and recession in space of surfaces; it provides (via visual fusion) an estimate of the distance in space from the viewer; and it helps to resolve motion when gross features and edges present ambiguous information.

Studies of movement of plaid patterns shows that textures are separated by visual frequency, and only merge if the frequency is roughly the same in all dimensions.

Where edges are lacking as region boundaries, textures can provide information to separate surfaces.

A simple but intriguing question is, how can we "recognize" or distinguish one kind of texture from another? For example, if you were shown a piece of paper printed all over with a single visual texture that was interrupted by a second, different texture, what visual characteristics would make that second texture easy or difficult to see? Some examples suggest the answers.

artificial texture contrasts top row: difference in values, difference in spatial frequency, difference in orientation; bottom row:

similar elements with random rotation, mirror reversal with random rotation, mirror reversal

These are some of the many kinds of artificial textures used in perceptual experiments. Most people find the contrasting textures in the top row immediately visible, while those in the bottom row require some scrutiny to identify. What seems to characterize textures that are easy or difficult to identify in this way?

As a rule, the "easy" texture contrasts rely on elements that can be discriminated with "low level" visual capabilities: contrasts in lightness, saturation, hue, spatial frequency, size or length, orientation, thickness, density, grouping and movement. The "difficult" textures are composed of separate elements that have to be discriminated in terms of how they are shaped or combined, and the most difficult are those that have to be discriminated in terms of orientation or mirror reversal. But these units become visible if they related to each other in larger patterns. Quite often a simple linear or spectral frequency pattern is sufficient to do this. The example at right makes it easier to see the rotated elements in terms of the contrasting pattern they form with the parallel lines.

// Lights are rather poor depth cues, and they cannot be used to distinguish distance unless luminance corresponds very closely to a perspective gradient. Thus the droplets in a fountain illuminated by the sun, or fireflies at

night, appear as a scattered mass of vague depth; stars in the sky, despite variations in brightness, seem to shine from the interior surface of a dome. City lights receding over flat land, such as Los Angeles viewed from the Hollywood Hills, convey an atmospheric sense of perspective; randomly spaced lights, or lights across a hilly geography, seem vaguely at the same distance. // The Boundary of Texture and Form. This brings us to perhaps the most important attribute of texture: its boundary with form. In visual perception any kind of boundary or edge is a form of focus or attention created by what we see clearly and what we don't, and textures help us actually see the boundary between seeing and recognizing or remembering.

surfaces dominate lights and shadows (left) image of corrugated metal projected onto a flat surface; (right) image of corrugated metal projected

onto corrugated metal

The basic feature of the natural world that is at issue here is that most natural forms have surfaces which are themselves natural forms — such as planes, bumps, ridges, crevises, curves, grooves — and usually this kind of surface texture is composed of miniature versions of itself. Planes are faceted, bumps are rough, ridges are creased, crevises are cracked, curves are variable, grooves are furrowed.

The example at right shows how these natural surfaces can be studied with a drawing or image processing program such as Adobe Photoshop. The starting point is an enclosed figure suggestive of the shape of a rock lying

a texture example created by

layering repeated forms ofdifferent sizes

on the ground. This form is reduced by 66%, tripled, and arranged in a triangular pattern below; this pattern is reduced by 33% and tripled again, and so on for two more levels. Then all the layers are arranged into a singe image that allows occlusion of overlapping forms. Many other natural forms are possible, depending on the shape of the basic unit, the amount of reduction between layers, and whether occlusion or perspectival changes in viewing angle are inserted.

The result is not simply a random texture of large and small units but an image highly suggestive of a rocky covering on flat earth, in which the units of different sizes play different roles. And this allows us to see more clearly the fundamental boundary between textures and forms.

Simulated patterns show two distinct boundaries between object and texture: in the example at right it is between (1) the forms that we can count at a glance or a few seconds of viewing (the largest two sizes of rocks in the example), and (2) the largest forms that define a texture (the smallest two sizes of rocks in the example). We can see at a glance that there are about a half dozen large rocks in the image, and below that a pebbly texture of various sized units; we get an impression of the largest forms in this texture and the amount of size reduction or texture gradient into the smaller sizes.

This boundary would show itself in a simple recognition test over a time delay of several hours, in which we are shown two images constructed in different ways from the same image elements. I believe we would find the same discrimination dimensions in these more complex images that apply to the textures described above. That is, if the smallest two texture elements were changed in lightness, saturation, hue, spatial frequency, size or length, orientation, thickness, density, grouping or movement, the image would be recognized as different. At the same time, the rectangle formed of the back rocks would perhaps not be noticed if it were rotated 90° in perspective, but omitting a rock would be.

Stabilized Images. A final condition in the definition of edges and regions is the situation

where edges and regions completely disappear.

The Ganzfield effect (German for "whole field") arises when the eye is presented with a continuous, monochromatic visual field. After a minute or two, the perception of edges and colors disappears completely. (In snowstorms or heavy fog the condition is called snowblindness.)

To stimulate a ganzfield,

This is a final indication of the importance of contrast and change in color vision.

The Craik-O'Brian effect reveals how the mind interprets the contrast at the edge to mean the two circular areas are different, then "fills in" each of the areas as suitably contrasting values. This "interpret the edge, then color the area" perceptual strategy is fundamental to the way we perceive color and light around three dimensional forms.

N E X T : the structure of vision (ii)

Last revised 03.28.2004 • © 2004 Bruce MacEvoy

the structure of vision (ii)

This page concludes our

survey of the structure of vision, from texture

and surface analysis to the more complex levels of depth perception, object recognition

and the overall structure of the visual field.

This section is technical, but includes

background relevant to basic design principles.

xxxxx

depth & volume perception

color

vision

depth & volume

perception

object & scene

recognition

the visual field

Textures are separated into discrete areas.

Visual Completion. Edges are so

fundamental to visual experience, in fact, that the mind will construct (perceive) a form even

where there is none, as the following example

demonstrates.

visual closure in an underdetermined pattern (Kanizsa illusion)

In this case the mind is simply presented with

three dark, incomplete circles. Yet the appearance of a white triangle standing in

front of or on top of the circles is so dramatic that some people will even perceive the

triangular area as whiter than the area outside it (the Ehrenstein illusion)! A "literal eye"

would simply see what is there.

Benary cross: pattern as form.

Benussi illusion in contrasted patterns.

DeValois checkerboard illusion

pattern contrast

The whole thing with pattern contrast.

Foreground/Background Contrasts. One of

the principal tasks necessary for depth

perception is to set the separate regions defined in the primal sketch at different

distances from the viewer. In effect, the regions are cut out as separate units, then

mentally located as near or far from the view in a third dimension, much as planes are

separated in the continuous flat surface of a bas-relief carving. This representation has

been called the 2.5 dimensional sketch (at right), because it shows depth without being

truly three dimensional: it does not define the

volume and mass of objects, only their relative distance from the viewer.

As part of this representation, color shifts can

be induced by a "foreground vs. background" pattern of the geometrical areas or color

shapes in an image (this is called White's

effect). The following example shows this clearly.

color shifts in a simple pattern

The two clusters of identical dull blue squares

(top) or red orange squares (bottom) are placed against a regular pattern of alternating

stripes. The edge contrasts for all the blue squares are identical — two sides of each

square border on green, and two on violet. The only difference is in the overall pattern:

the blue squares interrupt either the green or

violet stripes, which causes the other color to appear as continuous stripes.

The effect is enhanced if the space between

the stripes is narrowed (right). The spreading effect begins to take over and the squares

shift toward the color of the stripes on either side rather than the stripes that form the

"background".

The astonishing result is that hue shifts

emerge from the pattern alone: the squares that interrupt the violet stripes appear

lighter and less saturated than the squares that interrupt the green stripes. Visual

completion causes the squares to appear as horizontal blue bands, which means the eye

interprets the pattern as blue stripes behind

the uninterrupted colored bands and in front of the interrupted color, which acts as a

simultaneous contrast background. The squares that interrupt (are "in front of") the

green background (left) shift toward a violet hue and a darker value, while the squares that

interrupt the purple stripes (right) shift toward

enhancement of simultaneous

contrast in narrow patterns

a green hue and a lighter value.

lightness shifts induced by visual completion

You may suspect that somehow these shifts

are related to the center/surround contrasts of edge and region detection, but this is not

the case. In the above example, visual completion causes us to perceive the gray

cross in the center as a circle, which induces the perception that the circle is "behind" the

four squares and "in front" of the contrasting background. Even though the edges around

the circle are almost entirely with the four

squares, the lightness shift is toward the value of the squares and away from the contrasting

background. The 2.5 Dimensional Sketch. One of the principal tasks necessary for depth perception

is to set the separate regions defined in the primal sketch at different distances from the

viewer. In effect, the regions are cut out as separate units, then mentally located as near

or far from the view in a third dimension,

much as planes are separated in the continuous flat surface of a bas-relief carving.

This representation has been called the 2.5 dimensional sketch (at right), because

it shows the depth, slant and tilt of surfaces without being truly three dimensional (it does

not define the hidden sides, volume and mass of objects).

A standard method for showing this surface layout is a circular disk skewered by a short

rod and placed on a surface; the length and orientation of the rod shows the tilt and slant

of the surface, the size of the disk its distance from the viewer.

This would be fussy and cluttered to use in a

a 2.5 dimensional sketch

each point in the visual field is assigned

three values: a slant (in relation to the

direction of view), a tilt (in relation to

horizontal or vertical), and a distance (in

relation to the viewer)

drawing, but artists have used a variety of other line conventions to indicate surface

orientation and distance. Typically line thickness represents the distance of the edge

or object from the viewer (distant objects are more lightly drawn), or the approach of the

line to either a dark terminator or shadowed area. A variety of patterned lines, such as the

bracelet drawing used by etchers, convey contour by the path of the line across the

surface. The spacing of lines in relief

drawings shows the orientation of the surface in the spacing of the lines: imitating

foreshortening, the more slanted the surface, the more closely the lines are spaced. Finally,

in imitation of perspective gradients, lines across the same surface are drawn closer

together as they recede from the viewer.

Light and Shadow. Because saturation and

value are easy to confuse with each other, and tend to be disguised or shifted by the hue we

are looking at, it's important to observe the distinction between the two when modeling

three dimensional forms.

Translucency Effects. Color shifts can also

be induced by a pattern or "foreground vs. background" interpretation of the geometrical

areas or color shapes in an image (White's effect). The following example shows this

clearly, as it does not rely on color gradation and therefore is quite effective as a web

browser image.

The eye seems adapted to segregate image

regions using transparency or occlusion as a guiding principle. The illustration at right

presents an especially startling example.

(a) To begin, we arrange two rows of identical

gray bars so that they slightly overlap in their spaces. Note that they appear to be exactly

the same lightness — because they are.

(b) Light and dark squares can be added to

the ends of these bars, but the apparent lightness of the bars remains largely

unchanged. (I see a very slight shift to make the upper bars appear darker than the lower,

corresponding to the Craik-O'Brian effect.)

(c) Or, a lighter gray field can be added

around the lower bars, but this again does not

alter the apparent uniform value of the bars.

(d) However, when the two elements are combined, the mind interprets the continuous

horizontal edge created by the small squares

and the large gray field to mean there is a coherent spatial relationship among all the

color areas: the overall pattern resembles two rows of bars partially obscured at the bottom

by a shadow or a translucent filter. This spatial interpretation causes the mind to infer color

appearances that can "explain" the value contrasts in the apparent lightness

relationships — the upper bars appear much darker than the lower ones.

These effects are not limited to value (lightness) alone. The section on saturation

and value demonstrates similar and large shifts in apparent chroma and hue, simply by

changing the location of the colors within an apparently three dimensional figure.

We can conclude from these and many other specific demonstrations that the mind is

continually adjusting our visual experience to clarify the world's spatial structure —

specifically, the effects of illumination on three dimensional surfaces. That is, color shifts do

not arise "bottom up" through the local

contrasts of different color areas, as "color theory" assumes. They are imposed "top

down" by the mind, which first generates a three dimensional model of the world and the

illumination within it using lightness information alone, then adjusts or "paints

over" this three dimensional framework with color appearances appropriate to show the

inferred forms and contours.

The contrast effects described in this section

can only suggest the important effects of edge, pattern and spatial relationships on

apparent color. They confirm that (1) edge contrast, (2) the visual frequency or spacing of

a pattern, (3) the unity of colors in the

representation of a single object or surface, (4) the spatial illusion created by a design, (5)

simultaneous color contrast, and (6) visual contrast around a visual "average" are all

significant factors in modifying or enhancing the apparent colors in a painting or image.

lightness shifts in a transparency

illusion

The significance a viewer assigns to local color

information is dependent on his or her interpretation of the entire visual context in

which the color appears: the artist must build the unified effect of a design in the choice of

all its parts.

translucency

effects on patterns of different

lightness, saturation and hue

more about transparency.

Importance of light and shadow in form

perception and disambiguation of space.

object & scene recognition

The simplistic "square in a square" presentation of color contrasts suggests that

the effects are pretty much the same in any visual setting. But that is incorrect. It is

surprising how contextually dependent the contrast shifts in color can be.

Perhaps the major shortcoming of "color theory" prescriptions has been the assumption

that color effects arise only through the visual proximity of two differently colored surface

areas. In the suggestive and very influential color demonstrations of Josef Albers, for

example, suitable choices of different values or hues can produce effects of transparency,

translucency, spatial ordering, and so on.

Artists were until recently unaware that more

powerful contrast effects or color illusions actually work the other way: the three

dimensional or spatial interpretation of an image can strongly influence the apparent

colors of the image. This is a very complex

topic, but a few examples will illustrate the basic processes.

More about objects and scenes.

Canonical Views. One of the canons of American design theory is an emphasis on the

rule of good shapes, which Edgar Whitney stated as "a shape having variety in its length

and breadth dimensions, its directional thrust being a dynamic oblique, and with incident at

its edges interlocking with negative areas." What exactly that means in a specific painting

is not always clear, but one answer may be that a good shape is most informative

about the three dimensional form of the

object represented.

A relatively unexpected but artistically important aspect of visual recognition is the

role of "best" or canonical views of an object.

The figure below illustrates these viewpoints for some common objects.

canonical views of six common objects

These canonical views were identified by

asking experimental subjects to rate several photographs of a single object, each taken

from a different point of view, in terms of "how much it looked like the object." Unusual

views were downgraded in comparison to

more familiar views, and these canonical views rated highest of all. The canonical views

turned out to be recognized (named) most quickly when presented to different subjects.

Although it seems obvious that some views

are more recognizable or pleasing than others,

we'd like to find the rules that define a canonical view for a specific object. It seems

the basic rule is, "it depends." Some points of view, such as the clock or telephone, seem

determined primarily by the view during function or common use of the object —

how it appears when we use it. Others, such as the chair or teapot, seem to provide the

best three dimensional information about the object. In most cases, however, because

the object is familiar from many different points of view, the canonical view seems to be

a three quarters profile viewed slightly from above (the camera and shoe).

Interestingly, this viewpoint also seems to create the dynamic oblique directional thrust

and incident at edges valued by Whitney.

I suggest that the design requirements for

good shape can be thought of as a balance between six competing viewpoints and design

goals: (1) the habitual or functional view; (2) the view providing the best information about

the object's proportions in three dimensions;

(3) the view providing the most informative visual separation among the major parts of a

single object; (4) the view producing the most complex edges or outline against a

background; (5) the view producing the most dramatic perspective effects of height,

recession or profile; and (6) the view producing the most emphatic two dimensional

shape within entire image and its format. Balancing these competing criteria allows

considerable scope for esthetic and design

judgments.

Behavior Episodes. An equally important aspect of canonical views that artists are

rarely taught only emerges across time, in the behavior episodes studied by University of

Virginia psychologist Darren Newtson. Think of

any common physical activity, such as baking a cake, doing gymnastics or assembling an

Ikea bookshelf, as captured on film. Each frame of the film would present a snapshot

view of the activity unfolding over time. The unexpected result of Newtson's research is

that some frames of this film are far more "canonical" or informative about the activity

than others, because they show the key steps or processes of the activity in context. The

frames that show the egg dropping from its

shell into the mixing bowl, or the batter being poured into the baking pan, are immediately

comprehensible; the frames that show the cook looking for a mixing spoon or wiping

batter from her chin seem ambiguous and uninformative. Just as objects have canonical

views in space, activities have canonical views across time.

It turns out that nearly all human activities, from conversations to team sports, show the

same pattern of highly informative views separated by ambiguous intervals of rest,

distraction or transition. The artistic challenge is to find the most informative snapshot to

represent an entire activity or sequence of events as a single image. Photographers have

the luxury of choosing from among many negatives: painters must determine the view

through judgment and careful observation.

In athletic images or historical paintings, these

canonical views of action can represent a climactic point (as in David's Oath of the

Horatii) or can collapse several events in a

single view (as in Caravaggio's marvelous The Betrayal of Christ, which shows the traitor

kiss, the fleeing disciples and the arresting soldiers as a single moment). But the same

principles apply in quiet images: John Singer Sargent was a master at disclosing the

vitality and personality of his subjects through a gesturally expressive pose and a subtle

displacement of the artist's point of view.

It is also very instructive to study sports or

wildlife photographs, paparazzi celebrity shots, the photojournalism of Weegee (Arthur Fellig)

or Henri Cartier-Bresson, advertising images, and in particular the fabulous collections of

time series photographs by Eadweard Muybridge.

muybridge photos of a trotting horse

Although these twelve photos show different

aspects of the same animal activity, clearly

some of the snapshots are more informative or interpretable as "a trotting horse" than

others. Image 4 seems to show the horse lurching to a halt, while image 12 suggests the

wooden mount on a merry go round. Image 11 conveys a greater sense of speed than

image 2; image 7 is monumental and static where image 9 is dainty and flowing. Careful

comparisons such as these, using different kinds of photodocumentation, can help you

understand why some images are more

representative or characteristic than others, and to design figures and groups with a

greater feeling for moment and gesture.

One caveat: science can clarify, but it can't

prescribe. "Canonical" images are hardly the only view of the world. One of the main

attributes of Diane Arbus' photographs is her preference for catching her subjects within

transition moments, inside the detritus of action, creating an illusion of spiritual

disconnectedness, imbalance, and a lack of human warmth. Her contact sheets show her

decisions clearly.

Photographs structure the world in specific

ways. They can help you study more effectively the motionless form of water

ripples or running horses, but they cannot suggest the best way to represent water or

horses in a painting. I discuss this issue in the page on aids to drawing, but the main point

is simple: don't let dogmas dictate your

representations.

Beliefs and Details. This is perhaps the hardest problem in perception. We cannot see

the total individuality of everything in the world, or rather we see it but believe it does

not matter to the general beliefs we hold

about the world. So we float in a realm largely structured of ideas, interspersed with gleams

and pools of direct experience.

Speech is a classic and insightful example. Our

speech perception is entirely categorical, which means we can be confused by even

small variations from the sound patterns we have been habituated to believe are important

in speech production. Our perception focuses on specific sound details and discards the rest,

and this constitutes our "normal" perception of speech. It is thrown into slight disarray by

speech impediments, dialectics, or foreign accents, but at the borderline we are

completely deaf to what is said. All of us have had the experience of asking someone to

repeat something we don't understand, then once we "get" the misheard word reacting with

embarrassed recognition. "Oh, Irene, I thought you said I seen."

Embarrassment is an emotion of misplaced categories. When we paint or draw we have

similar difficulties finding the right graphical equivalent for a mental state, we are trying to

write down the communications of the world without complete knowledge of the means to

do so.

Attention during painting must be placed on

the good fit of the new marks, given what came before.

the visual field The many aspects of color psychology

discussed in this page share a remarkable

limitation: they are not put in the context of the visual field — the total visual panorama

that our eyes present to us.

In fact, our visual sense of the world is largely based on a psychological reconstruction of the

world, rather than a cameralike

documentation of optical events. Visual effects such as complementary color contrasts are

demonstrated with color stimuli that affect a very small part of the total visual field. Yet this

larger visual experience is usually involved when viewing a painting, and always when

viewing a landscape or figure, so its structure is important to understand.

Let's start with a simple illustration of the optical facts presented to us by our eyes. The

image below was made by superimposing two separate images taken about 4" apart, to

simulate the binocular view created by both eyes.

binocular parallax and depth of field in a visual field

In this situation the viewer is focusing on the

roll of paper towels standing on the bathroom counter, because at that point there is no

disparity between the binocular edges. The eyes report a combined image that is

misaligned for edges in front of or behind the focal object (the door jambs and the glass

shower doors).

Our visual system handles these problems in

two ways. First, it simply edits out the confusing visual facts: if we stare fixedly at

the center of the paper towel in the image, we don't really notice the misaligned or out of

focus details around it. We do if we look at them directly in the image — but this is

something that we cannot do in the real world.

Second, our mind replaces peripheral

optical facts with concepts — of a doorway, a shower stall, a window reflection. These

ideas cohere in our sense of being in a hallway before a bathroom, and the distances between

our view and the objects around us. These

ideas shift toward detailed perception only when we shift our direction of view — which

we do frequently and continuously — to explore the details of a new object.

The basic difference between optical facts and

visual experience is easiest to illustrate

through the problem of parallax, but other optical constraints contribute as well: the lens

of the eye cannot focus as efficiently along the

sides of the curved retina, and light falling on this part of the eye strikes at an oblique angle,

rather than head on, blurring the response across neighboring cones.

To cope with all these visual problems, the visual field is divided into three zones, as

shown in the figure (looking downward on a viewer looking forward).

geometry of the visual field hypothetical viewer seen from above; limits of

parafoveal and peripheral vision are approximate

Foveal vision occupies an area about 2° wide in the field of view. (A US quarter, or a circle

2.5cm in diameter, viewed at arm's length or

28" from your eyes, is about 2° wide.) The fovea is a small depression in the retina, with

a flattened basin called the foveola where blood vessels are absent; at its center is the

central island, where the visual receptors consist entirely of densely packed R and G

cones. The fovea has the most sensitive color discrimination capabilities and represents the

visual center of attention: whatever point we look at directly is within the foveal field. In

linear perspective the center of attention is

sometimes called the principal point, principal ray or axis of vision.

Parafoveal vision occupies an area about

20° wide (or 10° on all sides of the foveal field). Surrounding the parafoveal field is the

perifoveal field (not labeled in the diagram)

which is approximately 50° wide (25° on all sides of the direction of view). An object 2 feet

wide at arm's length, such as a large art book held open in both hands, is about 40° wide.

The parafoveal field provides the context for our attention, and typically frames in coarse

detail the point we are looking at — the book we read, a person, a TV screen. Color

discrimination poor in the parafoveal area and extremely poor in the perifoveal area.

Peripheral vision is the rest of the visual field, which in most people extends to

approximately 80° on either side of the center of attention (vision is limited above and below,

because our eyes are set far behind our eyebrows and cheeks). Hold your arms out on

both sides of your head and wiggle your fingers. Move your hands forward or back until

you lose sight of movement: now your hands

mark the width of your visual field. This peripheral field is primarily sensitive to

movement or change in environment, and contributes almost nothing to our perception

of object color, location or form.

Not really a zone within the visual field,

conceptual vision is the smoothing, enriching and seamless merging of visual

sensations with hearing, short and long term memory regarding our immediate

environment, and unconscious concepts about the world. It is the binding element between

the visual stimulus, the movement of our bodies, and the phyiscal world. In parafoveal

and especially peripheral vision, it creates the static assumption of specific objects located by

outlines or forms we barely see; this "concept

world" remains constant until we hear or see movement, or change our direction of view.

Conceptual vision acts in a number of ways to

suppress visible (or noticeable) but nuisance elements in the visual field. For example, it

provides closure over the blind spots in each

eye, deletes retinal "floaters" and our always visible nose from awareness, and links the

jerky movements of the eye (for example, when reading a book) into an experience of

uninterrupted flow.

If you want actually to experience conceptual

vision, do this: stand at night in a darkened hallway with the door to a lighted room behind

you. Begin to step gradually backwards into the lighted room, keeping your back turned to

the light and your eyes fixed straight ahead. At some point you will be able to see the

brightly lit door jambs on both sides and above you in your periperal vision. Keep

looking straight ahead, and continue to step slowly backwards into the room. When you

feel certain that you can see the jambs above and on both sides, stop and look directly at

them without moving your head. The jambs on either side are actually visible — but the jamb

over your head is not. You only saw it conceptually — where you thought it was.

Color vision is not structured equally within the visual field. Foveal vision shows a warm

color bias, because the fovea contains no rods and few or no B cones — only R and G

cones. It turns out, however, that these foveal

R and G cells are optimized to perceive edges and contrasts, which define our "center of

attention" and the visual acuity necessary to read text or use precise tools. Yet there are no

recognizable effects on perceived color. For example, demonstrations of color contrast

are typically larger than the foveal field: one part of the visual display is typically in the

foveal field, the other in the parafoveal field. We see the simultaneous contrast of colors,

but also the simultaneous contrast of two

different parts of the visual field. Yet when these images are reduced to fit entirely within

the foveal field, both the colors and the color contrasts remain unchanged.

contrast effects viewed entirely within the foveal field

view at a distance of two feet or more

Although the foveal field contains no B cones,

the color sensations for blues and violets also

remain subjectively the same as in the parafoveal field. However, careful observation

reveals that colors do shift somewhat toward blue because of the very high concentration of

B cones and rods in the parafovea, and this bias increases towards the peripheral limits of

view. (If you look directly at the righthand square in this chroma contrast diagram, it

will appear a bright red violet; move the eye gradually to the far right side, and it will

appear to shift toward blue, sometimes in

flashes of alternating color.) This effect is usually muted because colors also become less

intense in the outer areas of vision.

We rarely notice differences in detail, contrast

or color between the parafoveal and foveal fields in part because our concept of the

surrounding environment fleshes out what we don't directly look at. But we also seem to

function just fine within the fuzzy detail that the parafoveal field provides. For example,

during dark adapted scotopic vision, the fovea completely ceases to function because it

contains no rods. The functional "center of attention" then becomes the parafoveal field,

yet most people perceive objects in a

moonlight night as in focus.

The eye also builds an image through specific kinds of movement. The most common is the

saccade, which is a rapid, unconscious "jump and hold" of both eyes in tandem that causes

specific areas of the visual world to fall onto

the fovea or selective visual attention. Because of saccadic suppression we do not

visually experience these eye movements; that is, we don't experience a blur (as we do if

we shake our head) but a seamless flow of "snapshots" of the world. The "jump" is quite

fast, traversing up to 15° of the visual field in 10 milliseconds, and the "hold" or fixation

between saccades is usually 150-300 milliseconds — never less than that, to permit

the eye to register a distinct image, but

sometimes longer depending on the viewer's goal and level of attention. Saccades are

preprogrammed (ballistic) movements, computed from information in the foveal and

parafoveal areas of the visual field; a large saccade is often followed by one or more

smaller, "corrective" jumps. The "hold" of a saccade is refined by physiological nystagmus, tiny tremors,

flicks or drifts of the eye that constantly shift

the image over the fovea so that it is continuously stimulated by changing patterns.

(If this did not happen, the image would fade within a few seconds.) Sometimes these are

corrective movements, adjusting for an inaccurate saccadic jump or a drift in eye

direction.

In contrast to saccades, pursuit eye

physiological nystagmus

stare at the black dot for 30 seconds,

then shift your gaze to the white dot

movements are voluntary, tandem eye movements that smoothly track a moving

object in the visual field. They primarily function to stabilize moving objects on the

retina, which allows us to see the object in better detail. However, they typically require a

moving object to elicit, and are not under voluntary control. So they do not affect our

view of a painting.

eye saccades within a painting points show focus of eye saccades for 17 different

viewers

It's common in painting tutorials to find

misleading design statements such as, "the strong diagonals lead the eye." As the

example shows, viewers do not roll their eyes along geometric guides in the image, they leap

from one point to the next to explore the picture in a sequence of detailed views. In this

painting, which shows the execution of Lady

Gray, the saccades target image areas that help the viewer interpret what is going on: the

faces of the figures, the chopping block, the executioner's axe. If the viewer were asked to

examine the color mixtures, or inspect the costumes, the pattern of saccades would be

different. The interest a viewer brings to a picture, not abstract principles of design,

determines the movements of the eye around the picture.

eye saccades within a painting points show focus of eye saccades for 17 different

viewers

Peripheral vision emphasizes movement rather

than form. As we walk, objects in our direction of motion seem to expand slowly from the

center of view, but objects beside us, in the peripheral field, shear past us quickly. This

shearing movement is difficult for a precise visual system to track accurately. (To see

what shearing movement does to foveal vision, shake your head back and forth

violently ... but sit down first!) So the distribution of peripheral cones is sparser and

the cones are physically much larger than at

the fovea, to reduce visual resolution. The peripheral field makes sense of this rapidly

moving, coarsely defined information primarily by looking for differences in movement (those

wiggling fingers, or our tennis partner) at the edges of vision. Communication among

peripheral cells is more integrated — cones and rods are interconnected, for example —

which gives "resolution" in peripheral vision an entirely different meaning: we cannot see

forms or color at all, but notice movement

quite well.

The overall structure of the visual field (if we could see the whole field with foveal clarity)

might appear something like this:

structure of the visual field

I'm looking into the right eye of this endearing

infant, at arm's length, and her eye almost fills

my foveal field, which emphasizes contrast somewhat at the expense of color. The

parafoveal field is somewhat fuzzier but also slightly more brightly colored; these chunks of

color render the main forms. The peripheral vision is so vague that distinct forms are

almost lost, and colors shift toward a simple light/dark contrast with loss in both luminosity

and chroma.

This illustration makes clear that a large part

of the apparent visual field is not visual but conceptual. We don't experience the world as

a fuzzy tunnel. Instead, the mind creates a unified visual experience that replaces the

fuzzy objects in the parafoveal and peripheral fields with clear concepts or memories of what

we would see — if we chose to look directly in

that direction. So we can talk about a conceptal field laid over the visual field,

pulling it all together into a seamless, sufficiently detailed whole. We don't perceive

an image on the retina, but the world.

Our visual structure affects the way we

interact with works of art. We naturally approach a painting, photograph or sculpture

until the foveal field can examine specific passages of the work in detail, yet also move

back to bracket most or all of it within the parafoveal field. Our preferred "viewing

distance" is the balance between these two requirements. If an artist knows the intended

setting for a work, he or she can choose the level of detail — in the drawing, brushwork,

visual mixing and so on — that the viewer is

likely to be able to see at the viewing distance appropriate for the setting. Most drawings and

etchings, for example, assume a "portfolio distance" of only two or three feet.

When artists paint an image, they implicitly choose to emphasize one or another aspect of

the visual field. Drawings from the 18th century, and modern "photorealist" paintings,

where everything is in focus, there is no parafoveal fuzzing, and colors are rather drab,

emphasize the foveal and conceptual fields. Impressionist and postimpressionist paintings

are parafoveal in their coarse detail, visual color mixing, and intense color contrasts.

Painters that try to capture variations in visual

structure often keep highly chromatic colors out of the peripheral area of the painting and

paint objects there indistinctly or in shadow; the "center of attention" in a picture is often

finely detailed and strongly contrasted, with the area immediately around it more brightly

colored.

The story gets even more complicated when

we try to describe how eye movements assemble our visual experience — shifting the

foveal center of attention and the limits of the parafoveal and peripheral fields, and

continually refreshing and updating the conceptual field. Even this process has design

implications. When artists talk about how "the eye is led around" an image, they often are

describing the overall pattern of detail, color

and contrast within the image that would result from alternating parafoveal and foveal

views in the physical environment of the image. They make design choices that imitate

the variations in visual information that eye movements create — or they use

nonrepresentational forms and colors to mimic these variations abstractly. In particular,

critical commentary on the works of Pierre Bonnard emphasizes the ways in which his

color and drawing imitate the effects of

multiple foveal and parafoveal views.

N E X T : color in the world

Last revised 01.12.2004 • © 2004 Bruce MacEvoy

color in the world

Much of the previous discussion has

had a very narrow focus on the visual

response of the human eye and mind, and the relationship of color vision to the problems of

color mixing with paints.

This page describes color vision in the context

of the visible world and a variety of light effects that are common experience. These

are useful both to interpret the effects of lighting and color that we can see, and to

anticipate color effects that we must imagine.

In this discussion we take as given the surface

colors of objects: we want to know instead how light and shadow affect their apparent

hue. This means that almost everything discussed here is a direct consequence of the

cone sensitivity profiles (the trichromatic theory) and the color mixing effects predicted

by additive color theory, as interpreted in related color judgments.

We can put the total range of color in the context of physical explanations. All

these come down to ways that matter can affect or interact with light.

Electron Color. Throughout the pages on

color, light has been described exclusively in

terms of its wavelength, the distance between successive peaks or troughs in the

oscillation of a light wave (or the number of oscillations in a unit distance, such as one

centimeter). However, light can also be described by two alternative measures:

frequency and energy.

Light frequency is the number of wave

oscillations in a unit time, such as one second. In general, the higher the frequency, the

smaller the wavelength; but frequency depends on the medium light passes through

— the frequency of a given wavelength is higher in a vacuum than in glass. This

the causes of color

color

vision

the causes of color

the constants of light

surface & shadow color

special material colors

physical color changes

produces the refracting properties of transparent substances such as glass or water.

Most important for the present topic is the

energy of light, measured in electron volts

(eV). One eV is an extremely tiny unit of energy, but the key point is that each

wavelength or frequency of light also has a characteristic, fixed energy that is between 1.7

to 3.2 eV. So the electromagnetic spectrum can be described using three interchangeable

units, as shown below.

wavelength, frequency and energy across

the visible spectrum

The importance of light energy is that it can affect the behavior of electrons, which are

the lightest particles of matter, in a large number of ways. That is, the electrons that

normally form a cloud around the nucleus of every atom can interect with particles of light

(photons) through an exchange of energy, which changes the electron's behavior.

Normally the energy exchange amounts to this: the electron absorbs a photon, which

raises the electron's energy, or the electron emits a photon, lowering its energy. The

emitted photon carries with it the lost energy, and the exact amount (quantum) of energy

determines the wavelength of the light.

The important qualification is that electrons

within atoms are constrained to a range of fixed energy states, called electron shells, and

there is a limit to the number of electrons that each shell can contain, sometimes forcing

individual electrons to stick where they are, or

jump to a vacant position in a higher or lower energy electron shell. The dance between

electrons and light is shaped by this fixed energy ladder of shells and shell vacancies

within each atom.

quantum lines in gas emission spectra emission spectra for hydrogen (H, top), helium (He,

middle) and neon (Ne, bottom)

The table summarizes the major physical mechanisms of color. The point is not to

explore the details of physics, but to show the astonishingly large number of ways in which

color arises in the world.

The complexity of color producing mechanisms

depend on a variety of atomic structures and the integral role played by the electron in

chemical and crystal bonds. These are described in more detail on this page. It will

be useful to explain these further.

The electron can inhabit a variety of energy

levels, which are determined by the specific atomic structure of atoms and molecular

bonds of the material.

The energy levels may be separated by

relatively large or small intervals, and may represent relatively low or high levels of

energy. Usually, only untraviolet or x ray radiation can affect electrons at high energy

levels or cause them to jump across large

differences in energy.

Typically the energy thrown off by the electron is less than the energy absorbed, which shifts

wavelengths longer (from higher to lower

energy): from ultraviolet to visble blue, from blue to red, and from red to infrared.

Light Refraction. The most common optical

origins of color concern the effects of matter on light. These must be explained in terms of

the wave structure rather than the particle

energy of light: pigment colors and prismatic colors stand for the contrasting origins of light

in its particle and wave form.

Blah.

More familiar is sunlight refraction in

raindrops, which produces rainbows. Light

that strikes the raindrop anywhere near its center meets the surface of the water at close

to a perpendicular angle, so it passes through the raindrop just as it would through a lens

and is scattered out the opposite side. As the point where sunlight strikes the raindrop shifts

toward the side, some light is reflected off the back inner surface of the raindrop and exits on

the opposite side as a spectral refraction (C). This produces a primary rainbow. If the

incident angle is slightly less acute, the light

makes two reflections off the inner surface of the drop before emerging as a spectral

refraction. This produces a secondary rainbow outside the first.

Because the inner reflection and exit angle

depend on the incident angle of light, and the

surface of the drop is round, parallel beams of the same wavelength do not exit the raindrop

at the same angle. This causes the rays to diverge, producing a smearing in the rainbow

color (D). This smearing increases as drops get smaller, and in a fog or fine mist the

smearing blends the spectral colors back to white, producing a white fogbow.

Light Interference. Interference is produced by two parallel reflective layers, in oil (right).

interference produced by phase changes in light

the wavefront explanation

of light refraction

refraction in a prism

and in water drops

A: spectral colors from a

prism;

B: parallel rays of identical

color

remain parallel; C: spectral

colors

from a raindrop; D: parallel

rays of

identical color diverge

The light comes and goes, and sometimes it

cancels and sometimes it doesn't.

iridescence in an oil film

on wet pavement

This section draws in large part on the insightful

descriptions of photon and electron physics by Kurt

Nassau, including "The Physics and Chemistry of Color:

The 15 Mechanisms" in The Science of Color (2nd

ed.) edited by Steven Shevell (Optical Society of

America, 2003), and "The Fifteen Causes of Color" in

Color for Science, Art and Technology edited by

Kurt Nassau (North Holland, 1998).

The physical distinction between a

self luminous (light emitting) and illuminated

(light reflecting) object does not address the perceptual issues. The moon, planets and

satellites all appear as lights in the evening sky, even though they are reflecting bodies. A

flat panel television or computer monitor appears as a surface, much like a slide

projected on a reflecting screen, even though it is made up of thousands or millions of tiny

lights.

Constants of Spectral Mixture. The additive

color mixing.

an additive color mixing triangle

More about the additive color mixing.

the constants of light

Constants of Surface Reflectance. In most situations, human vision can distinguish a

potentially very large range of luminance contrasts between dark surfaces and/or lights

and reflections. For example, it is easy to see in daylight or at night the brightness difference

between a 60 watt incandescent light bulb and a "white" area on a computer monitor masked

to have an equal visual area; yet these differ in luminance by about 1200:1. A much larger

luminance contrast, on the order of

1,000,000:1, occurs when reflections of sunlight and clouds are visible side by side in

dark water. Visual experience comprises a very large range of brightness perceptions.

At the same time, human vision is always limited, in the perception of surfaces, to

lightness contrasts in which the luminance ratio between the lightest and darkest values

is never greater (and in natural surfaces is typically much less) than 100:1. These

lightness contrasts define a closed scale anchored on perceptions of white (pale) and

black (dark) produced by the local luminance contrast between to surface colors. This

lightness range is a completely reliable

physical constraint on surface luminance, because it depends only on the level of

illuminance as redistributed by the diffuse surface reflectance of physical materials.

Across both scotopic and normal (daylight) levels of illumination, it produces a constant

relative perception of light or dark values.

Ralph Evans found that a luminance contrast

of about 2:1 or greater between a small color area and its surroundings was sufficient to

produce the perception of self luminance, independent of the color chromaticity.

However, the color chromaticity has a large effect on blackness contrast, the

appearance of black or dull color caused by lightness contrasts. With these clues, the

overall luminance problem appears as shown

in the diagram.

contrast and luminance relations between

light and object colors

A much more common light effect is the result

of changes in luminosity on a surface. We can

move a surface from shadow to bright sunlight and back again. What is the effect on color?

The thing of surface diffusion.

light in diffuse reflection or specular reflection

The difference between actual and effective

light energy becomes important when we change our distance and/or viewing angle in

relation to the light source or reflecting surface. Both of these change visible light in

contrasting ways.

Light from a perfect light diffuser, also known

as a Lambert surface.

light diffusion by a lambertian and

semigloss surface

For measures of effective power (light as

received), illuminance and retinal

luminance (lux and trolands) decrease with increasing distance, because the

standardized surface area used to measure the light becomes a smaller and smaller part of

the many directions the light radiates. The rate of this decrease is governed by the inverse square law: light intensity decreases

by the square of the proportional increase in distance from the light source (double the

distance, and you cut the intensity by 1/4;

triple the distance, and you cut the intensity by 1/9, etc.). (Thus, when you compare light

sources rated in lux rather than lumens, it's important to make sure that the distances

used to make the measurements are the same.)

diffusion exactly

compensated by

foreshortening

Similarly, illuminance and retinal luminance decrease with an oblique angle

of incidence. That is, if a light shines

perpendicularly onto an evenly diffusing (dull or matte) surface, the amount of light

reflected from the surface is strongest in the perpendicular direction, and in oblique

directions it decreases — in proportion to the cosine of the angle from the perpendicular.

Thus, if someone standing several feet away from you at night shines a flashlight directly

down onto the pavement, it appears bright to

you because the beam is concentrated on a small circular area. But if he shines flashlight

onto the pavement far to one side, the illumination will appear much weaker to you

because the beam has been spread over a much larger surface area.

Constants of Illuminance/Luminance. For measures of actual power (light as radiated),

luminous intensity and luminance (lumens and nits) do not change with

viewing distance, even though lights or objects get fainter as they move farther away.

For objects that have a visible size, such as a searchlight or light bulb, the finesse is that the

visual size of the object also gets smaller and

in the same proportion as the distance (the inverse square law again), which means the

amount of light arriving to the eye remains constant for the visual area of the source. For

all evenly diffusing (dull or matte) surfaces, luminance does not change with viewing

angle either. The reason is that viewing the surface from one side foreshortens it, reducing its apparent

size, which exactly compensates for the

reduction in light diffused to that side. Thus, as long as someone else holds the flashlight

beam steady, it does not seem to change actual brightness as you view it from different

angles or different distances. And if you are holding the flashlight, the apparent brightness

of the beam does not appreciably change as you shine it on surfaces at different angles of

view, because your direction of view is the same as the line of illumination created by the

light. The beam seems noticeably fainter only

when you shine it on surfaces far away, because this reduces its illuminance.

luminance of white to luminance of light

This diagram extends the relationship between

relative luminace from a surface and its apparent lightness (shown here) to the

luminance necessary to match a diffuse light source of equal size.

The table below provides some context for luminance measures as the appearance of a

sheet of white paper under different lighting conditions.

luminance of white paper in different illumination contexts

illuminance

context

luminance level

(candelas/square meter)

cloudy night no

moon

0.0001

clear night no moon

0.001

clear night full moon

0.01

clear sky

1/2 hour after

sunset

0.1

clear sky 1/4 hour

after sunset

1.0

cloudy sky

at sunset10

subdued

indoor lighting

30

gray sky at

noon100

average office

120

bright

indoor office

240

precision

indoor tasks

480

the proportional luminance

of surfaces and lights

Because luminous intensity and luminance do not change across changes in viewing angle

and viewing distance, the eye can rely on these as invariants in comparing the relative

brightness of surfaces and lights in the world, at any distance or angle of view, provided we

know how far away they are and from what

angle we view them. In general, for a dull or matte 100% reflecting (pure white) surface, 1

lux of illuminance creates 1/π nits of luminance. That is, a white surface

illuminated from overhead at 100 lux will have a luminance of 31.8 nits in any direction.

(Luminance can also be used to describe extended light sources, such as light bulbs or

fluorescent light banks, provided the surface area of the light source is standardized at one

square meter.)

location of highlight and angle of reflection

The location of the highlight on a spherical

object, as a proportion of the distance from

typical

outdoor shade

960

cloudy sky

at noon1000

clear sky at

noon10000

noon sunlight

39,300

the center of the form to its visual edge, is equal to the sine of the angle of incidence for

angles from 0° to 45°, and the cosine of the angle of incidence for angles from 45° to 90°.

The figure shows some representative values. The simple procedure for estimating

complementary color contrasts is important to

learn for a second reason: it mimics the effects of a colored illuminant (colored light)

on the apparent color of a reflective surface.

A much more common light effect is the result of changes in luminosity on a

surface. We can move a surface from shadow to bright sunlight and back again. What is the

effect on color?

The reflectance curves we have used to

discuss paint mixing are designed so that the illuminant is not taken into account. But to

describe accurately the appearance of a surface, we have to know both the surface

color and the illuminant color. The color we actually see is the subtractive mixture of the

two.

the subtractive mixture of light and

surface color the product of a single illuminant on two

complementary colored surfaces; adapted from Jeff

Beall, Adam Doppelt & John Hughes © 1995 Brown

University

surface & shadow color

The figure above illustrates the basic

relationship: a red biased illuminant (right) acts to discount or proportionately reduce the

reflectance from the "red" end of the

spectrum. If the surface color is actually an ultramarine blue (center), its apparent

reflectance (right) will contain much less blue in comparison to red than it has under "white"

light. The resulting surface color will appear to be a dull red violet.

This is what we would expect if we mixed ultramarine blue with a red paint. So the

mixture of surface colors with illuminants is subtractive. In the comparison of color

mixing demonstrations, I mentioned that subtractive color mixing can be demonstrated

by passing a single beam of light through two colored filters. The colored illuminant is

"filtered" to begin with (its color is not white), and the colored surface subtracts from or

filters this light before the light reaches the

eye.

Metameric Colors. This subtractive mixing of surface and light source produces a

fundamental color ambiguity: it is possible

(and commonly happens) that (1) two different reflectance curves will produce the

same apparent color under the same kind of illumination, including pure white light, and (2)

colors that are apparently identical under one kind of illumination will appear different under

another kind of illumination, even if both light sources appear to provide "white" illumination.

These situations of metamerism involve metameric colors.

restricted light emission and metamerism the product of a single illuminant on two

complementary colored surfaces; adapted from Jeff

Beall, Adam Doppelt & John Hughes © 1995 Brown

University

The example above shows a simple but

commonplace example. The orange and blue paints shown in the previous illustration

appear to be very similar shades of green when illuminated by a predominantly green

light source. (A related problem arises in the

color of foliage greens under changes in daylight illumination.)

If you have already made some paint

wheels, these are very convenient to test

colors under different illuminations. A set of paint swatches of familiar paints or the

complete paint selection from a specific brand is also useful.

Visual metamers are the subtractive mixture

of the surface reflectance with the illuminant,

two surface colors that appear identical under one illuminant can appear different under

another illuminant. (This is the bane of automotive manufacturers, who have a

difficult time getting all the plastics and fabrics in a car interior to match under all kinds of

illumination.)

Object Shadows. The point with shadows is:

how much do they darken, how do they darken across a form, and what effects do

they have on apparent color or luminosity?

Shadows on a figure.

changes in chroma and hue in the

shadows across a figure

The end.

Complementary Shadow Contrasts.

Consistent with the general effect of chromatic adaptation is the specific phenomenon of

complementary shadow contrasts. If a yellow colored illuminant shifts the implicit white

point toward yellow, then an actual white or gray would appear to shift into the visual

complement, deep blue. Shadows are perceived to be color neutral, and therefore

they display this color shift — often quite

dramatically.

As Martin Kemp points out, the methods for producing the effect, usually attributed to

J.W von Goethe, were described several

times in the 18th century. The French naturalist Comte de Buffon reported on

complementary colored shadows and complementary afterimages to the French

Academy of Sciences in 1742. Similar descriptions were published in England by the

chemist Joseph Priestly and the entomologist Moses Harris in around 1780. These shadows

signal a shift toward the "internal" or

psychological consequences of color.

Buffon correctly I haven't experimented with a full range of

lights, but the effect is quite easy to produce with two lamps and several colored light bulbs,

such as large (exterior) Christmas tree lights or 50W colored floodlamps. (If possible, use

colored lights that are higher wattage than the white, to correct for the fact that the colored

glass blocks about half the radiated light, making the lights dimmer.)

The usual description is that the shadow cast by the colored light is the complementary hue

of the colored light. In fact the effect is more complex, and depends on the relationship of

the hue contrast to the CIELAB a*b* plane. the appearance of a

red/white shadow contrast

experiment

predicting the shadow

colors of contrasting

colored lights

shadow colors are a mixture of

shadow shine and light source

complementary color

A red light produces a beautiful pale turquoise

green (right), and a green light produces a rich middle violet, as we would expect from

the complementary color contrasts defined by

the visual color wheel. These hues have a significant contribution from the CIELAB a*

dimension, and therefore appear clearly.

However, an amber light produces a relatively pale blue violet, and a blue violet light (I used

a 60W blacklite bulb) does not produce any

visible yellow, but rather a cold gray. This is because the hue yellow requires both high

chroma and high lightness to be recognizable

daylight shifts

in shadow color

shown on the CIELAB a*b*

as such, but shadows by definition have low lightness. When darkened, the yellow appears

more like a gray raw umber. Thus, the CIELAB b* dimension creates qualitatively different

color contrasts — chromatically weaker at both ends, and more affected by a shadow's low

luminosity on the b+ (yellow) side of the color space.

The data are summarized in tabular form on this page.

A tangential question: why do watercolor artists a blue violet or purple as a foundation

for shadow colors? The answer is found in the mixture of skylight and the complementary

shadow hue that combine as the tint of all shadow colors (diagram, right).

Under midday sunlight, the visual complement of solar "green" (at about 550 nm) is a purple

(c550 nm), which our eye imputes to any absence of solar light (shadow). This

subjective color mixes visually with the shadow shine emanating directly from the blue

sky, which at midday has a dominant wavelength of about 470 nm. The result is a

mixed hue that appears to have a blue violet tint intermediate between the two.

However, this mixed hue can change significantly across daylight phases. In the

hours just after sunrise or just before sunset, the direct sunlight has a much lower color

temperature, giving it a deep yellow tint

(around 590 nm), which produces a visual complement equivalent to about 475 nm. At

the same time the sky appears to have a cerulean hue, matching monochromatic hues

above 480 nm. The resulting visual mixture is therefore closer to a middle blue or greenish

blue than the shadow color at noon.

For these reasons watercolor painters often

use a blue violet or even purple mixture (such as a dulled indanthrone blue or dioxazine

violet, or a neutral tint) to tint shadows created by bright or outdoor illumination, but a

greenish blue (dulled iron blue or phthalo blue, or an indigo convenience mixture) as the

shadow tint for indoor or late day illumination.

And concluding remarks.

plane

The interactive tutorial on color perception hosted

by the Brown University Computer Science Department

includes a java applet "Reflection" that explains the

combined effect of surface reflectance and illuminant

color on apparent color.

Several unusual color effects occur with special types of materials, our final topic.

Many of these were lovingly described by J.W. von Goethe in his Color Learning, but

without an adequate explanation.

Translucent Colors. Many materials can

appear translucent under certain circumstances, passing heavily filtered light.

This occurs in thin sheets of opaque materials (such as minerals or hides), and very thick

blocks of transparent materials (such as glass or ice).

Metallic Colors. We conclude with the phenomena of reflections and the specific

visual effects that make them compelling.

Reflectivity. A related attribute is the

reflective or "glossy" appearance of any surface, from window glass to lacquered

boxes. Vision researchers have established that the illusion of reflectivity is enhanced by

the following elements:

special material colors

• intensity of specular reflectance

• distinctness of image (when the eyes are

focused on the image behind the surface)

• increased contrast between light and dark

areas of the image

• absence of haze or fogging.

And so on.

Materials can easily change color

depending on how they are viewed or how the materials themselves undergo physical

change. As these materials can include paints, the artist needs to understand how these

changes occur.

physical color changes

reflectance curves for

characteristic surfaces

Color and Thickness. For partially transmitting substances, color changes with

changes in the material thickness.

The basic process is that the spectral

transmission curve can be established for any arbitrary (usually relatively small) thickness of

the material. This is the light transmitted from a "white" light baseline. If the material is

thickened, the effect is the same as passing the light through a second or third layer,

except that now the light is not white but is already filtered by the first layer. Essentially

the transmission profile is multiplied by itself, so any area of the spectrum that is not

transmitted at 100% is reduced each time.

This darkens the color and causes a characteristic hue shift.

the shift in color caused by increased

thickness of materials

In general "warm" colored (warm red, yellow or orange) substances become redder. "Cool"

red, violet and purple substances remain approximately the same hue, only darker.

Blues shift toward purple and cyans toward blue. Greens shift toward a middle green —

yellow greens become cooler and blue greens warmer.

Color and Illuminance. In this case the intensity of light is increased and passes

through what was an opaque appearing substance.

Color and Whitening. This shift occurs either because a paint has been diluted with water or

lightened by mixture with a white paint, which in watercolors is limited to chinese white

(PW4) or titanium white (PW6). In both

cases, the light reflected by the paint is mixed with a significant amount of white light, but

the either light reflected from the paper or the white paint. The hue shifts caused by white

paint are governed by additive color mixing, because the light from the paper and the paint

arrives separately to the eye, where it is

"mixed" by the averaging across millions of cone responses.

Why does merely lightening a paint cause

these shifts occur? Two separate processes are

at work.

The fundamental explanation is simply that hue is derived from the proportional

stimulation of the L, M and S cones, and these proportions change as white light or white

paint is added to a color. The figure below

shows how.

change in hue caused by adding white light

The reflectance curve at the top shows an

idealized spectral curve for a highly saturated orange paint, with a hue similar to perinone

orange (PO43). The cone response profile shows that the curve strongly stimulates the R

cones and less so the G cones, with no

response from the B cones.

Remember what the relative height of a reflectance curve means: when the profile is at

its maximum of 100%, all of the light from

those wavelengths is reflected by the paint. When the curve is at its minimum of 0%, then

none of the light at those wavelengths is reflected by the paint.

By adding reflectance from the paper, we do

not raise the maximum reflectance: if all

the "red" light is reflected by both red paint and white paper, we don't increase the

amount of reflected "red" light by mixing the two. Instead, we raise the minimum

reflectance, because light absorbed by the paint is supplied by the paper (or white paint).

This changes the cone response profile exactly as if we had started by shining a red orange

colored light on a sheet of white paper, and then lit the area with a second,

complementary (blue green) light.

direction and size of hue shifts caused

by adding white light

The diagram shows the net effect of these various changes for hues all around the color

circle. The basic rules are simple to remember: scarlet to yellow warmer, red,

magenta, blue and green cooler, scarlet, lemon and violet unchanged.

These are the shifts that occur while the eye is still daylight adapted. An additional shift

toward blue green occurs when the illumination is at the point where both the rods

and cones are active. The cones respond most to "blue green" wavelengths, and therefore

contribute a distinct blue green bias to apparent colors. This Purkinje shift causes

greens to appear relatively more luminous,

and oranges and reds to appear dull and even dark gray or black.

N E X T : tonal value

Last revised 01.12.2004 • © 2004 Bruce MacEvoy

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tonal value

Lightness or tonal value is the

light or dark of a color regardless of its hue.

Value arises from the relative luminance of surfaces or lights, the amount of light reaching

our eye from a specific color area in contrast

to the average or total illumination in our field

of view.

Lightness or brightness is only thing that the

oldest visual systems were designed to

perceive. Even when color vision appeared in mammals, it was basically a matter of long

wavelength light compared to short

wavelength light — yellow against blue —

which remain in our color vision as the hues that have, at their highest saturation, the

widest difference in lightness.

Given all the space devoted to hue in "color theory," it is surprising to learn that value is the most important design element of a painting. It is hard to overstate the

importance of good value structure to the

impact of visual art. This page explores in

depth the various ways artists think about,

measure, and control the value structure of

their paintings.

Value dominates our visual

experience. It is the strongest element of visual contrast and largely determines our

perception of form as we explore a picture. It

defines our perception of space through the

effects of aerial perspective and the

differences between the lighted and dark

surfaces of three dimensional objects. Even in

an abstract or pattern design, lightness

dominates hue as the patternmaking element

in a picture.

As a simple illustration, I've modified a

Winslow Homer watercolor to remove either

most of the color information or most of the

lightness information. (Lightness in the bottom

picture has been set to around 75, to match

the value of the sky in the original.)

The remarkable similarity between the original

color and the black and white versions,

compared to the noticeable impoverishment in

the unvalued version, demonstrates the

importance of value in a painting's overall

composition and visual impact. Notice how strongly the black and white image seems to

guide your eye!

no variation in hue, lightness unchanged

the dominance of value

colorvision

the dominance of value

the value scale

hue, lightnessand saturation

the artist's value wheel

grayscales & gamut mapping

painting values

the original painting (well, a picture of it)

no variation in lightness, hue unchanged

value versus hue in a painting by Homer

The comparison may suggest that a picture

with a limited value range will appear flat and

uninteresting. This is not literally true; a

painting with a reduced value range can be

visually exciting, as many paintings by Monet

or Whistler will demonstrate.

But if a painting has a poor compositional

arrangement of values within its value range,

there is little that color, texture, or line can do

to salvage it.

OK, but how do we measure the

differences in light or dark necessary to

recognize values with our eye or realize in

paints our intended value design? We use a value scale or photographer's grayscale.

Somewhere along the way between

psychology lab and art text, the rule developed that the eye can discriminate no

more than 9 distinct gradations in lightness,

from lightest to darkest. Of course, we can see

a much larger number of value differences

than that. The actual limitation is that a larger

number of value steps becomes impractical to

recognize across different situations and

match accurately with paints.

The nine step rule suggested the design of the

standard nine step value scale, originally

proposed by Denman Ross in 1907. His value

terms are useful and easy to memorize:

The convenient thing about this system is that

the labels work well for a basic three level

(light, midvalue and dark) or five level (white,

light, midvalue, dark, black) value structure

used in a value sketch; the remaining value

steps are "high" or "low" steps away from

"light" and "dark." In this framework one can

the value scale

Denman Ross nine step value scale

value sample value name

1 white

2 high light

3 light

4 low light

5 midvalue

6 high dark

7 dark

8 low dark

9 black

speak of the high lights, low lights or darks of

a painting with workable precision. The terms

are easy to remember, and easy to use as

reminders of the major value levels you can

use in a value composition. (Keep in mind that

a high light is the value step closest to white,

while a highlight is the bright reflection of a

light source from a shiny surface.)

Watercolor books typically explain values

using a 9 step value scale — but confusingly,

white and black are sometimes included in and

sometimes omitted from the range. The

standard in color models, for example in the

Munsell color order system, is an 11 step

value scale ranging from 0 (black) to 10

(white). (The CIELAB L* dimension is very close to a multiple of 10 of the Munsell scale:

a 6 on the 11 step Munsell value scale

corresponds to a 60 on the L* dimension.)

Both the 9 and 11 step scales are presented

below. Open the scale you prefer in a new

window by clicking on the link below it, print

on a good quality color printer (with print

options set to "black ink only"), and you have

a serviceable value scale for use in the field or

studio. (You can also buy preprinted value

scales, such as the "Don Rankin Perception

Kit" available from Cheap Joe's, or the

standard photographer's grayscale manufactured by Kodak and sold in most

camera stores — though the photographer's

scale crunches up the range of light values

and spreads out the darks.)

9 step value scale Click here to view the full size image on gray

background

11 step or Munsell value scale Click here to view the full size image on gray

background

How do the values of a value scale match to gray paint reflectance? There are three

approaches (also described below):

• reflectance interval scales are calibrated

to differences in relative reflectance from 0% to 100% (or as near to pure white and black

as can be reached by physical pigments), so

that step 10 is 100% reflectance, step 9 is

90% reflectance, step 8 is 80% and so on

down to the lowest value. These equal

reflectance scales produce finer apparent

gradations of value in the lighter values

(middle gray is at step 2).

• lightness interval scalesare calibrated to

differences in perceived lightness between

black and white so that each value step

appears to be equally different from the steps

above and below it. (This is the approach used

in the scales above.) This amounts to a power of the reflectance such as the square root,

cube root or logarithm. These power scales

produce finer gradations of value in dark values, and more closely match the

logarithmic scaling of light energy relevant to

film exposure. (Medium gray is at step 5.)

• media interval scales are calibrated to differences in the reflectance of art media —

differences in the darkness of photographic

prints produced by changing exposure or

developing times, differences in the darkness

of etchings produced by changing acid bath

times, and so on. These scales show large

intervals in reflectance and lightness at high

values, which grow progressively smaller in

darker values. The lightness of scale intervals

is not logarithmic but compounded, sometimes

at changing rates. For example, in a

photographic gray scale, if step 1 is white with

a lightness 99, then step 2 is 89 (89% of 99),

step 3 is 79 (89% of 89), step 4 is 70 (89% of

79), down to step 7 at middle gray (lightness

= 50). Then steps are compounded at 82%

down to the lower reflectance limits of the

media.

Painters are sometimes instructed to paint out

value scales for themselves, sometimes by

mixing different concentrations of color for

each step and sometimes by using the same

dilution of paint in multiple glazes (more

glazes for darker color). The glazing method produces the equal interval scales described

above. The exponent scales must be painted

using dilution recipes, and often the same

proportional mixtures will produce the same

intervals of value but anchored at a different

maximum darkenss depending on which paint

is used.

How large a value range should a painting

have? This depends mostly on the subject,

lighting, color scheme and painting style, but a

wider range in value will usually have a

stronger impact on the viewer. (Some artists

enthuse about "punching up a picture with

darks.")

The practice of landscape painters suggests a

starting point. Their rule is: for any object

outdoors and in direct sunlight, the shady side is 60% of the value of the sunlit side. So if you measure the lightness of the sunlit

surface, then take 60% of this value (whatever it is), you have the approximate

lightness of the shaded surface of the object.

With the 11 step value scale we can return to

the landscape painter's rule with more

guidance. The handy shadow ball (at right)

lets us illustrate basic lighting problems. If our

representation of the light source or highlights

on the object is given a value of 10, and a

white surface a value of 9, then the sunlit side

of a yellow or orange object has a lightness of

8 on the value scale. The shaded side will

therefore have a lightness of about 5 (8 times

0.6 or 60% is 4.8).

The cast shadows from the object depend on

the intensity of indirect illumination into the

shadow and the color of the shadow receiving

surface, but in daylight the shadowed area is typically about 40% the lightness of the sunlit

surface (that is, a lightness of 9 times 0.40, or

3.6), or 4 on the value scale for a white

surface at 9. On overcast days, when light falls

diffusely from all directions, all objects are less

brightly illuminated, but the only shadows are

cast shadows (underneath objects or in narrow

passageways), and the 40% applies here too.

These are only rules of thumb, but reasonably

accurate ones.

The shaded side of the object can be

considerably darker than 60% of the lit side, if

there is no indirect reflection onto the shaded

side from other parts of the landscape. (The

dark side of the moon is an extreme example.)

And cast shadows can appear significantly

darker than the shaded side of the object if they fall on a surface with a dark local color,

such as grass or asphalt.

There will always be some error in measuring the lightness of colored surfaces with a

monochrome value scale, and in estimating a

40% lightness reduction with only 9 or 10

value steps to chose from. But the goal is to

find the neighborhood of the correct value, not

its exact tone. Once you've located the

lightness of the sunlit side, just use the

lightness step that is halfway to black (or the

step just above halfway, if there are an even

number of steps to black) as the value of the

five value zones onthe shadow ball

the illumination value is 10, a white surface is 9.5, the object

8, the shadow side 5, and the

cast shadow 4; actual

reflectance shown below each value step

darkest part of the shaded side.

When we make the step

from estimating the lightness of various

shades of gray on a grayscale to estimating

the lightness of various colors, we confront a

new complication in color perception:

different paint hues reach their maximum saturation at different values. And because saturation is easily confused visually with

lightness, this means that we tend to misjudge

the actual value of different colors, perceiving

some of them as lighter or darker than they

really are.

The Value of Peak Saturation. The figure

below shows each of the 12 hues of the

tertiary color wheel with the value 0 (for

black) at the center, the value 10 (for white)

at the circumference, and value steps of 2

indicated by the concentric circles. The gray

squares show the approximate value of the

maximum saturation in paints that can be

achieved for each hue in the most extensive

Munsell Book of Color.

lightness of maximum saturation for different hues

based on the maximum chroma for hue sections in the

Munsell Book of Color (surface colors); concentric

circles show increasing lightness values from 0 (black)

to 10 (white)

The general shape outlined by these squares

— lopsided toward yellow and away from blue

violet — is worth careful study, because it can

guide your judgments of the actual value of

different hues, and assist in relating the

saturation of color areas to the basic value

design.

Before we get to that: why don't all hues

reach maximum chroma at the same value or

lightness? Because the eye is most sensitive to light in the middle of the spectrum rather

than at the ends. These differences in the

sensitivity of the color receptors to light of

different wavelengths creates differences in

the apparent luminosity of different parts of

the spectrum. The value of a color is always related to the total proportion of incident light

that is reflected by the color — but reflected

"green" light always appears much brighter

than the same amount of "blue" light, and

intense warm colors in general reflect much more light than equally intense greens or

blues. The next diagram shows how this

affects the value of different hues of paint.

hue, lightness and saturation

why the value of high chroma paints varies across hues

Colors from deep red through light yellow

have a "warm cliff" reflectance curve, so as

the reflectance curve moves from A to B —

from deep red to light yellow on the color

wheel — it is as if a curtain is drawn away

from a window. Bright reflectance expands

across the entire long wavelength side of the spectrum, and this rapidly increases the

value of color as the hue changes, while

always maintaining the maximum saturation.

The lightness starts at a dark value, since light

at the far "red" end of the spectrum is at

wavelengths where the eye is less sensitive to light — but lightness increases steadily as

the hue approaches orange and then yellow,

which at its maximum chroma has a high

reflectance almost indistinguishable from

white.

As the hue continues into green (the span

marked B to C in the color wheel), the "warm cliff" profile changes into a "hump" centered

approximately on the dominant wavelength of

the hue. The total area of reflected light has

been reduced, but the impact on the apparent

value is negligible at first, because the

maximum reflectance is in the "yellow green"

wavelengths where the daylight adapted eye is

most sensitive to light.

However, as the hue moves through blue

green and turquoise and approaches middle

blue (the span marked C to D in the color

wheel), we enter a part of the spectrum where

the reflectance curve is clipped on the short

"blue violet" wavelengths, and the center of

the hump moves into an area where the eye is

again less sensitive to light. So the value of

the intense blues begins to go down very rapidly.

The value of saturated hues reaches its lowest

point somewhere around a blue violet such as

indanthrone blue or dioxazine violet (D in the color wheel): these colors consist of

reflectance at the extreme "blue violet" and

"red" ends of the spectrum, so all the high

reflectance is concentrated in the areas where

the eye is least sensitive to light. This

produces the darkest valued colors.

Finally, as the hue continues to shift from blue

violet to red violet (D to A), stronger "red"

reflectance is added rapidly to the color as the

weaker "blue violet" reflectance is reduced,

which causes the value of intense red violet

paints to increase again. Value rises steadily

until we reach a deep red, and we have

completed the circle.

Hue and Apparent Value. Let's come back

to the fact that it's often difficult to judge the lightness of an intense hue. This occurs

because, in each case, the most intense hue is

at a different value. The next figure shows

twelve colored squares representing equally spaced hues around the CIELAB color space,

at the maximum saturation possible on a

computer monitor. Each gray square around

the hue sample is exactly the same value

(lightness) as the colored square it contains.

colored squares at maximum saturation outer gray squares are the same lightness as the

central color

The variations in the lightness of the gray squares show the differences in the value of

the maximum saturation of the different hues.

The apparent difference in lightness between a

colored square and the gray square

surrounding it indicates the difference in

apparent lightness caused by saturation alone

for that hue. Notice that most hues appear

lighter than they actually are, especially hues

at the spectrum extremes and mixtures of

them — purple, red violet and magenta

(bottom row), red and red orange (top row).

In contrast, mid spectrum hues such as yellow

and yellow green (top row) appear darker.

Only orange and the hues from green to blue appear at roughly their true value. (These

contrasts are similar but not identical in paints

or lights.)

These hue value relationships are easier to

remember in terms of the shadow ball (at

right). Two versions are shown, with similar

purple, red, orange, yellow or teal hues shown

at reduced saturation (top) and at maximum

saturation (bottom) for each hue (displayed on

a computer monitor).

The contrast between these two figures,

especially in the red and violet shadows, and

the similarity between the low saturation

version and monochromatic version (above),

suggests the distorting impact that high

saturation colors can have on our estimates of value. Perhaps it was this distracting, deluding

effect of intense colors that caused academic

painters to call color the enemy of good

design.

There is a simple relationship to the

warm/cool color contrast that can help you

remember the approximate relationship

between apparent and actual lightness for

hues near their maximum saturation:

• Hues at either end of the warm/cool contrast, such as scarlet, orange, deep

yellow, turquoise and green blue, appear to

the eye pretty close to their actual value.

• Intense hues that lie above the diagonal warm/cool color contrast, such as middle

or light yellow, all greens and cyan, generally

appear to have a darker value than they

actually do: to compensate, adjust your

judgment of the color's value slightly lighter.

• Intense hues below the diagonal warm/cool contrast, such as middle red,

magenta, violet and blue violet and middle

blue, generally appear to have a lighter value

than they actually do: to compensate, shift

your judgment of the color's value slightly

darker.

For example, in the Homer watercolor

reproduced at the top of this page, the beige

clouds and yellow buildings seem darker in

color than in black and white, while the middle

blue sky appears lighter valued in color than in

the shadow ball incharacteristic colors

in low saturation (top) and high saturation (bottom)

black and white. This is because the black and

white version shows the actual value separate

from the confusing effects of the beige (dull

yellow) and blue colors, which look darker or

lighter than they actually are.

Even with a value scale and an

awareness that high saturation colors can

mislead our perception of lightness, it's difficult to judge the value of watercolor

pigments by eye alone. So I created the

artist's value wheel as a help through these

difficulties. (I later learned in Martin Kemp's

The Science of Art that J.M.W. Turner described a very similar color wheel in his

Royal Academy lectures on perspective.)

This "wheel" is based on the fact that the

yellow/blue dimension of hue (b* in CIELAB),

and the light/dark dimension of value (L* in

CIELAB), are highly correlated — that is,

intense yellow hues are light valued, and

intense blue violet hues are dark valued. This

suggests replacing the chromatic dimension

b* in the artist's color wheel with the

luminosity dimension L. This separates

pigments vertically by value, but keeps the a* (red/green) dimension to show the chromatic

contrast between warm and cool pigments.

the artist's value wheel

This value wheel serves as a simple lookup for

the masstone value of specific pigments. The

vertical numbering is in units of the CIELAB L scale. Just divide by ten to get the equivalent

artist's 11 step (Munsell) value: ultramarine

blue has a lightness of 30, which equals a

Munsell value of 3.

click here for a full size view in a new window

click here for a printer friendly (Adobe Acrobat PDF) version of the artist's value

wheel (size 220K)

To print the value wheel, set page orientation to "landscape" and print to fit an 8.5" x 11" sheet of paper.

It's striking how well the luminosity and

a+/a- or red/green dimensions can

reconstruct the artist's color wheel. The

wheel reveals the close relationship between value and hue among intense

pigments on the "warm" side of the color

wheel (from cadmium lemon to quinacridone

violet). The top to bottom ordering of intense warm pigments (cadmium lemon to

quinacridone violet) in the artist's value wheel

is almost identical to the counterclockwise

ordering by hue in the artist's color wheel.

The important exceptions are among the high

chroma pigments at the extreme end of the

a+ (red) dimension — pigments between

naphthol scarlet (PR188) and quinacridone

magenta (PR122). Most of these paints are

"really red reds" that differ in how much

"yellow" or "blue" reflectance they contain,

which means these are hue differences that

require input from the y/b opponent contrast

to sort out. We can see this in the Coloroid color model (at right): the most intense hues

from scarlet to magenta have nearly the same

lightness (the Coloroid hue curve is flat), so

we can't use lightness alone to distinguish

among them.

A second area of confusion is the jumble of

dull earth and violet pigments across the

"warm" (a+) side of the wheel: we find

venetian red next to manganese violet and

cobalt violet next to quinacridone gold. A third jumble includes the "cool" pigments from

yellow green through deep blue on the a- side

of the wheel. In these pigments the y/b opponent contrast, specifically the

contribution from the B cones, is also

necessary to disentangle hue differences

within these color groups.

At the bottom of the scale are four very dark,

blue or purple pigments — dioxazine violet,

ultramarine blue, indanthrone blue, and

prussian blue. These are commonly used to

mix dark and near neutral shadow tones. They

are joined by a very dark brown iron oxide

(PBr6) and various carbon "black" pigments

(which are actually dark grays with a

reflectance around 20).

By grouping together the pigments that

appear well ordered by hue as opposed to the

pigments that are shifted out of their expected

hue location, the artist's value wheel identifies several pigment "families" defined on hue/value relationships: (1) the earth pigments and other dull yellow or red

pigments (low chroma, darker valued than

their yellow hue suggests), (2) the cobalts (low chroma, lighter valued than their blue

hue suggests), (3) the phthalocyanines (high chroma, darker than their green hue

suggests), (4) the red quinacridones (high

chroma, lighter than their bluish hue

suggests), (5) all other intense warm

pigments (ordered closely by value), and (6)

the dark pigments (including carbon black).

Interestingly, these are the same groups of pigments identified as having distinctly

different patterns of color change in the study

of dilution and saturation. In any case,

once you become very familiar with the paints

on your palette, these color "families" may

help you refine your judgment of paint

apparent values, and remember pigment

values in your value designs.

The value wheel is primarily a convenient reference to the value of a pigment and other pigments with similar lightness. It clarifies the relationship between a pigment's

most intense color and a specific,

characteristic value, so you can each value

step in relation to a specific pigment. By

reading across any horizontal band of the

wheel, you can identify the paints with a similar value, letting you first choose a value

and then select paints to match it. This can

help you to think about the scheme of a

painting as primarily gradations of luminosity

and saturation rather than hue, and to

overcome the visual illusions that make

orange appear darker than teal blue, or

phthalo green YS darker than quinacridone

rose, when they have exactly the same

lightness at optimal dilution.

The range and pattern of

values in a painting strongly determine how it

will affect the viewer. But the range of

lightness and saturation available in an artist's

medium is always more restricted than the

grayscales & gamut mapping

range of light and color in nature.

This schematic suggests the main differences across different media. If we take as our basis

of comparison the luminances that appear in a

daylit landscape (natural light gamut), and

compare these to a photograph of the same

scene, the photograph will have a much more

restricted gamut; the brightest whites in the

photograph will be much darker than the

matching surfaces in the real world, although

the darkest darks in the photograph will be

darker than the matching surfaces in the real

world. A watercolor painting is even more

restricted in chromatic range and along the

dark side of the gamut.

color gamuts in nature, painting and photography

Somehow the ideal range of natural color has

to be squeezed into a smaller range of paint

color. This problem is called gamut mapping

— squeezing a larger gamut range into a

smaller or different range in a way that makes

the squeezed colors appear "natural" or

"accurate" to most viewers. It is intensively

studied in color reproduction and imaging technologies, and it is an essential aspect of

painting skill and artistic vision. As Picasso

famously said, "some painters turn the sun

into a yellow spot, while others can transform

a yellow spot into the sun."

Gamut mapping is very familiar to

photographers, who learn how to use a

photometer to translate actual light values into

exposure time for a film emulsion, with the

knowledge that the exposure of light passed

through the negative onto photography paper,

and the amount of time the paper is exposed

to developing chemicals, will produce a

"natural" value structure in the final

photographic print. This serves as our point of

departure. We can also learn from research

that has been done on the gamut mapping

problem in the imaging industries.

A Painter's Basic Value Plan. All

professional photographers are familiar with

the zone system of photographic exposure and printing, developed by Ansel Adams. The

zone system links an ideal photograph — the

photographer's concept of how the finished

image should look — to the exposure

properties of their film.

Painters do not have the apparatus problems

of a photographer, but they do face a similar

value design problem: anchoring the middle

value of a painting in a way that

communicates the intended feeling of light or

dark without sacrificing a complete

representation of the tonal range.

Our visual system naturally adjusts to the

average luminance in our environment to

produce the best visual representation.

Because this adaptation also affects the

appearance of any physical gray scale, the key to the value design of a painting lies in the

distribution of gray values across the

luminance range.

What should this distribution look like? The

diagram at right shows a basic value plan that

can serve well in thinking about the value

range of any painting.

The CIELAB L* scale, which is a benchmark

measurement of surface reflectance and the

vertical scale used in the artist's value wheel, represents the basic reflectance

range; this is overlaid (in orange) with the

value range used to describe paints in the

guide to watercolor pigments. Against

these lightness benchmarks I've inserted the 9

steps of a simple design system.

The two important features of this value plan

are that (1) the reflectance range goes no

lower than 20, which is the effective value

range of watercolor paints; and (2) the

reflectance intervals are wide in the middle

and narrow at both the light and dark ends.

Indicated for each zone are some of the

physical surfaces that typically have that reflectance.

This scale can be linked to the method of

dilution recipes for value, which is probably

of most interest to painters who build their values through successive glazes, but for the

rest of us is a rough guide to the concentration

of paint necessary to produce any desired

value.

Creating a Value Scale (Grayscale). It will

be useful to explain how value scales are

derived from the apparent values of the

natural scene we want to represent.

Value scales or grayscales are usually

constructed to have perceptual interval

scaling: each value should appear to be

approximately midway between the values on

either side, and the middle value (middle

gray) should have an apparent lightness

roughly halfway between the darkest ("black")

and lightest ("white") values. The question is

how we get to those values, and how the

grayscale values relate to the original scene

values.

1. A Naive Value Scale. Let's start with the

naive assumption that differences in the

luminance (light intensity) in the scene we

want to reproduce should equal differences in

the luminance of the painting we look at, when the painting is displayed under optimal or

standard lighting. This suggests that the value

scale should space the lightness intervals

evenly across the luminance range — scene

luminance = painting luminance — as shown

below.

a naive value scale

The total range of light adapted visual response is bounded by a roughly 100:1 ratio

between the darkest and the lightest

luminances, so this applies to the scene as

well as the painting. The top end of the

luminance range would appear "bright" and

the bottom end "dark". Naively, we would also

assume that a middle gray is roughly in the

middle of the luminance span — in the

example, at around 2500.

There are obvious practical problems with this

a painter's basic value plan

value scale. As the luminance range changed

across different scenes (for example, from

sunlight to twilight), the luminance range of

each painting would change as well. But the

painting luminance patterns would have

different effects depending on the level of

surrounding illumination: a daylight painting

would have to be viewed in daylight, and a

nighttime painting in the dark. So each

painting would have to be displayed under its

own lighting conditions.

2. Visual Reflectance Steps. These practical

problems mean we have to make two

fundamental corrections to the naive value

scale. First, we have to shift to reflectances

relative to a standard white value. This limits all our value judgments to related color judgments, and also makes them more or

less independent of the viewing illumination

(within the normal range of indoor lighting).

Second, in order to get apparent visual

equality in the difference between two value

scale steps, the actual light intensity between

two steps must be unequally spaced to

compensate for the visual system's response compression to the light stimulus at higher

luminances. That is, as the stimulus intensity

increases, the changes in luminosity necessary

to produce an equal visual effect must

increase as well.

This gives the reflectance to value relationship

a characteristic downward sloping curve as the value increases.

visual response compression in the CIE L* (lightness) scale

The exact shape of this curve is different for

different color models, but all have a very

similar shape. The example shows the CIELAB

L* scale, which is also identical to the

Munsell value scale (with each value

multiplied by 10).

With a reflectance value scale such as CIE L*,

it is possible for some areas of the scene to

exceed the luminance of the white standard.

For example, a white porcelain bowl or the

surface of a lake may reflect sunlight as highlights, or a white paper displayed in a

darkened classroom will appear darker than a

white paper in sunlight seen through a

window. In such cases we either accept a

value of L greater than the white standard of

100, or we take the brighter white as the new

white standard and adjust all other values

accordingly.

3. Media Compression. However, in

photography, the film emulsion and print

paper have a fixed "white" transmision or

reflectance value. In natural scenes, random

highlights or contrasts in illumination can

produce a much wider range of luminance

values, so the media must compress this wide

range of values into the fixed range of

reflectances possible within the specific media.

This is the fundamental difference in luminance patterns between "real" scenes and

their representations.

Photographers use light meters and exposure

settings to adjust the light coming into the

camera so that a visible white in the scene

corresponds to a visible white in the finished

photograph. But brighter areas of the scene,

such as specular (reflected) highlights, do not

get an even higher white value — they are

rendered in the same white as the standard

"white" surface. So there is a specular compression in reflectance media, which

flattens extreme luminance values into the

same, top end "white" value.

flattening of specular values in photographic media

In most photographs, small changes in the

scene luminance at the low end of the visible

range are difficult or impossible to separate as

different darks in the photograph. In effect, a

single very, very dark value stands for all values from the darkest value of the media

range down to zero luminance. So there is

also media flattening of luminance differences

at the bottom end of the scale, which is too

small to see in the diagram.

By using the photographic example, we hold

onto the relationship between scene and

media values. If we know all details of the

camera exposure settings, emulsion speed and

development chemistry, it is in theory possible

to relate the photographic values back to the

approximate scene luminances.

An artist's value scale, for example the kind of

scale that painting students prepare by mixing

black and white paint to equal value steps of

gray, or the commercial grayscales available

from photography supply stores, will

approximately match the luminance curve of

this idealized grayscale. But those grayscales

have no relationship to the luminances in a specific scene.

4. Artistic Value Range. When we turn to

paintings, or the actual density range of

photographs, many significant changes enter the value scale.

If we stay with the example of watercolor

media, then the first change is that the range of values within the media is restricted in

comparison to the conceptual range possible in

the CIE L* scale. Watercolor paints on white

paper have a potential range from about L =

97 to L = 20, or a value range of about 75.

This puts the middle gray value at about L =

60. All media reflectance scales, including

photographic grayscales, restrict the range of

actual values in a similar way.

artistic interpretation in a painting's value scale

In addition, artists tend to interpret the values

in a scene as a distorted range of values in the

painting. Painters tend to assign a large range

of natural luminances at the extremes of their

visual range to a narrow range of paint values,

which flattens the value curve at both the top

and bottom ends.

They also tend to make fine discriminations

among the middle values, which assigns a

relatively wide range of paint values to a

narrow range of luminance values around the

middle gray. The result is a characteristic "S"

shaped curve.

Finally, artistic license means that we no

longer have the indirect but explicit

relationship between scene and image

luminances that we potentially retain in

photography. So there is no way to compare

painting values to natural values, or to judge

the actual luminances of the original scene.

If you compare this curve to the zone scale

shown above, you should be able to see why

the reflectance intervals are wide around the

middle value: this is where the curve is

steepest in relation to the reflectance scale and to the original values. Where the curve is

close to vertical, at either end, large changes

in the value intervals correspond to small

changes in the reflectance, but these

reflectance changes are smaller at the light

end of the scale. This also corresponds to the

visual effect known as crispening, where

values close to the background or average

reflectance of the scene appear more highly

contrasted than values at either end of the

visible range.

This general distribution of values — the

strongest contrasts in the middle range, with

reduced lightness variations at the extremes

of the range — produces the most gratifying

contrast across the widest range of values

possible with watercolor paints.

Industrial Gamut Mapping. The problem of

media value compression not only occurs

between the actual scene and its representation in a specific medium, but

between two different media representing the

same image. Gamut mapping in the printing

and imaging industries must tackle all aspects

of color transformations — chroma in

particular. The rules developed in these

applications provide a unique perspective on

the gamut mapping problem.

In this context, the image that the artist

intends to reproduce (landscape, still life or

abstract design) is source or original color

space, and the range of color mixtures

possible with paints applied to paper is the

device or media specific color space.

The media colors can be manipulated to

achieve different goals. For painters, the most

relevant are probably pleasing color reproduction (the image colors are not

necessarily accurate in comparison to the

source colors, but they are sufficient or

customary when judged in terms of the image

taken by itself) and preferred color reproduction (the colors are the best

possible, or the most commonly preferred, out

of many possible ways of color rendering the

same source image). To simplify things we

always assume that the colors in the painting

will be viewed under sufficiently bright, white

light.

The diagram at right shows the alternative

gamut mapping solutions. If we take a vertical slice through a color solid (such as Munsell or CIELAB) as our source colors, and look for

ways to represent its colors within the

somewhat reduced range of saturation and

lightness in watercolor paints, then we can do

the mapping in one of four ways: (1) chose a

color with the same hue and equal lightness at

a lower chroma (L in the diagram), (2) choose

a color with the same hue and equal chroma

at a lower or higher lightness (C), (3) choose

a color that is the nearest available color in

the media color space, whatever its lightness

and chroma (n), or (4) choose a color that is

the nearest available color in the direction of a middle gray in the media color space (G).

How do these different strategies fare when

judged across many different types of images? In general, the fourth strategy — shrinking the

source colors toward a middle gray value, until

the source gamut is mostly contained within

the media gamut — is the method producing

the most pleasing and most often preferred

results in all media. This is done by (1)

mapping the range of lightness values until the most extreme light and dark

contrasts in the source are matched by the

most extreme light to dark contrasts in the

media, and (2) preserving the middle gray value to be the same. Then (3) chroma values are clipped until all hues fall within

the media gamut.

There are many subtleties in the

implementation of these general rules. For

example, it may be permissible to alter the hue or lightness of the media color to achieve the desired saturation impact. A

yellow might be changed to a yellow orange if

a darker value at high chroma is needed; a

blue green might be made darker to increase

its saturation in the image.

The chroma of the media colors may need to

be reduced in order to match a reduced

chroma range in the source: few landscape

painters use their paints in pure form because

the pigment colors are more intense than

those in nature, especially in foliage greens.

Finally, the lightness of some media colors

may need to be reduced or increased to match

the overall balance of colors in the source. A

common problem arises with landscape

lighting, in which sky blue must be increased

in value to create sufficient contrast with

shadow and surface darks of the soil. This kind

of problem may require you to adjust the

distribution of light or dark across the entire image (see below).

The overriding rule is to match the middle gray as closely as possible, and adjust all

other values in relation to it and in proportion to the maximum range of light or dark

possible with white paper or dark paint. Once

this is done, the tendency of watercolors to

reproduce higher saturations in warm hues

and lower saturations in greens, blues and

purples must be compensated to match the

overall balance in the distribution of chroma in

the image; the specific hue of any color area

can be shifted to an analogous hue, or the

visual area of very intense colors can be

reduced (for example, from the entire surface

of an object to only the most brightly lit areas

of the object), to make this balancing act

work.

alternative solutions to the gamut mapping problem

High Dynamic Range Images.

Painterly Changes in Value Range. How does a painter incorporate these basic

mapping strategies into his or her technique?

The key is that the painter essentially works

the value design problem in a different

direction from the photographer. Both

visualize the "ideal" picture, but the

photographer must adjust exposure to ensure

the negative shows detail in all but the darkest

or lightest values, while the painter must use

paint mixing to anchor a middle gray at the

right luminance to define a visual style or a

specific luminance adaptation. In either

case, the middle value is shifted lighter or darker, which crowds one end or the other of the value scale.

As already discussed, high saturation appears

as an added luminance in a color, so painters must evaluate lightness in terms of

the combined luminance and chroma of the

color, rather than luminance alone. The

example below illustrates the basic problem.

The sample on the left retains the visual

lightness contrasts by combining lightness and

chroma as grayscale differences, producing

nice contrast between sky and trees, trees and

grass, and grass and flowers. The sample on

the right is produced by desaturating the color

(removing chroma information without

adjusting value), which produces

comparatively muddy grays.

difference between grayscale values (left) and desaturated values (right)

A second issue is the location of the middle

gray value in relation to the total value range

of the media. Design approaches that

emphasize a restricted or imbalanced

luminance range are a traditional method for creating a distinctive, atmospheric mood.

Three versions of the same photograph show

the typical effects.

shifting the middle value lighter (left) or darker (right)

The typical watercolor resembles the image at

left, in which the landscape mid values are

reproduced at a higher value in the painting,

creating a luminous, sun drenched effect. This

kind of gamut mapping suggests vision overwhelmed by light. We have come out of

a dark cellar, and our first impression is that

everything is bathed in intense light. Every

detail in the shadows is crisp and clear, but

the brightest areas of the landscape blaze and

blur together.

In contrast, the example on the right, in which

the landscape mid values are much darker in

the painting than in the actual scene,

illustrates the typical Claudean landscape, which exploits the ability of oil paints to

produce rich darks. The Claudean alternative

suggests vision overwhelmed by shadow.

This is why the sun is always near the horizon

in a Claude landscape: because the light is

rapidly fading, our light adapted eyes can't yet

see into the encroaching shadows. Usually

cloud detail in the sky is crisp and clear, but

forest shadows are dark and difficult to penetrate.

In fact, most watercolor painters would spread

out the middle values and push areas of near

dark toward the bottom limit of the painting media, resulting in the ogive "painter's value

plan" described above. Here is the same

photograph using that gamut mapping

strategy. Note that it lets the painter show a

sun drenched landscape while suggesting the

same visual contrasts within a smaller

lightness range.

lightnesses corresponding to the painter's value plan

A painter who wants to imitate either effect

starts by shifting the middle value lighter or

darker. For example, to produce a lighter

valued painting, tanned skin and weathered

wood would be painted at a reflectance of 70

or 75, rather than the 55 of normal vision. To

produce the Claudean darks, the same woods and skin would be painted at a lower

reflectance, around 45 or so. These

adjustments can be worked out using the

artist's value wheel to select the appropriate

paints, and the paint dilution recipes to work

out the appropriate paint dilution. There are

three contrasting techiques to do this.

The first, recommended by painters such as

Trevor Chamberlain, is to paint the middle values first, to establish the overall tonality

and the range of values from the middle

toward light and dark, and to reduce the

amount of white paper showing, as white

paper makes the paint you're applying appear

darker than it really is. The problems with this

approach are that the white paper will make

you misjudge the initial gray anyway, and that

the color will seem to fade because of watercolor paint drying shifts. Both narrow

the differences you can show at the top end of

the value range. You must have excellent

paint control to navigate these problems.

The second approach, recommended by

Joseph Zbukvic, is to work methodically from lightest to darkest values, without

skipping a step. This allows you to correct as

you go, pushing the middle values darker if

the lighter values already established demand

it. The problems with this approach are that

lighter values appear to grow even lighter as

darker values are added to the painting, and

by incrementally increasing the values you

may run out of room to show differences at

the dark end of the range.

Painters like Chamberlain and Zbukvic are

alike in their ability to nail a value on the first

pass. Given the natural tendency of

watercolors to fade as they dry, we'd expect

Zbukvic's method to be the better one for watercolor painters to use — at least, until

they become as skilled as Chamberlain.

The last method for gaining control of the

value range is to use many glazes to build

up the painting, adding more and more layers

to the middle and dark values until you've

pushed them down far enough to resemble the

middle picture above. I find this method is

excellent for precise modeling of subtly

contoured forms, and can flesh out the full

value range, but tends to look overworked or

bland if the goal is delicate color effects.

After drilling down on the topic

of color values, we can formulate a few basic

rules for modeling shadows. (These should be

studied along with the section on modeling forms).

In an artificial setting, as colors move into

shadows from a single light source, the

surfaces of objects do not usually change in

saturation: the shadow area is a lower value

of the same color at the same relative

saturation. This is modeled by simply adding a

dark near neutral paint, such as neutral tint, ivory black or lamp black to the color. This

reduces the saturation in the same proportion as the value.

In natural light the effects are more complex.

Direct light from the sun appears as close to

white, while indirect light (scattered from the sky) is colored blue. If an object is directly lit

by the sun, its shadow areas will receive some

light from the sky, and this acts to raise the

shadow value from the dark value created by

direct indoor lighting, and also to mix blue

with the local (surface) color.

If the local color is warm (red through yellow),

this added blue acts to lower the saturation of

the surface color, just as mixing blue in the

red paint will neutralize it. If the local color is

a cool green or blue, the saturation is

unaffected or may even slightly increase. This

indirect light also shifts the hue, in general

toward blue.

When painting these effects, mixing shadows

with the mixing complement of the local color

is almost always wrong: it desaturates the

color without shifting the value. Mixing with a

blackish color, such as neutral tint, is better,

since it shifts value primarily but also

saturation (because colors lose saturation in shades).

But the more common solution, especially for

landscape artists, is to use as the "cool" shadow hue a dark blue violet (such as

dioxazine violet, indanthrone blue, or any

dark mixed violet), or a dark, near neutral

convenience mixture with a blue tint (such as

payne's gray or indigo). This method shifts

value very effectively, since the small amount

of blue hue acts to reinforce other blues and

greens but to desaturate warm hues. But it

also shifts the hue: for most warm colors and

greens, these dark shadow colors shift the

mixed hue toward blue. Usually this hue shift

is quite small because the shadow color is so

unsaturated that is almost equivalent to gray.

So some artists go the extra mile and actually

model shadows by shifting the hue towards a

cool color: the shadow of a green object is

painted blue, the shadow of a red object is painted maroon. Many artists get similar

effects by using a less desaturated dark blue

(ultramarine blue or prussian blue) as their

shadow color, since these colors appear "cool"

in relation to all warm and most green hues.

This "purple shadow" method is often good to

represent the complex chroma and lightness

shifts of shadows in natural light. But other

artists use other methods. Christopher Schink

painting values

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models both light and shadow by shifting the

hue of the local either color warmer or cooler

(a red becomes a warmer orange in bright

light, a cooler magenta in shadow), which is of

course the method innovated by Paul Cézanne for rendering form without using

value changes. Jeanne Dobie thinks shadows

must always be the same hue as the local

color, neither warmer nor cooler; she reserves

warm or cool color changes for the highlights

and the transitions from light to shadow,

depending on the type of light.

These different approaches suit different

painting styles, but also different types of

illumination. For objects under other lighting,

the technique may be too simplistic. In particular, if the indirect light is colored by its

source (for instance, a red wall, or a green

neon sign), then the hue shifts and

desaturating effects have to be worked out as

if this hue were "mixed" with the local color of

the objects the light falls on.

The quality of shadows depends on the

amount of light, the color of the direct light,

the colors of indirect or reflected lights, and

the value and saturation of the surface color of

the objects. The only general rule is that

lightness, chroma and hue (color temperature) may all change from light to shadow. And if it's any consolation, these

effects have been among the most difficult

problems for color psychologists to

understand!

Anyway, to conclude with tonal values: many

books recommend that you squint to see the value structure of a painting or scene. This is handy for daylight and quick assessment of

values, but it requires practice to learn.

Actually, the most accurate way to judge the

value structure of a painting is to look at it

under very dim light, such as moonlight, when

only the rod receptor cells (which cannot perceive color) are active. If you get up at

night for some reason, use the opportunity to

look at the value structure of your paintings!

This will help you to use the "squint" method

on the same paintings during the day, and

from there to apply the "squint" to other

objects in all kinds of light.

N E X T : color temperature

Last revised 12.27.2004 • © 2004 Bruce MacEvoy

�¿F�Microsoft Word Documentœ���NB6W�Word.Document.8

color temperature

Blue mountains are distant from us, and so cool colors seem to recede.

— J.W. von Goethe

The concept of color temperature or warm and cool colors is

important to artists yet often poorly understood. This page provides an in depth

review of the topic.

Goethe provides the headnote because it was

his observation in the Farbenlehre, which struck me as ridiculous when I first read it a

decade ago, that launched me on my study of color and, by an arduous path, led to the page

you are reading now.

I begin with the conventional wisdom about

the attributes of warm vs. cool colors, then explain why the effects ascribed to warm

colors are not caused by their hue or by optical problems with our eyes but by their

typically higher lightness or chroma in comparison to other surface colors.

The earliest artistic applications warm and cool appear in the modeling of light in Baroque

landscape painting. I argue that the perceptual origin of warm/cool contrasts lies in the

mechanism our color vision uses to adapt to changes in the color of natural illumination

due to weather and time of day — effects that

are most obvious in landscape observation.

I develop a definition of "warm" color in paints, define the warm/cool contrast using

three reflectance criteria, and finally show

how these criteria are related to different hues around the hue circle. Finally, I show how the

phenomenon of unsaturated color zones, warm colors that appear only through

luminance contrasts, arise because of the limited span of S cone sensitivity.

These elements of the warm/cool contrast can be summarized as guidelines for painting

warm or cool, which depend primarily on whether the painting style is landscape or not,

and representational or not. Each situation

color

vision

warm vs. cool colors

warm/cool contrast

effects

the origin of warm/cool

the warm/cool contrast

in paints

unsaturated color

zones

painting warm or cool

should use warm/cool color contrasts in a different way.

Let's begin at the beginning. The concept of a

warm/cool color contrast seems to have entered the artistic vocabulary during the 18th

century. The earliest attestation in the Oxford English Dictionary (1890) for an artistic usage

of warm — The canvas glow'd, beyond e'en Nature warm — is from a poem by Oliver

Goldsmith dated 1764. Cold (the original

contrast adjective for warm) appears earlier, in an English translation of Cours de peinture

par principes (1708) by the French art historian Roger de Piles.

Warm and cold were, with dry and moist,

terms used from the Middle Ages through the

18th century to describe a variety of animal and physical qualities. Warm described

animation, exertion, ardent feeling or a complexion glowing with fever; cold described

a lack of enthusiasm, sociability, life force or energy. There was a long tradition of

metaphorical "warmth" from which the artistic usage grew.

warm vs. cool colors

Although the warm/cool contrast was familiar to artists since at least the early 18th century,

it was to my knowledge first presented within a color wheel by the English artist Charles

Hayter, in his Introduction to Perspective (1813). This shows that pairs of colors

opposite each other on the hue circle are

complementary colors, and that the warm/cool contrast is a "metacomplementary"

relationship — "the mother of all complementaries" — between warm hues

(from yellow to red violet) as a group and the cool hues (from yellow green to purple) as a

group.

the first warm/cool color wheel diagram from Hayter, 1813 (sky blue is placed at top, because in

Hayter's time it was defined as the "purest" or most

fundamental color; note the 19th century contrast with

cold rather than cool)

Whenever you see a tidy geometrical icon in "color theory" writings, you can be sure that it

represents something well cooked but only half baked! Despite the assurance and

certainty expressed by Hayter's diagram,

there are four questions that the traditional warm/cool usage has not clearly answered:

1. What are the warm (warmest) or cool

(coolest) hues?

2. Is every hue in the color wheel either warm

or cool, or are some hues excluded as neither warm nor cool?

3. What explains the visual or design effects created by warm or cool colors?

4. Why is the warm/cool contrast fundamental to our visual response to color and to the

manipulation of colors in painting?

The rest of this page tackles these questions one by one.

What Are the Warmest (Coolest) Hues? As Hayter's diagram indicates, the most common

choice for the warmest hue is usually a red orange with a CIELAB hue angle between

35 to 45. This includes pigments such as perinone orange (PO43), naphthol scarlet

(PR188), pyrrole scarlet (PR255), cadmium scarlet (PR108) or pyrrole orange (PO73).

TRADITIONAL

warmest

pyrrole orange

naphthol scarlet

coolest

Some artists prefer a slightly yellower, lighter valued color such as cadmium orange (PO20)

or benzimida orange (PO62). The choice of a redder color, such as cadmium red (PR108)

or naphthol red (PR170) is less common, because these reds are too dark valued.

The coolest color is whatever provides the complementary contrast to the warmest hue

already selected — colors opposite red orange in a visual hue circle, such as found in the

Munsell color system or CIECAM. These show the coolest hue is usually a blue

green with a CIELAB hue angle between 215 and 225. There are few pigments in this region

of the color wheel, but the closest matches

include manganese blue (PB33), phthalocyanine cyan (PB17), phthalocyanine

turquoise (PB16), cobalt turquoise (PB36) or cobalt teal blue (PG50). Together, these hues

define a vermilion/cyan contrast as the axis of warm/cool effects.

manganese blue

cobalt teal blue

But artistic practice has not been unanimous.

An important and fairly common alternative is to choose yellow as the warmest hue. This

usually means choosing an intense deep

yellow such as hansa yellow deep (PY65), a dull deep yellow such as yellow ochre or raw

sienna (PY43), or an intense middle yellow such as hansa yellow (PY97), cadmium yellow

(PY35) or nickel azomethine yellow (PY150) as the warmest pigment. A blue violet such as

ultramarine blue (PB29), indanthrone blue (PB60) or cobalt blue (PB28), or a dark blue

such as prussian blue (PB27) seems to work best as the cool complement. These choices

define a yellow/blue violet contrast as an

alternative axis of warm/cool effects. It makes all hues containing yellow (from scarlet red

through yellow green) warm colors, and all hues containing violet (from purple through

middle blue) cool colors.

This approach is attractive when the artist

intends to use yellow as the symbol of light. This matches our experience of color

variations in three ways. First, the hue contrast is aligned with the largest value

contrast — the lightest saturated hues are yellow, and the darkest hues are blue violet or

purple. Second, most colors shift toward yellow as the luminance on or through them

becomes more intense: blue violets become

ALTERNATIVE

warmest

hansa yellow

hansa yellow deep

coolest

ultramarine blue

indanthrone blue

blue, blues become blue green, greens become yellow green, oranges become deep

yellow, and "spectrum" reds become orange. (Purples shift either toward red or toward

blue, depending on the balance of the color.) Third, the effects of reflected, filtered or

shadowed light transition in the opposite direction, from yellow to red or green blue to

blue. Thus, layers of translucent yellow material redden as they become thicker, cyan

tropical shallows darken to blue as waters get

deeper.

J.M.W. Turner provides some classic examples of this approach. In many of his

paintings, the lightness of colors is closely

aligned with the color temperature (yellow is the lightest color, blue violet or gray the

darkest), so lightness and warmth go hand in hand. Jan Vermeer's paintings also show a

career shift in color design, from a red/green contrast in his earlier paintings to a more

austere, atmospheric yellow/blue contrast in his later works. The palette by Lucy Willis is

a good example among contemporary watercolorists.

However, the fact that artists define and use the warm/cool contrast in different ways

shows that there is no such thing as a universally "warmest" color — or "coolest"

color, either. Color attributes such as lightness, hue or chroma are inherently

defined by context, so the best choice of warm or cool colors will depend on the design

goals or painting purposes (abstract, expressionist, representational) for which the

colors are used.

Is Every Color either Warm or Cool? The

second question is whether every color should be described as either warm or cool, or only

reds and yellows as opposed to blue greens and blues. This is really a matter of how one

talks about color.

There are two conventions: one assigns an

absolute quality to a color (this color is always warm) or a relative quality to a color (this

color is warm in comparison with that color).

MODERN

warmest

it depends

coolest

it depends

I feel there are good reasons why purple and

green should not be described as either inherently warm or cool, as explained in a

later section. But common usage is to throw them in with everything else, and divide the

color wheel into warm and cool halves (as Hayter did), which gives us the scheme shown

below.

warm vs. cool colors in the color circle

Whatever your views on this dichotomy, it's common practice and often useful to describe

a color as warmer or cooler in comparison with another color. This simply indicates

whether the color is closer to red orange (warmer) or to cyan (cooler) than the

comparison color — or, closer to yellow or blue

violet, if you prefer the alternative yellow/blue violet contrast. Thus, red is a warmer color

than magenta, because red is closer to red orange, even though both are warm colors in

comparison to blue violet.

These relative comparisons are most often

applied to analogous colors (of similar hue) — a "warm blue" (compared to other blues) or

a "cool red" (compared to other reds). Thus:

• quinacridone red (PR209) is a cool red and

naphthol scarlet (PR188) a warm red

• hansa yellow deep (PY65) is a warm yellow and hansa yellow light (PY3) a cool yellow

• chromium oxide (PG17) is a warm green and viridian (PG18) a cool green

• cobalt blue (PB29) is a warm blue and cobalt teal blue (PG50) a cool blue

• cobalt violet (PV14) is a warm violet and

ultramarine violet (PV15) a cool violet.

Occasionally a wider comparison is made

across two or more hues, but it is still decided by the relative distance in a color wheel

between the two colors and the warmest/coolest hue. Hooker's green is warm

(closer to red orange or yellow) when

compared with viridian, but is cool (farther from red orange or yellow) when compared

with green gold.

What about dull (near neutral) colors? If all colors must be either warm or cool, the

common 19th century practice was to assign

"gray" to the cool hues (as in a gray or overcast day). This is primarily because most

grays or dark neutral mixtures used in painting, including payne's gray, indigo and

neutral tint, actually have a distinct blue or green tint.

If colors are judged in relative terms, then a grayed color is either warm or cool using the

same "distance in a color wheel" comparison as before. That is, a grayed blue green is

warmer than a saturated blue green, because the gray is closer to red orange across the

center of the hue circle. In paint mixing terms, some red orange has been mixed with the

blue green in order to gray it, and this red

orange appears as a warming of the color.

In general, all dull cool colors are warmer than their saturation hue match, and all dull warm

colors are cooler than their saturated hue match. Thus, burnt sienna is cooler than

cadmium scarlet, because it is less saturated

(closer to gray).

The same principle applies if you are using the alternative yellow/blue violet contrast:

ultramarine blue is made grayer (and warmer) by the addition of some burnt sienna, and

burnt sienna is made cooler by adding some

cobalt blue.

warm/cool contrast effects

Now we can address the third question raised above:

what explains the visual or design effects created by warm or cool colors? In "color

theory" writings the two most commonly described effects are:

• warm colors "advance" in an image — that is, they seem to stand out or attract

attention, or seem spatially closer to the viewer, while cool colors "recede" or seem to

melt into the background: they have a depth effect.

• warm colors are active, arousing or cheerful, while cool colors are passive, restful

or subdued: they have a mood effect.

Visual Associations. "Color theory" typically

explains these effects through absurd color associations — "ice is blue, and so blue seems

cool," or (my favorite), "a distant mountain appears blue, so blue seems to recede from

us."

These fictions completely fail to explain the

visual effects, because there are numerous and obvious counterexamples. For example, in

landscapes the blue sky above us appears much closer than the whitish horizon, so why

doesn't blue advance or white recede? If a sunset appears behind those blue mountains in

the evening, why doesn't red appear to recede more than blue? On a hot summer's day a

noon blue sky radiates far more heat than the

reddish sunset, so why isn't blue warm and red cool? Why don't we say "snow is white, so

white seems cold"? Or why is red warmer than white, if white hot is much hotter than red hot?

It's astonishing that "color theory" writers have repeated these nursery rhymes, generation

after generation, without any regard for the facts.

Indeed, thoughtful artists rejected this "color theory" nonsense almost from the beginning.

Here for example is John Ruskin, writing in 1862 about the depth effect:

It is a favourite dogma among modern writers on colour that 'warm colors' (reds and yellows)

'approach,' or express nearness, and 'cold colours' (blue and grey) 'retire' or express

distance. So far is this from being the case,

that no expression of distance in the world is so great as that of the gold and orange in

twilight sky. Colours, as such, are ABSOLUTELY inexpressive respecting distance.

It is their quality (as depth, delicacy, etc.) which expresses distance, not their tint [hue].

An Optical Illusion. Undeterred by Ruskin's critique, Joy Turner Luke offers an

explanation for the depth effect that has become popular recently: warm colors are

"advancing" because their focal length is longer than cool hues, which is the cause of

chromatic aberration.

All hues cannot be perfectly focused at the

same time. The eye focuses slightly differently on long wavelengths (reds) than on short

wavelengths (blues). The lens becomes slightly fatter and more curved to focus on red

in comparison to when it is focusing on a blue or green. ... When the eye focuses on nearby

objects it makes a similar, but larger, change

than it does when focusing on red; ... the muscles that control the lens are most relaxed

when we gaze off into space. This small difference in focus may account for the fact

that blue and green seem more relaxing and to recede slightly in space.

This explanation doesn't work for three reasons. First and most important, our eyes

are adapted in many ways to eliminate chromatic aberration from visual experience.

Depth perception is critical to primate perception and objects that "advance" or blur

because of their surface color would destroy that acuity. We simply never see aberration

effects, unless they are produced by cheap artificial optics. The focusing of our eyes, the

appearance of objects and our color

associations cannot be influenced by optical effects we never see!

Second, optical accommodation (the focusing

of the lens) is an extremely weak depth cue

(note Luke's use of "slightly" and "small"). In studies that have looked at various depth

cues, optical accommodation to object distance (even though it is a "larger change" in

the lens) has an inconsequential effect on depth judgments for objects more than a few

feet away.

Finally, in everyday experience we see red and blue objects together, as part of a unified,

three dimensional world. Luke's "relaxation sensation to invisible aberration" could only be

experienced by focusing on monochromatic lights viewed in isolation — first a pure "red"

pattern and then a pure "blue" one. And in that context humans are nearsighted to

blue light.

chromatic aberration and focal length humans are nearsighted to "blue" light, which means an

object comes into focus as it moves closer to the eye

The optical contrast is equivalent to an

enormous depth contrast. That is, if you cover

one eye and focus on a line grating of monochromatic "red" light 100 yards away, a

line grating of monochromatic "blue" light just two feet away would be in focus at the same

time. Wherever we looked, our experience of the world would be of near, in focus blue

objects or refractions popping out of a field of view anchored on distant, in focus warm

objects.

This separation is visible in rare situations,

such as an ultraviolet light viewed in darkness: the physical source, which appears

in shades of pink or red, is surrounded by an unfocused, but apparently closer, violet

nimbus. But this peculiar effect is clearly unusual, so it too cannot provide the

hypothetical associations claimed to produce

warm/cool contrast effects.

Lightness and Chroma. OK, so what does explain the qualitative differences between

warm and cool colors? As with any

complementary color contrast, lightness and saturation strongly influence our color

judgments, and in my view lightness and saturation explain the depth and mood

effects associated with warm or cool colors.

In fact, Alfred Munsell noted the "advancing" effect of light valued and saturated colors and

developed principles of color harmony around them.

The proof is that when the lightness and/or chroma of warm colors are made less than the

lightness and/or chroma of their cool complements, those special warm color depth

and mood effects either disappear or shift over to the cool colors!

warm color effects caused by lightness

and/or chroma cool colors can easily appear "advancing" or "arousing"

if they are lighter and/or more intense than the warm

colors around them; a white disk appears "closer" than

a black disk

But what makes lightness and saturation "attention getting" or "advancing"? The

luminance: they are the most luminous or

chromatic objects in the visual field, and our visual system perceives extreme brightness or

chroma as similar.

Vision continually isolates contrast or novelty wherever it appears, as a primitive

strategy to identify unusual (attention getting)

features in the environment and bring them (advancing) to our attention. Even in an urban

consumer environment, intensely saturated colors are infrequent in our routine visual

experience. We occupy a fairly gray world, colorimetrically speaking: saturated colors

stand out because they are unusual.

I think the conventional wisdom about warm

colors evolved primarily from comparisons between pure pigment paints. In general,

warm colored pigments achieve a higher chroma and lighter value than their cool

complementary equivalents. (Ultramarine blue is a spectacular exception.) A saturated yellow

or orange paint is much lighter valued and more intense than any green or blue paint.

But if the yellow or orange is mixed with black so that its lightness and chroma are matched

to a complementary iron blue, the color is

transformed into a raw umber or burnt umber. And I have never heard anyone claim that

brown is "advancing," "attention getting," "cheerful" or "arousing"!

Most of the warm/cool color effects do not appear in color comparisons made with single

wavelength or prismatic colors. For example, "violet" monochromatic light has the highest

saturation of any hue and appears extraordinarily "advancing" and "arousing" in

comparison to "yellow" light, which is bland and dull. Just the reverse is true in paints.

Because cool colored paints are typically darker and less intense than their warm

complements, they make effective background colors for warm colors. The

warm colors capture our attention and seem to stand out from the cool background; like

the setting for a jewel, the background provides an enhancing contrast. But these are

jewels of chroma and lightness, not hue. The

same arousing, advancing contrast appears in the last fiery orange leaves that remain in a

tree of autumnal brown — even though the red orange and brown are both warm colors

and are in fact the same hue.

By assigning warm color depth and mood effects to lightness and chroma, it

might seem that the warm/cool contrast is illusory, just a crude way to summarize the

lightness and saturation differences between

different hues.

But that's the wrong conclusion. The depth and mood effects were grafted onto the

warm/cool contrast by late 18th and 19th century "color theorists"; they were not part of

the origin of warm/cool

the contrast as it was applied in Baroque landscape painting. So we still have the

fourth question to answer: why is the warm/cool contrast fundamental to our visual

response to color and to the manipulation of colors in painting?

The first step to an answer is that the warm/cool contrast originates in diurnal

or climatic changes in illumination, specifically as seen in landscape settings. Thus

the Oxford English Dictionary describes 18th century usage to include:

Cold - applied to tints or colouring which suggest a cold sunless day, or the colder effect

of evening; esp. to blue and grey, and tints akin to these.

Warm - suggestive of warmth, said especially of red or yellow ... to become 'warmer' or

more ruddy: "On a bright morning of July, when the grey of the sky was just beginning to

warm with the rising day". These and similar 18th century sources, unpolluted by later "color theory"

misconceptions, show clearly that the warm vs. cool contrast originated in observations of

the changing illumination produced by sun

and sky. Specifically:

• changes in the sun's altitude during the day cause the color of daylight to shift from a cool

(bluish) tint at high noon to a warm (yellowish

to reddish) tint after sunrise or before sunset

• changes in the sun's declination cause seasonal changes in the sun's maximum

elevation above the horizon, causing the average illumination and temperature to

increase from winter to summer

• the atmosphere produces changes in

illumination intensity and color through the filtering effects of smoke, dust, water vapor

and clouds.

The examples (right) illustrate the changes in

natural light from dawn through midday to late afternoon. (These changes are best

observed through the window of a darkened room, as Monet did when he painted his series

of Rouen Cathedral facades.) The color

color changes in daylight

(top) noon; (bottom) late

afternoon; note change in the

sky color

changes are clearly from warm (yellow) to cool (blue). As the sun declines in the sky, the light

dims and the sky color shifts from deep blue to cerulean; in surface colors, reds and

yellows become more saturated, yellow greens become warmer and lighter valued, and blues

or blue greens become grayer and darker.

color changes across daylight phases by Hiroshi Yoshida

The Japanese artist Hiroshi Yoshida made a

fine set of three woodblock prints illustrating these color effects (above).

These changes physically occur because the

daylight spectral power distribution

contains different proportions of "red", "yellow" and "blue" wavelengths at different

times of the day, different seasons of the year and different geographical locations, and

under different atmospheric conditions. These variations in the color of the illumination mix

subtractively with surface colors, producing familiar changes in the appearance of our

environment. Hues appear to shift warm or cool, colors become more or less saturated,

lighter or darker, and complementary

shadow colors change from violet to blue green.

Blackbody Color. The obvious next step is to

find a method that can describe or define the

relative amounts of yellow or blue bias in a "white" light. A simple way to do this, for

natural light and most "white" artificial lights, is by the light's blackbody temperature.

In 1900 the Austrian physicist Max Planck

mathematically described the spectral power

distribution that would be produced at different temperatures by a perfectly radiating

color changes in daylight

(top) morning; (bottom)

midday

diurnal color changes are best

observed through the window

of a darkened room

object, called a "black body" because no light would reflect from it. (This work led to the

development of quantum mechanics, which won Planck the Nobel Prize in 1918.)

These blackbody curves approximately match the spectra radiated by many natural

light sources, including heated metals, electrical discharges and stars. In all these

cases, an entire spectral emission curve can be specified by its blackbody temperature

alone.

blackbody spectral emittance curves for temperatures of 2860°K, 5000°K and 6500°K,

corresponding to CIE illuminants A, D50 and D65; as

the blackbody temperature increases, the peak

emittance increases and shifts from infrared to

ultraviolet wavelengths

Shown above are the blackbody curves

corresponding to three standard "white" illuminants published by the CIE. They

illustrate the three characteristics of all blackbody radiation: (1) a continuous,

smooth curve with a single peak emittance; (2) a shift of the peak emittance as

temperature increases, from a peak in the far infrared (7200 nm) for a blackbody at room

temperature to a peak in ultraviolet (30 nm) for a blackbody at 100,000°K (degrees

Kelvin); and (3) an enormous increase in total

radiant flux as temperature increases.

If we convert the blackbody emittance to lumens, then standardize the vast energy

differences to get light profiles of equal luminance, these relative spectral emittance

profiles (or illuminants) can be assigned a hue and chroma location in a CIE chromaticity

diagram, just like any other colored light. The changes in the shape and peak energy of the

blackbody curves then produce a

characteristic color sequence as temperature increases — a curved line called

the blackbody locus (right).

The essential features of the blackbody locus

are: (1) the curve is closest to the equal energy white point at a temperature of about

5800°K; (2) above 5000°K the curve is nearly straight; (3) this straight portion is aligned

from blue to yellow (approximately from 470 nm to 575 nm); (4) below 4000°K the

curve arcs sharply into orange and red, and becomes much more saturated, as

temperature decreases; (5) an equal temperature difference defines a smaller color

difference as the blackbody temperature

increases; and therefore (6) blackbody radiation never reaches a violet or purple hue:

at an infinitely high temperature, the blackbody chromaticity has a dominant

wavelength of about 470 nm (CIELUV hue angle of 249).

Correlated Color Temperature. The blackbody locus provides the method

necessary to specify the color of almost any naturally occurring light source. The

temperature (curve shape) of the blackbody is adjusted until its standardized spectral

emittance curve produces a visual or metameric match between the blackbody

and light source — their chromaticity points

blackbody locus in the CIE

UCS

chromaticity diagram

adapted from Hunt (2004)

are the same. Note that the match is not between the shape of the two spectral

emittance curves, but between the apparent color of the two curves as they appear, at

equal luminance, to a normal observer. Then the temperature of the blackbody curve,

expressed in degrees Kelvin (K), is the correlated color temperature (abbreviated

rK or CCT) of the matching light.

The blackbody temperature has proven very

useful to specify the chromaticity of a wide range of artificial "white" lights and natural

daylight phases, as summarized below. Note that an equal temperature change produces a

smaller color change at higher temperatures.

correlated color temperatures for common illuminants and light sources

rK° color correlated illuminant or light source

1000 lower limit of blackbody curve

1850 candle flame

2000 sunlight at sunrise/sunset (clear sky)

2750 60W incandescent tungsten light bulb

2860 CIE A: 120W incandescent light bulb

3400 photoflood or reflector flood lamp

3500 direct sunlight one hour after sunrise

4100 CIE F11: triband fluorescent light

4300 morning or afternoon direct sunlight

5000 white flame carbon arc lamp

5003 CIE D50: warm daylight illuminant

5400 noon summer sunlight

6400 xenon arc lamp

6500 average summer daylight

6504 CIE D65: cool daylight illuminant

7100 light summer shade

To facilitate the comparison of color samples within modern color models, a series of CIE

standard illuminants are commonly used to define the white point in a chromaticity

diagram. Changing the white point in a chromaticity diagram changes the predicted

and actual distribution of colors and the calculation of color matches (metamers).

7500 indirect northern skylight

8000 deep summer shade

9300 white point of a CRT (television screen)

10640 clear blue sky

Sources: Mitchell Charity, MIT; Kodak USA

Note: Color samples illustrate approximate hue and chroma at nearly constant luminance.

The CIE standard illuminants are based on averaged photometric measurements that

characterize common light distributions. The 2860°K (A) illuminant represents light from a

standard domestic incandescent light bulb; the 5000°K (D50) illuminant represents a warm

daylight distribution and is preferred in graphic arts applications, and the 6500°K (D65)

illuminant represents a cool daylight distribution that is preferred for industrial

colorimetric applications (for example,

matching automotive colors or architectural paint colors).

Notice the fact inconvenient for "color theory"

and sometimes confusing when using CCT values in lighting and photography: as the

temperature becomes warmer, the color

becomes cooler! To avoid confusion, photographers instead use the mired (M),

defined as:

M = 1,000,000/rK

The mired has two desirable properties: values

increase as the color becomes warmer (diagram, right), and an equal numerical

difference on the mired scale represents an approximately equal visual change in the color

temperature across the practical range of CCT

values.

blackbody (rK), mired (M)

and

mired deviation (dM)

values

mired deviations specify

wratten filters used to

neutralize light temperature

for color film balanced at

5500°K

Solar & Daylight Color. How well do correlated color temperatures describe the

chromaticities of actual landscape illumination? The diagram below shows that

the blackbody locus closely parallels the aggregate chromaticity variations across a

large sample of daylight spectra, the colors of natural light, measured across different

seasons and at different times of day.

loci of daylight and blackbody spectra chromaticities of daylight spectra measured by Budde

(1963), Condit & Grum (1964) and Henderson &

Hodgkiss (1963), CIE illuminants D50 and D65, and

solar CCT (5780°K) in the CIE 1931 Yxy chromaticity

diagram; adapted from Wyszecki & Stiles (1982)

In general there is an extremely close fit between the

daylight and blackbody curves. This is not surprising,

because the solar spectrum is among the natural light

sources that resemble a blackbody radiator. But the

most essential point is that the blackbody locus

describes the entire sequence of landscape

illumination across diurnal and seasonal cycles.

However, there is one problem. Compared to

an "unbiased" or equal energy illuminant, the blackbody locus and the path of all daylight

spectra are shifted toward green by a small, consistent amount. This occurs because the

equal energy illuminant is perfectly flat, while

the daylight spectra are peaked in the center of the spectrum. When these chromaticities

are reproduced at luminances matching your

chromaticities of CIE

illuminants when eye is

adapted to equal energy

"white" (EE)

computer screen, they produce a distinct yellowish green or bluish green tint (right);

the wavelength that matches sunlight is about 530 nm. Sunlight is not yellow, it is green!

Can the correlated color temperature describe lights that do not exactly match a blackbody

chromaticity? The answer is yes, provided the color difference is not large. We simply

determine the closest matching CCT to the light we want to describe. In a uniform color

space, such as the CIE 1976 UCS, a line through the light's chromaticity that is

perpendicular to the blackbody locus passes through the closest matching CCT value. In a

nonuniform color space, such as the CIE 1931

Yxy chromaticity diagram used above, these lines (shown in green) are not perpendicular

to the blackbody locus but slanting to it.

The subtle chromaticity differences between the blackbody curve and the aggregate swath

of daylight spectra can be compared in the

daylight color series shown below. This represents the actual colors of light that mix

with and alter landscape surface colors.

blackbody and daylight color series chromaticities of blackbody spectra under D65

adaptation; adapted from Charity (1997)

The major difference between the blackbody

and daylight color series (when defined against a D65 "white" standard) is the visibly

increased "green" component in the daylight colors from deep yellow to white, and from

white through middle blue, which produces the noticeable yellow or cerulean tints around

daylight colors close to white. These colors

appear because "green" light shifts all "red"

wavelengths toward yellow and all "blue" wavelengths toward blue green (cerulean).

The yellow is visible in afternoon sunlight,

especially in shafts of light into a darkened room, and in this range does not match the

orange color of the blackbody spectrum. Ceruleans and very subtle greens are often

visible in the sky close to the horizon, especially around sunset when the "violet"

component of daylight is heavily filtered. At

these times the low sky can appear to shade from a grayish deep yellow into scarlet (photo,

right).

It is intriguing that green and rose hues

(shown in the diagram immediately around the white point) appear in the afterimage colors of

specular reflections, and commonly in the glint of iridescence or refraction colors in water and

high altitude clouds near the sun, and the rose colors of dawn. These are subtle shifts in

"white" color that are not within the daylight series of colors but are perpendicular to it

(along a magenta/green dimension).

The artist can only marvel that the solar light

and atmosphere can weave such a narrow chromaticity path and yet create so many

landscape color changes and light contrasts. The color variations between dawn and

sunset, or the sky seen from a seagoing ship and a mountain peak, or a desert sky before

and after a cleansing cloudburst, or the light of

spring and fall, or noon and twilight, or the colors of rainbow and iridescent sundog, are a

source of abiding pleasure and fascination for landscape painters.

Lighting "Mood" Depends on Luminance.

However, the important missing piece in this

discussion is the luminance or intensity of the light source. The actual light color depends

on light intensity, especially for chromaticities close to white, which means

lights with the same CCT can have a very different visual impact, depending on how

bright they are.

The CCT does not literally stand for a unique

color, and the apparent color of the object does not necessarily match the "color" of its

CCT. In addition, luminance affects our visual response. For objects at low to moderately

natural display of the

daylight color series

looking east during a Maine

sunset

high luminances, the blackbody color sequence seems to correspond to our

experience of heated metals — from the feeble red to yellow glow of heated iron. But metals

heated above 1700°K appear to be a brilliant white, even though this "white" might be

described by an "orange" CCT of 2000°K or more.

For slightly different reasons, solar light does

not appear to be green, but either white or

faintly yellow. In part this occurs because our eyes easily adapt to the total daylight

illumination as the standard for "white" light, and this adaptation is to a white point that

resembles one of the CIE daylight illuminants, usually D65, that are slightly bluer than direct

sunlight, which by contrast appears a pale amber or orange. But it also occurs for the

same reason that very luminous hot metals, such as the filament in a domestic tungsten

bulb, appear "white": the "yellow" or "yellow

green" chromaticities are closest to the eye's native achromatic point, so the feeble

chromaticity is swamped by the light intensity.

The joint effect of adaptation and illuminance

level explains why the same incandescent lighting appears "white" to someone inside a

room at night, but appears "yellow" when the light is viewed on a window shade from

outside. Similarly, a television screen or computer monitor, which typically has a white

point approximating 6500°K, appears to produce a balanced light to the viewer in a

darkened room indoors, but glows with a distinctly bluish tint when viewed on a window

screen from outside.

chromaticities of CIE

illuminants when eye is

adapted to noon daylight

(D65)

However, even when all the illumination

comes from a single light source with a constant relative spectral power distribution,

and chromatic adaptation is therefore minimal, illuminance changes produce contrasting

mood effects. We commonly experience these variations in invigorating effect of a

bright sunny day (high CCT, high illuminance) in contrast to the gloomy, cold demeanor of a

heavily overcast day (high CCT, low

illuminance), or the intimate or comforting effect of candlelight or a night campfire (low

CCT, low illuminance) in contrast to the motivating or clinical effect of indoor task

illumination (low CCT, high illuminance).

A study by A. Kruithof (graph, right) suggests that an incandescent (tungsten or halogen)

source matching illuminant A provides "pleasing" illumination between 100 to 300

lux; sources that are rated cooler (higher CCT) should be used at proportionately higher

illuminances (above 300 lux). Recently Steven Weintraub determined that museum

and gallery displays of many different styles of paintings were perceived as most attractive

under a CCT of 3700°K at 218 lux. Presumably

a slightly cooler illumination would appear most attractive at higher illuminances.

To my knowledge these effects have not been

explained, but the range of minimum

illuminances in Kruithof's graph (up to 500 lux) is too high to make increased rod

intrusion a likely explanation. It may be that exposure to the diurnal cycle during

development causes the visual system to associate the white balance with average

illuminance levels, so that it expects "warm" (sunset) spectral distributions to be

relatively dim.

Different CCTs are accepted as the best white

standard for different lighting or colorimetric applications. Lighting with a CCT of 3500°K or

less is considered "warm" and is used in the subdued lighting of restaurants or bars, while

lighting at 4000°K is considered an attractive "white" for kitchen or office lighting, which is

usually above 200 lux. The range of daylight

that appears as "white" does not go much below 3500°K, but a photoflood or high

wattage incandescent bulb, with a CCT below 3500°K, can appear perfectly "white",

especially at night when it is the only light source.

Daylight and the Warm/Cool Contrast. We now have ample evidence and context to link

the variations in landscape light to the geometry of color vision.

"preferred" light intensity

for different illuminants

yellow shows zone of preferred

intensities for each CCT;

adapted from Kruithof (1941),

Weintraub (2004)

Just as light/dark adaptation is a visual adaptation to diurnal variations in light

intensity, the y/b opponent function appears to provide the primary chromatic

adaptation to diurnal changes in the yellow/blue balance of daylight. The r/g

opponent function provides adjustments in

the relative balance of the L and M contribution to the Y component of the y/b

function, which restores the perception of "pure white" illumination as light shifts farther

into the "red" wavelengths.

The arrow indicating the direction of "yellow"

wavelengths (around 575 nm) shows that the y/b opponent function can easily compensate

for the daylight shifts in chromaticity down to about 5000°K. But under extreme "blue" or

"red" (late afternoon) daylight phases the r/g function is also involved. This is easier to

see if the chromaticities of daylight CCTs (disregarding their typically low saturation and

huge differences in luminance) are shown as

hue angles in a color wheel.

color analogs to daylight spectra

chromaticities the hue of blackbody temperatures illustrated as

spectral locations on the CIELAB a*b* plane

This diagram allows comparison of the color

shifts in natural light with the traditionally defined warm/cool contrast: the match is

quite good. It also suggests the relative

contributions of the r/g and y/b opponent functions in chromatic adaptation. The y/b

function makes the major adjustments around the average solar "white", while the r/g

function tracks hue changes at lower temperatures. In video production, there are

analogous Y/B and R/Y controls to adjust the image white balance; digital artists use

green/magenta, red/cyan and yellow/blue

the warm/cool contrast

and the opponent

dimensions

relative visual response to

illuminants A and D65

controls that change the balance between the three complementary contrasts that define the

secondary color wheel.

Warm hues (matched by CCTs below 5000°K)

are smeared across the hue range from yellow to red; cadmium pigments represent this

range very well. The solar and daylight CCTs above 5500°K start at a cerulean blue and

shift to a middle blue at 6500°K, the coolest white standard; this range is represented very

well by cobalt pigments. The artist can conveniently orient his judgments of

warm/cool in relation to specific cadmium or cobalt paints.

The color of the clear sky (skylight) varies substantially by geographic latitude, altitude,

season, humidity, distance from the zenith, time of day and concentration of atmospheric

ice, dust or smoke. The distribution of chromaticities is again roughly parallel to the

blackbody locus, but the average sky

chromaticity is usually above a CCT of 10,000°K, corresponding to a dominant wavelength of

about 470 to 475 nm (CIELUV hue angle of about 235° to 245°). The best paint matches

to the typical blue sky color are a dulled cobalt blue (PB28) or iron blue (PB27), both visual

complements of light yellow.

The luminance of sky colors vary widely. As an

upper bound, cumulus clouds that appear "pure white" have an albedo (reflectance) of

around 70%-80%, equivalent to a moderately light gray or dull white. In contrast, the

background sky typically appears relatively dark, with a luminance near the zenith that

approximately matches a middle gray (reflectance 30%). Again, moderately diluted

cobalt paints reproduce these values well.

The hue of daylight or direct sunlight never

reach a blue violet or purple, although these sometimes appear during twilight as a result

of subjective adaptation or complementary

contrast effects.

Color Rendering Index. The orientation of the lines of constant CCT (above) shows that

artificial lights with the same CCT can have a definite yellow, green, blue or purple tint,

even though rated as "white" lights. This

ambiguity is introduced in two ways: (1) by

defining CCTs as metameric matches between a blackbody curve and a light, which

can ignore radical irregularities in the spectral curve of the light, and (2) by defining CCTs as

the nearest blackbody chromaticity to the chromaticity of the light, even when there is a

visible color difference between them. Lights with the same CCT and even the same "white"

chromaticity can have very different spectral emission curves, which will produce different

appearances in surface colors.

These differences represent the color

rendering quality of a light. The color rendering index (CRI) is a numerical rating of

how closely the color appearance of surfaces

viewed under the light matches the color appearance of the same surfaces viewed

under a blackbody light of the same CCT. It is calculated by averaging the colorimetric

differences (if any) between the reflectance of 8 to 14 standard colors as illuminated by the

test light and a correlated light source of equal luminance and a flat, smooth emission profile,

after chromatic adaptation to each light.

Fluorescent lights generally have reduced

CRIs. They emit a broken spectrum that has an undulating shape across the spectrum and

contains very high, sharp spikes at specific wavelengths (right). These hardly match the

smoothly curving, domed curve of a blackbody spectrum, and the surface color reflectances at

the "spike" wavelengths are grossly inflated in the total color appearance, producing a

greenish or bluish cast that has an especially dulling effect on warm colors. "Cool white"

fluorescent lights have a CRI from 65 to 85,

"daylight" fluorescents around 80, and "warm white" fluorescents from 55 to 75. Metal halide

bulbs range from the mid 60's to the mid 90's; and those beloved sodium vapor lamps, which

transform all colors into a yellowish, cadaverous gray, have CRIs close to zero.

The best light sources are those that make all colors — all hues at all levels of chroma and

lightness — appear "natural" or completely untinted. These are broadband, smooth

spectral power distributions with chromaticities close to the daylight spectral

path: incandescent lights (tungsten or halogen lights), propane lanterns, carbon or xenon arc

lamps, burning magnesium. Incandescent or

spectral emission curve of

a

fluorescent "daylight" bulb

with a CCT of 4370°K

from Wyszecki & Stiles (1982)

tungsten halogen bulbs all have a CRI of 100 and deliver a "true" color balance.

How can a light source that has an off white or

"warm" color (such as a 120 watt

incandescent bulb at 2860°K) still have a CRI of 100? As long as the light approximates a

high temperature blackbody source, it generates light across the entire spectral

range without spikes or gaps, and our eyes will be able to preserve the perception of

"white" illumination by chromatic adaptation. That adaptation is the origin and principal

basis of our warm/cool color sensitivity.

Sumanas Inc. provides a simple web based Java

applet that calculates the emittance spectrum and peak

energy for a blackbody of any temperature across any

spectral range. Mitchell Charity has posted several

useful pages on blackbody colors with links to additional

resources.

I have explained why lightness

and chroma are responsible for the "advancing" (depth) or "arousing" (mood)

effects attributed to warm colors, and why the warm/cool contrast is a visual adaptation to

changes in natural light. The last piece of the puzzle is to explain how the warm/cool

contrast appears through our perception of surface colors such as paints.

Unfortunately no modern color model represents the warm/cool contrast as a

distinct dimension of color perception, so the answer has to expressed in terms of paint

reflectance curves and their colormaking

attributes.

The warm/cool contrast is also fundamentally a color judgment, not a color sensation: it is a

judgment about the relative quality of light, color in comparison to our notion of a pure

white.

the warm/cool contrast in paints

Green Is Neither Warm Nor Cool. If we

compare the visible spectrum to the daylight color spectrum shown above, we

immediately notice a glaring omission: there is no "green" in the daylight color spectrum.

The reason is that most noon daylight

phases, with CCTs between 5800°K and 5000°K, are actually slightly green in hue

(right, and above). Green is also the range of maximum reflectance in chlorophyll (which

absorbs only short and long wavelength light) and therefore is the color of landscape

vegetation. Green is not perceived as a sky color.

This green hue is briefly visible in the positive afterimage caused by glancing at the sun or

staring at its reflection in a dark glass or water; but we are adapted to accept it as

"white" light. (The afternoon sun appears yellow because atmospheric filtering has

reduced its brightness and begun to shift the

color toward red.)

As a result green is neither warm nor cool, because it is (at high luminance) associated

with solar light and our perception of the white point or an equal balance between

short and long wavelengths of light. So the

warm/cool contrast is fundamentally a judgment of the balance in a light mixture

between the wavelengths shorter than green (blue and violet) and longer than green

(yellow and red).

Reflectance Criteria for "Warm" Colors.

The next point is whether there are consistent attributes in the reflectance of surface colors

perceived as warm or cool. There are, in particular for "warm" colors. These are

apparent in the difference in color perception between lights and surfaces.

For all parts of the emitted spectrum — that is, for colors of lights — the relative saturation

increases as the wavelengths of light are limited to a narrower band of color. At the

extreme, a spike of single wavelength (monochromatic) light is the most saturated

color stimulus physically possible for any hue at any brightness. And this is true no matter

whether the hue is red, orange, yellow, green

or blue.

Despite this, we find in artistic practice the consensus that only lights in the hue range

from red through yellow to white are considered warm. A green or blue light, by

itself or as the source of illumination in an

architectural space, is not identified as warm

daylight spectral power

distribution and blackbody

curve at 5500°K

D55 curve from

Wyszecki & Stiles (1982)

and may even be termed cool. So although chroma or saturation may explain the

arousing or advancing effect of warm colors, it does not by itself define an essential

warm or cool color attribute. The same reasoning applies to the brightness or

lightness of a color.

However, for reflected colors — the colors of

the real world — the perception of chroma is more complex. As we saw in the discussion of

optimal color stimuli, the maximum possible chroma for a surface color is defined by its

lightness or total reflectivity, which means as colors become lighter they necessarily become

duller. So the general rule for hue purity in

surface colors should be: high saturation signals high reflectance within a limited

part of the spectrum, although this means intense surfaces will also be relatively dark

surfaces; pastel (light valued) colors typically have muted saturation.

But for warm surface colors even this rule does not apply: warm surface colors retain

chroma across increasing lightness. This is apparent in the diagram of MacAdam limits:

purple, blue or green hues contract toward the white point (become less saturated) as

lightness increases, but for hues from yellow green through red the maximum chroma

boundaries remain at maximum saturation, along the spectrum locus — although the

range of hues gradually contracts toward

yellow.

The reason for this unique quality is what I call the "warm cliff" reflectance curve that is

characteristic of all saturated red, orange and yellow paints. Invariably, all intense warm

hues have three reflectance attributes:

(1) a distinct "cliff", or abrupt increase in the reflectance curve between "cyan" and

"orange", (2) consistently high (90% or above) reflectance on "red" side of the cliff,

and (3) consistently low reflectance (20% or less) on the "blue" side of the cliff. This locates

warm colors in the hues from deep red to light yellow (approximately CIELAB hue angles 30°

to 90°)

the "warm cliff" reflectance curve (a sampling of intense red to yellow pigments (left to

right): hansa yellow light PY3, hansa yellow deep PY65,

perinone orange PO43, naphthol red deep PR170)

This sampling of reflectance curves shows how

consistent this "warm cliff" is across all highly saturated warm color pigments, from lemon

yellow (hansa yellow light, PY3) to deep red (naphthol red deep, PR170). These curves

roughly bracket the wavelengths where there

is a "plateau" in the photopic light sensitivity curve, which means that

luminances in this range will appear brighter than equal radiances at higher or lower

wavelengths. If we examine the average chroma of different watercolor pigments (in the artists' color

wheel), the highest available chroma appears in red to red orange hues. Comparison of

these reflectance curves with the idealized

warm profile for a matching optimal color stimulus (right) shows how closely intense

red, orange, yellow and yellow green pigments match the ideal and therefore can reach a

chroma nearly equal to the chroma of monochromatic lights.

The key feature here, in awkward language, is that warm colors can retain saturation

sideways — increasing the width of the wavelengths of maximum reflectance does not

lower the saturation of the color. No other surface hues have this property.

Warm and Cool in Paints. Now consider the effect this warm cliff must have on the

lightness of different warm hues. As we read these reflectance curves from right to left, it is

as if a luminosity curtain were being drawn back from a window of light, revealing more

and more reflectance as the apparent hue shifts from deep red to orange to yellow.

There is a close relationship between

lightness and hue for intense colors across the warm color span.

theoretical and actual red

orange reflectance curves

optimal color in white;

pigment curves in color

bracketing CIELAB hue angles

32 to 48

We can see this clearly if we plot the measured lightness of commercial watercolor

paints against their hue angle in the CIELAB color space. (Use this chart to identify the

pigments located at a specific CIELAB hue angle.)

masstone lightness and hue angle CIELAB C and h measured in 600 commercial

watercolor paints displayed at maximum chroma

The line of yellow colored points on the left spans the warm colors from hue angle 20

(quinacridone pyrrolidone, PR N/A) to hue angle 95 (cadmium lemon, PY35). (The

dark blue points above this curve at left are

lighter valued rose pigments; those below the curve are earth pigments and dull synthetic

organic pigments such as perylene maroon.) This curve peaks at a light or lemon yellow,

because the lightness of light yellow paints is around 95 and white paints are at 98.

Increasing the reflectance further quickly causes yellow to desaturate into white as the

warm cliff crosses into the darker "blue" and "violet" wavelengths.

The chart also shows a reverse relationship between lightness and chroma in the most

intense cool colors, shown in pale blue from approximately hue angle 200 (cobalt teal

blue, PG50) to hue angle 290 (ultramarine blue, PB29). The saturated blue hues lose

lightness as the hue shifts from "blue green"

toward "violet".

This is obvious if we plot the chroma of these paints in relation to their hue, which shows

that as warm pigments lighten (from red to

yellow) and as cool pigments darken (from turquoise to violet), they both increase in

chroma. But the range of chroma is greater, and the maximum lightness of chroma is much

higher, for warm colors in comparison to all other hues. This contrasting relationship

between lightness and chroma is partly why the warm hues have qualitatively

opposite effects in color experience.

masstone chroma and hue angle CIELAB C and h measured in 600 commercial

watercolor paints

If we just multiply the lightness of a color by

its chroma, the highest values are in the warm

colors around CIELAB hue angle 30 (roughly from pyrrole red, PR254 to pyrrole orange,

PO73), which includes many brands of cadmium scarlet. In those hues specifically,

the edge of the reflectance cliff is right on the wavelength of maximum sensitivity for the

L cones, while its base is at the wavelength of maximum sensitivity for the M cones.

Throughout this hue range, for maximally intense colors, there is no significant output

from the S cones.

Reflectance Criteria for "Cool" Colors. By

examining these pigment plots, and partly by reversing the "warm" color reflectance

attributes, I can suggest that all cool hues have three reflectance attributes: (1) a

"cliff" in the reflectance profile located between "cyan" and "yellow"; (2) high or

maximum reflectance from this cliff into the "blue" end of the spectrum; and (3) minimum

or no reflectance from this cliff to the "red"

end of the spectrum. The only qualification is

that the "violet" wavelengths (below ~460 nm) must be excluded from the

judgment, as these stimulate the r+ opponent function (as shown here) and therefore

appear to contain some "red" light. This locates cool colors in the hues from bluish

green to deep blue (approximately CIELAB hue angles 180° to 270°).

This implies that, for cool hues, the cone response profile is always S > M > L. (Note

that, for surface warm hues, the reverse is not always true, because L and M can be added

together without substantially reducing the chroma of the color, whereas a blue green

formed by S+M is always duller than a blue

from S alone.) In cool hues, adding L output acts subtractively on the M output and thereby

reduces the saturation of the color. In other words, as the S output increases, the color

effect of L+M changes from luminance increasing to chroma reducing (as explained

below).

Warm/Cool in Color Space. Finally, we can

compare the actual chroma of modern artists' pigments with the maximum possible chroma

of any surface color that does not fluoresce. The diagram shows this comparison on the

CIELAB a*b* plane, based on data for the optimal color limits published by the ASTM as

aim colors for the Munsell color system (published as ASTM D1535-97). (The

boundaries for optimal colors at different

lightness levels are illustrated in this diagram.)

artists' pigments and Munsell color limits on the CIELAB a*b* plane

CIELAB a* dimension has been reversed to match the

artist's color wheel.

It's intriguing that the pigment gamut is closest to the theoretical color limits (pigments

appear most intense) roughly along the warm/cool hues on opposite sides of the color

space, even though the widest variation in hue purity is in the perpendicular direction,

between green to purple. This is clearly visible

as the diagonally elongated scatter of pigments in the CIECAM a

CbC plane (which

is not reversed left to right).

The optimal color limits may be closest to the pigment limits along the orange/blue direction

of the color space because this is the direction of variation in daylight phases. Since surface

colors appear as the subtractive mixture of the

surface and illumination spectral profiles, changes in light chromaticity will have the

strongest effect on colors in this direction. This would arise during development through

experience with the naturally occurring variations in daylight and with the change in

surface colors between light and shadow. The development would in turn build on the "hard

wired" opponent functions.

There may be other factors involved, because

our perception of surface chroma hardly takes advantage of our actual saturation range in

blue or purple hues, as stimulated by

monochromatic light. However, extremely intense blue or purple surface hues may be

hard to form for basic chemical reasons, and would therefore not appear in the domain of

natural colors; most natural greens are relatively dull. So the pigment examples

probably represent very well the range of color experience produced by surface colors, which

leaves the daylight phases as the main source for the color adaptation.

What about Purple? Finally, all the evidence discussed above suggests that violet is

neither warm nor cool. I argued above that green is neither warm nor cool because the

gamut of daylight spectra contains no green,

and the same is true for violet or purple in all blackbody curves — no matter how intense a

blackbody radiator, it never achieves a color beyond blue violet.

As the green/purple dimension is

perpendicular to the warm/cool contrast

(defined on red orange), these hue seem unrelated to color temperature. In fact, a

magenta/green contrast seems to be associated with different levels of brightness

adaptation, and is therefore related to changes in the illuminance, not changes in the light's

spectral profile.

Exclusion arguments can also be based on

reflectance curves. The reflectance curves of blue green and blue pigments do not

conform to any of the three criteria characteristic of warm hues — a warm cliff

reflectance profile, maximum reflectance on "red" side of the cliff, and no reflectance on

the "blue" side. Rather, they have subdued "hump or bump" profiles, maximum

reflectance in the short wavelengths, and no

reflectance in the "red" wavelengths. This makes them visual complements to the warm

colors. In contrast, the reflectance curves of violet pigments and green pigments show

some of these warm color attributes but not others. So those hues do not clearly belong on

either side of the warm/cool contrast.

In paints, then, warm colors are limited to

the range from deep red to light yellow. If we consider only colors that violate all three

criteria, then cool colors are limited to the range from blue green to deep blue. This

means, as argued elsewhere, complementary color effects that involve green vs. purple

should be qualitatively different from the contrasts around warm vs. cool colors.

A major feature of the warm/cool

color contrast is that certain kinds of lightness or chroma contrast cause perceptually unique

colors to appear among reds and yellows but not among blues, greens or purples. These

new colors are brown, ochre and green gold.

They cannot be produced by manipulating the

brightness or colorfulness of an isolated red, orange or yellow color area; they only appear

in the contrast between related colors. Yet they appear perceptually very different from

the saturated hues: brown looks nothing like

orange, and green gold nothing like yellow.

I've called these unsaturated color zones. (There doesn't seem to be a standard name

for them; some texts refer to them as

"grays".) The chart below suggests the color variety they produce, in comparison to two

shades of green.

unsaturated color zones warm colors at optimal lightness (L) and chroma (C,

middle row), with reductions in lightness (top three

rows) or in chroma (bottom three rows) to 80%, 65%

or 50% of the optimal values; focal locations of green

unsaturated color zones

gold, ochre and brown are outlined

In fact, as shown above, these colors can be

produced by reducing either the lightness or chroma of the pure hue, although lightness

has a greater impact than chroma across

all hues, and lightness contrast is most important and chroma contrast least important

in light yellow hues.

Boundary of Unsaturated Color Zones. The

unsaturated color zones only appear within a limited span of the color wheel, roughly

centered on the warm end of the warm/cool contrast at a CIECAM hue angle of about 35°.

This splits the color wheel into two parts: the relatively small area between red and yellow

where the unsaturated color zones appear, and the much larger circuit of violets, blues

and greens where they do not.

The diagram shows the approximate extent of

these browns, ochres and green golds as a proportion of the lightness of "pure" (most

saturated) colors in a typical artists' color wheel, which puts the pure pigments at the

circumference. Color markers are indicated by pigment color index name. The boundary of

the unsaturated color zones defines an

involute starting at the neutral tone for a magenta, increasing rapidly in relative

lightness through the reds and red oranges, and finally intersecting the most saturated

yellow green color at a hue angle of around 110°. The approximate location of focal

brown, ochre and green gold are shown for reference.

unsaturated color zones in a generic color wheel

boundary of unsaturated colors as a proportion of the

lightness of pure pigment color, at hues anchored by

common pigments

The boundary is difficult to summarize in

terms of chroma or saturation changes. The gist is that:

• Mixing the pure color with white never

produces these new colors; it only produces a

pastel or tint of the color and typically shifts the hue as well (toward yellow for oranges or

deep yellows, toward violet for reds and bluish reds).

• Mixing the pure color with black ("lightness boundary", above) always produces these new

colors, as it reduces both lightness and chroma; the impact of added black is

strongest in light yellows (where a 5% reduction in lightness will shift the pure color

into green) and weakest in bluish reds.

• Mixing the pure color with a gray of equal

lightness ("chroma boundary", above) typically produces these new colors, as it reduces

chroma only; the effect is strongest in hues from yellow to scarlet. Added gray does not

produce a categorical change among light yellows, as these already have a lightness

close to white.

• An interior boundary between the

unsaturated colors with a reddish or greenish appearance crosses underneath all yellows and

turns toward the achromatic center of the color wheel at around a hue angle of 60°,

approximately the location of isoindolinone yellow (PY110) or nickel dioxine yellow

(PY153). Colors near this green boundary

have a greenish appearance (for example, raw umber or green gold) will usually shift back to

a yellow appearance if sufficiently diluted or mixed with white.

A variety of color labels have been attached to various shades or tones within the unsaturated

color zones in the CIECAM aCbC plane. This

table provides a guide.

As with any color, the label applies to a

category or cluster of similar colors that are centered on a focal color with a specific

lightness, chroma and hue. Just lightness or chroma by itself does not adequately locate

the color changes. For example, an extensive study by Bartleson put the focal color of

"brown" at around Munsell 5YR 3/6, which corresponds to a CIECAM JCh of about 25, 32

and 52°, respectively — very near the location

of burnt umber (PBr7).

The difficulty for artists who want to mix an unsaturated warm color is that they must

recognize a specific brown not simply as an

orange hue, but an orange of a specific lightness and chroma. Because hue is very

hard to identify in unsaturated warm colors, this results in a lot of fruitless mixing back and

forth to create a specific dull warm hue from more saturated paints — a problem that is

most commonly encountered when mixing skin tones.

What Causes Unsaturated Color Zones? The subjective qualities of the unsaturated

color zones are barely mentioned in the color vision literature. Joy Turner Luke explains

unsaturated color zones

CIECAM hue angle

pure color J* - pure color name

reduced lightness J - new color names

90 >90 - med. yellow 70 - green gold 50 - olive 30 - green gray

70 75 - deep yellow 60 - yellow ochre 50 - mars yellow 30 - green umber

50 65 - orange 50 - gold ochre 30 - raw umber

30 50 - scarlet 45 - burnt orange 40 - burnt sienna 35 - venetian red 30 - burnt umber

20 40 - deep red 30 - maroon 20 - mars violet

*J = CIECAM lightness. Unsaturated color zones only appear in surface (related) colors at moderate to low lightness (moderate to high contrast with white surface luminance).

the "strange case of yellow and brown" this way: "Apparently when the combined

response from the L and M (Y) cones is below a certain level, perception is more affected by

the signal from the L-M channel than the signal from the Y-B channel."

This offhand explanation doesn't do the job. Why do green golds, ochres, siennas, umbers

and maroons only appear in related color judgments, if the r/g and y/b opponent

functions also apply to the perception of unrelated light colors? And why does the

signal from the "L-M channel" affect only the appearance of reds and yellows, and not

symmetrically the appearance of greens, when

the y/b ("Y") response is "below a certain level"?

The starting observation is that unsaturated

color zones are produced by the lightness contrast that characterizes the related

colors of reflecting surfaces. This makes green golds, ochres and browns behave in the same

way as grays: they only appear through lightness contrast.

The example at right shows that the same color area can appear brown when viewed with

a high luminance contrast (white) background (diagram, right bottom), but will appear yellow

orange if the luminance contrast is substantially eliminated by the appearance of

shadow (diagram, right top). The reverse is

also true: an orange surface can be made to appear brown if the luminance of surrounding

color areas is substantially higher. A similar effect appears in yellows and scarlets. The

unsaturated color zones are produced by luminance contrast. They are not intrinsic to

a specific combination of trichromatic outputs or opponent functions.

What causes this odd color change? The key factor is the span of the S cone sensitivity,

which at wavelengths above ~570 nm ("greenish yellow") is less than 0.01% of the

peak S cone response (or 1 part in 15,000 of the total chromaticity signal). Compare this to

intuitive benchmarks for "invisible" light: in the Stockman & Sharpe cone fundamentals, the

S cone sensitivity at 570 nm is less than 2% of

its sensitivity at 400 nm, the conventional short wavelength boundary of the visible

color and lightness

induction in a

"brown" colored tile

from Purves & Lotto (2002)

spectrum, and it is less than 0.05% of the combined sensitivity of the L and M cones at

700 nm, the conventional long wavelength boundary of light.

When a luminance contrast reduces the S cone weighting in the "green" and "blue"

wavelengths (because the cones are adapted to respond at the higher luminance of

surrounding surfaces), the extremely small S cone signal is pushed below the detection

threshold, and our eyes become functionally dichromatic in "yellow" to "red" wavelengths.

In effect, brown signals a contrast induced colorblindness (tritanopia) in normal vision.

This divides the spectrum into two parts

(below): the monochromatic hues where the S cone outputs do or do not significantly

contribute to color discrimination. In long wavelengths (yellows and reds) only the L and

M cones can be used to discriminate spectral

hues.

cone mixture curves across spectral hues curves show the proportion of the total chromaticity

information contributed by normalized 10° cone

fundamentals

A background issue is that the maximum

chromatic intensity of a surface color is uncoupled from lightness in warm colors, in

the sense that increasing the luminance of a warm surface color does not significantly

reduce its chroma (as happens in all green, blue, violet and magenta colors). This is

because, lacking outputs from the S cones, the L and M cones must provide both

luminance (L+M) and chromaticity (L–M) information (diagram, right). Adding any short

wavelength reflectance increases both the lightness (L+M) and shifts the hue toward

white instead of green, because the S cone provides separate chromaticity input.

In this predicament, the visual system apparently imposes a chromatic induction (in

comparison to the luminance of a "white" standard) that assigns a different perceptual

quality to long wavelength (Y) luminance that is near, or alternately much below, the

luminance value expected for a ("warm cliff")

reflectance of matching hue.

So experienced "hue" becomes dominated by lightness contrast. However, the reflectance

profiles of yellows or reds can become darker valued (the lightness contrast with white is

increased) if they are:

• blacker, having a maximally saturated

"warm cliff" reflectance profile but with reduced reflectance in the "yellow" and "red"

wavelengths.

contrasting sources of

luminance and chromaticity

in

warm vs. cool colors

• redder, having proportionately more

reflectance in the longest wavelengths where the L and M cone sensitivity is much weaker.

(This is shown by the way the spectrum locus dives toward the achromatic center along a

constant hue angle of about 35° in the diagram, right.)

The combined effects of decreased hue sensitivity and the ambiguous interpretation of

darkened color (increasing blackness or redness) means there is a

disproportionately large number of metamers among dark, dull, red or yellow

surface colors — a third perceptual justification for unsaturated color zones.

How does color vision represent these ambiguities? Just as it does in tritanopia — by

anchoring the hue sensation in the opponent balance between red and green (the r/g

opponent function).

Recall that, at high reflectance with a "warm

cliff" profile, a roughly equal mixture of red

involute of "warm" hues in

CIECAM

a dimension reversed to

match artists' color wheel

and green produces the perception of yellow. Yellow is the perceptual token for a surface

color that approximately balances the r/b function at high surface reflectance. Any

yellow is a signal of both high chroma and high reflectance in warm surface colors,

which means the color is near or above the red boundary shown above. Increasing the

lightness and/or chroma of any color from yellow green through scarlet takes it toward

its affinity hue (diagram, below) and produces

a clear perception of the proportion of yellow hue in the color. Adding any S cone response

shifts the color toward white (or green), so whiteness or greenness becomes the warm

color signal for short wavelength reflectance — yellow and blue really do make green.

the r/g balance in unsaturated warm

colors

For darkened colors below the red boundary, as chroma and lightness decrease, the

"yellow" sensation weakens and then disappears. It is no longer possible to describe

the color in relation to yellow, except

intellectually (by studying color vision). In this case the color appears as a brown or ochre

that seems to lean either toward red or green. This red/green balance signals

indirectly the relationship of the color to the saturated affinity hues:

• If the color appears to contain more red than green, then it is at a hue angle below

60° (see diagram, above right), and would if made brighter shift toward a red (orange or

scarlet) color.

red > green orange or scarlet

• If the color appears more green than red,

then it is located somewhere at a hue angle above 60°, and would if made brighter shift

toward a yellow or greenish yellow color.

red < green medium yellow or green

• If the color appears neither red nor green,

then it is at a hue angle of about 60° and

would shift toward a deep yellow or light orange if made brighter.

red = green deep yellow

"Made brighter" means brightened by lightness contrast, that is, at a higher

lightness and higher chroma. The effect of lightness contrast is to increase lightness

proportionately more in greenish (yellowish) unsaturated colors, but to increase chroma

proportionately more in reddish unsaturated colors. This is because a pure red orange is

much darker valued, and also more intense,

than a pure yellow.

The perceptual quality of brown as a red/green mixture is the same as that of green as a

blue/yellow mixture. Greens appear either cool

(bluish) or warm (yellowish), and similarly browns, ochres, umbers and siennas can

appear either cool (greenish) or warm (reddish). The difference is that a balanced

green and blue mixture appears as a dull green, but a balanced red and green mixture

appears as a brown or umber.

In this section I emphasize the key points argued in this long and somewhat

speculative page, and offer some guidance on manipulating the warm/cool contrast in

painting.

I don't provide a separate discussion for

manipulating colors in digital or video media, because these are created by light projection

systems and additive light mixtures, not

illuminated surface colors and subtractive

painting warm & cool

pigment mixtures.

What is the origin of warm/cool contrast? The perceptual importance of the warm/cool

contrast probably arises in the capability of

the human visual system to adjust to changes in the color and intensity of natural

illumination under different phases of daylight. In response to these illumination changes,

color vision changes both its relative sensitivity to light (chromatic adaptation) and

its relative judgment of colors (color constancy) to maintain a consistent

appearance in surface colors.

A heightened awareness of the warm/cool

contrast in painting technique probably dates from the representation of diurnal and climatic

changes of light in late 17th century landscape paintings, and was explicitly extended in

artistic practice during the 18th century.

What are these changes in natural light?

Natural daylight changes in two ways: brightness and chromaticity (color). Under

clear skies, brightness ranges from a high around noon to a low just after sunset. The

chromaticity changes, as defined by the correlated color temperature, range from a

greenish white at noon to an intense scarlet at

sunset (for direct sunlight), or from a cerulean or greenish blue at noon to a deep yellow at

sunset (for sunlight and skylight combined).

Light intensity also has specific warm/cool

effects as it interacts with different kinds of materials. In general, as the intensity

(illuminance) of light on or through materials increases, the apparent color of the materials

shifts toward yellow: blues become blue green, greens become yellow green, oranges

become yellow, reds become orange; violets shift either toward red or toward blue,

depending on the hue balance. The effects of reflected, filtered or shadowed light change in

the opposite direction, from yellow to red or

green blue to blue. (For example: layers of translucent yellow material redden as they

become thicker, greenish pools darken to blue green as waters get deeper, etc.)

What are the warmest (coolest) hues?

There is no such thing as a "warmest" or

"coolest" hue in colorimetry. Two traditions

have developed in representational painting. Emphasizing the chromaticity changes across

natural daylight phases suggests a warm/cool contrast anchored on red orange. This makes

the warmest hue a paint such as pyrrole scarlet (PR255) or pyrrole orange (PO73); the

coolest hue is a greenish blue such as phthalocyanine cyan (PB17) or phthalocyanine

turquoise (PB16).

Emphasizing the intensity changes in natural

light suggests a warm/cool contrast anchored on deep yellow. This makes the warmest hue

a paint such as hansa yellow deep (PY65) or quinacridone gold (PO49); the coolest hue is a

(dark) blue violet such as ultramarine blue

(PB29) or cobalt blue (PB28).

Are there objective criteria for a warm/cool judgment? Yes. All warm

surface colors have three reflectance attributes: (1) a sharp transition or "cliff" in

reflectance located between the "cyan" to

"yellow" wavelengths; (2) maximum reflectance from this cliff to the "red" end of

the spectrum; (3) little or no reflectance from the cliff to the "violet" end of the spectrum.

This locates warm colors in the hues from light yellow to deep red.

The "cool" hues are defined in nearly complementary terms: (1) a "cliff" profile

located between the "cyan" to "yellow" wavelengths, (2) maximum reflectance from

this cliff to the "blue" region of the spectrum, and (3) little or no reflectance from the cliff to

the "red" end of the spectrum. The "violet" wavelengths must be excluded from the

judgment, as these stimulate the a+ opponent function (appear to contain some "red" light).

This locates cool colors in the hues from bluish

green to deep blue.

Is every color either warm or cool? No. I feel that greens and purples are in themselves

neither warm nor cool, because they do not

conform to all three of the three criteria just listed for a warm or a cool color, and because

they are not salient in the orange to blue transitions of daylight colors.

However, any color can be relatively warmer

or cooler in relation to any other color,

depending on which color is closer to the

arbitrarily chosen warmest (or coolest) color around the hue circle. These judgments must

be made in context with the other colors in the image or scene, including the scene

illumination, and not as abstract comparisons between color wheel locations.

Are warm colors advancing or arousing? No. The illusion of relative depth or a specific

mood effect are not consistent attributes of warm or cool hues. Colors typically "advance"

or come forward in an image because they are (1) light valued and/or (2) highly saturated.

These confusions developed because warm pigments as a group are lighter valued and

more saturated than cool pigments.

Mood effects depend on combinations of both

lightness and chroma: strongly saturated hues at medium lightness are usually "arousing" or

"vibrant"; highly saturated hues at high lightness are usually "cheerful"; low saturation

hues at high lightness are typically "restful";

and low saturation hues at low lightness are "somber" or "subdued". These effects are

mostly independent of hue, but are strongly dependent on the image, usage or scene

context. (Audrey Hepburn is not somber and subdued in those slim black pants!)

What are the unsaturated color zones? These are relatively dark (nonreflecting), low

chroma colors perceived as categorically different from light valued and high chroma

colors of the same hue. They only occur among "warm" hues, and include maroon

(dark red), brown (dark orange), ochre (dull deep yellow), raw umber (dark deep yellow)

and green gold (dull or dark light yellow).

What causes the unsaturated color

zones? In warm surface colors, color appearance is strongly affected by the

lightness contrast between a color area and surrounding surfaces.

This seems to be a compensation for the lack of S cone response (similar to tritanopia) to

long wavelength light. Because there is no third cone sensitivity across the "yellow" or

"red" wavelengths, the surface color chromaticity (the ratio between L and M

outputs) is not significantly altered by

increased luminance (L+M outputs), coupling

chromaticity and lightness perception in yellow to red surface colors.

However, because of the remarkable

consistency of the "warm cliff" reflectance

profile in all yellow to red material colors, the visual system is able to compensate for this

deficiency. It compares a color's lightness (L+M) to the lightness expected for a

matching optimal color of the same hue, which represents the physical limit for a "pure"

color of the same hue (L–M). If the contrast lightness is near this maximum for a given L–

M balance, perception signals this fact by adding a distinct "yellow" color sensation to

the color appearance.

A warm color can only exceed this optimal

contrast ratio through the addition of short wavelength reflectance, which both increases

the color lightness (L+M response), which preserves the yellow sensation but mixes it

with a chromaticity shift toward white or green

(separate S response). (In other words, L+M and S really do make green!)

When the color's lightness falls substantially

below the lightness expected of a maximally saturated color of the same hue, the yellow

sensation disappears and the color can only be

characterized tritanopically, as a balance between red and green sensations. These

yellowless mixtures of red and green create the unsaturated color zones.

Saturated blue reds (such as the quinacridones) that reflect some "blue"

wavelengths make a dark violet when mixed with black paint or illuminated by a broadband

blue or near UV light, while a "spectrum" red given the same treatment turns deep brown or

black. Browns and ochres do not appear in surface colors illuminated by a broadband

orange or red light source, because this provides no S stimulating "green" or "blue"

light and therefore no ambiguity in the "warm"

part of the spectrum. Brown, ochre or green gold colors appear in any darkened color

where the reflectance almost entirely stimulates the L and M cones and the

S contribution is small enough (in relation to quantity of S stimulation in the light) to be

ambiguous.

Does the apparent warm/cool contrast depend on the illumination? Absolutely.

Brilliant, balanced natural light occurs under a high sun and a clear sky. All hues are

rendered perfectly, and both the colorfulness contrasts and lightness contrasts are

optimal. All directly illuminated surface colors appear in their unbiased local color and can be

painted in that way.

In daylight shadows are tinted with a

desaturated red blue (such as indanthrone blue, PB60 or a grayed cobalt blue, PB28),

not a purple. A general yellowing of color — or a slightly increased saturation from orange to

yellow green and a decreased saturation from

magenta through cyan — can be used for expressive emphasis or to show variations in

illuminance intensity produced by the angle of surfaces to the light source ("brighter"

illuminance = yellower or, for warm hues, more saturated color).

Dim light either means greatly reduced illuminance or filtered (chromatically altered)

light. If the light is dim, the chromatic balance among colors, measured in the spectral

composition of the reflected light, is roughly the same. However, it produces very different

mood effects than bright light of the same chromaticity. Dim light seems softer, more

intimate and pleasant if it has a "warm" chromaticity, but seems cold, gloomy and

depressing if it has a "cool" chromaticity. In

either case the average value may be darker, but values always contract toward the average

value (extreme lights and darks disappear, with the larger shift toward gray occurring in

the dark values).

If the light is filtered, the color depends on the

tinting layer that produces the filtering. Overcast clouds produce a darkening that is

approximately the same chromaticity as unfiltered daylight, or slightly bluer. In

painting this is commonly represented as a shift toward blue, with a loss of colorfulness

(graying) and contrast in all colors, but especially warm colors (which shift toward

green).

Near sunset, short or "blue" wavelengths are

strongly filtered from sunlight by atmospheric dust and smoke, causing the "blue"

component in all colors to darken and the "red" component to appear unnaturally bright.

This causes greens to shift toward yellow and the dull yellow or red of tree bark and wood to

appear unnaturally red.

Night light is is viewed under scotopic vision,

which means colors are principally symbolic rather than imitative. Even so, the typical

representation of night relies on a near monochrome palette of blues or blue greens,

with yellow accents contributed by isolated artificial lights and the near surfaces they

illuminate.

How do I make a color warmer or cooler?

The answer depends on whether your axis of reference is the illumination or the hue circle.

If you want to make a color warmer within a certain kind of illumination (that is, the light in

any representational landscape or portrait), then the "warmest" color is typically shifted

from red orange toward the color of the

illumination. Greenish light makes oranges and yellow warmest, because reds are dulled

almost to blacks; orange light makes oranges warmest, and dulls magentas and yellow

greens.

If the axis of reference is in terms of the hue

circle (as would be used in nonrepresentational color design, for

example), then "warmest" color depends on all the colors in the image. However, given the

way our visual system is structured and the range of available pigments, a red orange

located at a CIELAB hue angle of about 40 — or darkened, whitened or dull paints of similar

hue, such as burnt sienna, burnt umber, convenience "naples yellow" paints, or

quinacridone orange — are good standards of

comparison.

When you "cool" a warm color in paint mixtures, it is important to use a blue that

contains no red reflectance and no green

hue. In paints, only indanthrone blue (PB60), phthao blue (PB15 or iron blue (PB27) meet

these two criteria. All paints compounded with ultramarine blue or cobalt blue contain some

"red" reflectance and give the mixture a purple tint. At the same time, paradoxical

shifts can result if you use a saturated "blue" red that contains some "violet"

reflectance. This paints will shift toward purple, rather than gray, when mixed with a

blue paint.

In most representational works, the coolest

hue is the visual complement to the color of the illumination. As landscape light declines

toward sunset, for example, the color of the sky becomes more greenish, appearing

cerulean just before sunset.

For representational modeling, the most

versatile shadow colors are iron blue (PB27) and indanthrone blue (PB60). Both are

remarkably versatile and effective shadow colors; iron blue is appropriate for shadow

tints under "red" or late afternoon light or weak incandescent lamps, while indanthrone

blue is best for shadows under intense incandescent or natural daylight. For more

expressive or coloristic effects, almost any paint from perylene maroon to phthalocyanine

green can be effective.

How do I mix any specific color to make it

warmer or cooler? Again, this depends on whether you want to model the effects of

natural light or create an abstract color design, and which specific color you intend to

shift.

All warm hues are made warmer if they are

darkened, dulled or mixed with any paint that does not contain "green" or "blue" reflectance,

which can raise the S cone response. Oranges

or yellows make a brown color similar to burnt sienna or yellow ochre if mixed with purple,

which warms them, but these mixtures characteristically shift toward red rather than

yellow when lightened. The saturated "blue" reds (which include all quinacridones and

many naphthols, perylenes and pyrroles) shift toward blue when diluted or mixed with white

paint, sometimes by as much as –20° hue angle.

Warm hues are made cooler if they are neutralized by any green or blue paint, which

shifts them toward gray without proportionately darkening the color.

Blues are warmed by mixture with any magenta, red or orange paint, up to the point

where they become purple. Blues are

generally cooled by mixture with yellow, but greens are warmed by it. Greens are cooled by

mixture with purples or blues.

How do I decide if a color is relatively

warmer or cooler than another? There are three possible definitions of "warmer": (1)

contains more yellow; (2) contains more scarlet (red); (3) is closer to gray.

If you want to convey luminance, then yellow

mixtures and yellow bias in reflectance curves

is the key; you need to know how to increase or decrease those in any color by paint

mixtures and how to harmonize the yellow content of paints in a total painting.

if you want to convey dryness, lack of

moisture, heat, intensity, then the same is

true, only now your focus is on red (any scarlet or red with no blue reflectance —

cadmium red deep is ok, quinacridone red is not).

N E X T : color wheels

Last revised 08.01.2005 • © 2005 Bruce MacEvoy

color wheels

A color wheel is a schematic

hue circle that artists use to guide color

mixing and color design decisions.

Isaac Newton's hue circle was intended to

explain light mixtures only, and did not contain "primary" colors as we think of them

today. Eighteenth century "color theorists" substituted paint mixtures for light mixtures

and replaced factual color relationships with simplified, symmetrical and idealized "color

theory" icons. This distorted Newton's concept of the hue circle and completely

misrepresents subtractive color mixing. This page explains how artists' color wheels:

• promote a rigid conception of "primary" paints

• adopt an incorrect definition of complementary colors

• distort the actual mixing relationships

between paints

• disguise the dependence of the paint

gamut on paint selection

• ignore the complications created by

substance uncertainty that occur in all paint mixtures.

We'll also discover that six paints are sufficient for effective color mixing, and the

paints in a more complex color wheel are often unnecessary. This makes it clear that the

color wheel is not a "color theory" — it's just a crude way to anticipate the often

complex or confusing results of mixing artists' pigments. Experienced artists learn to use the

color wheel as a compass to color improvisation.

The page concludes with a basic guide to color naming and common watercolor paint names.

creating a color wheel

color

vision

creating a color wheel

"primary" color wheel

secondary color wheel

tertiary color wheel

more is less? a gamut

comparison

color names

Artist's color wheels represent the color mixing characteristics of paints as

markers around a circle. This is a radical simplification of paint attributes. Before we get

into color wheels, it is useful to see how this simplification is done.

The first step in making a color wheel is to locate paint colors in a color space (such as

CIELAB), which is done by spectrophotometric measurements of standard

paint samples. (The earliest color wheels were created by judging a paint's hue by eye; this

produced less reliable hue circles.) In any modern color model, a paint's hue

and chroma can be represented on a two dimensional hue/chroma plane. In CIELAB

this plane is defined by the a* and b* dimensions. The diagram (right) shows the

location of 37 frequently used watercolor paints as small colored circles; other less

popular paints are indicated by small dots.

(The positions of the four unique hues are indicated in italics.) This a*b* plane

represents the hue of a paint as the proportion of red (a+), green (a-), yellow

(b+) or blue (b-) in the color. Thus, orange is a combination of red (a+) and yellow (b+), so

orange appears in the upper right (a+/b+) part of the a*b* plane.

The distance of a color from the center (where the a* and b* dimensions cross) indicates the

chroma of the paint. A paint that is dull or gray has low chroma and is close to the

center, while paints that are bright or intense have high chroma and are near the edges of

the diagram. Note the significant imbalance of

chroma across hues: most of the highest chroma paints are in the a+b+ (yellow to

red) part of the plane, while the least intense paints are opposite these, in the a–b– blues.

the a*b* color plane

position of the four unique

hues

shown in italics; red in CIELAB

conventionally shown on the

right

Unfortunately, black and white are placed

together at the center of the a*b* plane, even though they are opposite colors. This is

because we're missing the third dimension, the L* or lightness dimension, that separates

light colors from dark. If we view the a*b*

plane from the side (diagram, right), or examine the artists' value wheel, we can

see how much important information is lost. Yet it is common in conventional artist's color the a*b* plane viewed

wheels to ignore lightness differences among paints.

Worse, many color wheels ignore chroma

differences among paints as well — burnt

sienna and cadmium scarlet would both be considered the same red orange. When that is

done, we also discard the location of the colors as near or far from the neutral center. Then

what's left? Only the hue angle of the paint, which (in CIELAB) is the angle of the paint's

location measured in counterclockwise direction from the a+ dimension.

from the side

And thus we have the traditional method for

creating an artist's color wheel: define hue by

drawing a line from the origin of the a*b* plane (where the two dimensions cross)

through the location of the paint. This line defines the hue angle in relation to the a* and

b* dimensions. Then simply push the paint location away from the origin along this line

until it is located on the circumference of a circle. Do this for every paint color you want

to represent, and you have the template for an artist's color wheel (diagram, right).

The hue circle rests on a "pure" conception of hue, an abstraction, because "red" is not light

or dark, or intense or dull, it's simply the hue "red" separate from any of the other visual

attributes that characterize a sunset, a brick, or a drop of blood. So we have thrown away

quite a lot of the information about paints we

started with. In particular, the hue circle mingles colors of different chroma or

lightness. This is problematic in warm colors, where dull and intense reds, and light or dark

yellows, produce very different color mixtures.

a hue circle with hue angle

(red is now shown on the left

to match conventional color

wheels)

Some artists address these problems by removing dull or dark valued colors entirely,

leaving only intense colors along the circumference; or by creating concentric hue

circles, with the duller or darker colors

grouped in rings closer to the center. But these are somewhat arbitrary ways to put

back into the color wheel the information that was already thrown away.

A few "color theorists" don't stop here. The

paint locations in CIELAB (or most other color

models) do not correspond exactly to geometrical symmetry and the principles of

tidying up the hue circle

"primary" color mixing. So the hue circle location of paints is tidied up a bit by moving

the color markers around until they fit into a triangle (diagram, right). The NCS color

model shifts the markers around until the four unique hues are at the ends of the horizontal

and vertical dimensions. Some color wheels adjust the location of paints around the hue

circle so that certain hues fall neatly on evenly spaced "spokes". In each case, the color

locations are manipulated to represent a

color theory. At this point the artist is no longer throwing away information — he's

creating symbolism.

The backbone of the traditional painter's color wheel is the subtractive

"primary" triad. "Primary" colors have been part of the professional lore of painters and

dyers since at least the 17th century.

The diagram shows a simple color wheel

divided into three equal sections by three "primary" colors. At the center of the wheel,

the black square symbolizes the dark neutral color that results from mixing all three

subtractive "primaries" together: this is a color wheel for paints, not for light.

The geometrical symbolism of the color wheel is a pervasive feature of traditional

"color theory". Paints are shown as ideal colors, not real substances, and the mixture

relationships between them are shown as

balanced, symmetrical and harmonious. This symbolizes esthetic purity and intellectual

control, but it also badly misrepresents the actual mixing relationships of paints.

"primary" color wheel

the "primary" (three hue) color wheel

"Primary" Colors and Paints. This bare

bones color wheel comprises three "primary"

colors: magenta (M), light yellow (Y), and cyan (C). By convention, light yellow is

always placed at the top of the wheel (at "12 o'clock"), and magenta (red) on the left (at "8

o'clock"). Thanks to modern intense and lightfast pigments, we can choose much more

effective paints than were available to artists of the past, and as a result the traditional

"primary" triad — red, yellow, and blue — is obsolete and should not be taught.

Before reading further, you may want to experiment with your own "primary" triad

palette to experience for yourself the gamut or range of colors it can mix. (This is also a

great way to familiarize yourself with the basic mixing behavior of watercolors.) I suggest the

following paints (click on the color index name to identify the paint marketing names

for the pigment used by different manufacturers):

• "primary" light yellow : benzimidazolone yellow (PY154) or hansa yellow medium

(PY97) • "primary" magenta : quinacridone

magenta (PR122) or quinacridone rose ("permanent rose", PV19)

• "primary" cyan : phthalocyanine blue GS

(PB15:3) or phthalocyanine cyan (PB17).

It's worth the trouble to explore what happens

if you use different pigments for each of these "primary" colors. These substitutions introduce

you to the substance uncertainty that comes with the choice of specific paints, and

help you understand why some "primary" paints are better than others for a minimal

(three paint) palette.

For example, the quinacridone magenta can

be swapped for quinacridone violet (PV19), quinacridone red (PR209), or anthraquinone

red (PR177). (Don't bother with alizarin crimson [PR83] or genuine rose madder

[NR9], as these are too fugitive for professional art; I also feel quinacridone

carmine [PR N/A] has borderline

lightfastness, especially if used in tints.) These different pigments create distinctive reds,

oranges and deep yellows when mixed with a medium or light (lemon) yellow paint.

The phthalo cyan color can be replaced with

cerulean blue GS (PB36), cerulean blue

(PB35), phthalocyanine turquoise (PB16), or even cobalt blue (PB28). These choices

produce dramatic changes in the quality of mixed purples and greens.

The alternatives for the "primary" yellow color

are especially numerous. I prefer hansa yellow

because it a very intense, pure yellow pigment, neither warm nor cool. Some artists

prefer a warmer yellow (such as a cadmium yellow medium), while others like a cooler,

"light" or lemon yellow (bismuth yellow PY184, benzimidazolone lemon [winsor

lemon] PY175, hansa yellow light PY3, or cadmium lemon yellow PY35). Artists such as

Trevor Chamberlain prefer a dull deep (orangish) yellow, such as yellow ochre PY43

or raw sienna PBr7, to create subdued orange

and green mixtures.

Why Use "Primary" Colors? These many alternative paint selections highlight the

fundamentally arbitrary nature of

"primary" colors. I use the word "primary" in quotes to remind you that you can choose a

wide range of paints for a palette: there is nothing fundamental about one paint as

opposed to any other. In fact, artists have for many centuries used palettes that contain no

"primary" colors at all. So why do artists choose "primary" colors over any others?

The two key attributes of any "primary" palette is that (1) it can mix every hue in

the color circle (we cannot do this with just two paints, no matter which two we choose),

and (2) it can mix a sufficiently large number of colors for the painter's artistic

objectives.

The first and most important reason for using

magenta, yellow and cyan "primary" paints is that they can mix every hue at the highest

possible chroma — that is, they have the largest gamut in comparison to any other

selection of three paints. As we saw in the page on subtractive mixing theory, this is the

same as saying these "primary" paints

maximally stimulate two receptor cones but not the third.

Why do we focus on chroma? The gamut of a

palette is the total possible range of color mixtures that the palette can make, including

all the shades, tones and tints of every

color. However, these are created by diluting the pigments with water (to reveal the

whiteness of the paper) and/or with a black or dark neutral paint. These adjustments

produce the same lightness range in almost any watercolor palette, and always reduce a

color's chroma, so the most effective way to increase a palette's gamut is to increase the

chroma of the paints. For this reason it is useful to focus exclusively on color

intensity in undiluted paint mixtures as a

standard way to define a palette gamut and to compare the gamuts of different palettes or

different versions of the color wheel.

A second reason the "primary" triad has been so popular is that any color within the gamut

can be analyzed into a simple color recipe or

proportional mixture of the three colors, plus black paint and water or white paint:

color = % Cyan + % Yellow + % Magenta

+ % Black + % White (Water)

or, in comparison to the NCS color formula,

color = %C(p1+p

2+p

3) + %S + %W

where the percentages or proportions always add up to 100. These formulas are especially

useful in the printing industry, which relies on

standardized "primary" inks, color mixture recipes (such as the Pantone system), and

halftone screens of different densities to mix the inks in the desired proportions. When the

emphasis is on mixture recipes, the "primary" triad palette is usually represented as an

equilateral color mixing triangle rather than a circle, but this has been carried into color

wheels as an equal spacing of the three "primary" colors.

The third and last reason the "primary" triad palette has been used is because a limited

palette creates an effective or desirable harmony of mixed colors, adding a

distinctive tone or light to the finished

painting. Painters who follow this strategy often do not choose intense paints for their

"primaries," in order to get a cohesive, understated color range instead. They are

usually less concerned with "color theory" than with the paints' handling attributes —

transparency, staining, pigment texture, tinting strength and lightfastness.

Other reasons are sometimes given in traditional "color theory" texts for treating

"primary" colored paints as more important than other paints. These either derive from

the 18th century color dogmas, as described on another page, or they come down from

early 20th color theorists such as Johannes Itten and Wassily Kandinsky, who attributed

spiritual or "moral" qualities to various colors,

including the "primary" colors. However, statements such as "you can't mix a 'primary'

from other colors" or "the 'primaries' are fundamental to color vision" or "the 'primary'

colors are the primary colors of the universe" are either misleading or crackpot.

Only three criteria — large gamut, analytical mixing recipes and desirable

color harmonies — justify the choice of paints for a "primary" palette.

Mixing Step Scales. At this point it will be extremely useful for you to compare the actual

"primary" triad gamut with the full range of colors possible in watercolor paints.

To do this, make a mixing step scale

between each "primary" pair of paints you

have chosen to use. Mixtures of two "primary"

paints define the chroma limits or brightest colors within the palette's mixing range; any

mixture of three "primaries" will be somewhere inside the gamut, duller or closer

to gray.

Then compare your mixed colors to the most

intense pure pigment paints of similar color. This comparison will show you how well the

"primary" colors reproduce the entire range of colors, and how much their mixtures suffer

from saturation costs — the reduced color intensity that results from mixing paints that

are far apart on the color wheel.

To make the mixing step scale, first mix up a

generous quantity of the two "primary" paints you want to test. Paint each test color on a

watercolor paper as a 1" square of color, separated by 8" of blank paper (this allows

seven 1" mixing steps between the two colors, separated by 1/8").

With your clean brush, draw off a very generous amount of each "primary" color and

mix the two together until you get a hue that appears to you exactly equally different from

both paints; add one or the other color until you get this right. Paint this mixture as a 1"

square in the middle position 4.

With your brush, draw off roughly half of this

mixture into a new mixing area, and add more of the righthand "primary" paint until the new

mixture appears equally different from the

"primary" and the middle mixture; paint this as a square in position 6. Again, draw off

some of this mixture and add the righthand "primary" a third time to obtain a new hue,

halfway between colors 6 and 8, and paint it in square 7. Take what remains of mixture 6 and

add the lefthand "primary" paint until this mixture appears to be exactly between

mixtures 4 and 6; apply this as square 5. Then finish squares 1 to 3 in the same way, starting

with what remains of mixture 4, to mix color

2.

Don't worry if the dried colors appear different from the hues you thought you had mixed.

This happens because of drying shifts in the color appearance of the paints. Record this

shift by drawing an arrow above the square

showing the direction of the hue shift (toward

one or the other "primary" paint); this will help you learn how mixed colors change as

they dry.

Finally, paint below each mixed square any

alternative paints of the same hue that you want to use for color comparisons. Your

finished test page will look similar to the illustration below.

mixing step scale between quinacridone

rose and benzimidazolone yellow

Alternative pure pigments (middle row, left to right):

quinacridone magenta, quinacridone carmine, pyrrole

red, cadmium scarlet, cadmium orange, nickel dioxine

yellow, cadmium yellow; (bottom row): quinacridone

violet, venetian red, burnt sienna, gold ochre, yellow

ochre, raw umber

The illustration shows mixing steps for the

rose to yellow mixtures on the warm side of the color wheel. The middle row shows the

most intense alternative single pigment paints for each mixed hue; for comparison, the

bottom row shows the major earth pigments (with dark quinacridone violet at far left).

Many artists are surprised to discover that these mixed warm colors are almost as

intense as pure pigment paints. This supports the choice of "primary" magenta and

yellow for a palette, and suggests that pure

pigment colors between rose and light yellow may actually be convenience paints — they do

not significantly add chroma to hues on the warm side of the color wheel, and are included

only to provide a specific warm hue without mixing.

As it turns out, most other yellow and magenta/rose paints will produce substantially

duller mixtures, especially in the orange to deep yellow hues (as we'll see below). As

small differences in chroma are very

noticeable on the warm side of the color wheel, and single pigment colors are useful as

readymade mixing complements to the cool colors (blues and greens), few artists would do

without their customary selection of paints on the warm side of the color wheel.

mixing step scale between phthalo blue

GS and quinacridone rose

Alternative pure pigments (bottom row, left to right):

tint of phthalo blue GS, cobalt blue, ultramarine blue,

dioxazine violet, quinacridone violet

The mixing steps from phthalo blue GS to

quinacridone rose present a very different

picture. Here the alternative pure pigment paints (bottom row) provide a superior color

alternative to each of the mixed hues — a difference that is especially striking around

ultramarine blue. (Note the obvious: ultramarine blue literally "cannot be mixed

from other colors," but it is not a "primary" blue!)

The pure pigments clearly have a higher chroma (are more intense), in some cases by

as much as 50%. So the magenta and cyan paints are inadequate to get the full range

colors through this side of the color wheel: pure blue and violet paints would be necessary

to extend the intensity of color mixtures.

mixing step scale between phthalo blue

GS and benzimidazolone yellow

Alternative pure pigments (bottom row, left to right):

tint of phthalo blue GS, cobalt turquoise, phthalo green

BS, phthalo green YS

The mixing steps for the greens give similar results: even the dull cobalt turquoise is a

more intense color than the equivalent blue green mixture of the "primaries" cyan and

light yellow. The blue green and green side of the color wheel could also be augmented with

brighter paints to produce more intense color mixtures.

These simple mixing step scales have demonstrated the high cost of using a

"primary" triad palette.

True "Primary" Color Relationships. We've

found that the "primary" triad produces lopsided mixing results for different hues

around the color circle: bright orange and scarlet mixtures, relatively dull green and blue

green mixtures, and very dull purple and blue violet mixtures. Because saturation costs are

greater for paints that are farther apart on the color circle, these mixing studies imply that

light yellow and magenta should be closer

together in a color wheel than cyan is to either.

actual mixing distance between

"primary" colors spacing matches the maximum saturation cost

(dullness) of "primary" mixtures

The diagram shows how the "primary" colors

should be spaced in a color wheel if we wanted the distance between them to represent

accurately the maximum saturation cost

(dullness) of their mixtures. (Surprisingly, a nearly identical spacing of "primary" red,

yellow and blue was proposed in a color wheel by Louis Bertrand Castel, in his L'Optique des

Couleurs of 1740, but his insight was discarded in favor of geometrical

simplification.) Obviously, the traditional, equally spaced color wheel misrepresents

the actual mixing relationships among the "primary" paints.

Would choosing a different "primary" blue or

"primary" magenta produce more balanced

mixtures? Well, yes and no.

Yes, if the blue or magenta paints were significantly more intense (saturated) than the

ones available to us today. Because there is no artists' pigment more intense than a

phthalocyanine for the cyan hue or a

quinacridone for the magenta hue, we don't have that choice. The most intense yellow,

orange, red and rose paints are all lighter valued and have a significantly higher

chroma than currently available green, turquoise, blue or purple paints (with the

exception of ultramarine blue, PB29), so the pigment choices are imbalanced to begin with.

No, because we are forced to place the magenta and light yellow paints closer

together, in order to keep their mixtures highly saturated, because the "warm" hues

from red through yellow seem to change hue at lower saturation — red and orange become

brown, yellow turns into dull green or gray — in what I call the unsaturated color zones.

Choosing a blue that is closer to violet doesn't

solve our problems, either: shifting the cyan toward magenta would improve the intensity

of blue violet mixtures, but would make the green mixtures duller than they already are.

All these problems are symptoms of the fact that three "primary" colors cannot mix all

visible colors, no matter which three "primaries" or paints we use. The only way

around these limitations is to add more colors to the palette.

Once we've chosen our three

"primary" or fundamental colors, then "color theory" introduces a second step: derive three

new colors as mixtures of any two "primary" colors in equal proportions at

equal tinting strength. In the "primary" triad

color mixing formulas:

new color = 50%M + 50%Y + 0%C

secondary color wheel

new color = 0%M + 50%Y + 50%C new color = 50%M + 0%Y + 50%C

These are the secondary colors of the color

wheel.

Unfortunately, as we've already seen, these

"secondary" mixtures will be the dullest mixtures that any two "primaries" will

produce, because they are halfway between two "primary" colors and therefore suffer

the greatest saturation costs.

If dull mixtures don't make us happy, then our

only remedy is to replace the dullest "primary" color mixtures with new

paints. As we've just seen, there is certainly justification for adding a green paint, to

brighten up the dull mixed greens, which

would give us the artist's primaries palette suggested by Leonardo da Vinci. A blue violet

paint would also boost color chroma in mixed purples and maroons. So we may as well

replace all three secondary mixtures with the most intense paints of similar hues. These

become our new secondary colors, and join with the "primary" paints to make a six paint

secondary palette.

Notice that our focus is on the second

colormaking attribute, chroma: by adding three more paints, the gamut of color

mixtures is increased. "Color theory" obscures this issue with its emphasis on the

balanced "primary" composition of the new

colors, and its interest to create a geometrically symmetrical color wheel.

the secondary (six hue) color wheel

Secondary Colors and Paints. We end up

with three secondary colors: red orange (ro), green (g), and blue violet (bv).

This six color secondary palette is a classic (and classy) minimal paint selection. To take it

for a test drive, I suggest you try the following six paints (again, click on the pigment color

index name to identify the paint marketing names used by different manufacturers):

• "primary" light yellow : benzimidazolone yellow (PY154) or hansa yellow medium

(PY97) • secondary red orange : pyrrole orange

(PO73) or cadmium scarlet (PR108) • "primary" magenta : quinacridone

magenta (PR122) or quinacridone rose ("permanent rose", PV19)

• secondary blue violet : ultramarine blue

(PB29) or cobalt blue deep (PB73) • "primary" cyan : phthalocyanine blue GS

(PB15) or phthalocyanine cyan (PB17) • secondary blue green : phthalocyanine

green BS (PG7) or phthalocyanine green YS (PG36); the best color match to magenta falls

between these two greens.

These six paints provide a substantial

increase in mixing power over the three paints in a "primary" palette, specifically in the

intensity or purity of the most saturated mixed hues, as the following color mixing comparison

makes plain.

"primary" and secondary paint mixtures most saturated hue mixtures using three "primary"

paints (left) or six secondary paints (right)

Although the "primary" triad paints are

identical in both wheels, the addition of three saturated secondary paints significantly

enhances the intensity of the deep yellow, yellow green, middle green, middle blue, blue

violet and violet mixtures. (Notice that the violets and greens mixed from the "primary"

triads are also darker valued than the equivalent pure pigment paints, and this

darkening makes them look duller than they

actually are — but either way the eye easily notices a difference in color intensity.)

The secondary palette creates a lighter valued,

more festive array of mixtures with much more evenly balanced chroma all around the

color wheel. At the same time, the secondary

palette can easily create rich darks (compare the center swatches) and simulate all the

earth pigments. Nearly every hue in the color circle can be mixed with a chroma that rivals

the brightest pure pigment paint available for that hue.

Complementary Colors. In the standard "color theory" account, the three new paints

we've added to the color wheel are the complementary colors to the three

"primaries," and this is a fundamentally new color relationship. "Color theory" places a lot

of importance on complementary color relationships in color mixing and design, so it's

worthwhile to explore that story and see what

it's worth.

In the standard (18th century) "color

theory," complementary colors are said to act as color opposites, creating a new kind of color

relationship, which is said to be either a color contrast or a color antagonism. Color contrast

is demonstrated by viewing colors side by side or in simple visual patterns. Color

antagonism is inferred from complementary afterimages or paint mixtures in which two

complementary colors produce a neutral or gray mixture, each destroying the hue of

the other. The two interpretations can be

combined, for example by Ogden Rood: "Any two colors which by their union produce white

light are called complementary. An accurate knowledge of the nature and appearance of

complementary colors is important for artistic purposes, since these colors furnish the

strongest possible contrasts."

Let's start with the process: how exactly do

we find the two "colors" that mix to white? The answer is different for additive or subtractive

color mixing: • In additive color mixing, we take a white reflectance curve (or "white" emission

profile) and divide it in two along any

arbitrary boundary (illustration a at right). The two new profiles precisely define two new

colors, so the light from these two colors by definition must add back together to make

white. We would place these colors opposite each other on a visual color wheel. (In

practice, either two or more different wavelengths of light are combined, trial and

error, to find the complementary wavelengths that mix to white, or two or more paints are

combined, trial and error, using an adjustable

color top, to find the combinations that mix to gray.)

• In subtractive color mixing, we first find the

exact mixture of three "primary" paints that creates an achromatic (light or dark gray)

color. Then, we arbitrarily split this recipe into

two new mixtures, for example:

complementary paint mixtures

"primary" paints

gray

recipe

(in drops

of paint)

one possible

complementary

mixture

(in drops of

paint)

complementary colors

defined two ways:

(a) additive

complementaries

for color vision, by splitting a

"white" spectrum in two;

(b) subtractive

complementaries

for mixed substances, by

splitting a

"gray" mixture of three or

more

"primary" paints in two

These mixtures must by definition make a pure gray when combined (illustration b at

right), so the separate mixtures are complementary colors, and would be placed

opposite each other on a mixing color wheel. (In practice, usually two paints are

mixed together, trial and error, to find pairs that produce an achromatic or near neutral

gray or black.)

Complementary colors can be identified in

many other ways. In subtractive color mixing, we can use colored filters, or dyes in

solution, or colored powders, or oil or acrylic media to create similar mixtures and with

these mixtures identify complementary hues.

Each of these matched colors or mixtures would also be mixing complements.

In additive color mixing, we can find the

monochromatic (single wavelength) lights that perfectly neutralize any single monochromatic

light or emittance profile. We can use a

polarizing filter to produce complementary colored fringes of any hue. Or we might even

try to match the afterimage color that appears after we stare for a long time at a

single color area. Color pairs identified in any of these ways would also be visual

complements.

Now, if we try several of these different

methods — different mixtures of paints, powders and filters, or different mixtures of

colored lights or spinning colored surfaces — we might ask: are the complementary colors

defined in these different ways the same? The answer is "no"!

color

1

color

2

phthalocyanine

cyan33

0 .

. 33

benzimidazolone

yellow33

28 .

. 5

quinacridone

magenta33

20 .

. 13

The first surprise is that the mixing complement will often be very different

from the visual complement; even the visual or mixing complements will differ

among themselves, depending on the exact method we used to define them. The

differences are summarized in this table, using the major cool paint colors as the

standard of reference. The second surprise is that substance

uncertainty creates insurmountable problems for subtractive color mixing. The issue is not

just that the "mix to gray" results are dependent on the media used — we could just

accept watercolor paints as our standard. The problem is that when we use paints, the "mix

to gray" results are not consistent across hues — different colored paints will happily

mix to gray with the same "primary" color! (The problem is described and illustrated in

the section on painting in neutrals.) So we

often end up with several different hues as mixing complements for a single paint —

which means the different hues must all be located at the same point on the color wheel!

So "complementary" color relationships depend on the media used to create the color

mixtures, and in many media used for subtractive color mixing, complementary

mixtures may not show a consistent relationship to the hue of the mixed

substances.

A Complementary Grain of Salt. At the

beginning we heard that "mix to gray" antagonism is proof of "the strongest possible

[color] contrasts." We now can identify several problems with that claim:

• paint mixtures cannot identify visual contrasts (visual complementary colors):

antagonism does not define contrast

• paint mixtures cannot identify unique color

contrasts: a single paint may have several different colors that are "antagonistic" in

mixtures with it

• mixing antagonism by itself cannot identify the visual color relationships that produce the

best color harmonies in a visual design

• there are many different color wheels, each based on a different plausible definition

of complementary colors.

There is, then, no reason to accept "color

theory" claims for fixed complementary color schemes. Color harmonies are often arbitrary

symbol systems to begin with, and color combinations are a matter of taste and style,

not color dogma.

If painters do want a complementary color

framework, then the visual complementary colors are most relevant to color design.

These are, in fact, the complements advocated by Chevreul, Rood, and other classical color

theorists. Viewers of paintings only see the finished color, not the work of color mixing, so

the visible contrast between colors, not the mixing antagonism of paints, is what affects

the design harmony.

Where does that leave the color wheel? As a

helpful but arbitrary construction that distorts as much as it clarifies the facts of color. Some

artists bridle at this realization, and defend the geometrical clarity of "color theory" — it's so

symmetrical, so perfect! Others embrace the realization as permission to open their eyes to

the marvelous richness of color mixing with

actual paints instead of color ideas.

The final step to a wider range of geometrically symmetrical colors takes us

to the tertiary colors. These are defined as equal mixtures (at equal tinting strength) of a

"primary" color with a secondary color next to it on the color wheel. This is identical to a

mixture of two "primary" colors in the proportions 3:1 or 1:3, for example:

These tertiary colors form six new complementary color pairs — each tertiary is

tertiary color wheel

new color =50% magenta + 50% red orange

new color

=

50%M + 50%(50%M + 50%

Y)

=50%M + 25%M + 25%Y

=75%M + 25%Y

directly opposite from another tertiary color. They also in theory divide the color wheel into

twelve equal hue steps around the color circle.

the tertiary (twelve hue) color wheel

Tertiary Colors and Paints. Reading clockwise from "primary" yellow, we have the

following six tertiary colors: yellow green (YG), blue green (BG, also called sea green

or turquoise), middle blue (B), red violet (RV, or purple), middle red (R), and yellow

orange (YO, also called deep yellow). These new colors define twelve equally spaced color

points around the color circle, conventionally

numbered from 1 ("primary" yellow), counterclockwise to 12 (yellow green).

If you want single pigment paints for each

point on this new color wheel, I suggest using

this palette (again, click on the pigment color index name to identify the paint marketing

name used by different manufacturers):

• "primary" light yellow : benzimidazolone yellow (PY154) or hansa yellow medium

(PY97)

• tertiary deep yellow : cadmium yellow deep (PY35) or hansa yellow deep (PY65)

• secondary red orange : pyrrole orange (PO73) or cadmium scarlet (PR108)

• tertiary middle red : pyrrole red (PR254) or cadmium red (PR108)

• "primary" magenta : quinacridone magenta (PR122) or quinacridone rose

("permanent rose," PV19) • tertiary red violet : manganese violet

(PV16) or dioxazine violet (PV23) • secondary blue violet : ultramarine blue

(PB29) or cobalt blue deep (PB73) • tertiary middle blue : phthalocyanine blue

RS (PB15:1) or cobalt blue (PB28) • "primary" cyan : phthalocyanine blue GS

(PB15) or phthalocyanine cyan (PB17)

• tertiary turquoise : cobalt turquoise (PB36) or cobalt turquoise light (PG50)

• secondary blue green : phthalocyanine green BS (PG7) or phthalocyanine green YS

(PG36) • tertiary yellow green : a permanent green

light or phthalo yellow green (both convenience mixtures listed under PG7 and

PG36).

This may seem like a large expenditure in

paint, but it is worthwhile to use a large, systematic selection of colors. The experience

will fine tune your paint mixing skill, and it will help you appreciate the strengths of a smaller

palette.

Old & Modern Tertiary Colors. Here I

should explain the conflicting definitions of tertiary colors that have appeared over the

past two centuries.

The modern definition (as given, for example,

in the American Heritage Dictionary) is that tertiaries are a mixture in equal proportions of

one "primary" color with a secondary color next to it. Because these tertiaries are

actually the mixture of just two "primary" colors (in 1:3 proportions, as shown above),

they are, like the secondary colors, the most

intense mixtures possible for that hue around the edges of the "primary" triad gamut.

(Whether they actually look intense or dull is another matter.)

These tertiaries stand for the modern conception of the color space as a hue circle

that can be conveniently divided into 12 equal hue increments, like the hour marks on a

clock face. These equal divisions help the painter to anticipate the hue and saturation

cost of any two paint mixture: the greater the number of intervals between the paint hues on

the tertiary color wheel, the duller their mixture will be.

The older (original) definition was different,

and derives from the 18th century color

mixing idea that a tertiary color is a mixture of all three "primary" colors in

which one "primary" dominates. (A mixture in equal proportions would produce a color close

to gray or black.) So in Victorian era painting treatises (as quoted in the Oxford English

Dictionary), only three tertiary colors are referenced, as the mixture of two secondary

colors in equal amounts — which gives the new colors russet, olive and citrine.

These 18th century tertiary colors stood for the dull, unsaturated or near neutral colors

inside a color triangle, not the hues of maximum chroma or saturation along its

sides. By mixing two secondaries, painters had a simple and reliable way to create a familiar

series of dulled colors across the interior of the

color space, which could be intermixed to create countless dull color variations.

However, as shown in the diagram (right), the

mixture of two secondary colors is, in the analytical primary color calculus, identical

to the mixture in equal proportions of a "primary" color and its complementary

secondary color. So although "color theory" defines a tertiary color mixture as different

from a complementary color mixture, in fact

they contain identical proportions of the three "primary" colors:

In fact, the error here is that attempting to

tertiary

[russet] =

50% secondary[orange]

+ 50% secondary[purple]

=50%(50%R + 50%Y) + 50%(50%R + 50%B)

=25%R + 25%Y + 25%R

+ 25%B

=50%R + 25%Y + 25%B

neutral [gray] =

50% primary red + 50% opposite secondary

[green]

=50%R + 50%(50%Y + 50%B)

=50%R + 25%Y + 25%B

the alternative "color

theory" definitions of a

tertiary color

mix a gray or neutral color with a 50%/50% mixture of a primary and its complement

assumes a color wheel geometry where all hues are equally far from the neutral center.

In a primary triad triangle the red "primary" (because it is more saturated) is

twice as far from the neutral center as the green mixture (diagram, right). Therefore only

half as much red is necessary to neutralize the green:

But it is more accurate to say that the problem lies in the attempt to make color mixing

geometrically neat. Actual paint proportions will typically not resemble any of these

abstract recipes from a circular or triangular geometry, because the relative tinting

strengths of the red and green "colors" will vary depending on which paints are used.

This illustrates the confusions that are created by "color theory" principles formulated in

terms of colors rather than paints. The novice painter gains a much clearer grasp of paint

mixing by learning through experience the effects of saturation costs between the

specific paints on his or her palette. There is little benefit in memorizing abstract "color

theory" mixing concepts that are presented

as the logical effects of abstract "primary" colors.

Now comes a surprise:

although it's bursting with colorful paints, the tertiary color wheel is rather uninteresting. It

does not create a fundamentally new color relationship, in the way the "primary" triad

wheel creates all mixed hues, or the secondary color wheel creates complementary

color pairs. It just adds six new

complementary pairs to the three in the secondary color wheel.

What's more, although there are trivial

neutral [gray] =

33% primary red + 33% primary yellow +

33% primary blue

=33%R + 66% secondary [green]

more is less? a gamut comparison

saturation costs among the mixtures of adjacent colors on this twelve color wheel, the

saturation costs in mixtures of adjacent colors on the secondary wheel are not any worse.

Rather than prove the point by the visual comparison of paint wheels, we'll do it

using the more formal method of a gamut comparison based on spectrophotometric

measurements of actual watercolor paint mixtures. Gamut comparisons are common in

the color imaging and color printing industries, and painters should be familiar with the basic

concept. A gamut (at right) is the domain of all colors

that can be mixed from a specific set of fundamental colors — which may be the

traditional three "primary" colors or may be four or more palette colors. In a gamut these

"colors" are always actual physical colorants: watercolors on a palette or inks in a print job

or dyes in a color film or phosphors in a television monitor. Always, the gamut

depends on specific colorants in the media used to mix the colors, and changing

from one medium to another or exchanging

one fundamental color for another almost always changes the gamut, sometimes

drastically. Measuring whether or how much color mixtures will be affected by a change in

colorants or media, and computing how to translate image colors from one medium to

another so that the image "looks the same" to an average viewer, are the major reason for

gamut comparisons in color rendering technologies.

The gamut boundaries represent the most intense or saturated colors that the colorants

can mix from the lightest to darkest values. These boundaries come to points or corners

defined by the "primaries" or fundamental colorants, and form mixing lines or mixing

planes between every pair or triad of adjacent

"primary" colorants. If the fundamental or "primary" colorants are chosen so that the

gamut contains a white point or neutral gray mixture, then the fundamental colorants can

mix all hues. Any color that can be matched by a mixture of two or more fundamental

colorants is said to be inside the gamut; any color that cannot be matched — because it is

too intense, too light or too dark — is said to

a gamut showing the

chroma limits but not the

lightness range

be outside the gamut and is an unmixable color.

Gamut comparisons are made by representing

different gamuts within the same standardized colorimetric space. Usually CIELUV or

CIELAB is used for this purpose. The CIE color models enclose the space of all possible

colors, and define color locations by spectrophotometric measurements, which

provides an objective frame of reference to

judge the shape and size of a gamut and to compare different gamuts with each other.

The example at right compares in CIELAB the "millions of colors" Apple RGB (computer

monitor) gamut, its subset the 256 color ("web safe") gamut, and the CYMK (printing

ink) gamut, with contouring lines to suggest their three dimensional shape. Note the range

of purples, reds and greens available in a computer monitor but unmixable in the CYMK

system. Because monitor colors are created by

tiny colored lights, they can produce greater luminance contrasts, and higher color

saturation, than reflective prints.

The lightness or brightness range of the

media is always part of the gamut, although in most gamut illustrations (like the one at right)

it is the dimension perpendicular to the viewer. But the gamut of a "full color" process

in any imaging media is always three dimensional, like a sphere or cube. (The

gamut of a black and white printer or grayscale image is simply a line, like a value

scale, from its darkest to lightest values; the gamut of a duochrome process is a triangle,

with the third corner representing the pure

colored ink.) And gamuts are always sensitive to the specific context in which colors are

measured or judged. The gamut of a television is reduced if sunlight is falling on the screen,

just as the gamut of a printer's ink system becomes smaller if colors are printed on gray

paper, or with coarse halftone mixtures, or the print is viewed in dim light rather than

sunlight.

Now that you understand what a gamut is

good for, here is the gamut on the CIELAB a*b* plane of the 12 tertiary colors in

watercolor paints. The colors are either the most saturated single pigment paint available

for that hue (as listed above for the tertiary

a CIELAB comparison in

three dimensions of the

RGB, CYMK and "web safe"

gamuts

palette) or is the matching color mixture using the two best paints listed for the

"primary" triad or secondary palettes. In each case, the actual paint locations are

indicated by large dots.

the gamut or maximum chroma of

tertiary colors chroma of the twelve most intense tertiary paints (light

blue line), and the same paints also found in or mixed

with the "primary" palette (dark blue line) or secondary

palette (red line). (Chroma calculated on the CIELAB

a*b* plane, with CIELAB red placed at left to match

the standard color wheel.)

As you can see, the twelve fundamental colors

in the tertiary color wheel do not furnish any

improvement in chroma over the six fundamental colors in the secondary color

wheel (with the sole exception of purple, which represents the addition of dioxazine

violet). So we don't gain either a new color relationship or more intense color mixtures by

doubling the number of paints in the palette!

If our philosophy is "bang for the buck," then

the secondary palette is clearly the most efficient of the three. It achieves the greatest

range of color chroma with the smallest number of paints, and it provides a powerful

set of three readymade complementary color pairs that are easier to work with than the

paints in either the "primary" triad or split

"primary" palettes — where all visual or mixing complements and all near neutral dark

grays, must be mixed from at least three paints.

Artists Mix Paints, Not Colors. So why don't all artists use this best of all possible palettes?

Because our focus all along has been on maximum chroma — and for many artists

chroma is not by itself important. What matters to them is the specific selection of

paints.

Some artists use a large palette in order to

tackle complex design problems, or introduce wider variations in pigment texture,

transparency, or handling attributes, or simply to minimize the task of mixing paints to

produce specific colors. Others use a reduced palette of four or six paints to create a more

cohesive color harmony, or they choose paints

with lower chroma in order to achieve subdued, classicizing landscape effects.

Most artists seek a middle ground: they rely on a preferred set of about 10 or 12 paints

to meet most of their painting needs, but occasionally add one or more paints to this

basic palette to get a specific saturated hue, pigment texture, or color effect.

By itself, a "color theory" color wheel can't guide your paint choices or palette design. It

emphasizes hue over value and chroma, geometrical symmetry over gamut shape, and

abstract color concepts over actual paints. It tells you nothing about paint selection

strategy. So by negative example the tertiary wheel illustrates that there is more involved in

palette design than abstract color geometry:

artists mix paints, not "colors".

The tertiary color wheel does serve one useful purpose: it divides the hue

circle into equal hue steps defined by explicit color mixtures, which allows us to locate

specific color names and match them to specific paint examples. The tertiary colors can

be used as reliable landmarks, like Paris metro stops, to map out a convenient and standard

color nomenclature that can locate a hue

or color just by naming it.

The color names available in any language include the basic color categories and color

names acquired through the demands of the technologies or knowledge domains that

color names

require colors to be mixed, identified or labeled. There are conventional ways to qualify

or combine these basic color terms in order to name colors blends or color variations in

chroma or lightness. These conventions control how names are attached to colors and how a

color is identified or recognized from its name.

The Universal Color Language. Probably the most widely recognized standard naming

system in English is The Universal Color Language (UCL), first published by the Inter-

Society Color Council and the National Bureau of Standards (USA) in 1955 and extensively

revised for the 6th edition in 1976. Each of the

267 UCL color names is mapped onto 267 unique color samples in the Munsell Color

System. An object color is compared to the set of 267 Munsell color samples, and the

closest color match identifies the standard color name that should be used to describe the

object color.

The UCL system is designed as follows:

• There are 13 basic color names: red, pink,

orange, brown, yellow, olive, green, blue, violet, purple, white, gray and black.

• The basic color names of colors that are next to each other in the Munsell color space

combine to form 34 compound color names: reddish purple, reddish gray, reddish

orange, reddish brown, reddish black, pinkish

white, pinkish gray, brownish pink, brownish gray, brownish black, yellowish white,

yellowish pink, yellowish brown, orange yellow, greenish yellow, olive brown, olive

green, olive gray, olive black, yellowish green, greenish white, greenish gray, greenish black,

bluish green, greenish blue, bluish white, bluish gray, bluish black, purplish blue,

purplish white, purplish gray, purplish black, purplish pink and purplish red.

• The 47 basic and compound color names are modified by a system of overlapping lightness

and/or chroma adjectives:

—vivid for the color at maximum chroma

(which defines a specific lightness for every hue);

—brilliant, strong, deep or very deep for the

light to dark lightness variations at high chroma;

—very light, light, moderate, dark or very dark for the light to dark lightness variations at

average chroma; and —whitish, very pale, pale, grayish, dark

grayish or blackish for light to dark lightness variations at low chroma.

The actual combination of lightness/chroma modifiers is different for every color name, but

all possible object colors can be assigned a color label.

The UCL nomeclature has been used to standardize color terms in biology, botany,

horticulture, agriculture, interior design, marketing, textiles, colorant manufacturing,

plastics, geology and even stamp collecting. This Azalea Society page shows how a

variety of flower descriptive names can be clarified, standardized and compared through

the UCL nomenclature — note that cinnamon,

bronze, buff, tan and tawny are all essentially the same color.

The UCL is a useful reference for artists, as it

establishes a consistent usage for terms such as deep, pale or brilliant and objective (if

arbitrary) boundaries between color categories

such as orange and yellow pink, or blue green and bluish green.

Commercial paint names. Most artists learn

color names as defined by paint companies.

So it is necessary for artists to learn the naming conventions that art materials

manufacturers generally rely on to devise their paint marketing names or paint "colors".

The diagram locates the most important and

consistently used color names within the

tertiary hue circle.

standard hue names around the hue circle

In general commercial paint color names can

be interpreted as follows:

1. There are six basic color categories: red,

yellow, green, blue, black (dark) and white (light). Three mixture colors, orange, purple

(or violet) and gray are commonly added in English, for a total of nine basic colors. These

are located in capital letters in the diagram.

2. Within each color category, the "typical",

"best" or "pure" hue in the category has claim to the unmodified color category name: red or

blue. If you want to emphasize that the color is not tinted with any other color, add middle or

medium to the color name: medium red, middle blue. (Pure or true — "pure blue" or

"true red" — are not used.)

3. Within each of the six basic hue categories,

a hue that is shifted toward "primary" yellow is "light" and a hue that is shifted

toward blue violet is "deep". For example: cadmium red light is a red shifted toward

yellow (orange), or a scarlet red; cadmium red deep is a red shifted toward blue (maroon); a

bluish violet is a violet deep. That is, light and

deep describe hue rather than lightness or value. To mark this, they are usually placed

after the hue name, to avoid confusion with luminance related lightness. Thus, red light

(scarlet), not light red (pink); or orange deep (scarlet), not dark orange (brown).

4. Alternately, a color that is close to an adjacent color is named by putting the

adjacent color name first, in the same way we put adjectives before nouns. Sometimes

"ish" is added to clarify which term modifies which. Thus, a blue that is close to green is a

green blue (or greenish blue); a red that is close to orange is an orange red or orangish

red. (Yellowish red is acceptable, but unusual and ambiguous. See for example this Hue

Indication Chart used by the Society of

Dyers and Colourists (SDC) to describe pigment or dye color.)

5. The adjectives pale (sometimes light) and

dark (sometimes deep) are used to denote

colors that are relatively light or dark valued, respectively. Usually pale colors are whitish

and therefore relatively unsaturated; deep colors are usually saturated; dark colors may

be either intense or dull.

6. Colors with high chroma are sometimes

(but not consistently) labeled vivid, brilliant or bright; pale is sometimes used to indicate

a pastel (whitened) color, and deep a saturated, dark valued color. In general,

blackened or whitened colors are not explicitly named as such (dull having the negative

connotation of "inferior" or "lesser quality").

7. Many color terms are tied to hues of a

specific lightness: rose is a light valued bluish red, magenta is a mid to light valued red

violet, cyan is a mid to light valued greenish blue, ochre is a mid valued deep yellow, and

so on.

If a paint name is outside these naming

conventions, then you are in much less certain territory. However the following points are

useful:

8. Many of the dull, dark valued or whitish

colors between yellow and red are broken out as specific color categories: olive (dull yellow

or yellow green), tan (dull yellow), gold (dull deep yellow), brown (dark or dull deep yellow

or orange), maroon (dark dull red), pink (light red), crimson (dark blue red) or rose

(light blue red). These color names can modify or be modified by other color names ("yellow

gold," "violet rose," etc.), or by adding "light"

or "deep" as defined in rule 3 ("deep gold" for

"orangish gold").

9. A second group of specialized color names includes the family of earth colors — almost

always golds, tans and browns made from iron

oxide pigments. These are by far the paints most often sold under traditional or historical

color names, including raw sienna, burnt sienna, yellow ochre, gold ochre, french ochre,

raw umber, burnt umber, indian red, english red, venetian red, red ochre, mars yellow,

mars red, mars brown, brown madder, brown ochre, naples yellow, brown stil de grain,

cassel earth, caput mortuum, mummy, dragon's blood, vandyke brown, sepia, pozzouli

earth, violet umber, rose madder, and so on ad

nauseum. In nearly all cases these paints are actually made of modern synthetic iron oxide

pigments, not the natural earths that gave the "color" its traditional name.

10. Most green paints are convenience

mixtures of a green and yellow or (nowadays

rarely) blue and yellow paint, and these paints are also given historical color names that

provide vague guidance about the actual color quality — emerald green, permanent green

(light or deep), hooker's green (light or deep), terre verte, sap green — as well as descriptive

color names such as olive green, leaf green, vivid green, bright green, etc.

11. Historically there have always been more pigments available on the warm than on the

cool side of the color wheel. As a result, nearly all red, orange or yellow pigments are modified

by hue names, but the violet, blue and green pigments are simply called after their chemical

or mineral names — manganese violet, ultramarine violet, cobalt violet, dioxazine

violet, indanthrone blue, ultramarine blue,

cobalt blue, prussian blue, phthalo blue, cobalt turquoise, phthalo green, viridian, chromium

oxide green, cobalt green, cadmium green, prussian green, etc. (Blue convenience

mixtures are infrequently offered.) You must learn the characteristic color implied by each

pigment name: ultramarine blue is a dark, high chroma reddish blue, manganese blue is a mid

valued, high chroma greenish blue, and so on.

12. Chemical sounding synthetic organic

pigment names (phthalocyanine, benzimidazolone, pyrrole, dioxazine,

indanthrone) are commonly replaced by the moniker permanent, which is a 19th century

labeling convention that has nothing to do with the actual lightfastness of the paint!

Pigment names are also commonly replaced by proprietary or brand names (winsor,

blockx, scheveningen, australian, thalo, etc.). Occasionally the term spectrum is used to

denote a "primary" red, yellow or blue that has a balanced hue and high chroma.

Because these color names are primarily chosen for their marketing impact, and the

pigments they name are so diverse, you eventually learn that this is an area where

systematic color naming is hard pressed by

marketing creativity. To find your way through this labeling clutter you have to learn by

mixing experience (or study of color paint brochures) what these different color labels

actually mean.

Despite this, the terms shown in the figure

and the labeling conventions described tend to be widely recognized and consistently used.

N E X T : mixing with a color wheel

Last revised 08.01.2005 • © 2005 Bruce MacEvoy

mixing with a color wheel

Finally we get to the first practical application of color: how to mix colors with paints, using a color wheel as a guide.

A simple but powerful mixing concept, the geometrical mixing method, lets us visualize color mixtures within a traditional color wheel. This method uses the distance and midpoint between any two paints on the color wheel to estimate the saturation and hue of their mixture.

The geometrical method explains saturation costs, the unavoidable dulling of color created when we mix any two or more colored lights or paints, regardless of their hue. We encountered saturation costs in the demonstration of mixing step scales for primary triad mixtures.

The geometrical method works very well for mixtures of light in additive color mixing. It is much less precise for subtractive color mixing because of the many significant differences between the two color mixing processes. Assuming a color wheel can be used equally well in both cases is the color wheel fallacy.

The solution is not to discard the color wheel, but to use it intuitively and alertly, as a compass to color improvisation. This is the basic mixing method explained here.

The key issue is that artists mix paints, not colors. Nearly all the magic in a painting — and the difficulties in color mixing — arise from the richness and complexity of the color materials, not from the abstract experience of color itself. It's important not to let "color theory" or an abstract mixing method distract you from thinking in terms of specific paints and their unique effects when combined on paper. The split primary palette is one example of color dogma getting in the way of effective paint selection.

color

vision

saturation costs

the color wheel fallacy

basic mixing method

split primary palette

unequal color spacing

The easiest way to understand color mixing with a color wheel is through the study of saturation costs — the reduction in the hue purity (chroma or saturation) that results from the mixture of two or more colors.

Newton's concept of a hue circle was devised specifically to permit a geometrical definition of the colors that result from additive mixtures of light. It builds on these concepts:

• the hue of a color is defined by its hue angle or location around the circumference of the hue circle (usually measured in degrees from a zero point at red)

• the chroma of a color is defined by its distance from the center of the circle

• pure neutrals (white, gray or black) are at the center, and therefore have no hue angle and no saturation

• complementary colors (which mix to a pure neutral) are directly opposite each other on the circle

• the color of a mixture is found as the "center of gravity" of all the hues (light wavelengths) in the mixture, which is found as the geometrical mean of the separate wavelengths weighted by their brightness (proportional quantity) and tinting strength.

Let's first demonstrate Newton's method as it would apply to the mixture of different colors of paint on a typical artists' color wheel.

saturation costs

saturation costs on a hue circle

We start with the locations of different hues on Newton's familiar hue circle: middle red (R), yellow orange (YO), and yellow green (YG) paints. These colors will all be mixed with a magenta (M) or red violet paint. For reference, the third subtractive "primary", cyan blue, is shown as well.

In each case, to estimate the appearance of the color mixture, we draw a mixing line that connects the two colors being mixed. The "center of gravity" or geometrical mean between the two colors must always be on this line. If the paints have equal tinting strength and are mixed in equal proportions, then the mean will be the midpoint or halfway point between the two colors. Then:

• The hue of the mixture is defined by the hue angle, a line drawn from the center of the wheel through the midpoint to the circumference. The location of the line at the circumference identifies the hue of the mixture.

• The chroma of the mixture is the distance of the midpoint from the center of the wheel to the circumference: the closer the midpoint is to the center, the duller or grayer the mixture will be.

Now we can show that colors spaced farther apart on the color circle will produce

duller mixtures. Compare the distance from the black center of the wheel to the midpoint of the three mixing lines in the figure. The mixture of red (R) and magenta (M) is close to the outer edge of the wheel, and so will have a high saturation; the hue angle of the midpoint suggests the mixture will be a deep red. The mixture of magenta and yellow orange (YO) is somewhat displaced from the circumference of the wheel, so it will have a moderate saturation and a scarlet red hue. The mixture with yellow green (YG) is very close to the center of the wheel, and will be a very dull yellow orange.

Complementary colors would be exactly opposite each other on this color wheel, so the midpoint of their mixing line will be at the center — they mix to make black or gray.

It's also obvious that dull paints produce dull mixtures, because they are already closer to the neutral gray center of the color wheel. Venetian red and yellow ochre will produce a much duller orange mixture than cadmium yellow deep and cadmium scarlet, which have the same hue angles on the color wheel, because the two cadmiums are much more intense paints.

Notice that saturation costs have nothing to do with whether or not two paints are "primary" colors, or whether the mixture crosses a "primary" line, or any other artificial rule of artists' "color theory".

This is the unavoidable, universal rule of saturation costs in paint mixing:

the farther apart two colors are on the color circle, and the duller their average chroma,

the duller their mixture will be.

Saturation cost means that mixed colors will always be less intense than one or both colors they are mixed from. We pay a cost in reduced chroma whenever we create a new color through mixtures.

Newton's color circle was adapted to describe paint mixtures in the early 18th

the color wheel fallacy

century, at a time when the differences between additive and subtractive color mixing were either unknown or only vaguely recognized. However, even after subtractive color mixing was clearly understood, artists still used a color triangle to describe paint mixtures, exactly as Maxwell had done with light mixtures.

Unfortunately, the simple color wheel geometry that Newton used to explain saturation costs does not apply to paint mixtures. This problem represents the color wheel fallacy: that subtractive color mixtures with paints behave in the same geometrically simple and predictable way as additive color mixtures with lights. Unfortunately they don't, and if we look at the reasons why they don't we can understand why color wheels are relatively poor at predicting paint mixtures.

When Newton devised his hue circle to explain color mixtures, he made the claim that a simple geometrical model could predict the mixing behavior of spectral lights. This has turned out to be true, provided that we are not too fussy about the equal brightness of the mixtures, and that we define the hue circle as a shape more like a triangle, called a chromaticity diagram.

However, the same approach, using paint locations on a color wheel, fails very badly to explain paint mixtures. This occurs for two reasons: (1) the mixing relationships among different colors of paint are not geometrically simple; and (2) the mixing behavior of a paint is not predicted by its location on a color wheel.

the color mixture problems in a color

wheel

The diagram shows the most important problems that arise when attempting to predict subtractive color mixtures with a color wheel.

• If we want to explain color mixtures of light in terms of a single geometrical figure, they can be very adequately represented by a lopsided triangle with a rounded green corner, called a chromaticity diagram. However there is no geometrical figure that can represent paint mixtures with equal accuracy. In fact, "color theory" color wheels or color triangles are usually drawn as geometrically perfect because a lopsided or quirky geometrical shape would not be any more accurate.

• In both monochromatic (single wavelength) lights and in artists' pigments, there is wide variation in apparent saturation or chroma across different hues. A chromaticity diagram represents this fact through its irregular shape, and by shifting the white point or point of neutral mixture away from the center of the triangle and closer to the green edge of the chromaticity space. In a color wheel or color triangle, this is represented by shifting the location of paints toward the center of circle, while keeping the achromatic point (white or gray) at the center. But the problem is that paint chroma changes as paints are

diluted, changing their mixing relationships. Lights in contrast can be made brighter or dimmer without altering the color of their mixtures.

• The mixture of two lights in a chromaticity triangle will always lie on a straight line between their points. In contrast, as we will see on a later page, paint mixing lines are erratic rather than straight in a color wheel. Typically green mixing lines are curved outward, and if magenta and yellow are placed one third of the circumference apart, as is commonly done, then mixing lines between them are curved as well.

• We might try to remedy this mixing line problem by spacing the hues around the hue circle so that all mixing lines are approximately straight (for example, by putting blue and yellow closer together). But this only creates new problems. Most important, making the mixing lines straight in one part of the color wheel only makes them curved somewhere else. And any respacing will destroy the complementary color relationships on opposite sides of the color wheel.

• If we forge ahead anyway, and find the hue spacing that produces the best compromise in terms of straight mixing lines and complementary color relationships, then we discover that the same "colors" of paint will mix very differently with other colors around the color wheel: the hue of a paint doesn't reliably predict the color of its mixtures. Two paints of the same hue can create very different mixtures with other paints, a problem I call substance uncertainty. This is most obvious when we try to find the mixing complement of each paint: the same paint can mix a pure gray with very different hues on the color wheel. Paints can only be given a "fuzzy" location on the color circle, because this location changes depending on the other paints we choose to mix with it. In contrast, two monochromatic lights with the same hue will always produce identical color mixtures with every other hue on the chromaticity diagram.

• Finally, mixtures of spectral hues (including red violet and purple) always create the

appearance of other spectral hues, though these mixed lights can appear whitened or pale: mixing a green light with a red light creates a whitened yellow or orange. In contrast, paint mixtures within the magenta to yellow part of the color wheel seem to create entirely new colors not in the spectrum — tans, browns or maroons — that define unsaturated color zones. Thus, a mixture of cadmium red and chromium oxide green is actually a very dull red orange, but we see and describe the hue as a dark brown. This effect only occurs in one part of the color wheel, which again shows that paint mixtures are not geometrically consistent.

All these problems make it impossible to "predict" subtractive color mixtures with

a color wheel. Normally, "color theory" simply ignores these issues in pursuit of geometrical purity and mixing rule simplicity, but the inconsistencies are clearly visible in the paint mixtures and create a great deal of confusion for painting students.

The complexity of subtractive mixtures in particular make all color wheels unreliable predictors of paint mixtures. And any attempt to make them geometrically consistent (as for example in Stephen Quiller's mixing color wheel, or my artist's color wheel) will be half measures at best.

The solution to the color wheel fallacy is not to throw away the color wheel, but to use it as a rough guide — as a compass to color improvisation.

It's really very simple: let the color wheel help you choose the mixing paints and approximate paint proportions you need ... then rely on your eye (and your color mixing intuitions) to get the mixture just right.

Now let's use the color wheel to plan and guide a color mixture. This section describes the concepts behind color mixing: the physical methods for paint mixing are discused in the page on working with paints.

This tutorial is more detailed and explicit than

basic mixing method

the intuitive procedure you will learn to use: conscious planning and alternative paint choices will eventually be replaced by your habitual palette and mixing experience. As this happens, your ability to improvise and "go with the flow" will increase as well.

planning color mixtures on a color wheel

The diagram shows how to decide on the best color mixture to obtain a mid valued, somewhat dull bluish green color (indicated as the mixing point). It is sometimes possible to mix a color using only two paints, but it is always possible to mix a color using three

paints — provided you choose the right ones.

The hidden difficulty in color mixing is not getting the right proportions of paint in the mixture, it's choosing the right paints to start with. So paint selection is the first step in improvising that blue green color mixture: • Locate the color you want to mix on the artist's color wheel. You must first identify the approximate hue you want as a point on the circumference of the wheel; then identify the chroma of the mixture by shifting the point toward the center (black) of the wheel, and finally identify the value (lightness) you want. (Keep in mind that watercolors, especially intense or dark valued colors, lose saturation and lightness as they dry.) This is your mixing point.

click here for an illustrated version of the

mixing procedure

• Identify any mixing lines that pass through or near this mixing point from any pair of paints available on your palette. (Two lines between different pairs of paints are shown in the figure.)

• Identify all combinations of three paints that enclose the mixing point in a mixing triangle. (A single triangle shown in the figure.) This is usually a mixing pair that comes pretty close to the right color, plus a third, complementary color (opposite from the color you want) to pull the color toward gray or toward a darker value.

• Think about the value, transparency, texture or other handling characteristics desired of the mixture. For example, will two paints mix a color that is dark enough? Will the mixture be too saturated, or not saturated enough? Will the mixture have the right texture, transparency, or staining characteristics? After considering all these issues, choose the mixing pair or mixing triad that will give you the attributes you want.

In the example, mixing phthalocyanine green BS (PG7) with ultramarine blue (PB29) will produce a darker blue green than mixing permanent green light with phthalocyanine cyan (PB17) or manganese blue (PB33). The manganese blue mixture will be lighter, but have an interesting, granular texture with patches of light green. The mixture with ultramarine blue will have a slight flocculating texture and will be slightly less staining than the mixture of the phthalos green and cyan. The point is that you can choose different combinations of paints in order to get the paint behavior you want in the mixture, or the visual effect you want in the finished color. Color mixing lets you to choose the material attributes of paints as well as

paint color.

• Use the location of the mixing point along the line to estimate the approximate proportion of the two paints in the mixture, assuming the two paints are of equal mixing strength. This is important to estimate the amount of paint you need to mix (for example, in a wash).

The relative proportion of paint required

depends on several paint attributes, described below.

• Start with the weaker paint (the paint with less tinting strength, weaker concentration, lighter value, or more transparency), and mix it with water to give the desired concentration of paint, in a sufficient volume of liquid to cover the total color area you want to paint. (Starting the mixture with enough liquid to cover the total area prevents you from mixing too little paint, especially for a wash.)

• Now improvise. Add the dominant paint very gradually, from a mere touch of color up to the proportions you estimate will create the desired hue. Observe the mixture carefully, and stop when the hue is close to correct.

• Test the mixture on a piece of paper; a mixture on the palette will not look the same on paper. Nearly all paints present a drying shift between the wet and dry color, so if accuracy is important, let the test patch dry for 10 minutes before committing the mixture to the painting. Observing the direction of color changes as the mixture dries can also help you adjust the mixture accurately.

• If the color is the incorrect hue, adjust toward the exact hue required by adding one or the other (but not both) of the mixing colors. Add water as needed to return to the correct concentration.

• If the color is too intense, or if you are mixing with three paints, add the third (complementary) color (in very small amounts) to make final adjustments to the saturation or value of the mixture. This can also work to make a final adjustment to the hue.

As mentioned above, typically one paint will be dominant in an equal mixture of two paints. So you need to know the relative mixing strength of your paints, for each pigment and brand of paint you use, in order to improvise confidently. This is something you pick up with experience, but a few paint attributes can help you anticipate how much one paint will dominate another:

1. Concentration. Obviously, the paint that is more concentrated (less diluted with water) will be the dominant or stronger paint in a mixture. The paint concentration depends not only on the amount of water you add to the mixture, but also on the proportion of pigment to vehicle that the manufacturer puts in the paint. (This is noticeable when comparing different brands of the same single pigment paint, especially the strongly tinting phthalocyanines, quinacridones and dioxazine violet.)

2. Tinting strength. The dominant paint will have a higher tinting strength. Phthalocyanine blue has a tinting strength 40 times greater than ultramarine blue, which means that phthalocyanine blue is much more powerful than ultramarine blue in producing a noticeable color change in a mixture. Manufacturers attempt to minimize these differences — by increasing the amount of pigment in ultramarine blue, and/or by adding fillers to phthalocyanine blue — but these workarounds only reduce the clarity and depth of the color.

3. Value. Darker valued paints usually dominate a mixture. When two paints of equal mixing strength are mixed in equal proportions, the mixed color will lean toward the darker paint. This has less to do with paints than with the eye: equal lightness changes are more noticeable in light valued colors than in dark ones. Darker colors must be added carefully to a mixture, and it is more difficult to alter a mixture by adding a lighter color.

4. Color Temperature. Warm colors tend to dominate a mixture, especially hues from magenta through orange. This occurs partly because modern warm colors are almost entirely synthetic organic pigments (which have a high tinting strength), and partly because warm hues have a higher chroma (are more intense) than cool hues.

5. Opacity. Opaque pigments tend to dominate over "transparent" pigments in a mixture, simply because opaque pigments are more concentrated. The transparent pigment shows an opaque pigment behind it, but the opaque pigment covers the

transparent pigment underneath.

These are only guidelines: experience must teach you how much of a paint to use in mixtures with other paints. You will also learn to adjust differences in value, opacity or tinting strength by how much you dilute paints out of the tube. But the principal and safest rule is always this: only add a small quantity of dominant paint to the weaker paint, and increase the dominant paint slowly until you get the exact color you want.

All these issues are simplified when using a consistent and limited palette, so you can learn the distinctive mixing proportions for every pair of paints.

The range of effects you can get from your mixing combinations depends on your choice of paints. More variety is possible if you select both organic and inorganic pigments from both the warm and cool side of the color wheel, and include a few earth, granulating and opaque pigments as well. The basic palette discusses some of these alternatives.

However, the more paints you select for your palette, the harder it is to learn all their combinations. In a 6 color palette there are only 15 possible mixing pairs; in a 12 color palette there are 66; in an 18 color palette there are 153! You will master color mixing more quickly if you start with fewer paints in your palette.

Color mixing strategies inevitably leads to the issue of special paint selections or palette designs intended to make color mixing simpler, more effective or downright foolproof. Perhaps the most popular among these is the split primary palette.

The Dogma. If the artist limits his paint selection to the traditional primary triad palette, then the saturation costs in secondary color mixtures (orange, purple and green) are so severe that even some artists committed to their primary color dogma look for a way to reduce them.

split primary palette

The common remedy has been to split each "primary" color into a pair of colors, each leaning toward one of the other two "primaries." So the single primary yellow paint is replaced by two paints: a warm (deep) yellow that "leans toward" (is tinted by) the red "primary," and a cool (light) yellow that leans toward blue. Similar replacements are made for the other two "primaries," which doubles the palette from three to six paints.

the split primary palette

the version proposed by Nita Leland

According to Nita Leland, a representative split primary palette would consist of:

• cool yellow : cadmium lemon (PY35) or benzimidazolone lemon (PY175) (leans toward blue)

• warm yellow : cadmium yellow (PY35) or nickel dioxine yellow (PY153) (leans toward red)

• warm red : cadmium scarlet (PR108) or pyrrole red (PR254) (leans toward yellow)

• cool red : quinacridone carmine (PR N/A) or quinacridone rose (PV19) (leans toward blue)

• warm blue : ultramarine blue (PB29) (leans toward red)

• cool blue : phthalocyanine blue GS (PB15:3) (leans toward yellow)

The "color theory" logic for these substitutions goes like this: a yellow that leans toward blue is a yellow that actually contains blue, and a blue that leans towards yellow is a blue that contains yellow. So the blue and yellow reinforce each other when mixed to make green. But if either color leans toward red, then red is carried into the mixture through the yellow or blue paints. This isn't good, because mixing all three primaries creates gray or black, and this dulls the remaining green mixture.

This becomes a rule: when mixing two primary colors, choose the paints that lean toward each other to get the most vibrant mixture. The slogan is, "never put the mixing line across a 'primary' color" — that is, don't choose either two primaries leaning toward or tinted with the third primary, because mixtures containing all three primaries mix to gray. Split primary advocates call these mixtures "mud."

Of course, the painter can intentionally choose one or both of the primaries leaning toward the third primary, if he wants less intense or near neutral mixtures. But then "color theory" painters will call his paintings mud.

The Critique. Where did these muddled recommendations come from? Straight out of the Newtonian color confusions of the 18th century. Essentially the same color concepts appear in the color wheel text by Moses Harris, and are accepted without serious challenge in Michel-Eugène Chevreul's The Principles of Color Harmony and Contrast (1839). Chevreul describes color mixing beliefs that must have been widely accepted by artists of his time; one passage is worth quoting at length:

We know of no substance [pigment or dye] that represents a primary color — that is, that

reflects only one kind of colored light, whether pure red, blue or yellow. ... As pure colored

materials do not exist, how can one say that violet, green and orange are composed of two

simple colors mixed in equal proportions? ...

Instead we discover that most of the red, blue

or yellow colored substances we know of, when mixed with each other, produce violets,

greens and oranges of an inferior intensity and clarity to those pure violet, green or orange

colored materials found in nature. They [the authors of color mixing systems] could explain this if they admitted that the colored materials mixed together reflect at least two kinds of

colored light [that is, two of the three primary colors], and if they agreed with painters and dyers that a mixture of materials which

separately reflect red, yellow and blue will produce some quantity of black, which dulls

the intensity of the mixture. It is also certain that the violets, greens and oranges resulting

from a mixture of colored materials are much more intense when the colors of these

materials are more similar in hue. For example: when we mix blue and red to form

violet, the result will be better if we take a red tinted with blue, and a blue tinted with red,

rather than a red or blue leaning toward

yellow; in the same way, a blue tinted with green, mixed with a yellow tinted with blue,

will yield a purer green than if red were part of either color. [1839, ¶¶157-158; my translation]

There you have the color ideas behind the split primary palette. Unfortunately, most of them are factually wrong or logically unrelated.

Chevreul is criticizing the idea that "primary" colors can be represented in paints by observing that these primary paints can't mix all the hues of nature with sufficient intensity or chroma. From that he concludes that paint pigments do not reflect "only one kind of light". A yellow primary paint must reflect "yellow" light mixed with some "blue" or "red" light, which dulls the pure yellow color. As we can't avoid this color pollution, we minimize it by mixing colors tinted with each other — so the thinking goes.

However, paint colors do not simply represent spectral "colors" as Chevreul believed: a primary yellow paint does not just reflect a lot of "yellow" light. Nor is color "in the light" as colored light; there are no "magenta," "red violet" or "purple" wavelengths in the spectrum, so those colors cannot be "in" the light. The same surface colors can result from very different light mixtures: yellow results

from a "red" and "green" mixture, and red violet from a "blue violet" and "red" mixture. These confusions were clarified later in the 19th century through the popularizing science books by Hermann von Helmholtz and Ogden Rood. Surprising, then, that the "paint color equals light color" fallacy is still widely believed by painters today — Michael Wilcox teaches it as the basis of his color mixing system.

In addition, you can never find a paint, a crystal — or a light — whose color is "pure enough" to match a primary color. This is because primary colors are always imaginary or imperfect: they can never be matched by visible lights or paints, and visible lights or paints can never mix all possible colors. The reason for this lies in the design of our eye — in the overlapping response curves of the L, M and S light receptors. The "impurity" of the light reflected by the paint certainly aggravates the problem, but is not the cause of it. The "color theorist" dogma that paint mixing problems arise because paints are "impure colors" is bogus.

Choosing two paints or inks that are more similar in hue does increase the intensity of their mixture, as Chevreul says. But these saturation costs again have nothing to do with the contamination of one primary color with another. They appear even when we mix monochromatic (single wavelength) lights that are completely free of tint by any other hue. In fact, mixing pure spectral lights was how Newton discovered saturation costs in the first place!

In brief, the split primary palette is based on 19th century color ideas that have nothing to do with the facts of color perception and color mixing as we understand them today.

The Demonstration. But the pragmatist may say: who cares? Just because the justification is murky doesn't mean that the split primary palette isn't an effective selection of paints.

Fair enough. So let's hold the split primary palette to its two key claims: (1) that red and blue (rather than magenta and cyan) are the most effective primary colors; and (2) that splitting these primary colors allows us to mix

the most vibrant secondary colors (orange, purple and green). It's easy to show that both these claims are false.

A "pure" red or blue makes an ineffective primary color because these colors fail the basic requirement for a subtractive primary paint: it must strongly stimulate two receptor cones but not the third. A pure red and pure blue paint mix dark, grayed purples, for example, because they have almost no reflectance in common; for the same reason, the blue and yellow make very dull greens. So the split primary palette starts out with an inaccurate definition of the primary paints most useful for subtractive color mixtures.

We can evaluate the second, "vibrant color" justification for the split primary palette by comparing it to any other palette of six paints, for example the secondary palette, to see which paint selection is superior. There are two ways to do this.

A simple "back of the envelope" approach is to draw a circle, divide it into twelve equal segments, then mark on the circle the location of each paint in the palette according to the location of the paint's color category in the palette scheme. (Use the complete palette to assign specific pigments to the correct color category.) Then enclose all these category markers inside the largest possible, straight sided closed figure (see examples below). The closed area is the gamut of the palette — the approximate range of hue and saturation that it is possible to mix with that selection of paints. The palette with the larger gamut will create a wider range of color mixtures.

comparing the gamut of two palettes split primary palette (left) and secondary palette (right)

The split primary palette (at left) creates a narrow lozenge of color mixtures that is skewed toward the "warm" colors of the palette, and puts the heaviest saturation costs (dull mixtures) in the mixed greens and violets. In contrast, with the equally spaced secondary palette (at right), we get a substantially increased range in color mixtures. This is because a single intense pigment anchors each primary and secondary hue, which pushes back the limits of the color space as far as possible (particularly on the green side). Same number of paints, very different gamuts.

The alternative (and better) way to compare palettes is to use each one to mix the twelve colors of a tertiary color wheel. Display these mixtures either side by side or as matching paint wheels (below), and see what you get.

comparing paint wheels made with two palettes

split primary palette (left) and secondary palette (right)

This side by side comparison confirms the gamut differences identified with the palette schemes. The mixed red orange in the split primary palette (left) is so dull it is close to brown; the purple is dark and grayish, and the mixed greens are drab across the entire range. In contrast, the secondary palette (at right) is obviously much brighter in the greens, produces a more evenly saturated range of warm hues, and gets juicy purples as well. If you don't want "mud," then the split primary palette is not the one to choose!

Can we fix these problems by changing the selection of split primary paints? Yes we can,

and the solutions people choose are revealing. The palette scheme for the Wilcox six principle [he means principal] colors shows that his split primaries have turned into the secondary color wheel, but with green omitted in order to provide two very similar yellows.

palette scheme for the Wilcox "six principle colors"

from "Blue and Yellow Don't Make Green" (2001)

Wilcox has widened the split between the red and blue primaries to the point where they are completely different hues (scarlet and magenta, or blue violet and green blue) — yet he still hangs onto his two similar "primary" yellows. This is a funny and revealing example of how a color dogma accepted without question (you must use primary colors!) can trample on color mixing common sense (hey, mixtures look so much brighter if you add a scarlet, blue violet and green paint!).

Not only have we found that the split primary palette fails to meet its claims, and its "color theory" justifications are inaccurate, I've proven by demonstration and explanation that the secondary palette is the superior mixing system. And because it lets the painter choose many different paints for the three contrasting pairs of complementary pigments, the secondary palette offers the largest gamut and value range, and the greatest alternative choices of transparency, staining, granulation, texture, and handling attributes in paints that are possible with a six paint palette. Try it for yourself and see.

The logic of the split primary

unequal color spacing

palette contains the germ of an important idea: that you can explicitly control the saturation costs of your color mixtures by the grouping or spacing of the most saturated paints in your palette.

Increasing the color wheel or hue circle distance between two paints increases the saturation cost or dullness in their midpoint mixtures, and within the "primary" triad or split "primary" frameworks this effect is most pronounced in orange, purple and green colors. By manipulating the bright or dull mixing potential of these purples and greens, the artist can shape the fundamental color dynamics of his painting palette.

unequally spaced colors and the implied illuminant

The color wheel schematic (above) shows the two main variations painters are likely to use: when the illuminant — the color of light — shifts warmer (toward longer wavelengths, becoming yellowish or reddish) or greener (the color of intense noon sunlight).

The basic principle is that when the illuminant has a distinct color, it brightens similar hues and dulls complementary hues.

Warmer Color Shifts. In this case, typical of late afternoon light or artificial light from a candle or incandescent light, warm colors

become more saturated and cool colors become darker and duller.

This suggests choosing warm color (red to yellow) paints that have higher saturation and cool color (blue) paints that are relatively darker and duller. Burnt sienna would be replaced by cadmium orange, and phthalocyanine blue by iron [prussian] blue or a red shade of phthalo blue.

Provided the light yellow is not too pale (greenish), all mixed yellows will be very saturated and light valued. If the "cool" red is shifted from a bright quinacridone magenta to quinacridone red, and the "warm" red into red orange, the saturation of mixed warm hues will be consistently at maximum saturation.

The greens mixed from yellow and blue will be moderately dull and somewhat dark. These muted greens yield dominance to the more intense reds and oranges, reducing the fundamental visual tension between red and green. Because all the greens must be mixed, they will be more varied and interesting.

The blue paints are typically grouped close together, so the mixed middle blues will be relatively bright, but quickly become muted as they are mixed with the "cool" yellow or red. This gives the range of blues a chromatic emphasis around the sky color, surrounded by a range of less intense green blue and blue violet mixtures for foliage and shadows. The mixed violets will be somewhat dull, and dull dark blues (the visual complements of yellow or red orange), not purples, should be used to tint shadows.

Greener Color Shifts. A "green" color shift is characteristic of colors under intense noon sunlight. Daylight does not appear green to our eyes because of the color balancing effect of chromatic adaptation, but the relative color emphasis that results can be modeled by different palette choices.

The main effect of this greening is to brighten greens and to dull purples (because purples are the complementary hue of the light). As there are few useful purple or green pigments, the most common method to produce this bias is to shift the yellow and blue paints toward

each other — by choosing a lemon or greenish yellow as the "cool" yellow, and a greenish or turquoise blue for the "cool" blue — thereby increasing the saturation of green mixtures. The greenish blue should also be somewhat lighter valued, if possible: cobalt turquoise or cobalt teal blue (PG50) are very useful alternatives.

In contrast, the hue circle distance between the "cool" red and "warm" blue should be increased, and one of the colors should be dark valued, if feasible — for example, by choosing a phthalo blue red shade or a quinacridone carmine. These will produce dull dark purples that are usefil to tint shadows with the complementary hue of the illuminant color.

Other imbalanced distributions are possible, which might contrast a broad range of blues against dull earths, vibrant greens against dull reds, and so on in many combinations. But the palette shown in the figure, with most of the saturation costs in the violets and greens, is one of the most popular; dozens of palettes are variations on it.

Why not just choose a large number of paints that are very closely spaced all the way around the color wheel? You can, if you want. These colorist palettes are useful for a bright and lively style of painting that specifically does not give the impression of a certain kind of light. The point is that saturation costs can buy you expressive resources, particularly in landscapes and portraits. Forcing some color mixtures to be dull confers a light giving power to the pure colors they are mixed from, which can create a deep color harmony across the value structure of a painting.

N E X T : testing the color wheel

Last revised 08.01.2005 • © 2005 Bruce MacEvoy

testing the color wheel

The previous pages explained

the traditional color wheel and how to go

beyond it to a practical method of color mixing. We had to keep in mind that the color

wheel depends on a basic fallacy and contains mixing biases that appear in mixing

step scales among "primary" colors.

This page presents my research to measure

the biases in the color wheel more precisely, using color mixture measurements made with

a GretagMacbeth spectrophotometer. These are measurements that paint manufacturing

color technicians must have already done many times, but I have never seen similar

results published before.

My test results clarify the significant biases in

color wheel geometry, and also explain our color experience as we mix paints. We will get

a clearer picture of the biases in the color wheel, but will also find it is not so easy to

"fix" these biases in a systematic way.

To begin, let's translate

the basic assumptions of the geometrical mixing method into something we can

measure precisely.

If we make allowances for differences in the

relative tinting strength among paints, then the color wheel assumes that the hue and

saturation of color mixtures can be described by a straight line between the two mixed

colors.

The figure below shows a straight mixing line

between the "primary" colors magenta (M) and light yellow (Y). Five mixing points are

shown along the line. Each point marks the hue angle of a magenta+yellow mixture, as

these pass from magenta through carmine, middle red, red orange, deep yellow and

middle yellow to light yellow.

testing the mixing method

color

vision

testing the mixing

method

mixtures between two

"primary" colors

mixtures among all

tertiary colors

changes in chroma along a mixing line

The seven gray lines drawn from the center of the wheel to the mixing line indicate the

chroma of the mixtures at each mixing point, and the chroma of the "primary" colors yellow

and magenta. We observe two things as colors (paint mixtures) shift along the mixing line:

• As a small amount of one paint is mixed with the other, there is a sharp drop in the chroma

of the mixture, because the mixing line is at an angle close to the center of the wheel.

• The chroma reaches its minimum at the midpoint of the line, and here changes in

chroma are quite small across large changes in hue, since the mixing line is at a tangent to

the center of the wheel but roughly parallel to the hue gradations along the circumference.

So the basic rule is roughly:

drop in chroma —> change in hue —> rise

in chroma.

If we stand these seven chroma lines in a row, spaced horizontally by hue angle, the tops of

the lines describe a curve like a chain hanging

between the two "primary" color poles (chroma is represented by the height of the

chain).

changes in chroma across a mixing line

And this hanging chain is what we would expect to appear between any two widely

spaced, saturated paints, if we measure both

the hue angle and chroma of their mixtures. We will test to see if this is true.

I should clarify an apparent contradiction in

color mixing that seems hidden in this "hanging chain." The subjective experience of

mixing one intensely colored (saturated) paint

with another seems to the eye to produce strong changes in color in mixtures near the

original paints, but rather small changes in color across the middle hues between them.

Does this contradict what I just said about the sharp drop in chroma near the original colors

and large changes in hue across the middle mixtures? No: chroma or saturation is

basically our ability to discriminate hues, and hue differences near the intense colors are

brighter and so easier to see. The hanging

chain really tells us that accurate color mixing is difficult for two completely different reasons

— near the "primary" colors, because small quantities of paint will have large effects on

the apparent color; near the middle mixtures, because they are significantly duller and

therefore harder to identify visually.

Now the test is easy to design.

We simply pick three "primary" color paints (a light yellow, a magenta, and a greenish blue),

and mix pairs of them in various proportions. A spectrophotometer measures the chroma

and hue angle of these mixtures, and the chroma can be plotted against the hue angle

mixtures between two "primary"

colors

to see how well the "hanging chain" describes changes in chroma across the hues from one

"primary" color to the next.

I actually chose two different paints for each

of the three "primary" colors, to minimize effects peculiar to any single pigment. The

paints were: Winsor & Newton cadmium lemon (PY37) and benzimidazolone yellow (winsor

yellow, PY154) as the "primary" yellows, Winsor & Newton permanent [quinacridone]

rose (PV19) and quinacridone magenta (PR122) as the "primary" magentas, and

Winsor & Newton phthalocyanine blue (winsor blue GS, PB15:3) and Holbein phthalocyanine

cyan (peacock blue, PB17) as the "primary"

blues.

Each "primary" paint was mixed with the four paints in the other two "primary" colors,

creating 12 unique mixing combinations. For each combination, seven test swatches were

prepared from mixtures in the approximate

proportions (paint 1/paint 2) of 1/7, 2/6, 3/5, 4/4, 5/3, 6/2 and 7/1, or 13%, 25%, 38%,

50%, 63%, 75% and 88%. (Actual paint proportions varied slightly depending on the

tinting strength and darkness of the paints, and my errors in making the mixtures.) Then

the actual chroma and hue angle of these 84 mixtures, and the 6 pure "primary" paints,

was measured with a GretagMacbeth Spectrolino™ spectrophotometer. The

results were plotted using Microsoft Excel

spreadsheet software. The following graph shows the results.

saturation costs between "primary" color mixtures

The vertical scale shows the chroma of the six

"primary" paints and their mixtures; the horizontal scale shows the hue angle in the

CIELAB space where 0 (360) degrees is approximately the position of a "primary"

magenta color. Each color measurement is plotted as a blue point, with the average of

the measurements shown as a red line.

The expected "hanging chain" curve appears

between the "primary" color pairs, but we also see several imbalances in the color wheel

geometry:

• The "primary" colors should be separated by

approximately 120°, or one third of the total circumference of the color circle, but the

distance between "primary" yellow and "primary" blue is around 160°, and the

distance between yellow and "primary" magenta is less than 90°. The "primary"

colors are not equally spaced around the

color circle.

• The "primary" paints are not equal in chroma to begin with: magenta is significantly less

intense than yellow, and cyan is less intense than magenta. Placing these paints equally on

the circumference of a color circle disguises

the fact that "primary" colors are not equal in chroma.

• As shown by the vertical dip in the three

"hanging chains," the "primary" colors are

not equal in saturation costs. This is not simply because they are not equally spaced on

the color wheel: the chroma of mixed greens (between yellow and blue) is higher than the

chroma across mixed violets (between blue and magenta), even though yellow and blue

are slightly farther apart on the color wheel than blue and magenta.

What do these biases mean to practical color mixing? First, saturation costs are attributes

of specific paint colors; they depend on which paints we are talking about, as well as how far

apart the two mixed colors are on the color circle. Yellow tends to sustain and even raise

the chroma of paints mixed with it, while violet has the most intense dulling effect on all other

colors.

The change in chroma between magenta and yellow is quite small: the "hanging chain" is

almost flat, and never dips much below the chroma of the original "primary" magenta

paint. So yellow's "chroma raising" effect is much stronger on the warm than the cool side

of the color wheel. Notice also that the scatter of mixture measurements above and below

the average line is very large, indicating that there is a lot of variability in the measured

chroma. This variability probably comes from

very specific interactions between the different pigments — some mixtures are more potent

than others.

As reference, I've added markers for the hue

and chroma of burnt sienna and burnt umber, a moderately dull and very dull red orange.

Notice that "dull" burnt sienna has a higher chroma (is more saturated) than most of the

mixed violets and greens! All the mixed warm colors must all have higher chroma than the

burnt sienna, or else they would appear brown. (This is the real reason for the old

cliche that "warm colors advance and cool colors recede." If you leave browns and tans

and pinks out of the picture, then warm colors

are all more intense, and often lighter valued, than cool colors.)

Now, if we wanted to straighten out these

differences in the saturation costs between "primary" colors, how would we change the

color wheel to do that? First, we would have to

move magenta closer to yellow; yet most color wheels distort this side of the color space

by spacing the warm colors too far apart. Unfortunately, the variability above and below

the "hanging chain" shows that a mixing line won't predict the chroma of a warm hued

mixture very accurately.

In addition to a closer spacing of the "primary"

colors magenta and yellow, the "primary" yellow and blue must be spaced farther apart.

So why is the "hanging chain" here higher than the one between magenta and blue,

indicating more intense color mixtures? One way to get an answer is to look at the mixing

lines plotted on the CIELAB a*b* plane:

mixing lines on the CIELAB a*b* plane red is shown on the left, to match the standard artist's

color wheel

This shows that the lines between magenta and yellow are overall fairly straight: the

reason they dip so little in chroma is simply because warm colors are closer together in

the color space than blues or greens. (The mixing lines are also highly variable or wavy,

effects specific to the different pigment

combinations.)

The mixing lines between blue and magenta are straight and consistent, indicating that the

color wheel models mixtures in the violet and blue part of the space almost perfectly. This

may be due primarily to the fact that these are

also the dullest mixtures.

The surprise is that the mixing lines between yellow and blue are strongly

curved rather than straight. They bend away

from the neutral center of the wheel, making the mixtures of cyan and yellow more intense

than we would expect them to be. This effect also happens with other cool mixtures, for

example ultramarine blue and lemon yellow (which makes a dull green, even though the

mixing line between them suggests it should make a dark maroon) or between phthalo

green BS and cadmium orange. These funhouse mirror distortions in the cool mixing

lines are one reason that green mixtures are so hard to judge accurately.

You can make fairly accurate color mixing tests of your

own, if you have access to a color scanner and Adobe

Photoshop or similar image processing software.

Photoshop contains a color sampling utility that

provides the CIE L*a*b* coordinates for the color of

any pixel in an image, and these pixels can be sampled

from scanned images of your mixing tests and plotted

on graph paper or with a spreadsheet program. Scan

the unmixed paint colors, and a Kodak color test card,

as reference points for lightness, hue and chroma;

compare to the CIE measurements for paints in the

guide to watercolor pigments or the CIELAB color

chart. Use the "5 by 5" pixel sampling option to

average the color over several pixels in the test image.

This method will not give highly accurate absolute

measurements of color, but is quite serviceable for

measuring the relative changes in colors as they are

mixed.

Now let's try to map these color

wheel biases in more detail. To do this we will shift our focus to the relationships among

tertiary hues as a measurement framework.

The figure below shows the chroma of all paint

mixtures in one of my preferred paint wheels. Each line is color coded to the

pigment hue it represents; these are also noted at the bottom of the graph as equal hue

increments around the color circle. Follow any curve horizontally across the graph to track

the changes in chroma that occur in mixtures of that paint with all other paints.

mixtures among tertiary colors

chroma curves of mixtures around the color wheel

This graph represents the overall pattern of

saturation costs in the color wheel, and makes the following points clear:

• The colors move in two contrasted groups: a

"warm" group of colors that ranges from cadmium lemon yellow (PY37) to quinacridone

magenta (PR122), and a "cool" group of colors

that ranges from ultramarine blue (PB29) to permanent sap green (a dull yellow green,

labeled Sap in the figure). These two groups move in opposite changes in chroma around

the color wheel; the warm colors show very wide changes in chroma (from 90% to 25% or

lower), while the cool colors cycle within a narrower range. These differences affirm the

importance the warm/cool color contrast.

• Paints on the warm side of the color wheel,

from nickel dioxine yellow (PY153) to pyrrole red (PR254), lose little or no chroma when

mixed with other paints in the same group; the chroma of quinacridone magenta (PR122)

actually increases when mixed with other warm colors.

• Warm colors begin to lose chroma when they are mixed with either cadmium lemon yellow

(PY37), which contains a small amount of "cyan" reflectance, or with quinacridone

magenta (PR122), which contains a significant

amount of "blue violet" reflectance, so "blue" reflectance is the most dulling addition you

can make to any warm paint mixture.

• The warm colors cadmium scarlet (PR108) and pyrrole red (PR254) continue to shift in

the same way when mixed with cool colors.

However, cadmium lemon yellow (PY37) and nickel dioxine yellow (PY153), which reflect

significant amounts of "green" light, create fairly intense mixtures with the "green"

reflectance of phthalocyanine blue (PB15), cobalt teal blue (PG50), phthalocyanine green

(PG7) and sap green (Sap). As a result, the yellows and yellow oranges diverge from the

reds and red oranges in mixtures on the cool side of the color wheel. Mixtures of yellows

and blues increase in chroma, while mixtures

of reds and blues decrease in chroma. So the

"warm" colors seem to consist of two color clusters, split at around red orange, which

behave basically as a yellow or a red pigment in mixtures with all other colors.

• In contrast to the warm colors, the blue mixture curves are widely spaced rather than

moving as a close group around the wheel. (This spacing is caused by differences in the

amount of "green" or "red" reflectance each blue paint contains.) The blues also do not

have a large area of high reflectance in common, as the warm colors get with the

"warm cliff" reflectance curve. There is a similarly large separation between the greens.

In general, the "cool" colors form a natural

spacing of chroma curves, each acting as a different hue in relation to all the other colors:

there is no clustering.

• The curve for dioxazine violet (PV23) is separate from all other paints, showing very

even changes in the chroma of mixtures

across different hues in the color wheel. This verifies the dull and dark visual impact of the

color, and shows the systematic dulling effect it has on the lightness and chroma of mixtures

with every other paint. This is in fact the curve we should see among all the paints, if the

geometry of the traditional color wheel were true.

This graph affirms Leonardo's insight five centuries ago that red, yellow, green and blue

are the artists' primary colors. The red-orange cluster moves as a group, the yellows

as another group, and the blues and greens move independently in a range defined by a

red blue on one side, and a yellow green on the other.

The most important discovery is that the color wheel is biased in several ways as a

representation of color mixing. The chroma curves of different colors do not behave

consistently across different segments of the

color spectrum; warm colors cluster into two groups but cool colors do not; warm colors

move together and cover a wide range of chroma, while cool colors move independently

within a narrower range ... and violet doesn't seem to behave at all as we'd expect.

If we wanted to predict color mixtures with the

standard "primary" color wheel, we would have to use an outward bowing arc, and not a

line, to estimate the hue and chroma of mixtures on the green side of the space. We'd

use an inward bowing arc, and not a line, to estimate mixtures between magenta and blue.

We'd need to use another outward bowing arc to estimate the hue and chroma of mixtures

between magenta and yellow. (We could straighten out one side of the color wheel by

spacing the hues differently, but this only

creates worse problems across other hues.) And, because we depend on the

complementary relationships in the color wheel to define color design, the color wheel is

also flawed as a framework for selecting color harmonies. (Certainly, using the color wheel

in circular "color calculators" is highly questionable.)

All this reaffirms the importance of using the color wheel as a compass for color

improvisation rather than a geometrically precise framework for color calculations. The

many biases within the color wheel are not something we can learn abstractly. They are

part of the complex terrain of color mixing

that we grasp only after taking many journeys through it with many, many paintings.

N E X T : an artist's color wheel

Last revised 01.12.2004 • © 2004 Bruce MacEvoy

an artist's color wheel

An earlier page described

several modern color models, including the

latest CIE color difference and color appearance models, and a later page

explained how the hue circle from any color model can be used to create an artist's

color wheel.

This page presents my own color wheels, the

result of considerable study. My understanding of the problems involved has changed over the

past several years, so I present both the wheel originally published in 1999, and the

version I developed in 2006.

Both wheels show the color appearance

locations of all major watercolor pigments in use today. Both wheels are based on visual

complementary colors. The wheels differ in their chroma scaling of all colors, and in the

spacing and visual complements assigned to blue and violet colors.

Some artists, from force of habit, may prefer a color wheel based on mixing complements. I

try to dissuade you from that route, but if you choose it, I provide the information on

mixing complements you'll need to get started.

Because the visual and mixing location of pigments sometimes differ by a large amount,

this page tries to explain why those differences occur. It turns out they are

caused by the green reflectance in many

paints, and can be summed up in three simple rules.

To make a color wheel, we

have to tackle the problem first encountered with the secondary color wheel: how do we

define complementary colors?

To recap, complementary colors are two

hues with balanced or opposing color

visual vs. mixing complements

color

vision

visual vs. mixing

complements

the artist's color wheel

1999 version

2006 version

tour of the color wheel

why the difference?

making your own

color wheel

characteristics; that's why they're opposite each other on the color wheel. But the way we

define that opposition gives us different results.

In subtractive color mixing, complementary colors are two dyes, paints or inks that can be

mixed in some proportion to create a gray color. This usually means their reflectance

curves combine to make a metameric color or visual equivalent of gray, not the flat

reflectance curve of a true neutral. This approach closely ties complementary colors to

the problem of mixing paints.

In additive color mixing, complementary

colors are the two monochromatic (single wavelength) lights that can be mixed to

produce the perception of white light, or the two surface colors whose reflectance curves

can be combined (with a color top) to produce the same result. This method closely

ties complementary colors to a specific

chromaticity diagram and the problem of mixing lights.

Finally, in color appearance models based

on surface colors (painted color samples, rather than colored lights), complementary

colors are any two colors at opposite ends of a

straight line through the achromatic center of the color model's hue plane, or colors on

opposite sides of a perceptually defined hue circle. This approach closely ties

complementary colors to the actual visual impact of colors, and to our color psychology.

If we compare the results of subtractive paint mixing, additive light mixing and perceptually

defined color models, we find that visual and mixing complements are almost never the

same. The visual complement of ultramarine blue is a yellowish green, but the mixing

complement of ultramarine blue is a dull deep yellow; mixing ultramarine blue and greenish

yellow paints produces a dark bluish green.

The visual complement of phthalo green is close to quinacridone rose, but the mixing

complement of phthalo green is a middle red; mixing phthalo green and quinacridone rose

paints gives a muted dark violet, not a neutral tone. And so on. (These color circle

comparisons clarify the different hue relationships that appear in visual and mixing

color circles.)

So we have to choose from among competing approaches when we build a color wheel. The

easiest way to review these choices is to

compare visual and mixing complements side by side, using the major "cool" pigments as

the basis for comparison. (More extensive information is provided in the section on

mixing complementary paints.) This table is worth careful study!

visual vs. mixing complements

cool key colorwarm visual

complements

warm mixing

complements

Indanthrone Blue PB60

Hansa Yellow Medium PY97 Benzimida Yellow PY151/154 Cadmium Yellow Pale PY37 Copper Azomethine PY117/129

Raw Umber PBr7 Raw Sienna PBr7 Gold Ochre PY43 Benzimida Orange PO62 Hansa Yellow Deep PY65

Ultramarine Violet PV15 [blue shade, M. Graham]

Quinacridone Deep Gold PO49 Yellow Ochre PY43 Raw Sienna PBr7 Chrome Titanate PBr24 Cadmium Yellow Deep PY35

Ultramarine Blue PB29Hansa Yellow Deep PY65 Nickel Azomethine Yellow PY150 Antrapyrimidine Yellow PY108

Raw Umber PBr7 Quinacridone Orange PO48 Benzimida Orange PO62

Cobalt Blue Deep PB72

Raw Umber PBr7 Raw Sienna Quinacridone Orange PO48 Benzimida Orange PO62

Cobalt Blue PB28

Isoindolinone Yellow PY110 Nickel Dioxine Yellow PY153 Cadmium Yellow Deep PY35 Chrome Titanate PBr24 Yellow Ochre PY43 Raw Sienna PBr7 Raw Umber PBr7

Raw Umber PBr7 Benzimida Orange PO62

Prussian Blue PB27 Phthalo Blue RS PB15:1

Venetian [Mars] Red PR101 Quinacridone Gold PO48

Phthalo Blue PB15Quinacridone Gold PO49 Raw Umber PBr7

Venetian [Mars] Red PR101 Cadmium Orange PO20 Perinone Orange PO43

Phthalo Blue GS PB15:3Quinacridone Gold PO49 Gold Ochre PY42

Venetian [Mars] Red PR101 Gold Ochre PY42 Perinone Orange PO43

Raw Umber PBr7

Cerulean Blue PB35 [red shade, M. Graham]

Benzimida Orange PO62 Gold Ochre PY42 Burnt Umber PBr7

Burnt Sienna PBr7 Burnt Umber PBr7

Manganese Blue PB33 Phthalo Cyan PB17 Cadmium Orange

PO20 Burnt Umber PBr7

Cadmium Scarlet PR108

Cerulean Blue PB36 [green shade, Winsor & Newton]

Venetian [Mars] Red PR101

Phthalo Turquoise PB16

Pyrrole Orange PO73 Perinone Orange PO43 Quinacridone Orange PO48 Burnt Sienna PBr7 Burnt Umber PBr7

Perinone Orange PO43 Cadmium Scarlet PR108

Cobalt Turquoise PB36 Cobalt Teal Blue PG50

Quinacridone Red PR209 Quinacridone Pyrrolidone PR N/A Cadmium Red Deep PR108 Perylene Maroon PR179 Indian Red PR101

Pyrrole Orange PO73 Pyrrole Scarlet PR255 Quinacridone Maroon PR206 Cadmium Red PR108 Perylene Maroon PR179 Cadmium Red Deep PR108

Phthalo Green BS PG7

Quinacridone Magenta PR122 Thioindigo Violet PR88

Quinacridone Maroon PR206 Perylene Maroon PR179 Pyrrole Scarlet PR255 Pyrrole Red PR254 Cadmium Red PR108

Viridian PG18

Quinacridone Maroon PR206 Perylene Maroon PR179 Pyrrole Red PR254 Naphthol Scarlet PR188 Naphthol Red PR112 Naphthol Red PR170

Phthalo Green YS PG36 Permanent Green [Deep]

Manganese Violet PV16 Cobalt Violet PV49

Quinacridone Rose PV19 Quinacridone Red PV19 Benzimida Maroon PR171

Hooker's Green Permanent Green [Light]

Manganese Violet PV16

Dioxazine Violet PV23/37

Chromium Oxide Green PG17 Perylene Black PBk31

Cobalt Violet Deep PV14

Dioxazine Violet PV23 Cobalt Violet Deep PV14 Ultramarine Violet RS PV15

Sap Green Phthalo Yellow Green

Dioxazine Violet PV23 Ultramarine Violet RS PV15

Dioxazine Violet PV23

Permanent Green Yellowish Olive Green Cadmium Lemon PY35

Ultramarine Violet BS PV15 [M. Graham]

[none]

Note: Mixing complements depend on the pigments used by a specific brand of watercolor paint. The mixing complements listed here may not apply in oil or acrylic mediums.

Which Complements Are More Useful? Now, there are some artists who claim that

mixing complements are the correct or best

ones to use in a color wheel; Stephen Quiller even calls them "the true complements." So

here is my editorial for using visual complements instead.

The basic problem is insurmountable: it is

impossible to define a consistent color

wheel using mixing complements. (See the section on substance uncertainty for a

full explanation.) You can find some glaring examples in the table. Take venetian red

(PR101): it's an excellent mixing complement for iron (prussian) blue (PB27) and cerulean

blue (PB27)! Or perinone orange (PO43): it neutralizes both phthalo blue (PB15) and

phthalo turquoise (PB16). These blue paints are fairly far apart in hue, which means there

is only a fuzzy connection between paints that

mix to gray and visual complementary hues. You can marvel at this fuzzy relationship in my

mixing complement diagram.

Even worse, phthalo blue is neutralized to a

pure gray by venetian red (a dull scarlet) or by gold ochre (PY42, a dull yellow orange)

but is only neutralized to a near gray by the many saturated scarlet and orange pigments

between venetian red and gold ochre on the color circle! This makes the hue relationship

among mixing complements downright incomprehensible by itself, as both hue and

chroma affect the mixing complement relationship.

Don't take my word for it. Joy Turner Luke, in her notes to the New Munsell Student Color

Set, writes that:

It is impossible to create a subtractive color wheel where every color combined with the

color opposite it on the wheel will mix to gray. This type of color wheel, which is found in

many books for artists, (1) can only be approximate; (2) applies only to complex

subtractive mixture, not to color vision; and (3) precludes understanding many other

things about color.

Impossible to create? I present ample

evidence to support that claim in the section on mixing complementary paints. You can't

make a consistent color wheel based on subtractive color mixing.

The key issue is stated in Luke's second point: a mixing color wheel has little to do with color

vision. There is nothing contradictory or impossible about a visual color wheel. What's

more, the visual color wheel shows us the end, not the means, of artistic design. It

guides our painting decisions by showing us

how to effectively combine the colors we see, not how to mix gray colors from commonly

used paints.

Think about it: the viewer of your painting has no idea how you created a specific color. Was

that gray mixed with two paints, or twenty?

Were the paints orange and blue, or red and turquoise, or violet and green? The color

assembly decisions in paintings disappear, or leave traces that are too complex to interpret.

So why would you base your color design on the mixing relationships no viewer can see?

In contrast, the visual color relationships are inherent in the way we see color, and they

define natural contrast effects such as complementary colored shadows. They are

always right on the surface, in the immediate visual impact of the painting, no matter how

the paints that made the colors were mixed. To control that impact, painters should

understand and use the visual

complementary colors.

The mixing color wheel, at best, shows an artist how to mix gray colors — if he hasn't

figured that out already — and, as we've seen, it can't even do that very well. The visual color

wheel shows us the true color harmonies, the

color harmonies of the eye and mind, and so

unlocks the visual esthetic impact of any color image in every color medium.

With those points in mind, I set out

to make a visual color wheel adapted specifically to the needs of painters and

graphic artists, and drawing on as many reliable sources as I could find. I think this is

one of the best color wheels you will find for making both visual design and paint mixing

decisions.

It is useless to talk about color in the abstract,

because artists must deal with specific colorants made of specific pigments. So my

artist's color wheel represents the masstone color locations of the 90 most commonly used

watercolor pigments, rather than color

categories ("red orange") or clusters of similar pigments.

Paint Measurement. Spectrolino measures

380-730nm in 10nm intervals broken by

diffraction grating with 45°/0° viewing geometry, 10° observer, and neutral filter

over tungsten (A) light source in the apparatus. An equal energy (EE) illuminant

was used in the color models. I used my own spectrophotometric measurements of single

pigment watercolor paints and convenience mixtures.

1999 Version of the color wheel. located them on the CIECAM a

CbC plane, then

modified the hue spacing of these pigments to take into account the spacing of hues in the

Munsell color model, some known problems in the spacing of hue and chroma in

CIECAM (hue dominance and irregularities in the green and violet parts of the hue circle),

and the presence of curved mixing lines around the cool (green) side of the color

circle. However, I kept the visual complementary relationships exactly as

defined in CIECAM.

the artist's color wheel

click here for a full size view in a new

window

click here for a printer friendly (Adobe

Acrobat PDF) version of the artist's color wheel (330K)

To print the color wheel, set page orientation to "landscape" and print to fit an 8.5" x 11" sheet of paper.

Here are the main design features of the

artist's color wheel:

• The pigment markers show the hue and

chroma of pigments as measured in single pigment paints and averaged across all

brands reported in the guide to watercolor pigments. Pigments are indicated by generic

name and color index name; convenience

mixtures of two or more pigments are labeled in italics without color index names.

• Hues directly opposite each other (that can

be connected by a line drawn through the

center of the wheel) are visual complementary colors as defined by the

pigment locations on the CIECAM aCbC

plane. (Note that the CIECAM locations are

reversed left to right, to make the color circle consistent with Munsell and most artist's color

wheels.)

• The spacing of hues around the color wheel

has been altered to expand the range of scarlets and reds and compress the range of

violets and greens. The subtractive "primary" hues are located approximately at the color

wheel points 1, 5 and 9, and the paint equivalents of the additive primary hues (the

paints used by James Clerk Maxwell and Ogden Rood to perform additive color mixing

experiments) are located approximately at points 3, 7 and 11.

• The twelve spokes of the tertiary color wheel are inserted to guide your eye in

finding complements on opposite sides of the wheel. (They do not represent equal hue

spacing in CIECAM or Munsell.)

• The masstone chroma of paints is

approximately indicated by the distance of pigment markers from the center of the wheel.

(Pigments farther from the center are more intense or saturated.) However, I show the

mixing chroma rather than the actual

chroma of the paints to compensate for the distorting effects of hue superimportance

and unequal "primary" triad spacing on the estimation of saturation costs. This was done

by (1) compressing the chroma intervals at higher chroma levels, (2) bending or curving

the chroma curves on the warm side of the wheel closer to the center of the wheel, and

(3) inflating (shifting outward) the actual chroma of many paints. For example, these

corrections place the mixing line between

quinacridone rose (PV19) and hansa yellow (PY97) through quinacridone burnt orange

(PO48), which is approximately the correct chroma of an orange mixture of the two

paints. Without these corrections, the straight line mixture would appear to equal a burnt

sienna (PBr7), which is too dull.

• Straight mixing lines between any two paint

markers can be used to estimate the approximate saturation costs of the paint

mixtures. (Note that it is not possible to create a color wheel where all mixing lines are

straight, and this problem can't be fixed by shifting the location of hues around the color

circle.)

• The artist's color wheel does not show

mixing complementary colors. However, these are exhaustively listed in the page on mixing

complements.

2006 Version of the color wheel.These adjustments mean that the distance between

the colors in the artist's color wheel no longer

equals the perceived difference between colors of the same lightness or value, but this

information can be more accurately judged (at least for small color differences) from the

chart of pigment locations on the CIECAM aCbC plane.

Despite the care taken to make this artist's

color wheel as accurate as possible, and to compensate for differences in paint mixing

behavior, the word approximate is important

to keep in mind. The lightness of a paint or color mixture can significantly affect the

chroma or mixing behavior. Any subtractive color wheel is fundamentally a poor

predictor of paint mixing results, and as we've just seen, no amount of tinkering can

fix it. Treat the wheel as a starting point for your own color judgments with the brands of

paints you prefer to use.

I found that the most effective way to

learn the color wheel was to work through all

the major color categories around the circumference, sampling one or more paints at

each of the major points, and mixing these paints in all possible combinations. This

approach is described in the page on paint wheels.

If you know the hue, lightness and chroma of any paint, you will have a pretty good idea

of how that paint will mix with other paints. So part of the basic knowledge of any painter is

knowing the location of the major pigments in relation to the twelve major points of the color

wheel. Let's take the tour.

1 : LIGHT YELLOW (primary) : This hue is a

tangy, bright yellow, the color of lemons and canaries, which often takes on a distinct

greenish appearance, especially at darker values. It corresponds to the spectral hue at

around 575nm. The visual color wheel locates hansa yellow light (PY3), cadmium lemon

tour of the color wheel

(PY35) and the benzimidazolone yellows (PY151, PY154, or PY175) at the "primary"

yellow point. Artists differ in how much green they prefer in this hue; the Munsell color circle

picks a very lemony yellow as the exemplar. My own preference is for hansa yellow

(PY97) because it is very lightfast, intense, and has a hue that contains (to my eye) no

hint of orange or green. The historical pigment aureolin (PY40, not shown because it is

impermanent) is a slightly cooler and less

intense yellow, while bismuth yellow (PY184) is whiter and therefore less intense than the

usual cadmium lemon. Copper azomethine or green gold (PY117) and nickel titanate

(PY53) are relatively dull light yellows and therefore less suitable as a primary mixing

paint; all have a distinct green or greenish gray color. All yellows at this color point

quickly lose their characteristic yellow appearance as they are darkened or made less

intense, turning rapidly into a dull warm green

and then into a peculiarly lifeless gray. Note that none of these yellows can be used in

neutralizing mixtures with blue violet; they all make dull greens.

2 : DEEP YELLOW (tertiary) : This is the golden color of highway caution signs, school

buses and autumn squash. It corresponds to the spectral hue at around 585nm. The visual

wheel places hansa yellow deep (PY65), cadmium yellow deep (PY35) and nickel

dioxine yellow (PY153) at this location, but many cadmium paints labeled yellow orange

or yellow medium are also close to this hue. (The Munsell Book of Color chooses a color

slightly warmer than cadmium yellow deep for

this hue location.) A less intense but very lovely alternative is quinacridone deep gold

(PO49). This second hue point is interesting for several reasons. Mixing the hue from

yellow and red produces a duller mixture than expected, often duller than a red orange

mixed from the same paints. This is also the yellowest hue that can neutralize mixtures

with blue violet; mixing complements for cool colors really start at this hue point and

continue through purple. Finally, this is the

hue point at which the yellowest earth pigments are located — the many "yellow"

iron oxide pigments (PY42 or PY43, marketed as raw sienna, yellow ochre, mars

yellow or gold ochre). If this hue is made even

less intense, it turns into a grayish or grayish brown hue, typical of raw umber (PBr7). A

handy way to remember the yellow range of the spectrum is to remember that most

"medium" cadmium yellows are about half the distance from cadmium yellow deep to hansa

yellow light, and hansa yellow medium (PY97) is about half the distance from cadmium

medium to hansa yellow light.

3 : RED ORANGE (secondary) : This is an

especially intense and powerful hue, just at the boundary between scarlet and orange

(hues on either side of this hue point). It corresponds to the spectral hue at around

620nm. The best exemplars of this color are

perinone orange (PO43) or pyrrole orange (PO73), although I really like a slightly

warmer cadmium scarlet (PR108) or cadmium red orange (PR108). The less intense

pigments in this color category include the "red" iron oxide pigments (including venetian

red, indian red and light red, all PR101) and the synthetic organic equivalent quinacridone

maroon (PR206; Daniel Smith's quinacridone burnt scarlet and Winsor & Newton's brown

madder). It's also important to familiarize

yourself with the pigments that fall between the deep yellow and red orange color points:

cadmium orange (PO20) and benzimidazolone orange (PO62) are the most intense, while

among the duller but very useful paints are quinacridone gold (PO48) and the extremely

useful burnt sienna (PBr7), a moderately dull, orange iron oxide pigment that is a mixing

keystone in the "warm" color range. Even darker and less intense is burnt umber

(PBr7), which can be used in place of burnt

sienna in any mixture that you want to take to a darker and duller color (although it is oddly

ineffective at mixing true grays with most blue paints). Naphthol scarlet (PR188) and pyrrole

scarlet (PR255) are very intense pigments on the red side of this color point. It's interesting

that artists tend to have a distinctive preference in warm paints: some (Caravaggio,

Turner, Gauguin, Matisse) seem to like red orange focal hues, while others (Van Gogh,

Reubens, Rembrandt) seem to prefer a deep

yellow.

4 : MIDDLE RED (tertiary) : This is close to a "pure" red that leans neither toward orange

nor violet. Its closest monochromatic

counterpart is in the extreme red, around 720nm. The visual color wheel places

quinacridone carmine (PR N/A) or the historical pigment alizarin crimson (PR83, not

shown because it is fugitive) close to this location. Notice that cadmium red medium

(PR108) and pyrrole red (PR254) are close by, and the range from scarlet to deep red is

visually quite small — about the same as the distance between the yellow and green shades

of phthalo green. And there is quite a crowd of

"warm red" pigment alternatives between the red orange and red points on the wheel. These

include the cadmium reds (PR108), naphthol reds (PR112 and PR170), quinacridone reds

(PR209 and PV19), perylene scarlet (PR149), perylene red (PR178), perylene

maroon (PR179). Notice that in the visual color wheel the red and yellow spans of the

spectrum are approximately the same size: deep yellow is the middle boundary between

the two. Most of these reds mix strong blacks

with phthalo green BS (PG7), and strong dark grays with cobalt turquoise or teal blue. I find

it useful to divide the warm colors in two groups — the paints that can or cannot mix a

green color with a greenish blue paint such as phthalo cyan or phthalo blue GS. Yellows up to

cadmium yellow deep can, and reds up to benzimidazolone orange cannot.

5 : MAGENTA (primary) : This is a distinctive bright, bluish red hue that is easy

to recognize once you've seen it, and the best choice among existing pigments for a

"primary" magenta color. It has no spectral counterpart, but is obtained by mixing roughly

equal parts of "red" and "blue violet"

wavelengths. An excellent choice for this point is the Winsor & Newton brand of quinacridone

magenta (PR122); other paints sold under that name tend to be slightly darker and

duller, but also have a bluer hue. Permanent rose (PV19) is a slightly warmer hue; don't be

confused by the fact that this pigment also comes in a noticeably redder shade,

sometimes sold under the name quinacridone red. Quinacridone violet (PV19) is much

darker but with a rich bluish luster when wet.

It's remarkable that the entire color span from middle red to red violet, formerly represented

by a shoddy gang of fugitive organic pigments, has been handsomely replaced by different

shades of a single modern and lightfast

pigment: quinacridone. Manganese (mineral) violet (PV16) could be placed at this color

point, but it is too blue and too dull to make useful mixtures with the warm pigments. (I

don't consider the hues from quinacridone magenta to ultramarine blue, and the

complements from phthalo green YS to cadmium lemon, to be either warm or cool.)

Thioindigo violet (PR88) belongs at this point on the visual wheel; though too dark and dull

to make a suitable "primary" color, it mixes

lovely dark violets, oranges and browns. Some "accomplished" artists continue to use the

fugitive magenta and carmine pigments, including alizarin crimson and rose madder

genuine. But apparently they do so with a furtive conscience: posing as an interested

buyer, I've found that a few don't notify their collectors of the lightfastness issues related to

their choice of paints.

6 : RED VIOLET (tertiary) : A relatively rare

hue encountered most often in certain flowers or gems. It has no spectral counterpart, but is

obtained by mixing "red" and "blue violet" wavelengths. This location can be represented

by either dioxazine violet (PV23) or cobalt

violet deep (blue shade), depending on whether you want a red or blue bias to the

hue. Note that cobalt violet also comes in a redder shade that is lighter valued but similar

to manganese violet. Few artists use these pigments because they have poor tinting

strength, are not especially bright, and are strongly granulating. There is a lack of

effective pigment alternatives for this hue because nearly all natural and synthetic

pigment choices are fugitive; to avoid these

problems many paint brands offer the color as a convenience mixture of a rose or magenta

quinacridone and ultramarine blue. Points 5 through 7 of the wheel are also confusing to

learn because the apparent hue of a paint depends on its lightness and/or chroma:

magenta paints appear to redden with increased chroma, and blue violet paints

appear to shift toward purple. This is especially noticeable in quinacridone violet

(PV19), which has the same

spectrophotometric hue as quinacridone magenta (PR122), but appears distinctly

bluer because the color is darker and less intense. A similar hue difference appears

between indanthrone blue (PB60) and

ultramarine blue (PB29).

7 : BLUE VIOLET (secondary) : Here we enter the blue hues, corresponding to the

spectral hue at around 450nm. Cobalt blue is

the best visual complement for "primary" yellows at point 1 (ultramarine blue actually

matches up visually with a greenish yellow color), but artists are sometimes confused by

the mixing complementary relations, which match up cobalt, phthalo or cyan blue to an

orange or scarlet paint. The compromise is usually to shift all the blues counterclockwise,

so that ultramarine blue aligns with point 7, phthalo blue with point 8, and phthalo cyan

and turquoise with point 9 (the "primary" cyan

spot). The visual wheel identifies cobalt blue (PB28) or a red shade of phthalo blue (PB15)

as the representatives of this hue point, but most color wheels prefer ultramarine blue

(PB29). A beautiful pigment at this point is indanthrone blue (PB60), dark and dull, which

makes a superb substitute for "indigo" convenience mixtures and mixes beautiful

darks with benzimidazolone orange. The nearness of ultramarine blue to a violet color

is revealed by the fact that ultramarine violet

(PV15) is very close by. The mixing complements of blue paints tend to change

inconsistently from one blue to the next, but some good dark mixtures are possible,

especially with the ultramarine blue, the phthalo paints and prussian blue.

8 : MIDDLE BLUE (tertiary) : An unusual hue in nature, as sky blue falls between color

points 8 and 9. It corresponds to the spectral hue at around 480nm, which is exactly the

wavelength of maximum transmission (and therefore the color) of pure water, but most

natural bodies of water contain suspended matter that shifts the color toward green or

brown. The visual wheel puts cerulean blue (PB35) or a green shade of phthalo blue

(PB15:3) approximately at this color point.

Pay special attention to brand variations in color when selecting paints around points 8

and 9 on the color wheel, including cerulean blue (PB35 or PB36) and phthalo blue

(PB15). If you shift the blues counterclockwise (as described under color

point 7), then cobalt blue (PB28) may also work for this color point, especially if a bluish

ultramarine violet is chosen for point 7. Mixing

complements for the blues at point 8 are primarily deep oranges and scarlets, as well as

their dull "earth" palette equivalents.

9 : CYAN (primary) : This is a bright, light

greenish blue, also unmistakable once learned, representing the "primary" cyan in paint

mixing. It corresponds to the spectral hue at around 490nm. For that hue there is one good

pigment choice — Holbein's peacock blue (PB17) — although a very green phthalo blue

(PB15:3) or even the very dark phthalo turquoise (PB16) would also serve well,

depending on your palette requirements. Manganese blue (PB33) is more granular but

almost identical in hue, and many cerulean

blue paints (PB36) are also close to a cyan hue, though less intense and also less

transparent.

10 : BLUE GREEN (tertiary) : This hue, called "sea green" (meer graun) by the

Germans, is peculiarly neglected by most

artists. It corresponds to the spectral hue at around 500nm. The visual color wheel places

dark and dull cobalt turquoise (PB36) and brighter cobalt turquoise light (PG50, one of

my favorite paints) at this location. But most paint companies either do not offer any paint

of this hue, or provide a convenience mixture made from phthalo blue and phthalo green.

There is, in any case, no pigment other than cobalt (or a convenience mixture) that can

match this color. The mixing complements for

this point are also among the visual complementary colors (middle or deep red),

and the fact that red and blue green are such strongly antagonistic colors in color vision

(lying at opposite ends of the r/g opponent contrast) means that many of the neutral

mixtures are especially dark and intense.

11 : GREEN (secondary) : This green

corresponds to the spectral hue at around 540nm. The visual color wheel puts phthalo

green yellow shade (PG36) exactly at this point, and chromatically that has the highest

loading of green (a-) visual stimulation of any available pigment. However, in keeping with

some artists' preference to shift the blue stuff counterclockwise, phthalo green blue shade

(PG7), darker and with higher tinting

strength, is often chosen instead, and it is perhaps a better visual complement to

quinacridone magenta (thioindigo violet is the exact visual complement to phthalo green

yellow shade). Viridian (PG18) is visually identical in hue to phthalo green blue shade,

and Winsor & Newton markets a relatively bright version of cobalt green (cobalt titanate,

PG50) at this hue, as well. But be warned: all the other paints named cobalt green are

weakly tinting or dull colors that few artists other than botanical painters use. (The pros

and cons of these and other green pigments

are dished up in the page on mixing green.)

12 : YELLOW GREEN (tertiary) : To close out the color wheel, there is a long slog of

green and more green until we come back to

cadmium lemon. This yellow green corresponds to the spectral hue at around

565nm. Yellow green is an unpopular color in everything from clothing to cars to home

decor, and there are few pigments available to provide it: chromium oxide green (PG17, the

pigment used to make camouflage paints) is the only lightfast pigment at this color point.

Nearly all the commonly used paints at this color point are actually green convenience

mixtures. The most intense choice is a very

yellow shade of permanent green light (listed as a convenience mixture under PG7), but I

find sap green (listed as a convenience mixture under PG36) is more convenient to

use, and it is also an excellent mixing and visual complement for dioxazine violet. It's

surprising to recognize that the distance on the visual color wheel between phthalocyanine

green yellow shade and cadmium lemon is the same as that between ultramarine blue and

quinacridone magenta, the visual

complements. And I have actually reduced this space somewhat; it's even larger on the

Munsell color circle.

At first reading, this survey of the color wheel seems to cover a confusingly large number of

pigments and colors. The differences between

scarlet and brown, or yellow and ochre paints — what I call the unsaturated color zones

— also complicate color judgments on the "warm" side of the color wheel.

But don't despair. The simple exercise of

mixing paint wheels is a great way to learn

these color variations and the major color differences that result from mixtures of paints

from any two color points. And you will find that painting experience will gradually clarify

and strengthen your grasp of the color wheel, and with it your confidence at navigating the

complexities of color space.

Why does this difference

between mixing and visual complementaries occur? When we look at the differences in the

mixing and visual pairs around the wheel, we

discover a pattern of systematic bias. To make this bias clearer, draw lines connecting the

blue and green pigments with their mixing complements on the warm side of the wheel.

mixing lines between blue and green

pigments and their mixing complementary "warm" pigments

Nothing is precise in subtractive color mixing,

yet it's obvious the lines from the blue pigments (from the blue shade of ultramarine

violet PV15 to cobalt teal blue PG50) all converge on a small area of the wheel located

roughly around the pigment red iron oxide (venetian red, PR101). This is indicated by

the blue circle.

In contrast, the mixing lines for the few green

pigments and convenience mixtures all pass through a small area located near chromium

oxide green (PG17), indicated by the green circle.

why the difference?

The reason for these differences is not hard to find, if we consider the reflectance curves of

the different paints and the differences between additive and subtractive color mixing.

All the "green mixing" warm pigments (that is, the light yellow to yellow orange paints

that will mix a green color with a blue paint) contain significant amounts of "green"

reflectance — even though visually they seem to contain no green color. As the paint

hue shifts from yellow toward red, this "green" reflectance diminishes, but does not

completely disappear until the hue is around a scarlet red.

These "green" reflecting warm pigments are visual complements to paints from cobalt

blue to phthalo cyan, and these colors also contain a significant amount of "green"

reflectance, even though they appear primarily blue. This "green" reflectance increases as the

paint color shifts toward blue green, which

compensates for the loss of "green" reflectance as their visual complements shift

from yellow to scarlet.

When these blues are mixed with their visual complements, there is enough "green"

reflectance common to both paints that the

mixtures appear as various dull greens rather than neutral grays.

To remedy this problem and get a true gray,

we must neutralize this excess "green"

reflectance. We do this by adding the complement of green, magenta. It's exactly as

if we mixed the visual complement paints phthalo cyan and benzimidazolone orange, got

a dull green color, and realized we needed to add a little magenta paint to neutralize this

green toward gray.

So here's the trick: we could also mix the

magenta and orange first, which would result in the same gray when mixed with

phthalo cyan. But the magenta and orange mixture would itself be close to the pyrrole red

that is the mixing complement of phthalo cyan. The difference in hue between the visual

and mixing complements represents this added "red" or "magenta" reflectance, and is

the reason why the convergence point for the

mixing lines is shifted away from the center of

the wheel toward a magenta hue.

For the green to blue green paints that are visual complements to blue violet, purple or

red violet colors, the problem arises from an

excess of "red" and "blue violet" reflectance that magentas and red violets

all have in common. In these cases mixing the visual complements gives a dull blue violet

color. Now we have to choose a mixing complement to neutralize this "purple"

reflectance, and yellow green will do that nicely. It's as if we mixed the visual

complements, for example phthalo green BS and quinacridone magenta, got a dark violet

as a result, and had to add a little yellow

green paint to the mixture to neutralize it back to gray.

This comparison of visual and mixing wheels

leaves us with these three rules for mixing complements:

(1) You can ignore the yellow paints from cadmium lemon up to hansa yellow deep; they

are not effective mixing complements with any cool pigment.

(2) All blues, from ultramarine violet BS to cobalt teal blue, form mixing complements

with paints from hansa yellow deep to middle red, indicated by lines converging on the blue

circle. In general, dull (low chroma) warm pigments, such as quinacridone maroon or raw

umber, are more effective neutralizing paints

than very intense pigments.

(3) All greens, from phthalo green BS to sap green, form mixing complements with paints

from deep red to violet, indicated by lines passing through the green circle; the yellow

greens can all be neutralized with dioxazine

violet.

The simplest way to remember the mixing complementary relationships in the paints you

use is just to memorize the best neutralizing pigment for each blue or green pigment from

the table of mixing complements. The blue

and green circles can help you to find the most likely mixing complements for any cool

mixture, if you can identify the location of the mixture on the artist's color wheel (or the

existing blue paint it most resembles).

With this "complete color wheel," and the explanation of how other

artists have made their own color wheels, you can easily make color wheels of your own.

When you do this, you will keep the information about colors or paints that is

necessary to solve a specific artistic problem (identifying mixing complements; identifying

paints that mix well together), and throw

away the rest.

Your personal color wheel start with the actual selection of paints in your palette. You won't

include as many pigments as the scientific or generalist color wheels I've described on this

and the previous page.

Any artist can make their own color wheel by

following these five steps:

1. Decide on the colors (few or many, and

specific hues) that will be in the palette — this is the overall palette design.

2. Choose a paint for each hue with the chroma and lightness most appropriate for the

total color effect the palette should achieve. (The choice of tonal values determines the

relative lightness of all mixed colors and the value range of the palette as a whole.)

3. Choose either visual or mixing color complements as the basic color geometry

that the wheel will represent.

4. Position the paints around the color wheel

according to their hue or color mixing behavior.

5. Determine the additional information about

the paints (if any) to represent by the concentric placement of the paints inside the

wheel. (In Quiller's wheel, this extra

information is chroma and lightness; in Kosvanec's wheel, it is paint transparency and

staining.)

An artist can bring other considerations to

designing a color wheel than the ones I've shown (the texture of the paints, or their

making your own color wheel

behavior when they are rewetted or charged with clear water).

By now you should realize that there is no

"objective" color wheel, no "best" color

palette. There are many color wheels and palettes, each one suited to a particular artist

or artistic purpose. By working through the steps just described, you can make your own

color wheel.

Art means you do it whatever way makes

sense for you. One of the pleasureful puzzles of painting is the process of continually

rediscovering your personal color wheel, rather than memorizing somebody else's

"perfect" color system.

N E X T : toward a modern color theory

Last revised 08.01.2005 • © 2005 Bruce MacEvoy

toward a modern color theory

This is an editorial page

on topics of color perception, color mixing and "color theory" — the dogmas about color developed by artists rather than scientists.

When Jakob LeBlon in 1725 saluted Newton's Opticks as the source of the color wheel, science has been used to rationalize artistic practice. For artists this has always been an opportunistic relationship: many scientists enjoy art, few artists enjoy science.

The contemporary principles of "color theory" come down to us from two traditions. The artistic tradition was developed by three sources: (1) 18th century printers and academic painters; (2) 19th century art critics; and (3) 20th century Bauhaus artists and their cultural peers.

The scientific tradition includes 18th century natural philosophers and 19th century physicists and physiologists, whose ideas were important; and substantial 20th century research that has been too technical to digest.

The result is an artistic gloss on a simplified, outdated scientific framework. Most of the "color theory" ideas from this tradition are false, misleading, inaccurately explained, or not explained at all. An extraordinary amount of modern color research remains unknown to artists.

The opportunity for artists today is to create a contemporary color theory that reinvents the discussion between color science and artistic practice. This page suggests how that can be done.

First the matter of goals. "Color theory" announces the possibility of guiding the artist through principles of color harmony — the sensually pleasing or symbolically potent combination of colors in a

color harmony & design

colorvision

the research cleansing

words and deeds

artists mix paints, not colors

those pesky"primary" colors

color harmony & design

the dungeon of "color theory"

what color is

institutional failures

artist resistance

teach yourself to see

visual design.

This is a modern concept. Classical painters such as Claude or Poussin were known for their careful color balancing and use of color for symbolic purposes. But their design vocabulary and conceptual grasp of color were limited by the range of available pigments. Before the Industrial Age, institutional or occupational costumes and limited dyes and fabrics made color harmony principally a problem of choosing materials: colored stones, colored gems, colored minerals, colored dyes.

But after c.1780, the proliferation of industrially created colorants allowed a wider and cheaper diffusion of color into wallpapers, ceramics, textiles, printing inks, architectural paints and artists' colors. This awakened the fashion sense that some color combinations were more pleasing or striking than others. This transition appears in the founding texts of "color theory" by Michel-Eugène Chevreul, where the analysis of color in the abstract grew out of the imperative to understand textile manufacturing problems created by brighter synthetic colors and more demanding consumers.

Even in the 19th century, however, color harmony was typically an informal principle. The French painter Eugène Delacroix empirically worked out color designs by painting his mixtures on strips of canvas that he hung on his studio wall for careful study. If theory was wanted, most painters simply used the complementary pairs of the secondary color wheel — in those days defined as red/green, orange/blue, yellow/violet — and these complementaries remained the norm even in the paintings of "scientific" neo-impressionists such as Georges Seurat, who knew from reading Ogden Rood that red was not a visual complement of green and violet was not a complement of yellow. The artistic application of color science was still not very rigorous.

Rigor (or something that was supposed to look like rigor) came in the early 20th century. European artists focused seriously on color harmonies and the (entirely imaginary) analogous relationships between color and music or color and emotions. These studies

were linked to a revived interest in Goethe's color theories and to a mystical or ritualistic emphasis on "primary" colors. Even today, "color theory" clings to the assumptions and aims made explicit during this period.

The figure shows a typical offshoot of this effort: a color harmony interpretation of Goethe's six pointed color star, by the Bauhaus trained Yale University design professor, Josef Albers (1888-1976).

josef albers' "moral" color harmonies (1963)

Albers has reversed Goethe's color star and transformed it into a color triangle by folding the secondary color points inward (to mimic the trichromatic mixing triangle of color science). He then filled the remaining three spaces with mixtures of the "primary" and complementary colors, the primary dominating the mixture. (All "color theory" has this manner of childlike simplicity in the way it manipulates color concepts and color demonstrations.)

The "psychological" interpretation of these color harmonies, presented as bands or sections within the triangle, follows the example set over a century earlier by Goethe's

moralizing color associations ("scarlet is pleasing to impetuous, robust, uneducated

men"). But the new interpretations were developed by the consensus color associations of 20th century European artists and intellectuals.

The most striking aspect of this kind of harmonic diagram is its radical simplemindedness. A comparison of this color triangle either to the natural spectrum or to the sheer variety of painting pigments may open your eyes to the brutal disfigurement that this scheme inflicts on the natural experience of color. The confused status of complementary colors in different color models shows how arbitrary these abstract color systems really are. Brutal, abstract, arbitrary ... like the penal codes of a totalitarian regime.

In fact, rigor in the "color theory" literature consists of stating simplistic rules decisively, then refusing to concede that the rules are arbitrary. "Color theory" is attractive not because it is true, but because it replaces complex experience with simple rules.

In some cases these rules create a predefined symbolic code. They provide a way for an artist to say something that has already been said to an audience that expects to hear it. As such "color theory" is purely conventional, and coercive in the mild sense that it restricts the range of an artist's expression and limits the audience that can interpret it. That is often its goal, because that is the only way to endow color with communicative significance.

The select audience is a particular consumer market segment, social group or social class, and the class dimension of "color theory" comes through clearly in the emphasis on character terms or "color personalities" ascribed to individual colors and color combinations: red is male, green is peaceful, blue is mystical, pastels are modern, taupe is trendy, and so on. The artist first conceives a design goal as a "moral" state — for example,

the dungeon of "color theory"

"this will be a serene room" or "I wish to paint a serious picture" — then uses the theory to identify the appropriate colors or color harmony, and from there proceeds to the selection of colored fabrics or paints. (Colors have even been linked to male or female essences, to times of the day, to geometrical forms [yellow is a triangle], to musical intervals, and so on.) But what about "playful," or "nurturing," or "days of the week," or any other attribute not in the color symbol vocabulary? Those represent design issues that were irrelevant to the viewpoint of the male, technophilic, overintellectualized, mystical, humorless and misguided group of artists who invented the color codes in the first place.

Of course, if the viewer does not recognize this culturally dependent color symbol code, believes in a different code or comes from a different culture, or simply approaches color experientially rather than intellectually, then the symbolic aspects of "color theory" become irrelevant and impotent.

To refute the charge that their color codes might be arbitrary, "color theorists" argued that there are universal physical or psychological reactions to different colors. Colors must have a universal significance because they arouse our physiology or psychology in consistent ways: green calms and red excites, yellow makes cheerful and blue makes introspective. These hypotheses have been extensively tested by academic color research from around 1890 up to the present day; Bauhaus designers even sent out survey questionnaires to measure the collective emotional associations assigned to colors. The net result of this research? Just hundreds of publications to show that consistent physiological effects of color don't exist. (One well established finding: there are beneficial effects from white light exposure in the treatment of SAD or seasonal affective disorder.)

Lacking consistent proof for the physiological or psychological power of color, "color theorists" fell back on the idea that "primary" colors embody transcendental qualities of light or nature or spiritual being. (The tactic here is an old one: lacking empirical proof, fall

back on religion.) Some "color theorists" of the 19th and early 20th centuries linked the "primary" triad to the Holy Trinity. On those imaginary cornerstones rigid geometrical or symbolic models could be rebuilt; and within those models, the "primary" triad acquired a stupefying magical or pseudoreligious symbolism. Once humans get rolling on an allegorical or symbolic system, free of any concern for the facts, there is no end to their ingenuity.

The real problem? "Color theory" then becomes detached completely from the materials of color making or the facts of color vision. Color is an experience, a perceptual phenomenon, yet "color theory" talks about "blue" or "yellow" detached from any material circumstances, as abstractions or absolutes. There is an implicit appeal to the scientific premises of our technological culture, the 19th century expectation that all aspects of human existence could be (ought to be) reduced to simple universal principles: color obeys "laws." In fact, color is not like gravity, for the simple reason that living things are not the same as inanimate objects and neurobiology is completely different from physics. As I've shown elsewhere, "primary" colors are either imaginary or imperfect, they are either "colors" that are invisible (and arbitrary), or they are represented by physical colorants that, in the case of paints, can behave in surprising and erratic ways. It seems to me evident that most of the great painters, the painters I most admire, anyway — Titian, Caravaggio, Velàzquez, Vermeer, J.M.W. Turner, Monet, Degas, J.S. Sargent, John Marin, Fairfield Porter — there is an incredible sensitivity to and masterful handling of the color materials, the paints themselves, and the many amazing effects they can produce on the eye.

A related problem is that "color theory" is careless about controlling hue, lightness and chroma as separate sources of color effects: violet against yellow, or orange against blue, differ significantly in lightness and chroma as well as hue. When each colormaking attribute is tested separately, the same contrast demonstrations show that lightness and chroma have a much stronger contrast impact than hue, which

by itself has a weak effect.

As John Gage points out, the surest antidote to a dogmatic "color theory" is art history. There simply are no consistent color meanings in world art, no consistent methods for handling color materials, no universal optical effects embodied in painting techniques. Several movements in modern painting — for example the Pre-Raphaelites, Cubists and Fauves — used "shocking" or "forbidden" or "wild" color schemes to break out of conventional color codes and use color to say new things. After a brief period of argumentative turmoil, these practices became the new color norms, the new color codes, and color dogma rolled on as complacently as before.

Colors cannot be assigned objective meanings because cultural expectations and experience play a large role in a viewer's response. This is a good thing: it means the symbolic power of color is continually renewing itself, adapting to the range of color experience in a culture at any historical moment. "Color theorists" perversely want to fix this symbolic power once and for all as a universal language of color, a kind of chromatic Esperanto. Their theories (and Esperanto) haven't gained wide support because people much prefer to use the color codes (and color terms) that grow from their culture and social situation. Case in point: most German and French color symbolists claimed that red is a "sensual" or "earthy" color. The Russian Wassily Kandinsky used red as the "spiritual" color. Why? Well, in rural Russia, the "red corner" of devout peasant homes — that is, a corner actually painted bright red — is where religious icons were displayed.

"Color theory" describes color as an external fact with consistent properties, — when all the available evidence about color suggests exactly the opposite: color experience is completely dependent on the physical, visual, artistic and cultural context. Color is not an essence that inspires us directly, like a holy ghost or a jolt of electricity. Abstract color ideas divert attention from the material presence and power of a work of art. Artists paint with paints, not with colors: paint is on

the paper or canvas, color is in a viewer's mind.

A final problem, as explained in the page on tonal value, is that the perception of pattern and form has a powerful effect on apparent colors (and apparent values). Vision continually interprets color as part of three dimensional forms in an illuminated life space. Approaching color through the experience of flat color areas is a simplification useful only to a certain style of painting and crafts manufacture. It hardly represents the full range of our color experience — and that is the problem with "color theory" in general.

Put simply: "color theory" developed through contrasting colored squares may, in the end, only help you to understand ... colored squares.

This project arose from diverse 19th century attempts to anchor the fine arts to scientific principles. Writers from Charles Blanc and Auguste Laugel in the 1860's to Wassily Kandinsky, Paul Klee, Joseph Albers, Ernst Gombrich, Rudolph Arnheim, Richard Gregory, Semir Zeki and John Willats (among many others) in the 20th century have argued that art can be enhanced by scientific knowledge in at least four ways:

1. There are important constancies in the visible world, such as linear perspective, the contrast of light and dark, or the behavior of light. If the artist understands these realities, he can produce more convincing or impactful visual representations.

2. There are fundamental properties of the retinal image, including the opponent perception of colors, optical artifacts, afterimages or visual fusion, that arise from the workings of the eye. If the artist knows what these fundamental properties are, he can use his materials to enhance or simulate them in an artistic image.

3. Two dimensional images of a three dimensional world are ambiguous and complex; vision must rely on basic visual

the research cleansing

cues or strategies of interpretation, such as depth cues or the reliance on edges and textures to define objects, to make sense of what we see. If the artist understands these basic cues or strategies, he can use them creatively to control how viewers will interpret an artistic image.

4. There are universal meanings attached to visual signs that originate in our psychological or biological relationship to the world: a vertical line represents strength and a horizontal line repose; red signifies passion and blue relaxation. If the artist understands these deep visual codes, he can build a universal symbolism into his image.

These topics are usually brought into the art academy, with most of the science left out, through the study of elements of design, principles of composition or the symbolism of art. My aim is to go back to the science in order to clarify the basis of those academic principles, with the expectation that other resources remain undiscovered or unrecognized.

There needs to be a cleansing of art theory and "color theory" by anchoring every aspect in perceptual or cognitive science.

When this cleansing is done then new principles need to be added from practical experience, from psychology, from experimental esthetics.

Principles must be formulated tactically, as tools useful in specific situations, so that they do not encumber the artistic strategies on which styles and innovations are based. We must achieve a vision of art that releases rather than encumbers creativity.

two programs for linking art to vision science

In all aspects of artistic "color theory" there are usually four important questions to get answered:

• The most important is to clarify exactly what is meant by a specific term or concept, or what actually is the goal of an artistic process, or what exactly are the desirable attributes in artistic materials. This is done by surveying the consensus language and common practice of professional artists.

• Then we must explore how these terms, processes or materials relate to the domain of factual and theoretical knowledge in vision science, materials science, business realities, conservation techniques, and so forth. We must anchor the artistic practice in the way things really are, by deferring to science, fact and empirical demonstration.

• We then can use the scientific information as a corrective by which the terms or goals can be expressed more precisely, the goals limited, expanded, redefined, or identified as subjective or cultural and therefore arbitrary (the "meaning" of colors, for example)

New Painting Codes. The outcome of color research should be two: to show how far painting styles represent painting codes, and to identify in natural vision new features for new painting codes.

Gombrich described the invented and conventionalized nature of art. This implies that all art paintings by an artist can be distilled to a system of specific rules applied to the manipulation of specific materials; and the "style" of the artist would be reducible to a minimum or characteristic set of rules common to all.

The analogy here with a game such as chess is exact.

Problem is that this leaves the value of art in its "message". But I think art works by exemplification or showing, and what it shows is simply a group of goals or standards (values) applied to the manipulation of materials. These largely fall into the domains of skill, appeal, symbols and topic. Skill for example is exemplified by accuracy or control both in materials and in the other values; appeal by color or line or gesture, symbol by icons or optical images, and topic by historical themes or decorative motifs.

In this way the research cleansing would lay the foundation for a critical language that would allow description or evaluation of any work of art in terms that would be directly comparable with any other description and with viewer evaluations of the work of art. This could lead both to new and more effective painting styles and more aggressive exploration of existing painting styles.

The fundamental point is to tie words to practice and concepts to guidance in specific process situations.

The difference between talking because it creates an aura of structure and choice and control, and the process of discovery which is difficult and painful.

Every rebellion needs a slogan that announces what matters most. Speaking as an artist to other artists, with quite a bit of color studies behind me, I do have such a

words and deeds

artists mix paints, not colors

slogan: artists mix paints, not colors.

Many times I have emphasized that color effects in the natural world are not detached from material circumstances. I have also hit repeatedly the idea that color can be analyzed or described in the abstract, either as an abstract mental quality or as a quality independent of substances.

The distortions created by color abstraction include the spiritualizing of color and ignoring the ways that colors affect one another in context.

Ignoring the material qualities leads to marketing names and ignoring problems of permanency and lightfastness.

Ignoring the material qualities leads to an insensitivity with color materials and their properties.

Leads to a comparative ranking of media, rather than an understanding of the inherent qualities of media. Leads to ideas of "color copying" rather than context creation.

If you have read this far, you may feel impatience with the many complications in color, color mixing and color wheels. Isn't there some way to make color mixing simple?

Yes, there is. For the past 400 years, the drug of choice to combat those headachy symptoms of color complexity has been the "primary" color scheme. Ah ... what relief! Three paints are all you need to mix any hue! And thanks to intense modern pigments, convincingly too: the "primary" triad palette can be very effective in the hands of a skilled artist such as Jean Grastorf.

The 18th Century and Reification. After much study of the "color theory" literature, I came to a conclusion I hadn't expected and didn't like:

those pesky "primary" colors

all "primary" color ideas taught by modern "color theorists" represent 18th century color mixing ideas.

My objection is not that 18th or 19th century ideas are bad, just that 18th or 19th century ideas about color are wrong, and from that misguided tree have come many misguided apples of misinformation.

Contemporary "color theory" was developed during the century of Newtonian color confusions and became dogma in the 19th century. I critique some of these ideas in my reviews of books by J.W. von Goethe, Michel-Eugène Chevreul, Ogden Rood and Michael Wilcox, and in my comments on Newton's color circle, artist's color circles and the split "primary" palette. But as a summary statement of the misleading concepts, here is the color catechism preached by English architect Charles Hayter (1761-1835):

First — That Yellow, Red and Blue, are entire

colours of themselves, and cannot be produced by mixture of any other colours. ... Secondly,

Yellow, Red and Blue, contain the sole properties of producing all other colours

whatsoever, as to colour [hue]. ... Thirdly —

Because, by mixing proper portions of the Three Primaries together, black is obtained,

providing for every possible degree of shadow. Fourthly — And every practical degree of light

is obtained by diluting any of the colours ... by the mixture of white paint. Fifthly — All

transient or prismatic effects [of light mixtures] can be imitated with the three

Primitive Colours, as permanently considered, but only to the same degree or compensation

as white bears to light. Sixthly — There are no

other materials, in which colour is found, that are possessed of any of the foregoing

perfections. ["A New Practical Treatise On the Three Primitive Colours," 1826]

These pronouncements are a blend of special pleading, false reasoning, and ignorance of the facts. The first point claims that the color yellow in paints is an "entire [pure] colour" of itself, when in fact yellow always consists of both "red" and "green" reflectance. The second point, the "unmixable from other colors" proof of "primary" colors, is only valid

in the limited sense of color as hue; this claim is refuted in the next section. The fifth point uses an obscure evasion ("as permanently considered but only to the same degree or

compensation as white bears to light") to claim that "primary" paint color mixtures duplicate light mixtures, which is simply false. The sixth and first points suggest that Hayter considered color in subtractive color mixtures only, disregarding the color mixtures in light.

Hayter's example invites us to add a seventh "primary" color principle inherited from the 18th and 19th centuries: All "primary" color

dogma is based on false reasoning or false

information. The false reasoning appears in the reification of "primary" colors — the belief that abstractions must be real, and therefore can be used to explain things outside the limited problem they were originally used to answer.

I've explained elsewhere why the concept of "primary" colors is only a useful fiction, and why "primary" colors must be either imaginary or imperfect. A limited number of "primary" colors can be a cost effective method of color production (in video, printing or painting) or a mathematically elegant way to predict additive color mixtures and apparent color matches from an idealized retina. In those situations, as shortcuts or fictions adapted to solve specific problems, "primary" colors are harmless because they are specific solutions to a specific problem.

The flaw in artistic "color theory" is that the reasoning goes in the other direction: the various limited, practical solutions that use "primary" colors have led "color theorists" to leap into the imaginary realm of "pure" color, declare that "primary" colors are real, and use "primary" colors to explain every aspect of color experience. The result is that "primary" colors degenerate into the rigid thinking that is inadequate to describe color facts and too limiting to guide artistic intuitions. In fact, subtractive color mixing can never be precise or geometrically simple and, in the abstract, doesn't even exist!

I put "color theory" and "primary" colors in quotes because "color theory" and

"primary" colors do not signify anything theoretical or primary. The "theory" distorts painting experience more than ignorance does, and the "primary" color explanations distract the painter from learning the quirks of color vision, the peculiarities of actual pigments and paints, and the adventure of exploring color experience without labels or dogmatic ideas.

The Coincidence of "Unmixable" Primaries. One way to dismantle the grip of "primary" color dogma (and double talk) is to examine the claim that the subtractive "primary" colors cannot be mixed from other colors. The usual "color theory" justification for this claim is that the "primaries" are "pure" and cannot be broken down into or mixed from other colors, or as Hayter says, they are "entire colours of themselves." But before we leap to that conclusion, we must recognize that any paint color that can be mixed from two other paint colors must satisfy three conditions (diagram at right):

1. the matching surface color can be produced by wavelengths from a limited band of the spectrum

2. it is possible in theory to produce the necessary chroma in the narrow reflectance band from the subtractive mixture of two overlapping reflectance curves, and

3. two pigments actually exist that come close to the required overlapping reflectance curves.

Point 1 has to do with the fact that subtractive paint mixtures destroy reflectance, so paints cannot create broad bands of high reflectance through mixture. Point 2 stipulates that the desired narrow band of reflectance is not so high or sharply defined that it cannot be produced by subtractive mixture. Point 3 says you can't mix a color if you do not have pigments with the right reflectance curves.

Now, instead of resorting to spiritual or mystical explanations for color behavior, we can ask whether the subtractive "primary" colors satisfy these three conditions.

the three requirementsfor subtractive mixture of

any specific color

Yellow. Let's start with the subtractive "primary" yellow, which is the color that seems unquestionably fundamental. Every painter has had the experience of mixing an intense deep yellow and a bright yellow green only to come up with a dark grayish brown instead of the desired lemon yellow.

In surface colors, we can only produce a saturated yellow color through a very broad, high reflectance across both the red and green parts of the spectrum. There is no such thing as a dark yellow color: the lowered lightness produces a large contrast with the available illumination, and this turns the color to a dull green, tan, brown or gray. There is also no such thing as a yellow surface that reflects only in the yellow wavelengths: its reflectance again would be so low in comparison to the illumination that it would be a grayish brown.

Yellow is fundamentally a light valued color — in fact, it is the lightest valued hue in the color wheel. (The link between the hue and lightness of yellow is a specific example of the effect of the unsaturated color zones, explained above.) But this means yellow fails the first requirement for subtractive mixture: the color cannot be produced by a narrow band of spectral reflectance.

In fact, a yellow hue can be mixed — and very easily — from two other paints, for example from a yellow orange (like benzimida orange, PO62) and a yellow green (like a permanent green light). The green provides reflectance in the "green" and "yellow" sections of the spectrum, with relatively little in "red"; the orange provides reflectance in the "red" and "yellow" but not in the "green" wavelengths. When these hues are subtractively mixed in paints, they cancel each other out everwhere except in the "yellow" wavelengths.

mixing "yellow" from an orange and a green paint

But this mixture doesn't look yellow (in fact it looks sadly close to gray), because the mixture destroys the luminosity of the color and with it, the bright yellow appearance. So even though yellow does satisfy the second and third requirements for subtractive mixture, and yellow in fact can be mixed from other colors, failing the first requirement dooms every subtractive mixture.

It's worth mention that the same problem arises if we try to mix an orange color from "primary" yellow and magenta paints. The perception of orange also depends on high luminosity, and the orange mixture is also typically darker and duller than a true orange, which usually makes it appear to be a brown close to burnt sienna. So why isn't orange also a "primary" color? I think the answer is: because this is inconsistent with the "color theory" preconception that there must be only three "primary" colors.

Magenta. Surprisingly, at first glance it appears that all of the subtractive requirements can be met in a "primary" magenta mixture.

The color magenta remains relatively unchanged across reduced levels of color reflectance, so it can be produced by narrow reflectance in the spectrum. This reflectance is actually split across the two ends of the spectrum, because magenta is an extraspectral hue that does not occur in a prismatic spectrum and can only be produced by the mixture of "violet" and "red" wavelengths. In theory we could mix that kind of reflectance from a blue containing some red reflectance, and a red containing some blue reflectance. And in fact we have two pigments (if not more) that fit those requirements very well: ultramarine blue (PB29) and quinacridone red (PR209).

mixing magenta from a blue violet and a

deep red paint

So it turns out that we can mix magenta from two other paints. But, if we actually make this mixture, as a magenta it looks disappointingly dark and dull. This is because two hidden problems compromise all magenta pigments and mixtures.

The first problem: magenta pigments always stimulate the G cone to a significant degree, making the color relatively dull because all three cones are stimulated at the same time. The problem arises in the eye, in the overlap between the R and G cone sensitivity curves. This is obvious in the reflectance of quinacridone magenta (PR122, shown below), which is probably the most intense pure magenta pigment available in watercolors. Anything that affects a pure magenta pigment will also affect a magenta mixture.

green reflectance in a magenta paint (PR122)

We could try to eliminate this problem by limiting the reflectance to the extreme "red" and "blue violet" ends of the spectrum, where the G cones are least sensitive. But now we run into the second problem: these are also the darkest (least luminous) regions of the spectrum, so the resulting color would appear very dark, and this loss of luminosity would also destroy the color's chroma and mixing power in paints.

These problems are of a completely different kind than the problems that arise in mixing yellow, so the fact that yellow and magenta are both difficult to mix is no proof whatsoever that they share any fundamental, "primary" purity or uniqueness.

Cyan. According to "color theory," cyan should also suffer from the same problems as the

other "primary" colors. Yet those problems just don't seem to arise.

The cyan color can be created by a narrow to broad band of "blue" and "green" reflectance, and this reflectance matches the overlap between blue and green pigments. And in the mixing experiments designed to test the color wheel, I found that there is no abrupt change in chroma or lightness of blue green mixtures around the cyan (PB15) point on the color wheel, in the same way there is a loss of luminosity around yellow or a loss of chroma around magenta: the subtractive color mixing antagonism is simply not an issue.

In addition, blue green is near the center of the visible spectrum, so (unlike blue violet or deep red) blue and green pigments have the potential to be relatively luminous. But in fact there is a problem with available cyan pigments, which are rather dark valued (like phthalocyanine cyan, PB17), or reflect a substantial amount of "red" light (like cerulean blue, PB35).

The culprit may be limitations in contemporary chemistry or constraints in the atomic basis of color. In any case, we can mix a mid valued cyan from two other paints: cobalt teal blue (PG50) and phthalocyanine blue GS (PB15:3) . If more intense, lighter valued pigments are ever developed in the turquoise and middle blue parts of the color space, even brighter cyan mixtures will be possible.

"Primary" White (and Black?). Cannot get full range of color without a source of white. Example, mixing paints in a bowl.

White is always there, but in the interests of theory it is swept under the rug by assigning it to the background or, quaintly, to "the light shining through the pigment like a stained glass window."

"Primary" Orange, Violet and Green. The final problem is that many other pigments exist that cannot be mixed from other pigments (colors). For example, in watercolors, isoindolinone yellow deep, pyrrole orange, pyrrole red, dioxazine violet, ultramarine blue, phthalo blue, and phthalo green are all more saturated than any mixture

of two other pigments to a matching hue and lightness. This is especially obvious if you limit your matching mixtures to combinations of the three subtractive "primary" colors — try it yourself and see!

The same problem appears in all color media. For example, new color television technology uses specialized software to adapt the standard three phosphor gamut to include a fourth, blue green "primary". The result is an obvious and desirable increase in the apparent quality of the color picture. Yet no one has claimed cyan as a fourth additive "primary" color.

Conclusion. I've just demonstrated that the reason "primary" colors are unmixable has nothing to do with their function as "primary" colors in subtractive color mixing. "Primary" colors work in subtractive color mixing because they all stimulate two cones but not the third. Any problems in mixing the colors from other paints are irrelevant to this double stimulation requirement. Several pigments produce colors that are unmixable from any other known pigments, but this does not make them "primary" colors either.

Mixture is inherently impossible for yellow because our visual system ties its hue to its luminosity, and luminosity is destroyed by darkening subtractive mixtures; is disappointing for magenta because of obscure problems with G cone stimulation and darkness at the spectrum ends; and is technologically limited for cyan by the low chroma of available blue and green pigments. Three different "unmixable" colors, three completely different color mixing explanations.

The relationship between the mixing power of "primary" colors, and the fact that they cannot be mixed from other colors, is purely coincidental. And this coincidental "fact" only applies to one "primary" color, and was falsely asserted as true for the other two.

What have we learned from this examination of "primary" colors? That reasoning from coincidences and false assertions compromise the most basic concepts of 18th and 19th century "color theory".

We have reached the point where the story of color branches into several different topical areas discussed in the following several pages.

It is worthwhile at this point to summarize what we already know about color, and anticipate other issues to come, in order to contrast the actual dynamics of color with the common misunderstandings that artists have about it.

what color is

two color explanations available to artists

The 18th century explanation was relatively straightforward: there were three "primary" colors of light, which in their pure form appear as the colors yellow (Y), red (R) and blue (B). In vision these three different colors of light enter the eye in different proportions, where they affect the three types of color receptors adapted to them. The combined responses of these receptors "mix" the three "primary" colors in exactly the same way as paints mix.

The difference between additive and

subtractive color mixing was not clearly understood, so the importance of evaluating the illumination color and intensity separate from the surface color was generally ignored. Unusual color effects, such as complementary colored shadows and adaptation to strongly colored light, were all swept under the vague notion that the eye "strives for balance" or "seeks harmony" in its color relations. This mixed and adjusted sensation is sent directly to the small part of the "sensorium" or conscious experience where color perceptions appear; and this results in the color experience.

Under the cover of a few cosmetic changes, such as substition of the visual "primary" G for the subtractive "primary" Y, this is essentially the same "color theory" taught in most art schools today and believed by most artists. Art has made no significant advance in its understanding of color since the 18th century.

The modern color explanation is more complex, but this complexity is still less that what is required. The difference between additive and subtractive color mixture is clearly understood, and the fact that additive mixture is generally the same across all types of light, while subtractive mixture varies considerably depending on the type of substances that are mixed.

In the perception of surface colors, the illumination and surface spectra combine subtractively, which means both must be measured in order to understand the actual wavelengths of light reflected to the eye. The luminance level is important, especially at extremely low or high levels, as are the colors of the areas surrounding the surface color. From these outputs the visual system performs several transformations of the color information, first translating the three "primaries" into the four unique hues (plus a white/black or luminance channel), then, at some late stage, into the three colormaking attributes. This minimum of information, already discussed in previous pages, allows a satisfactory prediction of how the retinal light receptors will produce a color experience given the available illumination and background color.

However, during these transformations many other processes, discussed later, also significantly affect color appearance. Most important are luminance adaptation, which extends from the iris to the higher levels of the brain, and chromatic adaptation, which extends from the retina to the brain. The color information is also adjusted further to weave a cohesive image of the world. These adjustments include simultaneous contrast, visual fusion, edge sharpening, area filling or visual completion, the perceived spatial relations and illuminant direction of the surfaces in view, memory color (beliefs as to the color the surface should be), conventional labels attached to color experience, and so on. These cognitive or judgmental activities involve most of the brain, and all must be included in any explanation of color experience.

The situation can be summarized this way. In the 18th century (and among many artists today), "color" is something transmitted more or less directly from surfaces to the eye and from the eye to the brain, thanks to the cohesive linkage provided by three "primary" colors that remain constant throughout the whole process. This process can be reversed — a color from the brain through the eye to a page, via a "primary" color mixture of paints — which means that colors can be "copied" from nature into paintings.

The modern view is something different. Color is an experience that is profoundly affected by many dimensions of the physical world and by receptor and cognitive processes. Nowhere, at any step of the process, do absolute or unchanging "primary" colors enter into the explanation. This makes the "copying" of colors from nature into a painting implausible or impossible, and makes the creation of a painting highly dependent on the specific materials used to create color and the specific color relationships in the painting itself.

Although it is a more complex explanation, I hope to show you that the modern understanding of color has two enormous benefits. It clarifies the actual problems involved in the skill of painting, and it helps direct the painter to the best solution to those problems.

Failure of art schools to teach the appropriate.

Programs in lightfastness testing.

Empirical demonstrations of color effects.

Lack of historical awareness.

Partnership with campus perceptual and cognitive psychologists.

Over the past decade of developing and posting these pages on color vision, I'd had my share of emails from artists, scientists, curators, and philosophers. Weaving through the diversity of opinion on facts and their interpretation has been a consistent subtext: that a modern color theory is unnecessary.

This position is usually expressed in three ways. Probably the most frequent position is simple ignorance, indifference or laziness. These slackers paint what they see and see what they paint; whatever they mix is fine for what they do, and if the design or color is bad they just throw the painting away. Color theory is something like a tax code or market regulation that just gets in the way of their business, or one of those beach warning signs about tides and rocks that only get in the way of their summer fun. If they can work around it, or swim past it, they do so.

Slackers include many very talented and productive artists, and for them the fault is not learning color theory but not translating their skill into advice that can be passed on to others. When color theory confirms their practice, this proves that it is irrelevant; when color theory contradicts their practice, this proves that it is incorrect. Grounds, either way, to ignore it.

This is not a personal failing but an occupational trait. Artists are craftsmen with materials, and if they experiment with

institutional failures

artist resistance

materials they do it to solve a specific process problem, not to derive a general principle. They are not didacts or theorists, and putting their process into words and teaching it to others would be a huge diversion from their painting practice. And it is not something they can do well, if at all.

This is especially true of art school instructors, which brings me to the second category of reactionaries: the hacks. Hacks have incorporated the dogma taught to them by their teachers and pass it along unchanged to their students. The geneology here, generation to generation, goes all the way back to the 18th century.

Hacks have learned that color is a certain domain defined by explicit principles, and the task of the student is to learn those principles. "Primary" colors, color wheels, complementary contrasts, a whiff of Goethe, a heavy dose of Bauhaus, a little notan and lots of "color meaning" — the hack syllabus is immediately recognizable.

Finally, there is the fringe of individuals whom I call the whack jobs. It is a cultural fact that color attracts a certain kind of theoretical, abstracting mind not much different from conspiracy buffs and religious fanatics. They have their all explaining, all encompassing and all reductive view of things and no facts or practical alternatives will get in their way.

For many of these color theory enthusiasts, the basic equation is extremely commonplace: talking is easier than painting. Whether they are privately reading about color rather than painting, or posting color theory screeds rather than painting, or conducting arcane color mixing experiments rather than painting, they are doing something that is not painting.

For these folks there is a very simple question: how does this discussion relate to a specific painting problem? Many are brought up short to realize, well, they don't have a specific painting problem. And those that do are led to talk about color in practical, contextual terms, rather than to debate generalizations that treat color as an abstraction.

A few are passionate defenders of their individual faction of color theory, and are eager to ignite a debate around it. I've found the best recourse is simply not to engage.

I have to admit that my typology is rather like George Carlin's classification of people into stupid, full of shit or fucking nuts. And it was only by using Carlin's filter on my own color studies that I came to put much of it in perspective.

I cannot by any stretch be called a slacker, but I have certainly fallen into the camp of hacks and whack jobs. As someone who recycled scientific ideas about color without really understanding them or without clearly understanding how they apply to artistic problems, I have been a hack. And as someone who felt personally empowered to displace conventional "color theory" with my own I have certainly resembled, if not become, a whack job.

I think my salvation has been my persistent efforts to paint better, and to understand why painting progress occurred. And this, it seems to me, has to be the touchstone of a modern color theory: all students should prosper with it.

"Color theory" is the oddest mixture of confused and imprecise thinking I have ever come across. Sorting it all out has been huge labor of love and indignation.

Some of that confusion has been my own. I realized how frequently I use color terms or color concepts in a kind of trance or dream, seeing the concepts without actually grasping them.

In many cases, I adopted that confusion from the sources I consulted. Academic studies recognize the unusual nature of the unsaturated color zones, and some have even tested whether brown, maroon or pink are "fundamental colors" in the color space in the way red, green, yellow and blue are. (Apparently they are not.) But none seem to have pointed to the peculiar "sideways"

teach yourself to see

saturation coding of reflected colors as the fundamental qualitative difference between warm vs. cool colors. The eye is not a heat receptor: warm colors are not "warm like fire" as many "color theorists" will tell you — but because they are "brimming with light"!

Artists have been remarkably perceptive about color. Leonardo da Vinci identified the four unique hues over four centuries before the scientist Ewald Hering did. And long before artists had the terminology to talk about chroma in colors or value scales, they controlled these effects through the technique of grisaille underpainting — glazing transparent colors over a background of light and dark gray, essentially mixing the colors with gray or near black. Artists weren't interested in talking about color, but in developing practical techniques to control color effects. Artists have learned about color through experience and quite a lot of experimentation.

This is the heart of my strong distaste for "color theory" — it replaces color experience with color talk, and inhibits color experimentation by teaching simplistic schoolroom "color facts." Artists are experimentalists with materials and ideas; they use colors the way engineers use plastics, or scientists use mathematics — to realize whatever they can imagine.

Explanations of color should, I believe, stick close to the methods used to explore color, so that explanation leads directly back to exploration. My often tedious explanations of color phenomena are intended to make this link explicit. My view is that art is fundamentally a kind of meditative or physical practice in which you teach yourself to see. I have attempted to describe what I feel are the psychological consequences of artistic practice, but the means to those ends are always personal exploration — endless exploration.

The good news is that the color learning tools available to artists today have never been more powerful: computer graphics programs, spectrophotometers, digital cameras, process color manuals, color scanners, digital art reproductions, intense

pigments, spreadsheet programs to plot and graph color relationships. It's intriguing that most art departments are eager to encourage "digital media" as an art from, but neglect it as a tool for artistic training and exploration. Color scientists are more frequently using computer color monitors to study color vision — artists can and should do the same.

I've demonstrated all these tools on this site, to teach you methods of exploration and the confidence to trust in your own curiosity. I also recommend color theory books that describe other tools — "color tops" and exercises with colored paper — useful to color learning.

Personal experimentation is the only way to break out of the circular explanations of today's color theory. It's the only proven doorway to a genuine understanding of color. And this experience is universal, the process by which artists outgrow "color theory" toward an intuitive understanding of color effects.

That journey is the spirit of art. How wonderful to be human! How miraculous to see! What ripping fun to paint!

Last revised 08.01.2005 • © 2005 Bruce MacEvoy