Light and ColorCSC 292:Computer GraphicsRandal C. Nelson

Color Perception and Representation� Complex subject.� Involves Physics, Psychophysics, Physiology,Psychology, Art, etc.� Color Perception depends on properties ofobject, light, surroundings, and humanvisual system.� Hard to predict what color a person will\see"

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Achromatic Light� Black and white TV.� Only concerned with quantity of light.� Terms intensity and luminance -Physically de�ned.� Term brightness - perceived intensity,subjectively de�ned.� Deal with intensities on a 0-1 scale.

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Selecting Intensities� If we have (say) 256 intensities for a CRT,what should they be?� Not 128 from 0 to 0.1, and 128 from .9 to1.0...� Linear might seem a good idea but...� Perceptual brightness is much closer to alogarithmic process (step from .10 to .11seems the same as step from .50 to .55.� Steps should be placed logarithmically ininterval from lowest attainable intensity I0,to 1.0.

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� For example, 4 steps between 1/8 and 1would be 1/8, 1/4, 1/2, and 1.� In general I0 = I0; I1 = rI0; i2 = r2I0:::,where r = (1=I0)1=n.� Note critical dependence on I0. Lowestintensity is never zero. Typical values forCRTs are 1/200 up to 1/40.� Ratio between highest and lowest intensitiesfor a device is known as the dynamic range.

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Gamma Correction� Once we know the desired intensities,displaying them is a bit tricky, andrecording them on �lm even trickier.� This is because CRT intensity is related tobeam current N by a relationship of theform I = kN for constants k and .� Values sent to the CRT must thus begamma corrected, unless the display hasgamma correction hardware.� If logarithmic and gamma correction arenot done, then steps at the darker end ofthe range are much more noticeable thansteps at the bright end.

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Number of Steps� Total dynamic range of the eye is on theorder of 107 (!) with a number of adaptivemechanisms included (e.g. pupil dilation,slow dark adaptation etc.)� The human eye cannot distinguish valuesthat di�er by less than about 1%.�We can use this to determine the number ofintensities needed to cover a given dynamicrange.

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� The formula is:r = 1:01 = (1=I0)1=n ) n = log1:01(1=I0)Medium Dynamic nRangeCRT 50 - 200 400-530prints 100 465slides 1000 700newsprint 10 234� Blurring reduces n for print media. 64 canbe taken as a minimum for good results.

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Halftone Approximation�Many devices print only in black and white.� E�ect of gray can be obtained by usingspatial integration properties of the eye.� In print media, an array of variable sizeddots is used. This is called halftoning.� Spacing varies from 60 - 200 dots per inch.� In array output devices, gray tones areproduced by dithering.

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� One way is to use n� n subpatterns toprovide n2 + 1 intensity levels.� Tradeo� between spatial resolution andintensity resolution.� Patterns can be speci�ed by a dithermatrix, e.g. 26666666664 6 8 41 0 35 2 737777777775� To display intensity I we turn on all pixelsless than I .

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Clustered Dithers� If output device is poor at isolated pixels(e.g. laser printers) it may be necessary tocluster dots. Known as a clustered dotordered dither.� Patterns must be carefully designed not tointroduce artifacts{ Avoid linear patterns.{ Grow from center.{ Produce a growth sequence(automatically done with matrixrepresentation).� To produce equivalent of 150 dpi printedhalf-toning thus requires 8� 8 or 10� 10masks, and a pixel resolution of 1200 to1500 dpi.�We can dither with more than 2 gray levelsas well (e.g. 4). 10

Dispersed Dithers� On CRTs and some other devices, singlepixels work perfectly well.� On these we can use dispersed dot ordereddither.�Many possible patterns. Try to design toreduce texture artifacts.� Quite a di�cult problem.� Random is very bad (hence order).� Perfect order produces obvious patterns atsome gray levels.

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Other Issues� If we do not have extra pixels available, wecan still use these techniques, essentially bytiling image with dither matrix andapplying comparison rule at each pixel.� This allows the use of large, carefullydesigned dither matrices (e.g. blue-noisetechniques).� Another technique is known as errordi�usion.� Di�erence between displayed value anddesired value is passed to neighboring pixels(e.g. 7/16 E, 3/16 SW, 5/16 S, and 1/16SE).� Small images displayed on large windowsmay be interpolated to avoid blockyappearance.

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COLOR� Discussions of color perception Usually usethe terms hue, saturation, and lightness.� Subjective terms, not originally de�nedtechnically.{ Hue distinguishes shades such as red,green, blue, etc.{ Saturation refers to distance from grayof equal intensity (red is saturated, pinkis unsaturated).{ Lightness refers to total amount of lightor brightness.

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� Need a way of specifying and measuringcolors.� For re ected light, we can compare againsta set of \standard" color chips, organizedby hue, saturation and value (lightness), instandard lighting.� The Munsell system is one such standardset.

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Psychophysics� Chip-matching is somewhat subjective -depends on lighting, surrounds, etc.�More quantitative approaches are obtainedin a branch of psychophysics known ascolorimetry.� Any light signal can be described by acurve, the spectral distribution, graphingthe amount of energy present at eachwavelength in the visible spectrum(approximately 400 - 700 nm).� Describing such a curve requires many(in�nitely many) numbers.

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� It turns out that the visual impressionproduced by any spectral distribution canbe described by just three numbers.� This is due to the fact that color perceptionarises from the di�erential responses ofthree types of cone cells in the retina, eachwith a di�erent spectral response curve.� Peaks: \blue" at 440 nm, \green" at 545nm and \red" at 580 nm.�Many di�erent spectral distributions mustthus map to identical perceptual colors.� Distributions that map to the sameperception, as determined by colormatching experiments, are called metamers

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Color Matching� Basic experimental protocol is side-by-sidecolor matching experiments: Subject isshown two distributions, and asked whetherthey appear to be the same color.� Results are consistent within individuals: Iftwo distributions look the same now, theylook the same in later experiments.� Results are largely consistent betweenindividuals: Distributions that look thesame to one person, look the same to others(with the exception of rare people withanomalous color perception).� Results are not consistent between peopleand other animals: Certain spectra that aredistinguishable by humans are notdistinguishable by some animals, and viceversa.

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Color Speci�cation Systems� There are several methods of assigningthree numbers to specify colors.� The �rst attempts to formalize the oldartists' hue, saturation, and lightnessscheme.� Based on the observation that any spectraldistribution can be matched by acombination of white light and a spike of asingle wavelength. (Except purples, whichneed a red spike and a blue spike.)

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� The three terms are:{ Dominant wavelength, corresponding tonotion of hue. Equal to the wavelength ofthe added spike.{ Excitation purity, corresponding to thenotion of saturation. Equal to the ratioof the energy in the spike to the totalenergy.{ Luminance corresponding to the notionof brightness. Equal to the total energyin the sample, sometimes normalized bythe energy of a bright white standard.

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Tristimulus Theory� The second method is known as thetristimulus theory, and is based on theobservation that many colors can be exactlymatched by a mixture of threemonochromatic primaries.� Primaries are de�ned as the blue, green,and red lines at 438.1 nm, 546.1 nm, and700 nm respectively.� By performing a series of color matchingexperiments on monochromatic colors, threecurves called color matching functions isobtained showing the proportions of eachprimary required to match themonochromatic line.

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� The proportions required for mixed spectracan then be obtained by integrating theproduct of the spectral curve with thecorresponding color matching function.� Only drawback is that while most colors arematchable, some of the monochromaticcolors in the blue-green part of the spectrumrequire negative amounts of the redprimary. (Measured by adding red to thesample side in the matching experiment).

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The CIE System� A third method, the CIE Chromaticitysystem de�ned three primaries X, Y, and Zto replace the red, green and blue primaries.� All monochromatic colors, and hence allperceptible colors, could be produced withpositive combinations of these threeprimaries.� Spectra of the primaries themselves containnegative amounts of some wavelengths, andthus these primaries are \imaginary" insome sense.� A useful standard, nevertheless, since theperceptual representation for any spectraldistribution can be found by integrating theproduct of the spectrum and the colormatching functions, just as before.

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� Normalizing by dividing X, Y, and Z by (X+ Y + Z) to obtain x, y, and z gives arepresentation that depends only on hueand saturation, and can be given byproviding only two of the coordinates (e.g.x and y).� Plotting the monochromatic curve in x andy gives a chromaticity diagram that isuseful for illustrating color mixingproperties.� All perceptual colors lie within the curve� Any hue that can be obtained by mixingtwo colors lies on the line between them.� Any hue that can be obtained by mixingthree colors lies inside the triangle de�nedby them (and more generally in the convexhull).� Useful for determining how much of theperceptual range can be covered by certainsets of primaries. 23