JOURNAL OF THE OPTICAL SOCIETY OF AMERICA

Some Quantitative Aspects of an Opponent-Colors Theory. II. Brightness,Saturation, and Hue in Normal and Dichromatic Vision

LEO M. HURVICH AND DOROTHEA JAMESONColor Technology Division, Eastman Kodak Comnpany, Rochester, New York

(Received January 21, 1955)

A quantitative model for an opponent-colors theory of vision is presented that is based on the CIE colormixture data for the standard observer. The model is used to account for spectral brightness, saturation,and hue and some of their associated psychophysical functions in both normal and dichromatic vision.Special attention is given to an account of the Bezold-Brficke hue shift, and to changes in saturation andwavelength discrimination with changes in stimulus luminance.

I T has been shown that the spectral saturation func-1 tion can be predicted quantitatively on the basis ofindependently measured chromatic response and spec-tral luminosity functions.1 The agreement betweentheoretical prediction and experimental result has ledto the development of a quantitative theoretical modelfor the Hering opponent-colors theory, and the presentpaper is concerned with various aspects of this theo-retical model and their relations to other psychophysicaldata.

Since the chromatic valence curves measured for twoobservers show a strong similarity to functions derivedby Judd2 from the average color mixture values for theCIE standard observer, the latter data were used forthe present quantification. The transformation equa-tions used to convert the CIE tristimulus values X, Y,Z to the chromatic responses of an opponent-colorstheory are the same as those used by Judd:

y-b=0.4Y-0.4Z,r-g= L.OX- 1.OY.

The spectral distributions of these responses are givenin Fig. 1.

The chromatic responses (y-b and r-g) do notrepresent the total initial responses of the whole visualapparatus to the stimulus light. Rather, in the opponent-colors theory, they are assumed to result from differencesin excitation of opponent visual processes that areexcited, in turn, by the action of light on retinal photo-sensitive materials. The chromatic response functionsper se are not fixed in form for all states of chromaticadaptation. The shift of the so-called pure hues in thespectrum with changes in adaptation is the mostobvious illustration of this point.' That is, if the wave-length for pure yellow for a neutral state of adaptationis assumed to be, say, 578 mit, then r= g= at 578 my.(See Fig. 1.) For a red desensitized state of adaptation,however, the pure yellow hue will occur at a wavelength

1 D. Jameson and L. M. Hurvich, J. Opt. Soc. Am. 45, 546(1955).

2 D. B. Judd, Ilandbook of Experb)elal Psychology (edited byS. S. Stevens) (John Wiley and Sons, Inc., New York, 1951),pp. 811-867.

3 A. v. Tschermak, Handb. Norm. Path. Physiol. 12, 295 (1929),p.342 ff.

longer than 578 myu, and for the latter wavelength nowr<g5=O indicating that the red and green responsefunctions have undergone a change in form. Nor doesthe invariance of metameric color equations requirethat the forms of the chromatic response curves remaininvariant with changes in adaptation. This is truebecause these curves are the result of differences inlight absorption or excitation in receptor substanceswhose absorption or excitation curves do remain thesame in form but differ only in magnitude for differentadapted states. Consequently, in addition to thechromatic response functions, any quantification of anopponent-colors theory requires a postulated set ofinvariant spectral distribution functions for the photo-sensitive materials of the retina or what Hering calledthe retinal "Empfangstoffe." 4 A transformation of theCIE color mixture data was therefore carried out toprovide the excitation curves of the retinal Empfang-stoffe or light sensitive substances.

This transformation must meet a number of require-ments. The excitation curves must provide a basis forthe chromatic response curves already defined, that is,simple combinations of these receptor functions mustyield chromatic response curves of the forms

Yx-bx= 0.4 7x-0. 4 2x,rx-g = L.OXx-1 .OyX,

and they must predict rather large changes in thechromatic responses with changes in chromatic adapta-tion. The excitation curves must also provide a basisfor the achromatic and luminosity aspects of thesensations, and predict rather small changes in lumi-nosity with changes in chromatic adaptation. The basicassumptions of the theoretical model that yielded themost satisfactory transformations are as follows.

The y-bx response curve results from excitation ofopponent yellow and blue processes in the visual systemthat are initiated by the photochemical absorption oflight in two substances of different spectral properties,a "Y" substance and a "B" substance. The rx-gxresponse curve similarly results from excitation ofopponent red and green processes in the visual system

4 E. Hering, Grundzige der Lelhre vom Liclhtsinn (Julius Springer,Berlin, 1920), p. 112 f.

602

VOLUME 45, NUMBER 8 AUGUST, 1955

OPPONENT-COLORS THEORY. II

that are initiated by photochemical absorption of lightin two substances of different spectral properties, an"R" substance and a "G" substance. The excitationsin the B, G, Y, and R substances (decompositionreactions) combine in a specified way to activate awhite process in the visual system, and the activitiesinvolved in the re-formation of these four substances(B, G, Y, and R) are also combined in a specific wayto activate an opponent, black process. The white-black response (w-bk) is, like the chromatic responses,assumed to represent the residual of excitations, in thiscase in the opponent white and black processes. Thisachromatic response is assumed to have the same formas the spectral luminosity function, and to be the basiccorrelate of the achromatic aspects of the sensation,i.e., brightness and whiteness (grayness, or blackness).

A set of transformation equations that satisfies theaforementioned requirements is:

Bx= 13.0682gx+0. 267 2 2x, (1)

Gx -0. 6 7 36xx+ 14 .0018x+0.0040x, (2)

Ix= -0.0039xx+13.4680x-0.13272x, (3)

Rx=0.3329xx+1 3 .0012yx-O.OOllx, (4)

where ,x, g, and 2x are the CIE tristimulus values foran equal energy spectrum. These curves are shown inFig. 2. In view of the recognized inadequacy of the CIEvalues (particularly the gx tristimulus value) for theshort-wave spectral region, the transformations havebeen worked out for the spectral wavelengths from440 my to 700 mhz, and the region between 400 and 440m/u has not been evaluated.

The chromatic and achromatic response curves re-sulting from excitations of the B, G, Y, and R receiving

0.75

0.50

W

-0

p0C.)

+0.25

0.00

0.25

0.50

0.75

400 500 600WAVELENGTH-nW

FIG. 1. Chromatic response functions forthe CIE standard observer.

substances can be expressed as:

yx-bx =l( Yx-Bx),

rx-gx= k2 (Rx-Gx),

wx- bkx = k3 (0.5Bx+0.5Gx+ 1.0 Yx+ 1.0Rx)- k4 (0.5Bx+0.5Gx+ 1.0 Yx+ 1.ORx) .

In terms of the CIE tristimulus values,

wx- bkx= k5gx.

(5)

(6)

(7)

(8)

While transformation to four receptor substances isconsistent with the simplest conception for the arousalof the chromatic responses, there is no theoretical re-quirement that these substances be four in number.A mathematically equivalent system that agrees aswell with the phenomena to be discussed in the followingdevelopment can be based on the following alternativeset of transformation equations:

ax= 6 .534 19x+0.133 6 2x,

Ax= -0.3368zx+ 7 .0009gx+0.0020 2x,

-yx= 0.3329.x+ 6 .4 67 1lx-0.1347 2x.

(9)

(10)

(11)

The curves resulting from this transformation aregiven in Fig. 3.

In this case the expressions for the visual responsefunctions would be:

yx-bx= kl(ix+,yx-2ax),

rx-gx= k2(ax+,yx- 21x),

(12)

(13)

wx- bkx= k 3(ax+0x+Yx) - k4(ax+x+yx). (14)

The mathematical considerations permitting the ac-curate representation of trichromatic mixture data bytransformations to either three or four excitation curvesare treated in detail by Schrodinger, 5 and transforma-

0

I: 10

wO1

15.- .

400 500 600 700WAVELENGTH - mu

700 FIG. 2. Spectral distribution curves for four receptor substances.

5 E. Schrodinger, Sitzber. Akad. Wiss, Wien. th.-naturw,Kasse, 134, 471 (1925).

603August 1955

L. M. HURVICH AND D. JAMESON

o I

I-~ ~ ~~~WVLNT I a

5.0

-Jw

2.5

a-

0.0 400 50600 700

WAVELENGTH -mF

FIG. 3. Spectral distribution curves for three receptor substances.

tions to a four-dimensional system have also beenmade by a number of other investigators includingHiecke,6 Bruckner,7 Judd," and Schouten.9 Physiologicalconsiderations must ultimately be decisive in this matterof the number of different receptor substances thatmediate between the light stimulus impinging on theretina and the arousal of responses in the visualsystem.' The theoretical model proposed here is notimportantly affected by the number of these mediatingsubstances. On the other hand, the assumption of threepairs of opponent visual processes is basic to theproposed theoretical treatment. It should perhaps beemphasized here that although the opponent natureof the paired processes can be conveniently expressedin a quantitative treatment by the mathematical con-vention of negative and positive signs, these signs inno way imply the existence of a phenomenon of egativeresponse."

The general nature of the curves proposed here is, atleast, not inconsistent with what is known of visualphysiology. The absorption curves of all visual pigmentsidentified in biochemical investigations are very similarin form when plotted on a spectral frequency scale, anddiffer primarily in the location of the peak responses.'2These curves conform so closely to each other thatDartnall has devised a nomograph from which a closeapproximation to the spectral absorption curve of anyvisual pigment can be determined once the wavelengthof the absorption peak has been specified. A frequencyplot of the curves shown in Figs. 2 and 3, with the

6 R. Hiecke, Z. Sinnesphysiol. 58, 111 (1927).7 A. BrUckner, Z. Sinnesphysiol. 58, 322 (1927), p. 340 ff.8 Reference 2, p. 831.9J. F. Schouten, Proc. Acad. Sci. (Amsterdam) 38, 590 (1935).10 J. Guild, in Joint Discussion on Vision (The Physical Society,

London, 1932), pp. 1-26.1l M. H. Pirenne, Vision and the Eye (Chapman and Hall Ltd.,

London, 1948), pp. 159-160.12 H. J. A. Dartnall, Brit. Med. Bull. 9, 24 (1953).

absorption of the ocular media and the macular pigmenttaken into account, is in good agreement with curvesbased on Dartnall's nomograph for visual pigments.Moreover, the chromatic response curves shown inFig. 1 are consistent with the narrowly selective curvesof the sort measured by electrophysiological techniquesin various animals. The theoretical conception of therelation between the receptor substances and thechromatic responses is, furthermore, consistent withDartnall's notion that the electrophysiological responsesmeasured by Granit" and others may reflect onlydifferences in the various photochemical excitations,rather than the receptor excitations per se. 2 Althoughwe are not concerned here with specific neural andstructural correlates consistent with the antagonisticor opponent nature of the paired visual responseprocesses,' 4 such mechanisms have been discussed insome detail by Talbot."

Another important aspect of the model used hereconcerns the constants k, k2, k, and k4 in the equationsrelating the photochemical excitation functions and thechromatic and achromatic response functions. Theseconstants are not fixed in value, but are assumed to bedefined by different ascending functions of the stimulusluminance, or of the strength of excitation in thereceptor substances. Thus, different values assignedto these constants permit quantitative expression ofthe well-known fact that the three primary psycho-logical attributes of color sensations vary with thestimulus luminance level. For the reference luminancelevel in the present formulation (assumed to be approxi-mately 10 mL), k= k2= 1.0, k= 1.0, and k4= 0.95. Toaccount for the fact that yellow and blue hues predomi-nate in high luminance spectra, whereas red and greenhues are more prominent in low-level spectra, k isassumed to be greater than k for stimulus luminanceshigher than the standard level, and kl is assumed to besmaller than k2 for luminances lower than the standardlevel.

A more detailed discussion of these aspects of thetheoretical formulation will be presented in analyzingvisual phenomena specifically related to various levelsof stimulus luminance. The adequacy of the theoreticalmodel in integrating some of the measured propertiesof color sensation and discrimination will be discussedseparately in sections dealing with the three primarycolor attributes, brightness, saturation, and hue.

SPECTRAL BRIGHTNESS

In deriving the transformation equations based onthe CIE color mixture data, the w-bkx function wasmade equal in form to the luminosity function for the

13 R. Granit, Sensory Mechanisms of the Retina (Oxford Uni-versity Press, London, 1947).

14These responses may be related to different physiologicalstructures or, more likely, they may be correlates of differentphysiological states within the same structural elements.

'S S. A. Talbot, J. Opt. Soc. Am. 41, 918 (1951).

604 Vol. 45

OPPONENT-COLORS THEORY. I

standard observer (x-bkx= k5gx). Since the achro-matic response function has been required to representthe standard function describing spectral luminosity,by definition the theoretical model accounts for spectralbrightness.

In this formulation the achromatic visual response isdependent on a difference between the processes in-volving the breakdown and those involving the reforma-tion of photochemical receptor substances. Since theinitiation of the black response is dependent on a backreaction in the physiological mechanism, it is consistentwith the fact that a black sensation is aroused onlyindirectly by either spatial or temporal induction. Theformulation may also prove to be useful in resolvingthe apparent conflict between orders of magnitude ofphotochemical changes and changes in brightnesssensitivity. Qualitatively, it has been possible to relatechanges in brightness sensitivity to the bleaching bylight of visual photochemicals with a consequent reduc-tion in their concentration. Quantitative comparisons,however, have shown that extremely large changes insensitivity are accompanied by only very minor changesin chemical concentration. Rushton and Cohen, forexample, find that exposure of the eye to a light whichbleaches only about 2 percent of its rhodopsin raisesthe visual threshold about 100 times.'6 If brightness andbrightness sensitivity are determined by the totalamount of photochemical bleaching (or conversely, bythe concentration of unbleached material), it is difficultto understand the quantitative discrepancy.' 7 If, how-ever, excitation of the opponent white-black visualprocesses correlated with brightness and luminosity isdependent on a difference in the activities involved inphotochemical bleaching and reconstitution, such adifferential mechanism by its nature will magnify theeffects of changes in the photosensitive materials. Anexample of this magnification in the chromatic processesis given in a later paper concerned with changes inchromatic adaptation.

The nature of the excitation of the achromatic white-black visual process is conceived here as fundamentallydifferent from that of the chromatic processes. Theformer is correlated with two kinds of activity (de-composition-regeneration) in the same group of receptorsubstances, whereas the latter are related to theseparate excitations (decomposition reactions) in thefour different substances. Thus it is not surprising thatthe mechanisms for brightness and chroma appear tohave quite distinct properties when studied by psycho-physical techniques.'8 ' 9 On the other hand, since thephotochemical mediating substances (B, G, Y, and R)for the achromatic system are assumed to be the sameas those activating the chromatic processes, a complete

16 W. A. H. Rushton and R. D. Cohen, Nature 173, 301(1954).

17 G. Wald, Science 119, 887 (1954).18 H. Pieron, Annee Psychol. 40, 1 (1939).19 L. T. Troland, Trans. Illum. Eng. Soc. 11, 957 (1916).

0.25 F

0.20 F

I040.15-

0.101-

0.05 _

Z.00

,.75

.50

1.25

X

1-

IC

1.00

400 500 600 700

WAVELENGTH -mM,

FIG. 4. Variability of frequency-of-seeing functions. See text.

independence of achromatic and chromatic propertiesof the sensation is not to be expected. The relativelysmall but real effect of chromatic adaptation onthe threshold luminosity function illustrates thisdependence.2 0

Moreover, although it is assumed that thresholdmeasurements of the spectral luminosity function areprimarily dependent upon the responses of the w-bksystem, it is still possible that a subsidiary dependenceon the simultaneously excited chromatic responsesystems will be detected under certain conditions ofmeasurement. Such a subsidiary dependence may beresponsible for the several minor inflections and irregu-larities found in threshold luminosity functions forindividual observers.2 ' This dependence may alsoaccount for the changes with wavelength of the vari-ability of the frequency-of-seeing functions measuredby Crozier.2 Crozier's analysis of his visibility dataled him to conclude that the sigma variations hefound were probably related to the number of separategroups of excitatory elements responding to the near-threshold test stimulus flashes, and he illustrated somecorrelations between his o- functions and measuresof saturation and wavelength discrimination. To evalu-ate the likelihood that variability of this sort is adirect manifestation of the activities of both chromaticand achromatic response mechanisms, we have deriveda theoretical variability function for comparison withthe Crozier data. For the theoretical prediction, ourassumptions are: (1) that the a- logAIo, if determinedby response of the achromatic process alone, would beequal to a constant; and (2) that a subsidiary de-pendence on the chromatic responses would be reflectedby an increment to this constant at each wavelength,with the increment proportional to the total chromaticresponse at a given wavelength.

20 D. Jameson and L. M. Hurvich, J. Opt. Soc. Am. 43, 552(1953).

21 For a list of references see: L. M. Hurvich and D. Jameson,J. Opt. Soc. Am. 43, 490-492 (1953).

22W. J. Crozier, J, Gen. Physiol. 34, 87 (1950).

O-- O EXPERIMENTAL- PREDICTED

A

, I

605August 1955

L. M. HURVICH AND D. JAMESON

In Fig. 4, we have plotted the o- logAI0 data obtainedby Crozier for frequency-of-seeing functions for oneobserver and a very small foveal field (1.6'). These dataare plotted as open circles and are connected by adashed line. The ordinate values are given on the leftof the figure. (The data obtained by Crozier below400 mA and above 700 mA are not inclu&d in Fig. 4.)The solid circles and solid line represent the predictedfunction for the standard observer (20 foveal field).The ordinate values [K+2 (b+g+y+r)] for the pre-dicted data are shown on the right. Although the agree-ment is far from perfect, the similarity in the functions isstriking in view of the fact that we are comparing apredicted function derived originally from color mixturedata for a number of observers with experimental resultsfor a single observer and very small field size.

SPECTRAL SATURATION

In discussing the usefulness of our experimentallydetermined chromatic response curves a comparisonwas presented between predicted and experimentallymeasured saturation discrimination functions.' In thiscomparison, the ratio of the sum of the chromaticresponses to the achromatic response at each wave-length was found to predict a logarithmic functionclosely similar to functions determined experimentallyby measuring the amount of spectral light that mustbe added to white for an observer to detect a just-perceptible change in color. The experimental resultsare quite different, however, if the method of measure-ment is reversed. That is, if a just-detectible amount ofwhite light is added to a series of monochromatic

2.0

~JJII1.01-

EXPERIMENTAL

4.

A

PREDICTED

0.0 -

.5!

0.06

0.04

�20.02

a.0 EXPERIMENTAL

* - PREDICTED

a

a A 0 00 0 A 1

0 0 0 A A

400 500 600WAVELENGTH - mi

FIG. 5. Saturation discrimination for two experimental methods.

spectral lights, saturation discrimination seems to beindependent of wavelength. Wright and Pitt havesuggested that the difference between the two experi-ments might be related to the state of chromaticadaptation.2 3 When the initial stimulus is always awhite and increments of spectral color are added, thechromatic state should be the same for measurementsat all wavelengths. On the other hand, when the initialstimulus is a spectral wavelength and white light in-crements are measured, adaptation to each spectralstimulus might occur. In this case the resulting functionwould involve two variables, the stimulus variable,spectral wavelength, and the uncontrolled physiologicalvariable, chromatic adaptation.

This suggestion would seem quite reasonable if theexperimental procedure involved extended viewing ofthe spectral light stimulus before measuring the just-perceptible increment in white light. However, sincelong durating observations of chromatic stimuli areusually avoided in discrimination experiments, we have,without assuming any significant changes in the chro-matic state, worked out quantitative predictions for thetwo different experimental procedures.

The predictions were quantified in the followingmanner. The total chromatic and achromatic responseat each wavelength was first computed for the standardobserver for a constant luminance. The spectral lightincrements required for threshold saturation are ob-viously much lower than the 10-mL luminance takenas the standard reference level (see the foregoing), andsince the yellow and blue responses are very weak atlow intensities relative to the red and green, in thepresent computations the constant k relating theyellow-blue chromatic responses to the Y-B receptorexcitations was correspondingly reduced [see Eq. (5)and the related discussion]. In computing the chromaticand achromatic responses for spectral lights of a lowluminance, the following values were assigned to theconstants: k=0.5, k2= 1.0, k3= 1.0, and k4=0.95. Wethen computed the fraction of these spectral lightresponses that is required to be added to a constantachromatic white light response at each wavelengthin order to give a fixed saturation ratio equal to 0.1.It is assumed, of course, that a threshold saturationchange is correlated with a constant visual effect. Thecomputed values give the spectral light increment ateach wavelength for a just-noticeable change in satura-tion from an initial saturation of zero.

To predict the results for the other experimentalprocedure, where an increment of white light is addedin order to just noticeably decrease the saturation of aspectral color, a 10% reduction in the initial saturationratio was taken as the threshold change for each wave-length. Here it was assumed that the constant luminancelevel for the spectral lights is of the order of 10 mL, andhence k1 and k2 were set equal to 1.0.

23 W. D. Wright and F. H. G. Pitt, Proc. Phys. Soc. (London)47, 207-208 (1935).

| | l fi b

owoo tAm

606 Vol. 45

OPPONENT-COLORS THEORY. I 6

The results of both predictions are shown in Fig. 5,together with experimental data for the two differentprocedures obtained by Wright and Pitt. In the upperpart of the figure, log[(Lw+ALx)/ALx] is plotted asordinate. The open circles and triangles are the experi-mental values for Wright and Pitt, respectively. 24

The solid circles are the predicted values for thestandard observer. The experimental and predictedfunctions have been displaced arbitrarily along theordinate for clarity of presentation. These curves aretypical of the spectral saturation function as it is usuallyrepresented.

The lower part of the graph in Fig. 5 shows thepredicted and measured results for the experiment inwhich white light increments are added to spectralcolors.2 3 Here AL,, is plotted as ordinate. Again, the opencircles and triangles represent the data for Wright andPitt, respectively, and the solid circles the valuespredicted for the standard observer. The experimentaland predicted values shown all refer to spectral lightstimuli of uniform luminance. Wright's observationsalso include two very high values for AL, (beyond theordinate values encompassed in Fig. 5) at the long andshort wave extreme of the spectrum, but those valueswere also obtained at a different luminance level andhence introduce another stimulus variable. Clearly,the fact that a just-noticeable reduction in the satura-tion of all spectral stimuli is produced by a constantincrement of white light is a theoretically predictableresult.

Since our theoretical model postulates different ratesof increase with receptor excitations of the two pairedchromatic responses (different values for the constantsk1 and k2 at all luminances other than the standardlevel), it is possible to predict specific changes in theform of the saturation discrimination function fordifferent levels of chromatic excitation. Two such pre-dicted functions are shown in the lower part of Fig. 6.The values plotted as solid circles are those computedfor a low level of chromatic excitation, those plotted asopen circles refer to a higher excitation level. Onedifference in the theoretical functions occurs in thespectral region between 480 mu4 and 530 mAu. For a lowlevel of chromatic stimulation, where the blue-yellowresponse is weak relative to that of the red-greensystem, saturation discrimination is nearly constant inthis spectral region. At the higher level, however, forwhich the yellow and blue responses on either side ofthe pure green stimulus are stronger, a secondaryminimum occurs at about 500 m/.

The theoretical functions are compared, in Fig. 6,with Purdy's saturation discrimination data for twodifferent white light luminances.25 Purdy's measurementsare shown in the upper part of the figure. The solid

24 W. D. Wright and F. H. G. Pitt, Proc. Phys. Soc. (London)49, 331 (1937).

25, D. M. Purdy, "Chroma as a function of retinal illumination,"dissertation, Harvard University, 1-190 (1929), Table VI.

1.0~~~~~

I 0 b-g-y-

< \

0.0I- ~ 5I'

T.5 " '

1.0400 500 600 700

WAVELENGTH - mn

FIG. 6. Saturation discrimination for two luminance levels.

circles represent data obtained for a white luminanceof 200 photons, and the open circles, the data for awhite light of 700 photons. The lines describing theexperimental functions have not been joined in thespectral region between 560 m/u and 605 m,4, where nomeasurements were obtained.

The experimental functions show, in the 500-mAspectral region, the major difference that is predictedby theory. The measurements for the lower luminancelevel remain fairly constant in this region, whereas thosefor the higher level exhibit a secondary minimum atabout 505 mA. Moreover, both the experimental andthe predicted sets of functions indicate slightly greatersensitivity in the short-wave region for the higherluminance level at which the blue response is assumedto be relatively strong. The remaining spectral extentshows a general lowering in sensitivity for the higherluminance function, consistent with the relative weak-ness of the red-green chromatic response at this level.The theoretical curves also predict slightly greatersensitivity for the higher luminance in the region of thepure yellow stimulus. Data are not available in Purdy'smeasurements to evaluate this prediction.

SPECTRAL HUE

An opponent-colors theoretical formulation, withpaired chromatic responses directly correlated with thefour psychologically primary or unitary hue sensations,permits a direct expression of the relation between per-ceived hue and spectral wavelength. This expressionmay be quantified as the ratio of each separate chro-matic response to the sum of all the chromatic responsesat a given wavelength, and since it is a relative measure,is called here the "hue coefficient." The expressions forthe spectral hue coefficients are thus: b/(b+g+y+r),g/(b+g+y+r), y/(b+g+y+r), and r/(b+g+y+r).Since b and y, and g and r are opponent color responses,only one response of each pair can occur simultaneously

607August 1955

L. M. HURVICH AND D. JAMESON

for a given stimulus, and two of the values in thedenominators of the hue coefficient fractions arealways equal to zero. For the wavelengths stimulatingunitary hue sensations, three of the values in thedenominator are equal to zero and at each of thesewavelengths the single hue coefficient is equal to 1.0.

A graphical representation of the spectral huecoefficients is given in Fig. 7. The open circles connectedby dashed lines (--- ) represent the values for thehue coefficients b/(b+g+y+r) as a function of wave-length, open circles and dotted line (. ) representy/(b+g+y+r), the solid circles and dash-dot line(- * -) are the values for r/(b+g+y+r), and the solidcircles connected by a solid line represent the functionfor g/(b+g+y+r). These coefficients apply to thestandard luminance level assumed to be about 10 mLand the value for the chromatic response constants k1and k2 is equal to 1.0.

From the short-wave spectral extreme to about 475m/- (unitary blue) both red and blue hues are present,with the blue hue coefficient rising to a maximum of1.0 and the red value dropping to a minimum of zeroat 475 mis. Between 475 mys and 498 myu, blue and greenhues are present. The blue hue coefficient drops rapidlyfrom its maximal value to a minimum of zero at 498 mA,and the green rises from zero at 475 m,4 to 1.0 at thepure green stimulus wavelength. Beyond 498 mg, greenand yellow hues are present, with the green coefficientdropping rapidly at first from its maximal value,changing more slowly in the 530-560-m,4 region, anddropping rapidly again to zero at 578 mt. The yellowcoefficient values inversely image the green, risingfrom a minimum of zero at 498 mu to a maximum of 1.0at 578 mA, the pure yellow stimulus. Beyond 578 mg,yellow and red hues are seen, with the yellow droppingand the red rising rapidly from 578 m,4 to beyond620 mA, and the changes beyond 620 m,4 are progres-sively slower at the longer wavelengths.

WHITE ADAPTATION

1.0 o

.8

Z .7 . '

Li.L . 6I

W .5

wd .4 'M 0~~~~~~~

.30

.2

500 600WAVELENGTH - mjL

FIG. 7. Spectral hue coefficients. Standard luminance.

At those wavelengths where the two hue componentsare equally strong in the sensory response, i.e., blue-green, green-yellow, and yellow-red, the correspondinghue coefficients are equal (0.5). These intermediatehues occur at about 485 myu, 560 mu, and 595 mu.Although the wavelengths eliciting pure hues are inde-pendent of stimulus luminance for a neutral state ofadaptation.26 the intermediate binary hues are not. Awavelength eliciting a true orange, or an equal yellowand red hue at a luminance of 10 mL, will evoke a morestrongly reddish hue at a lower luminance, and a morestrongly yellowish one at a higher luminance. In ac-cordance with the theoretical postulates, these changescan be computed and expressed quantitatively byassigning different values to the chromatic responseconstants k and 2 for the yellow-blue and red-greenmechanisms.

An example of the hue coefficient functions for aa high-luminance spectrum is given in Fig. 8. For these

l`-'U

LL-

0

1.0

.9

.8

.7

.6

.5

.4

.3

.2Z

.1

0

WHITE ADAPTATINWHITE ADAPTATION

I d;

1 0b

I f I I

HIGH LUMINANCE SPECTRUM

~1W

___--- o-- blue..... - yellow

-..@..-.- red- green

400 500 600 7tWAVELENGTH - m

FIG. 8. Spectral hue coefficients. High luminance.

data, the assumed value of k for the yellow-blue re-sponse is 1.0, the value of k2 for the red-green responseis 0.8. The major difference in the functions in Fig. 8for the high-luminance level as compared with thosein Fig. 7 for the standard luminance level is a relativeincrease in the blue and yellow hue coefficients, and arelative decrease in the red and green. The pure blue,green, and yellow loci are unchanged, but the loci of theintermediate binary hues (coefficients= 0.5) have movedin the expected directions. Specifically, the wavelength485 mu which was equally blue and green for thestandard luminance is now more strongly blue thangreen, and the hue that is equally blue and greenoccurs at almost 490 m. At 560 m,u, where the hue forthe standard luminance was equally yellow and green,the hue is now more strongly yellow, and the equallyyellow-green hue is found at about 553 m. The wave-

2G L. M. Hurvich and D. Jameson, Science 114, 199 (1951).

'00

608 Vol. 45

OPPONENT-COLORS THEORY. II

length which formerly elicited the equally red-yellowsensation, i.e., 595 mit, now elicits a more stronglyyellow sensation and the wavelength for equal yellowand red hue coefficients has moved closer to 600 mit.

In a graph of the spectral hue coefficients for aluminance level lower than the standard level we should,of course, find differences in a direction opposite tothose just noted. At the low-luminance level, theblue and yellow chromatic responses would becomerelatively weak, and the red and green ones relativelystrong, the classical Bezold-Briicke hue shift. Again,the wavelengths at which hue coefficients of 1.0 and0 occur, namely, the loci of the psychologically pure orunitary hues in the spectrum, would be unchanged.An extreme of the yellow-blue chromatic loss at verylow levels of stimulation is illustrated for observerswith normal color vision, in the apparent yellow-blueblindness found for very small stimulus areas. Since thelevel of excitation is reduced with area as well as withluminance, the chromatic response factors k and k2

must also be assumed to vary with both of thesestimulus variables. This yellow-blue loss, usually re-ferred to as either foveal,"7 or small area tritanopia,'5 '9

has been the subject of considerable theoretical andexperimental interest in recent years.

On the basis of hue coefficient data such as thoseillustrated in Figs. 7 and 8 we have computed, for anumber of spectral loci, wavelengths giving identicalhue coefficients at a series of luminance levels. It issimply assumed that to match a spectral wavelengthat a luminance of, say, 100 mL, by a spectral stimulusat a luminance of, say, 10 mL, the wavelength of thelatter will have to be altered until it excites chromaticresponses having the same hue coefficients as the re-sponses excited by the 100 mL spectral stimulus.Calculations have been made for a luminance range ofthree log units. For the highest level, the chromaticconstants k and k are assumed to be 1.0 and 0.8,respectively. For the intermediate luminance the con-stants are both equal to 1.0 and for the low luminancethe constants are equal to 0.8 and 1.0, respectively.

The predicted functions are plotted in the lower halfof Fig. 9. Log luminance is shown as ordinate and wave-length in mg as abscissa. The open circles represent thewavelengths at the three luminance levels that haveidentical hue coefficients and the lines drawn throughthese points represent constant hue contours. The threewavelengths for which the hue coefficients are constantand independent of luminance are indicated by arrows.In the upper half of Fig. 9 we have plotted the huecontours as drawn by Purdy. 0 They are based on hisexperimental measurements of the amount of hue shiftthat occurs between various luminance levels. Thewavelength locations of the invariant points as given

27 E. N. Willmer and W. D. Wright, Nature 156, 119 (1945).28 H. Hartridge, Nature 155, 657 (1945).29 D. B. Judd, Natl. Bur. Standards (U.S.) 42, 13 (1949).3' D. M. Purdy, Am. J. Psychol. 49, 313 (1937).

3.0

W0

'CK

0

2.0

1.0

3.0

2.0

1.0

INVARIANT POINTS_4 t

EXPERIMENTAL |

PREDICTED 8 /

400 500 600WAVELENGTH -mu

700

FIG. 9. Constant hue contours.

by Purdy are also indicated by the three arrows in theupper part of the figure. The agreement between thelines of constant hue predicted on the basis of theoryfor the standard observer and the contours based onPurdy's experiment for a single observer is apparenton inspection.

The quantitative considerations involved in ourtheoretical prediction are essentially the same as thoseused by Judd for predicting the Purdy hue shift meas-urements for a single pair of intensities.3 Judd's calcu-lations are also based on the chromatic responses of anopponent-colors mechanism. There is a major difference,however, in the basic assumption made by Judd andthe one developed here. Judd does not assume, as we do,that the relation between strength of excitation and thechromatic responses differs systematically for the twochromatic pairs. Rather, he interprets the Bezold-Bricke hue shift as an adaptation phenomenon andassumes that the red-green chromatic system is readilyadapted whereas the blue-yellow chromatic system ismore resistant to adaptation. In the light of the avail-able evidence, the assumption of a differential depend-ence upon the level of stimulation seems to us to bethe more fruitful one. We refer, for example, to thepredictions of specific changes in the saturation dis-crimination function illustrated in Fig. 6 and to thewavelength discrimination functions to be discussedbelow.

The hue coefficient functions given in Figs. 7 and 8not only provide descriptions of the spectral hues, theyalso suggest the way in which spectral hue discrimina-tion might be expected to vary. In the regions where thehue coefficients are changing rapidly, for example, inthe region between 470 and 510 miu and again between560 and 590 m/i, a small change in wavelength producesa considerable change in the hue coefficients, and in

31 Reference 2, p. 855.

609August 1955

fI . r

L. M. HURVICH AND D. JAMESON

these regions spectral hue discrimination should bevery good. In the regions where the hue coefficients arechanging only very slightly, particularly at the twospectral extremes, a large change in wavelength pro-duces very little change in the hue coefficients and huediscrimination in these regions should, consequently,be very poor. In the middle of the spectrum between510 and 560 m, discrimination should be less goodthan at the two regions of maximal rate of change, butnot so poor as at the spectral extremes. Moreover, sincethe hue coefficient functions and their rates of changewith wavelength are not identical for all luminancelevels, these differences should be reflected to someextent in the observer's ability to discriminate changesin hue with changes in wavelength at different lumi-nance levels.

In experimental measurements of wavelength dis-crimination, however, the observer does not dependsolely upon changes in hue. In some of the very earlymeasurements of wavelength discrimination variationsin spectral brightness were not controlled and the resultswere consequently influenced by the observer's abilityto discriminate the brightness attribute. In later ex-periments the importance of controlling spectral bright-ness has been recognized. The saturation attribute,however, also varies with wavelength, and this varia-tion is not controlled in measurements of wavelengthdiscrimination.3 3 In fact, there is good reason tobelieve that the so-called hue discrimination functionsfor dichromats, except for the transition point where thespectrum changes from the one dichromatic hue to theother, are actually measures of their ability to dis-criminate changes in the saturation attribute alone.3435

In order to treat the problem of wavelength discrimina-tion, therefore, we have assumed that the changes inhue and saturation from one wavelength to the nextare both determinants of the measured threshold. Toexpress the saturation attribute on a quantitative basisequivalent to that for hue the saturation coefficient isused. This is a relative value representing the ratioof the chromatic responses to the sum of the chromaticplus achromatic responses, and is directly comparableto the expression for the hue coefficient. The saturationcoefficient function for the spectrum is very similarto the logarithmic saturation sensitivity functionsshown in Fig. 6, but the coefficient function, arelative measure, approaches a limiting value of 1.0(rather than infinity) in the regions of maximalsaturation.

The limiting determinant for a wavelength dis-crimination threshold is assumed to be some constantchange in the hue coefficient combined with a simul-taneous constant change in the saturation coefficient.

32 A. Konig and C. Dieterici, Ann. Phys. Chem. 22, 579 (1884).3 L. T. Troland, The Principles of Psychophysiology (D. Van

Nostrand Company, Inc., New York, 1930), Vol. II, pp. 142, 144.34 E. Hering, Lotos, Jahrb. Naturwiss. N. F. 1, 95, 96 (1880).35 S. Hecht and S. Shlaer, J. Gen. Physiol. 20, 83 (1936).

In our computations equivalent saturation and huechanges were postulated for the wavelength discrimina-tion threshold. It is quite possible that changes in thetwo attributes should be weighted differentially, butwe have made the simpler assumption here.

Predicted functions for the wavelength discriminationof the standard observer are plotted in the lower partof Fig. 10. The values plotted as open circles representthe just noticeable difference in wavelength for a spec-trum at the standard luminance level (10 mL). Thevalues plotted as solid circles and connected by dashedlines are predictions for a luminance level considerablylower than that of the standard. The function for thestandard luminance shows the usual characteristicsexhibited in measurements of wavelength discrimina-tion: two rather shallow minima, one between 460and 510 mj.i, the other between 560 and 600 myt, a mid-spectral maximum at about 530 mg and a rise in AX atboth ends of the spectrum indicating rapid deteriorationin wavelength discrimination. The function for the lowluminance shows magnified curvature, the minimumin the short-wave region is shifted toward the shorterwavelengths and is now lower than the 580-mA mini-mum. The mid-spectral maximum is not only exag-gerated but its locus is also shifted, occuring now atabout 510 mAs rather than at 530 my.

The upper part of Fig. 10 contains experimentalmeasurements for spectra at two luminance levels(foveal field, 50').36 The points plotted as open circlesand connected by the solid line are Weale's values for aspectral luminance of 9.5 efc (approximately 9.5 mL).The points plotted as solid circles connected by dashedlines are his values for a spectral luminance of 0.95 efc.The two experimental functions show differences ofthe same sort as those predicted by theory. In com-parison to the higher luminance function, at thelower luminance the short-wave minimum is shiftedtoward shorter wavelengths and has a lower value

5 [X --- ~t^ Ity , I

/ 'I I

5 t. 0- .r /..

S

"30

'5

to

5

9~~~~~~~~

I I I.- -

_ _ 1I I I $~~Il U/.jC

* I t I/1 I / "

400. 500 6CWAVELENGTH - mp

00 700

FIG. 10. Wavelength discrimination for two luminance levels.

36 R. A. Weale, J. Physiol. 113, 115 (1951).

11-

610 Vol. 45

OPPONENT-COLORS THEORY. II

of AX than the long-wave minimal value. The mid-spectral maximum occurs at about 540 my for the high-luminance function and is shifted to about 520 m inthe low-level function, and again, the curvature in thelow-luminance function is considerably exaggerated incontrast to the rather shallow curvature of the high-luminance function.

An additional psychophysical function that can bedetermined directly from the hue coefficients plottedin Figs. 7 and 8 is that showing the relation betweencomplementary pairs of wavelengths. The theoreticalfunction is specified simply by reading the magnitudesof the hue coefficients, say, red and yellow, for a givenwavelength, and locating a second wavelength forwhich the opponent hue coefficients, in this case, greenand blue, have the same values, respectively. The re-sulting curve approximates a rectangular hyperbola,and is, of course, identical to the function frequentlyillustrated or tabulated for the standard observer. 37

The hue coefficient functions make it apparent on in-spection why there are no complementary wavelengthsfor the mid-spectral region. It is also true, because ofthe paired nature of the chromatic processes, thatchanges in the hue coefficients with changes in lumi-nance have no effect whatsoever upon the complemen-tary wavelength function.

In general, the theoretical formulation presented herefor an opponent-colors theory on the basis of the colormixture and luminosity data for the standard observerwould seem to account rather well for the attributesof spectral brightness, hue, and saturation and theirassociated psychophysical functions. Up to this pointthe analysis has been limited to a single neutral stateof adaptation, and we have given no attention to theproblem of color blindness. The effects of chromaticadaptation for normal color vision will be consideredin a later paper. We should like now, however, brieflyto examine some aspects of dichromatic vision.

PROTANOPIA AND DEUTERANOPIA

Any theoretical formulation that purports to de-cribe the basic relations of normal color vision must, ofcourse, also provide a basis for the description of themajor classes of abnormal color vision. The mostcommon major color defect is red-green blindness, inthe forms that have come to be classified as protanopiaand deuteranopia. It is generally agreed that bothprotanopes and deuteranopes see only blue, yellowand achromatic hues in the spectrum,3 8 39 with the twoclasses sharply differentiated by the characteristics oftheir respective luminosity functions. The deuteranope'sluminosity function is very similar to the functionsobtained for observers with normal color vision, whereasthe protanope's function exhibits a loss of sensitivity

37A. C. Hardy, Handbook of Colorimetry (The TechnologyPress, Cambridge, 1936), p. 31.

38 E. Hering, Arch. Ophthal. 36, 1 (1890).39 D. B. Judd, Natl. Bur. Standards (U. S.) 41, 247 (1948).

0.50

0z

Cr

0.00 -d '2 -

Id_

II

1.00

0.75 -- 0

0.50

0.25-

0.00 I

40 0060/0

400 00 600WAVELENGTH - m,

FIG. 11. Chromatic and achromatic response functionsfor protanopia and deuteranopia.

in the long-wave spectral region, peaks at a lower wave-length than the normal function, and shows relativelyhigh sensitivity at the short wavelengths.4 0 To accountfor both types of color blindness, we assume either anabsence or complete loss of function of the red-greenchromatic system. For the deuteranope, it is assumedthat the B, G, Y, and R receptor substances are essen-tially the same as for the observer with normal colorsense. For the protanope, on the other hand, we suggestthat these four substances bear the same relation toeach other as for the normal, but that the whole set offour excitation curves has undergone a shift, on afrequency plot, toward higher frequencies (i.e., shorterwavelengths).41 The distribution curves still show thegeneral form characteristic of photopigments (seeDartnall"2 and our earlier discussion), but they all peakat lower wavelengths than do the curves for thenormals and deuteranopes. Since the red-green chro-matic processes are not functioning, the chromaticresponse curves for the red-green blinds are given bythe equations:

(deuteranope)(protanope)

The achromatic responses, and the luminosity func-tions, are equal to:

wx-bkx= k3 (0.5Bx+0.5Gx+ 1.0Yx+ 1.ORx)-k 4 (0.5Bx+0.5Gx+1.0Yx+1.0Rx)

(deuteranope)

wXP- bkxp= k3(0.5Bx +0.5Gx,+ 1.OYxp+ 1.0R p)- k4 (0.5Bxp+0.5Gx p+ 1 .OYx p+ 1 .0R p)

(protanope).

40 D. B. Judd, Documenta Ophthal. 3, 251 (1949).41 This assumption is not inconsistent with the established fact

that rod pigments peak at different wavelengths for differentlower organisms and even undergo a shift during development insome instances [G. Wald, Ann. Rev. Biochem. 22, 497 (1953)].

611August 1955

I -

11 . .1 ��- DP -

700

yx-bx=k1(Yx-Bx),yXP-bxp=k1(Yxp-Bxp).

L. M. HURVICH AND D. JAMESON

5.

4.5 -

4.0 -

3.5

3.0

2.5

2.0

1.5

1.0 F-

0.5

0.0

400 500 600WAVELENGTH- m1L

FIG. 12. Saturation discrimination forprotanopia and deuteranopia.

These functions are shown in Fig. 11. The chromaticresponses or valences are given in the upper part of thefigure, and the achromatic responses, or relativeluminosity functions are given in the lower part of thegraph. The values for the protanope are plotted as solidcircles, those for the deuteranope are represented byopen circles. In the chromatic response functions, theparts of the curve below the zero line are joined bydashed lines and represent blue response, the partsabove the zero line are connected by a dotted line andrepresent yellow response. Again, the mathematicalconvention of positive and negative signs is used toindicate the opponent nature of the chromatic system,and does not imply positive or negative qualities ineither the sensation or its physiological correlate.

As previously indicated, the deuteranope is assumedto have the same receptor substance curves as thenormal, and hence the yellow-blue chromatic valencecurve for the deuteranope is the same as the corre-sponding function for the standard observer (see Fig. 1).At the wavelength 498 mu, which appears unitarygreen to the standard observer, the deuteranope'schromatic responses are equal to zero, and this wave-length represents the locus of the deuteranope's neutralpoint in the spectrum. The protanope's neutral point,where the chromatic responses for this class of observerare equal to zero, occurs at a lower wavelength, approxi-mately 489 mg. The protanope's function shows asmaller blue response than the deuteranope's from theneutral point down to about 450 mu, and a larger blue

response than the deuteranope's at wavelengths shorterthan 450 m. The protanope shows a greater yellowresponse than does the deuteranope from the neutralpoint up to about 550 mjnp, and this response becomessmaller than that of the deuteranope beyond thiswavelength and continues so to the long wave spectralextreme.

Spectral Brightness

The two achromatic response functions show differ-ences characteristic of measured luminosity functionsfor the protanope and deuteranope. The deuteranopicfunction is like that for the normal observer, whereasthe protanopic function shows a decreased sensitivityat the longer wavelengths, the peak is displaced about20 mIn/ toward the short wavelengths from the deuter-anopic (and normal) peak, and there is a relative in-crease in sensitivity from about 550 m/t to the short-wave spectral extreme.

Spectral Saturation

Given the functions for the protanopic and deuter-anopic chromatic and achromatic response systems, itbecomes possible to predict the saturation discrimina-tion functions for these two classes. The same procedureis used as that already described for the standard ob-server with normal color vision and the function isgiven by the ratio of chromatic to achromatic responsesat each wavelength. Two such functions are shown inFig. 12. The functions have been displaced arbitrarilyalong the ordinate, and the curve shown in the upperpart of the graph is that predicted for the protanope,whereas that contained in the lower part of the graphis for the deuteranope. In both instances, they areplotted as solid circles and solid lines. The valuesplotted as open circles are measured results of satura-tion discrimination experiments for a protanopic anddeuteranopic observer. The experimental results arethose reported by Chapanis for the protanopic observerW.M. and for the deuteranopic observer L.P.,41 and, asFig. 12 shows, the theoretical functions describe fairlywell the measured results for these two types of dichro-matic vision.

Both functions are open ended at the observers'neutral points, illustrating the fact that when thespectral light itself elicits an achromatic sensation aninfinite amount of such light can be added to a whitewithout producing a change in saturation. For bothtypes of observer, saturation increases rapidly fromthe neutral point toward the short wavelengths. Fromthe neutral point toward the longer wavelengths, thefunction also rises rapidly at first but levels off fairlysoon and for both types of observer spectral saturationbecomes fairly constant from about 530 myu on. In agree-ment with the different neutral point loci, the wave-length region of minimal saturation occurs near 500 m,4

42 A. Chapanis, J. Exptl. Psychol. 34, 24 (1944).

PROTANOPEo EXPERIMENTAL* PREDICTED

DEUTERANOPEO EXPERIMENTAL* PREDICTED

: ̂aBu, | a i ] a - a

612 Vol. 45

0

-1'91

l

OPPONENT-COLORS THEORY.

for the deuteranope and in the vicinity of 490 m/t forthe protanope.

Spectral Hue

The spectral hues for both protanopes and deuter-anopes are simply blue, neutral and yellow as indicatedby the functions plotted in Fig. 11. A plot of the huecoefficient functions for the red-green blind dichromatswould show a coefficient of 1.0 b from the short-waveextreme to the neutral point, a precipitous drop to 0.0at the neutral point, and beyond this point a sharp riseof the y-coefficient to a value of 1.0 throughout theremaining spectral extent. Clearly, if the dichromatwere dependent on hue changes alone to discriminateone wavelength from the next, his wavelength dis-crimination would be infinitely poor except at theneutral point where the blue-to-yellow transition occurs.

It has been pointed out, however, in relation to thewavelength discrimination of the observer with normalcolor sense, that both hue and saturation changes occurwith variation in wavelength, and for the dichromatsthe variable of spectral saturation is of primary im-portance in wavelength discrimination. To predict thewavelength discrimination function for the dichromat,the saturation variable is treated in the same way thatit was for the normal observer. That is, for each X, theAX for a fixed change in the value of the dichromat'ssaturation coefficient was computed. Since the valuesof the dichromatic hue coefficients are invariant exceptin the immediate region of the neutral point, the wave-length discrimination function for this type of observeris almost exclusively determined by the variation insaturation from one wavelength to the next.

The predicted wavelength discrimination functionsfor the protanope and deuteranope are given in Fig. 13.The function for the protanope is contained in theupper half of the figure and is represented by the solidline. The values plotted as open circles are averages ofmeasurements obtained by Pitt for 6 protanopic ob-servers,43 and the values plotted as solid circles areaverage determinations made by Ladekarl for threeprotanopic observers.4 4 Ladekarl's data have beenmultiplied by a constant for purposes of comparison.

In the lower half of Fig. 13, the solid line representsthe theoretical function for the wavelength discrimina-tion of the deuteranope. The open circles represent theaverage experimental values determined by Pitt for 6deuteranopes, 43 the solid circles are averages for twodeuteranopic observers measured by Ladekarl,44 andthe open triangles are the data for one deuteranopereported by Brodhun.45 The Brodhun and Ladekarldata have both been multiplied by constants.

For both the protanopic and deuteranopic observers,the theoretical functions describe fairly well the AX

43 F. H. G. Pitt, Med. Research Council (Brit.) Spec. Rep. Ser.No. 200 (1935).

44 P. M. Ladekarl, Acta Ophthal. 12 (Supplement III) (1934).45 E. Brodhun, Z. Sinnesphysiol. 3, 97 (1892).

20

I0

E

I1

0

20

10

PROTANOPE

a} EXPERIMENTAL

- THEORETICAL

1a

DEUTERANOPE

* EXPERIMENTAL

-THEORETICAL

4'00 500 600WAVELENGTH - men

FiG. 13. Wavelength discrimination forprotanopia and deuteranopia.

700

functions obtained experimentally. Both functions arequite unlike those for observers with normal colorvision (see Fig. 10), in that they show only a singleminimum (at about 490 myu for the protanope and near500 mu for the deuteranope) and beyond this minimumdiscrimination deteriorates rather rapidly toward boththe short- and long-wave spectral regions.

TRITANOPIA AND TETARTANOPIA

Loss of the yellow-blue sense, although less commonthan red-green deficiency, is the second major colorvision aberration for which a theoretical formulation ofthe color sense must provide an account. Among theobservers who have shown this kind of loss, there are,again, two groups. One group, generally referred to astetartanopes, is known to have two neutral points in thespectrum, one in the region of the unitary blue for thenormal observer, and another in the region of thenormal's unitary yellow. These two neutral pointsdivide the tetartanope's spectrum into three regions,a short-wave red region, a central green region, and along-wave red region. Only rare instances of this typeof yellow-blue loss have come under investigation, andthere is, consequently, only fragmentary informationabout the psychophysical characteristics of this kindof dichromacy.

More data are available, particularly from Wright's

I 613August 1955

L. M. URVICH AND D. JAMESON

0.50

+

0.50

1.00

LU

1i-J

-'. TRTANOPE - I t. e4, -;,.4~~'/ 'N~~~~~~I

- TETARTAN0P

0.75 _

0.50 _.

0.25 _

0.00

- TRITANOPE

400 500 600 700WAVELENGTH - m,

FIG. 14. Chromatic and achromatic response functionsfor tritanopia and tetartanopia.

recent studies,46 concerning some of the characteristicsof the second group of yellow-blue deficients, namely,the tritanopes. This type of observer has one neutralpoint in the region of the normal's unitary yellow, andthe second neutral point is either absent or greatlydisplaced toward the short-wave spectral extreme. Thetritanope shows not only yellow-blue loss, but also amarked red anomaly. This anomaly is exhibited in thespectral region from about 400 m,4 to approximately475 mg, where the hues seen by the normal observerand the tetartanope have a distinct red hue component.The tritanope sees a weak red hue component, if atall, only in a very restricted part of this region near400 mit. It seems unlikely that the excitation curves forthe tritanope's receptor substances can have the sameforms as those for the normal observer. On the otherhand, the tritanopic luminosity function, while notidentical to that for normal color vision, does not indi-cate any major shift in excitation peaks of the receptorsubstances.4 7

In deriving a quantitative model for the two kindsof yellow-blue loss systems, a complete absence or lossof function of the y-b chromatic response systems isassumed. In view of the meager evidence concerningthe characteristics of tetartanopes, we have made thesimplest assumptions for these observers, namely, thatthe B, G, Yx, and Rx receptor curves are the same asfor the normal, and that the tetartanope's luminosityfunction is also the same as for the normal observer.Thus, for the tetartanope, the chromatic and achro-

46 W. D. Wright, J. Opt. Soc. Am. 42, 509 (1952).47 The measured luminosity function for one tritanopic observer

reported by Judd, Plaza, and Farnsworth did show a peakstrongly displaced toward the long wavelengths, but they attributethis exceptional case to abnormally heavy macular pigmentation.[Judd, Plaza, and Farnsworth, J. Opt. Soc. Am. 40, 833 (1950).]

matic response functions are:

rx-gx=Rx-Gx,wx-bkx k3(O.5Bx+0.5Gx+ 1.0Yx+1.ORx)

-k 4(0.5Bx+0.5Gx+ 1.0Yx+ 1.0Rx).

The transformation equations relating the Bx, Gx, Yx,and Rx excitation functions to the CIE standard ob-server are the same as those for normal color vision[see Eqs. (1)-(4).]

To account for the measured psychophysical charac-teristics of tritanopic vision, we have made two addi-tional assumptions. The first assumption is that theB-receptor substance is lacking. The second is that theform of the Rx-receptor function differs slightly fromthe corresponding function for the standard observer.The transformation equation used to relate the trita-nopic Rx function to the tristimulus values for thestandard observer is the following:

Rxtr. = 0.6658&x+ 12.93427x- 0.26942x.

The chromatic and achromatic response functions forthe tritanope then become

rXtr. - gXtr. = Rxtr. -Gx

WXtr. - bkxtr = k3 (Gx+ Yx+Rxtr.) - k4 (Gx+ Yx+Rxtr.).

It should be noted that the Rxtr. function defined hasthe same form as the y function (Eq. 11) defined in anearlier section where the equations were given for analternative set of receptor functions (a;,, o3x, and yx). Inthis alternative system, for the tritanope the a substancewould be lacking, and the chromatic and achromaticresponse systems would have the forms

rXtr. - gXtr. tx-flXy

WXtr.- bkxtr. k3 (x+yx) - k4 (X+7Y) .

These functions are identical in form to the tritanopicresponse functions defined in the preceding paragraph.

The theoretical chromatic and achromatic responsefunctions for the yellow-blue blinds are given in Fig. 14.(The values for both sets of functions at wavelengthslower than 440 m/ were obtained by extrapolation.)The values for the tritanope are shown in solid circlesand those for the tetartanope are represented by opencircles. As previously stated, the tetartanopic chro-matic response is assumed to have the same formas the normal red-green function, and the wave-lengths where the chromatic responses are equal tozero (475 mu and 578 mp) identify the two neutralpoints in the spectrum for this observer.40 48 For thetritanope, the red response function is very similarto that of the tetartanope in the long-wave spectralregion, but intersects the zero response line at asomewhat shorter wavelength (570 mn/). This displace-ment is in agreement with G. E. Muller's comparison

48 G. E. Mller, Darstellung nd Erkidrung der versc/hiedenenTypen der Farbenblindlheit (Vandenhoeck and Ruprecht, Gttingen,1924), p. 72 f.

.

___V.VU Ad i_ b r s

64 Vol. 45

OPPONENT-COLORS THEORY. II

of the long-wave neutral point locus for his tetartanopewith the measurements reported for cases of tritanopia.The green function peaks at about the same wavelength(530 myu) for both types, but the tritanope continues tosee green to about 415 myu, beyond which point there isonly a very slight red response again.46 49 On the basisof the functions shown in Fig. 14, the tritanopic ob-server should theoretically find a second neutral pointin the region of 415 mis, but in view of the very minorred response at the shorter wavelengths, it is difficult,at best, to isolate this achromatic locus experimentally.

Spectral Brightness

The achromatic, luminosity, responses for thetritanope and tetartanope are shown in the lower partof Fig. 14. As we have said, the tetartanope's luminosityfunction is assumed to be identical to that of the normalobserver. The function for the tritanope differs fromthe normal mainly at the short wavelengths, wherethis class of observer shows a loss in sensitivity relativeto the standard observer's luminosity function. Thetheoretical functions are consistent, in this respect, withWright's measurements for seven tritanopic observers.46

Spectral Saturation

Predicted saturation functions for the tritanopeand tetartanope are shown in Fig. 15. The functionshave been arbitrarily displaced along the ordinate, andthe theoretical function for the tritanope is given inthe upper part of the figure, that for the tetartanope inthe lower part. The functions differ for the two classesin accordance with the differences in the chromaticresponse functions shown in Fig. 14. For the tritanope,saturation discrimination is infinitely poor at about415 mya and again at 560 mu, whereas for the tetarta-nope, the curves approach infinitely low values atabout 475 myu and 578 my. Unfortunately, we knowof no reports in the literature that contain experimentaldeterminations of yellow-blue blind saturation dis-crimination with which to compare the theoreticalfunctions. The functions for the tritanope can, however,be evaluated indirectly in terms of the predicted wave-length discrimination functions, for which experimentaldata are available.

Spectral Hue

As we noted in discussing the psychophysical charac-teristics of red-green blinds, the spectral hue coefficientsfor the dichromatic observer are constant except atthe neutral point transition regions, and wavelengthdiscrimination for the dichromat depends primarily onperceived variations in spectral saturation. The pre-dicted functions are obtained by computing, for eachwavelength, the AX required for a fixed change in thevalue of the spectral saturation coefficient. For tri-

ll Fischer, Bouman, and ten Doesschate, Documenta Ophthal.5-6, 73 (1951).

50

4.5

JIZ51

20 -

'.5

1.0

0.5

0.0

400 500 600 700500 600

WAVELENGTH - m,

FIG. 15. Saturation discrimination for tritanopia and tetartanopia.

tanopes and tetartanopes, changes in hue are availablefor discrimination only at the neutral point transitionregions where there is a shift from reds to greens.

Wavelength discrimination functions predicted onthe basis of these considerations are presented in Fig.16. The theoretical function for the tetartanope, forwhom there are no comparable experimental data, isshown in the lower part of the figure. We need noteonly that the degree of curvature exhibited in thisfunction depends on the size of the critical value of thesaturation coefficient change selected arbitrarily forthe prediction.

The predicted wavelength discrimination functionfor the tritanope is shown both in the upper and middlesections of Fig. 16. The theoretical values are plottedas solid circles in both instances. In the upper graph,the theoretical prediction is compared with data(plotted as open triangles) obtained by Fischer,Bouman, and ten Doesschate.49 The scale for the experi-mental data is shown on the inner ordinate line. Thecontinuous line describing the experimental functionis copied directly from the figure presented by Fischerel al., and it can be seen that a very similar continuousfunction is fitted satisfactorily to the predicted AXvalues.

The experimental data plotted as open circles in thecenter graph are those obtained by Wright for oneof his seven tritanopic observers (Observer A).4 Again,the broken curve fitted to the experimental data iscopied from the function presented by Wright. Thesolid circles representing the theoretical AX values are

TRITANOPE

6 PREDICTED

I'

ITETARTANOPE

0 PREDICTED

l

615August 1955

700

L. M. HURVICH AND D. JAMESON

30

20

10

0

30

iLE

I3

201

10

0

30

20

I 0

TRITANOPE

| XPRIMENTAL |l *' PREDICT1

11 , , .I ~~~111/- I .`

TETARTANOPE* PREICTID

400 500 600

WAVELENGTH- ma700

FIG. 16. Wavelength discrimination fortritanopia and tetartanopia.

the same as those compared with the experimental dataof Fischer et al. in the upper part of the figure. In thiscase, however, the theoretical values have been fittedby a broken curve (dashed lines) similar to the functionplotted by Wright for his experimental values. Heretoo, the experimental and predicted functions are verysimilar, except for the spectral region between 470 mjuand 500 my, where the theoretical AX values are lowerthan the experimental determinations for Wright'sobserver. In both cases, however, the theoretical andexperimental functions for tritanopic wavelength dis-crimination show a short-wave minimum in the vicinity

of 430 mu, a maximum at around 460 mu, a broadshallow minimum between 550 mnu and 620 m,4, and asharp rise for wavelengths beyond this value.

In summary, a quantitative theoretical formulationbased on an opponent-colors theory of the visual systemcan be shown to provide an integrated account of manyof the basic facts of dichromatic color vision. Theauxiliary assumptions made in this account for thevarious dichromatic visual systems are, of course,neither the only ones possible, nor are our choicesnecessarily the best ones. We should like, for example,to have more experimental data on the characteristicsof both tritanopia and tetartanopia against which toevaluate some of the postulated functions derivedhere. We should like also to have more informationabout the relation of the deuteranope's luminosityfunction to that of the normal. While it is usually agreedthat spectral luminosity is the same in form for bothnormal and deuteranope, the assumption made in ourquantitative treatment, other evidence has been pre-sented which shows that there are significant differencesbetween the two functions.5 0 5 The account of dichro-matic vision of the various types is, therefore, presentedas a tentative one, subject to whatever modificationsmay be required in the light of further physiologicaland psychophysical information.

A similar theoretical account could be presented forthe various types of anomalous vision, and we havequantified theoretical predictions of some of the psycho-physical relations for anomalous color vision. Thisseries of papers is, however, concerned primarilywith the normal color sense, and hence a detailed exami-nation of the characteristics of different types of coloranomaly is beyond the scope of this discussion.

Changes in perceived brightness, hue, and saturationwith changes in chromatic adaptation will be consideredin the next paper of this series. A means for the quanti-tative specification of the perceptual attributes of colorswill also be presented.

so S. Hecht, Documenta Ophthal. 3, 289 (1949).1 C. H. Graham and Y. Hsia, Science 120, 780 (A) (1954).

V - _ In

616 Vol. 45