changes in luminance affect dichoptic unique yellow

Vol. 6, No. 9/September 1989/J. Opt. Soc. Am. A 1297

Changes in luminance affect dichoptic unique yellow

Jeffery K. Hovis

School of Optometry, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada

S. Lee Guth

School of Optometry, Indiana University, Bloomington, Indiana 47405

Received November 28, 1988; accepted April 17, 1989

An extension of the Benzschawel-Guth ATDN model [Color Res. Appl. 9, 133 (1984)] predicts that, for dichopticpresentation, the green-to-red (G/R) ratio required to obtain a unique yellow percept should decrease withincreasing luminance, because the green postreceptor hue response increases faster than the red postreceptor hueresponse with increasing intensity. However, for monoptic presentation the model predicts that the G/R ratioshould remain invariant, because the neural responses from the receptors increase at the same rate with increases inluminance. Data from four subjects confirmed these predictions.

INTRODUCTION

Dichoptic color mixing has been a controversial subject foralmost two centuries. The early disputes focused on wheth-er dichoptic mixtures represented real neural processing ofdisparate chromatic information from each eye or an experi-mental artifact.",2 It is now generally accepted that, underappropriate stimulus conditions, dichoptic color mixturesdo occur and that they represent central neural processing ofinformation from each eye.2 4 A later debate arose regard-ing whether dichoptic color mixtures supported the trichro-matic color-vision theory or the opponent-colors theory.7 '8

This controversy has been resolved by the general accep-tance of zone color-vision models, which incorporate aspectsof both the trichromatic and opponent-colors theory.

Despite these theoretical disputes, studies generally agreeon one aspect of dichoptic color mixing. That is, relative tomonoptic mixtures, dichoptic mixtures of red and greenlights require less of the green primary to match a yellowishstandard; therefore dichoptic mixtures of red and greenlights appear greener than the corresponding monoptic mix-ture.3 -9'1 0 The one exception is the study by Livshitz,"1 whoreported that the hues of monoptic and dichoptic mixturesare identical.

This generally agreed on result and several other huedifferences between monoptic and dichoptic mixtures can bepredicted by an extension of the ATDN model' 2 ofBenzschawel and Guth."3 The dichoptic ATDN model isrepresented schematically in Fig. 1. The first three levelsare similar to those of the Benzschawel-Guth model. Thecone photoreceptors, L, M, and S, compose the first stage.They provide input to the second-stage mechanisms, whichare the nonopponent achromatic mechanism A, the oppo-nent T mechanism (similar to the classical R/G channelj,and the opponent D mechanism (similar to the classical B/Ychannel). In a departure from previous opponent-colorsmodels, the two outputs of each postreceptor opponentmechanism have different nonlinear responses. That is,blue, yellow, red, and green each have different intensity-

related response functions. These four different postrecep-tor nonlinear response functions are the relevant property ofthe Benzschawel-Guth ATDN model that allows for thepredicted monoptic and dichoptic hue differences.

At a third central level, the red-green responses from eacheye are added together, as are the blue-yellow responses.For present purposes, red and blue responses are assignedpositive values, whereas green and yellow responses are as-signed negative values. Ratios of the blue-or-yellow to red-or-green responses represent the predicted hue of either thedichoptic or monoptic image. (Rules for combining achro-matic information and an achromatic nonlinear responsefunction are not necessary for the current treatment.)

FORMULATION OF THE MODEL

Photoreceptor sensitivities are from Smith-Pokorny funda-mentals as cited in Ref. 13:

L = 0.24x' + 0.85y' - 0.052z',

M = -0.40x' + 1.2y' + 0.084z',

S= 0.62z',

(la)

(lb)

(Ic)

where x', y', and z' are Judd's 1951 modifications of the 1931CIE color-matching functions.

The following equations give the outputs of the postrecep-tor mechanisms for the unit luminance spectrum:

A = cl,

T = c2(0.96L - 1.3M + kS)/(0.60L + 0.37M),

(2a)

(2b)

D = C3 (-0.025L + k2M + k8S)/(0.60L + 0.37M). (2c)

These equations were derived by normalizing each postre-ceptor mechanism's unit radiance response by the A me-chanism's unit radiance response for a given wavelength.

In Eqs. (2), A corresponds to the achromatic system,which signals whiteness (or luminance) information, T cor-responds to the R/G channel, and D corresponds to the B/Y

0740-3232/89/091297-05$02.00 © 1989 Optical Society of America

J. K. Hovis and S. L. Guth

1298 J. Opt. Soc. Am. A/Vol. 6, No. 9/September 1989

LEFT EYE RIGHT EYEFig. 1. Diagram of the dichoptic ATDN model described in thetext.

channel. The kl coefficient for Sin Eq. (2b) was adjusted byBenzschawel and Guth to optimize intensity-dependent pre-dictions of small-step hue-discrimination data, but they sug-gest that the coefficient may be constant when one is pre-dicting large color differences and color appearances in gen-eral.

So that data from various dichoptic color-mixing studiescould be predicted, the S coefficient for the D mechanism inEq. (2c) was changed from the constant of 0.048 to a variable.In addition, the M receptor (with a variable coefficient) wasadded as an input to D. These variable coefficients for Sand Mare dependent on the light-adaptation level.'2 At lowlevels, the M coefficient is large relative to the S coefficient,whereas the converse is true at high levels. This modifica-tion of the D mechanism's inputs was proposed by Inglingand Tsou14 to account for the shift in the spectral location ofunique green with changes in light adaptation. However,for the present predictions, it is not necessary to derivevalues for the receptor coefficients k2 and k3. The cl, c2, andC3 coefficients serve as scaling factors and adjust theamounts of A, T, and D that are operated on by subsequentnonlinear neural functions.

The individual-hue nonlinear intensity-response func-tions of the Benzschawel-Guth second-stage outputs are

R = T 09 3/(T 09 3 + 1.3)

G = -[T" l/(T1 1 + 0.83)]

B = D0.75/D0 75 + 3.0)

for T > 0,

forT < 0,

for D > 0,

Y = - [D'l2 /(D' 2 + 0.68)] for D < 0,

(3a)

(3b)

(3c)

(3d)

where R, G, B, and Y represent the red, green, blue, andyellow responses, respectively.

PREDICTIONS

A prediction that follows from this model is that, for dichop-tic presentation, the green-red (G/R) luminance ratio re-quired to obtain a unique yellow percept (i.e., adjusting thered response from one eye to equal the green response from

the other eye) should initially decrease with increasing lumi-nance, because the green postreceptor hue response in-creases faster than the red postreceptor hue response asluminance increases. However, at the higher luminancesthis trend should reverse, and the ratio should increase withfurther increases in luminance, because the green responsereaches its asymptotic value while the red response is stillincreasing. The nonlinear red and green hue responses as afunction of the T channel's output are illustrated in Fig. 2.For monoptic presentations, the model (as do most models)predicts that the G/R ratio required to obtain unique yellowis invariant (i.e., adjusting the receptor inputs into the oppo-nent T mechanism so that the output equals zero), becausereceptor neural responses increase at the same rate withincreasing luminances. 15

In addition to predicting a decrease in the dichoptic G/Rratio with increasing luminance, the model indicates thatthe dichoptic G/R ratio may be greater than the monopticratio at low luminances but less than the monoptic ratio athigh luminances. This second possibility is illustrated withthe following example.

In order to obtain unique yellow from a monoptic red-green mixture, the receptor inputs into the T mechanismmust sum to zero. According to Eq. (2b), when a mixture'sT response is zero the T responses of the individual wave-lengths are equal but of opposite sign. If these two lights,which produce T responses that are equal in magnitude, arenow presented dichoptically and the absolute values of theirT responses are below -1.0 log unit, then Fig. 2 shows thatthe red response will be greater than the green response;therefore the fused mixture appears reddish, and, in order toobtain a unique yellow percept, the subject will require adichoptic G/R ratio that is greater than the monoptic ratio.At higher luminances (or for T values greater than -1.0 logunit), Fig. 2 shows that, for equal inputs, the green responseis greater than the red response, so that the fused perceptappears greenish, and the subject requires a dichoptic G/Rratio that is less than the monoptic ratio.

These predictions were tested by determining the amountof a 550-nm light required to obtain a unique yellow percept

04

(0

0a-

0-j

l - -I I- I I I I I I I I X

0.0 GREEN RESPONSE

-0.4 o<~~~~~~~RD RESPONSE

-0.8 - ,

-1.2 _-v

-1.6 //

-2.01 / , I I I I I I I I I I I I -2.0 -1.5 -1.0 -0.5 0.0

LOG of T INPUT

Fig. 2. Intensity-response functionsresponses.

0.5 .0 1.5

for the red and green hue

. . . . . . . . .


.


when admixed with 610-nm light at various luminances forboth dichoptic and monoptic presentations.

METHOD

ApparatusAs diagrammed in Fig. 3A, lights from two monochromators,Ml (Oriel) and M2 (Bausch & Lomb), were imaged ontodiffusing screens DF1 and DF2 by lenses Li and L2. Ra-diances were adjusted by either the subject or the experi-menter, using servo motors that rotated balanced Inconel-type neutral-density wedges Wi and W2. A long-wave-length pass filter was always present in the 610-nm channel.For monoptic trials (Fig. 3B), mirror MR2 was lifted fromthe light path so that light from the two monochromatorswas combined at beam splitter BS and imaged onto DF2.Synchronized shutters, S1 and S2, were placed at the mon-ochromators' exit slits in order to flash the lights at 0.5 Hz.

Luminances of the lights from the diffusing screens weremeasured by the portion of the light from Ml transmittedthrough the partially silvered mirror MR1 onto photodetec-tor PD1 (PIN-lOAP, United Detector Technology) and byreflecting (from BS) a portion of the light from M2 onto anidentical photodetector PD2. Output voltage of the detec-tors was displayed on a Tektronix 502 oscilloscope. Thevoltage-versus-luminance relationship was calibrated forthe two wavelengths by measuring the luminance of eachdiffusing screen with a Spectra Pritchard photometer placedat the subject's viewing distance. Photometer readingswere reference to an external source traceable to the Nation-al Institute of Standards and Technology.

Stimulus fields for each eye subtended 30' within a darksurround at the 50-cm viewing distance. The fields wereimaged at optical infinity by +2.00 lenses located at thesubject's spectacle plane. The lenses' optical separationwas varied to obtain comfortable and stable fusion. Sub-jects viewed the fields through 3-mm artificial pupils, whichwere positioned to obtain maximum brightness of each testfield. The subjects' head positions were stabilized with ad-justable chin and forehead supports.

In order to provide fusional clues in addition to the testfields' borders, four white lights, each subtending 9', wereplaced peripherally to each stimulus field. These lightswere produced by fiber optics and positioned 0.50 from thestimulus field's border so that they appeared to be at onecorner of an imaginary square centered around each testfield.

SubjectsThe three male subjects and one female subject had normalcolor vision in each eye and a minimum of 30" stereothre-shold. Color vision was evaluated by the Nagel Anomalo-scope and Farnsworth 100 Hue Test. Stereothresholds weremeasured with the Randot Stereo Test. Each subject had atleast 4 h of practice in obtaining dichoptic and monopticunique yellows.

ProcedureAfter 5 min of dark adaptation, subjects adjusted the lumi-nance of the 550-nm light until the mixture with the 610-nmlight appeared neither red nor green. (Except for the lowest

APD2

7 7 1e 0.00 I ARTIFICIAL

j DF I PUPIL

E~~~~~lt~~ -/ 4 R

SI

| D2

E~ ~~L W2 BS 4------ .A RTIF---°CIAL-Sli L2 W2 ! es DF2 PUPIL

LI WI PDIS2

Fig. 3. Schematic of the apparatus.

dichoptic luminance condition, the residual hue appearedunique yellow. At the lowest luminance, two subjects re-ported that the residual hue of the dichoptic mixture wasgray, and the other two reported that the hue appearedunique yellow.)

For a given session, the luminance of the 610-nm light wasfixed at a luminance ranging from 0.63 to 10.0 cd/M2. The610-nm luminance range was limited because subjects no-ticed rivalry at brighter levels. The session viewing condi-tion was one of four possibilities: (i) 550-nm light presentedto the right eye and 610 nm presented to the left eye (R550-

L610), (ii) 550 nm presented to the left eye and 610 nmpresented to the right eye (R6, 0-L550), (iii) both stimuli pre-sented to the right eye, and (iv) both stimuli presented to theleft eye. The first two conditions permitted evaluations ofocular dominance, and the last two conditions permittedevaluations of between-eye differences in color processing.

During a session, subjects made four settings, with theexperimenter randomly adjusting the 550-nm luminance af-ter each setting. There were five replications of each view-ing condition. The viewing condition and 610-nm lumi-nance level for each session were randomly chosen.

RESULTS

Figure 4 shows the mean logarithms of monoptic and di-choptic G/R ratios for three subjects. Each mean is onesubject's pooled monoptic or pooled dichoptic data, sinceanalyses of variance did not reveal significant (p S 0.05rejection level) between-eye or ocular dominance effects forthese three subjects. Only subject CC showed between-eyeor dominance effects. Figure 5 shows that she requiredmore green to obtain a unique yellow when viewing with herleft eye and relatively more green to obtain unique yellow forthe R 6,0-L5 50 dichoptic condition. Analyses of variance


1300 J. Opt. Soc. Am. A/Vol. 6, No. 9/September 1989 J .HvsadS .Gt

0

zz

-J

0-J

-0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2

LOG LUMINANCE of 610 nm

Fig. 4. Mean monoptic and dichoptic G/R ratios required to pro-duce unique yellow as a function of the 610-nm light's luminance forthree subjects who did not show between-eye differences. Eachsubject's functions are arbitrarily shifted along the ordinate. Unitson the ordinate are 0.1 log unit. Values listed in parentheses are theactual log ratios for the above point. Errors bars represent 1standard error.

0

ILdUzz-

(90-J

0.6

0.4

0.2 I-

0.0

-0.2 I-0

I I I I I I ISUBJECT CC

...MONOPTIC R E0 L E

- DICHOPTIC U 610 (R E)550 (L E)

- 0 610 (L E)550 CR E)

I I I

.4

T -L -

I 7 I '

-0.2 0.0 0.2 0.4 0.6 0.8

LOG LUMINANCE of 6I0nm

1.0 1.2

Fig. 5. Mean monoptic and dichoptic G/R ratios required to obtainunique yellow for subject CC. Error bars represent -Ii standarderror.

showed that these differences were significant (p 0.05).Nevertheless, both the R55o-L6 ,o and R610-L550 dichopticfunctions are below both monoptic functions at the threehighest luminance levels, whereas, at the lowest levels, dif-ferences between the monoptic and dichoptic functions arenot so apparent. Therefore, despite the between-eye differ-ences, her data show the same trends as did those of theother three subjects.

The important finding revealed in these figures is that, forthe range of luminances evaluated, all four subjects showed asystematic decrease in the dichoptic G/R ratio required toobtain a unique yellow (neither red nor green) percept asluminance increased, whereas the monoptic G/R ratio re-mained invariant, thus confirming qualitatively the model'spredictions. (Because of the rivalry experienced at brighterlevels, it was not possible to evaluate the cancellations atluminances where the response functions begin to asymp-tote.)

DISCUSSION

The result that, at most test luminances, the dichoptic G/Rratios required to obtain unique yellow were less than themonoptic ratios confirms the general finding reported in theIntroduction that dichoptic mixtures require less of thegreen primary to match a yellowish standard. The excep-tions that, at the lowest luminance, the monoptic and di-choptic ratios are equal for subject LK and the dichopticratios are relatively greater for subjects JH and CC are con-sistent with the model's predictions and with results from aprevious dichoptic red-green-cancellation study.' 2 In thisearlier green-to-cancel-red experiment, the reddish testlight's luminance was constant and its wavelength was var-ied. For test wavelengths with a small T component (e.g.,590 and 600 nm), the dichoptic G/R ratio was either greaterthan or equal to the monoptic G/R ratio. However, as wave-length (and the T responses) increased from 610 to 660 n,the dichoptic G/R ratio systematically decreased.

The present result that subject LR's dichoptic ratios arealways less than the monoptic G/R ratios suggests that his Tresponses for these test wavelengths are greater than thoseof the other three subjects.

The present results also suggest that the relative contribu-tion of a green light to the resultant dichoptic mixture's hueincreases as luminance increases. This implication dis-agrees with the conclusion of de Weert and Levelt 6 that, asluminance increases, lights from the midspectral region (540nm) contribute less to the hue of the fused impression whenmixed dichoptically with a longer-wavelength light (600nm). However, because their standard may not have ap-peared unique yellow, Bezold-Bruecke effects and blue-yellow nonlinearities may have affected the appearance ofboth the monoptic and dichoptic mixtures' hues, thus mak-ing comparisons with the present experiment difficult.

QUANTITATIVE PREDICTIONS

For monoptic unique yellow to be obtained, the T responseproduced by 550-nm light must be equal, but of oppositesign, to the T response produced by 60-nm light. That is,the T response of the 550-610-nm mixture must equal zero.

SUBJECT LKK - - - - ~~~~~~~~~~(0.19)-

SUBJECT LR

(0.16)-

- ~~~~~~~SUBJECT JH

- .-.-- ~.---.. - -' .- -' (0.24)

-*@MONOPTIC-

--- DICHOPTIC



0t 0.3

L'i 0.2 …

< 0.1 _Zi 0.0 MONOPTIC * OBTAINED

D ~~~0 PREDICTED

- DICHOPTIC * OBTAINEDz 0.1 0 PREDICTED

( -0.2( -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2

LOG LUMINANCE of 610nm

Fig. 6. Predicted and mean G/R ratios required to produce uniqueyellow as a function of the 610-nm light's luminance. The obtainedfunctions are the means of the individuals' data shown in Fig. 4.

Predicted monoptic G/R ratios were determined by usingEq. (2b) to calculate the relative luminance of 550-nm lightthat produced a T response equal in magnitude to the Tresponse produced by 610 nm at unit luminance. The L andM receptor coefficients in Eq. (2b) were adjusted to give apredicted G/R ratio that equaled the mean of the threesubjects' monoptic ratios shown in Fig. 4. (Because of thebetween-eye differences, subject CC's data were not mod-eled.) The receptor coefficients were 0.90 for L, 1.3 for M,and 0.2 for S.

For dichoptic unique yellow to be obtained, the rednessresponse, R, elicited by 610-nm light from one eye mustequal the greenness response, G, from the other eye. Thatis, redness and greenness cancel centrally. Dichoptic G/Rratios were calculated by substituting Eq. (2b) into Eqs. (3a)and (3b). After rearranging Eq. (3b), we calculated therelative luminance of 550-nm light required to produce a Gvalue equal to the R value calculated for 610-nm light. Al-though the scaling factor in Eq. (2b) does not affect thepredicted monoptic ratios, it does affect the dichoptic pre-dictions, because the equality between R and G varies withscaling changes in T. Furthermore, the c2 value will bedependent on which test luminance corresponds to the unitluminance value; therefore the c2 value was chosen to pro-vide the best visual fit to the mean of the dichoptic datashown in Fig. 4, with the lowest test luminance correspond-ing unit luminance.

Figure 6 shows the mean monoptic and dichoptic func-tions and the model's predictions. The c2 value was 0.45.As is evident from the figure, the model provides an excel-lent fit to the data.

This study has shown that the dichoptic G/R ratio re-quired for unique yellow to be obtained decreases with in-creasing luminance, whereas the monoptic G/R ratio re-mains invariant. This result confirms the prediction madeby an extension of the ATDN model and suggests that adifference in monoptic and dichoptic mixing may reflect

differential postreceptor nonlinearities in the opponentmechanisms that occur before the information from the twoeyes is combined, even if receptor neural inputs to opponentmechanisms increase equally as intensity increases.

ACKNOWLEDGMENTS

This research was supported by a grant from the NationalSciences and Engineering Research Council of Canada.

This paper was presented at the annual meeting of theAssociation for Research in Vision and Ophthalmology, Sar-asota, Florida, 1988.

S. L. Guth is also with the Department of Psychology,Indiana University.

REFERENCES AND NOTES

1. J. Southall, ed., Helmholtz's Treatise on Physiological Optics(Dover, New York, 1962), Vol. 3.

2. E. Hering, Spatial Sense and Movements of the Eyes, translat-ed by C. Radde (American Academy of Optometry, Baltimore,Md., 1942).

3. W. Trendelenberg, "Versuche ueber binokulare Mischung vonSpektralfarben," Z. Sinnesphysiol. 48, 199-210 (1913).

4. W. Trendelenberg, "Weitere Versuche ueber binokulare Mis-chung von Spektralfarben," Pfluegers Arch. Ges. Physiol.Menschen Tiere 210, 235-246 (1923).

5. F. H. Thomas, F. L. Dimmick, and S. M. Luria, "A study ofbinocular color mixture," Vision Res. 1, 108-120 (1961).

6. Ch. M. M. De Weert and W. J. M. Levelt, "Comparison ofnormal and dichoptic color mixing," Vision Res. 16, 59-70(1976).

7. S. Hecht, "On binocular fusion of colors and its relation to thetheories of color vision," Proc. Natl. Acad. Sci. (USA) 14, 237-241 (1976).

8. L. M. Hurvich and D. Jameson, "The binocular fusion of yellowin relation to color theories," Science 114, 199-202 (1951).

9. G. Rochat, "Etude quantitative du fusionnement binoculariedes couleurs complementaries," Arch. Neerl. Physiol. 7, 263-267 (1922).

10. C. S. Hoffman, "Comparison of monocular and binocular colormatching," J. Opt. Soc. Am. 52, 75-80 (1962).

11. N. N. Livshitz, "On the laws of binocular color mixture," Dokl.Akad. Nauk. SSSR 28, 429-432 (1940).

12. J. K. Hovis and S. L. Guth, "Dichoptic opponent hue cancella-tions," Optom. Vision Sci. (to be published).

13. T. Benzschawel and S. L. Guth, "ATDN: toward a uniformcolor space," Color Res. Appl. 9, 133-141 (1984).

14. C. Ingling and B. Tsou, "Orthogonal combinations of the threevisual channels," Vision Res. 17, 1075-82 (1977).

15. Recent data [e.g., C. H. Elzinga and Ch. M. M. De Weert, VisionRes. 24, 1911-1922 (1984); Y. Ejima and S. Takahashi, VisionRes. 24, 1897-1904 (1984); Vision Res. 25, 1911-1922, 1985]prove that the assumption that the receptor neural responsesincrease at the same rate is untenable for blue-yellow cancella-tions and for red-green cancellations that result in a uniqueblue percept. However, the large number of studies reportingthat wavelength of unique yellow is invariant with intensityindicates that this assumption is reasonable for red-green can-cellations that result in a unique yellow percept.

J. K. Hovis and S. L Guth

changes in luminance affect dichoptic unique yellow

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