Simultaneous color constancy: papers with diverse...

Vol. 8, No. 4/April 1991/J. Opt. Soc. Am. A 661

Simultaneous color constancy: papers with diverse Munsellvalues

Lawrence E. Arend, Jr.

Eye Research Institute, 20 Staniford Street, Boston, Massachusetts 02114

Adam Reeves

Northeastern University, 360 Huntington Avenue, Boston, Massachusetts 02115

James Schirillo

University of Chicago, 939 East 57th Street, Chicago, Illinois 60637

Robert Goldstein

Eye Research Institute, 20 Staniford Street, Boston, Massachusetts 02114

Received November 28, 1988; revised manuscript received August 14, 1990; accepted October 11, 1990

Arend and Reeves [J. Opt. Soc. Am. A 3, 1743 (1986)] described measurements of color constancy in computersimulations of arrays of colored papers of equal Munsell value under 4000-, 6500-, and 10,000-K daylight illumi-nants. We report an extension of those experiments to chromatic arrays spanning a wide range of Munsell values.The computer-simulated scene included a standard array of Munsell papers under 6500-K illumination and a testarray, an identical array of the same papers under 4000 or 10,000 K. Observers adjusted a patch in the test array inorder to match the corresponding patch in the standard array by one of two criteria. They either matched hue andsaturation or they made surface-color matches, in which the test patch was made to "look as if it were cut from thesame piece of paper as the standard patch." The test and the standard patches were surrounded by a single color(annulus display) or by many colors (Mondrian display). The data agreed with those of our previous equal-valueexperiment. The paper matches were often approximately color constant. The hue-saturation matches were inthe correct direction for constancy but were always closer to. a chromaticity match (no constancy) than to thechromaticity required for hue-saturation constancy.

INTRODUCTION

Color constancy refers to invariance of perceived surfacecolors under changes of illuminant color. In recent yearsthere has been renewed interest in color constancy.'- Mostof this new research has been theoretical: analyses of theo-retical limits of color constancy and proposals for computa-tional strategies. Empirical studies of simultaneous colorcontrast and chromatic adaptation are not directly inter-pretable in terms of surface-color constancy for several rea-sons discussed below.

We have recently begun a series of experiments specifical-ly designed for directly examining human color-constancycapabilities in complex images." 9 Our observers viewed acomputer-simulated scene consisting of two identical arraysof patches of Munsell papers. The standard array was illu-minated with a constant source. The test illuminant variedfrom trial to trial. Observers adjusted one patch in the testarray in order to match the corresponding patch in the stan-dard array.

Our experiments improved on previous studies in severalways:

(1) We made a clear procedural distinction between twokinds of judgment. The first is judgment of the hue, satura-

tion, and brightness of the light that is coming to the eyefrom a point in the scene. We will refer to this variable asunasserted color, short for perceptually unasserted color.10

The observers were instructed to match the hue, saturation,and brightness of the test patch to those of the standardpatch, disregarding all other areas as much as possible. Thesecond kind of judgment is judgment of surface color, aproperty of the surface at a point in the scene. The observ-ers were instructed to make the test patch look as if it werecut from the same piece of paper as the standard patch.

Color constancy refers to perception of surface color rath-er than to sensory appearance. Under some viewing condi-tions there may be a close correspondence between per-ceived surface color and unasserted color. Under other con-ditions there may be a discrepancy. Indeed, one canimagine two kinds of visual system, both having perfect colorconstancy but producing two different appearances: A sur-face might produce identical hues, saturations, and bright-nesses under different illuminations, with no direct sensoryrepresentation of the illumination difference. Alternative-ly, the surface might produce different unasserted colors butbe recognized as the same surface under perceptibly varyingillumination. For example, consider a yellow surface in thegreenish illumination under a tree. In the first kind ofvisual system it would produce the same hue as a yellow

0740-3232/91/040661-12$05.00 © 1991 Optical Society of America

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662 J. Opt. Soc. Am. A/Vol. 8, No. 4/April 1991

surface under full sunlight. In the second visual system itwould have a yellowish-green hue (easily distinguished fromthe full-sunlight hue) that is correctly perceived to be ayellow surface in greenish illumination.

(2) We limited chromatic adaptation to rapid processes,with time constants less than 1 sec. When integrated overtime intervals of the order of minutes, exposure was con-stant, preventing changes in slow adaptation processes.The distinction between rapid and slow adaptive processeshas a long history in vision research.1"1 2

Rapid constancy mechanisms are needed in natural vi-sion. Shading and indirect illumination make uniformlyilluminated scenes rare, and eye and head movementschange focal scenes rapidly. Slow adaptation cannot beappropriate for all regions in a single scene and alters sensi-tivity too slowly to compensate for natural environmentalscanning. Chromatic illumination varies from surface tosurface within scenes because of variation in surface orienta-tion with respect to various light sources. The illuminationvariation can be as large as chromatic reflectance differ-ences. For example, Maximov13 has shown that a yellowdandelion blossom in north skylight has the same chroma-ticity as grass in direct sunlight. Even larger chromaticillumination changes can occur when an object is partiallyilluminated by light that has been reflected from nearbycolored objects.

(3) We used identical reflectances in the test and stan-dard arrays. By providing the same reflectance context forthe test and standard patches, we limit the experimentalindependent variable to illuminant color.

In our first experiment9 we studied simultaneous lightnessconstancy and brightness in simple and complex achromaticpatterns. We found that matches of the brightness of a graytest patch varied substantially as the illumination levelchanged, but matches of its surface color, i.e., lightnessmatches, were remarkably invariant over our 19:1 illumi-nance range. The need to distinguish lightness from bright-ness has often been noted14 but has also often been neglectedin discussions of constancy. The consistency of our obser-vers' data further confirms the multidimensionality of a-chromatic color perception.

In a second experiment' we studied simultaneous constan-cy in simulations of chromatic papers and illuminants. Ourilluminants spanned the chromatic range of normal day-lights. We wished to examine the effect of chromatic inter-actions independent of any effect of luminance variation.We therefore kept the luminance range small by simulatingonly Munsell papers of Value 5.

The observers' unasserted color matches were slightlyshifted in chromaticity from the chromaticities of the stan-dard patches. While the shifts were mostly in the correctdirection for constancy of unasserted color, in all cases theywere small relative to the shifts required for invariance ofunasserted color. On the other hand, our subjects' surface-color matches did approximate constancy of perceived sur-face color, though not nearly so precisely as in the achromat-ic case. Nevertheless, the data qualitatively agreed with theachromatic data: Our observers had approximate constan-cy of perceived 8urface colors in pite of oubotantial differ-ences of unasserted colors.

Various studies of simultaneous color contrast in simple

patterns differ regarding the effects of luminance differ-ences. Some early investigators found maximum inducedhue and saturation when the luminances of the test field andinducing fields were equal,15 while more recent researchershave reported either larger effects when the test-field lumi-nance was below that of the inducing field1'8 or no effect ofluminance.'9 It is therefore possible that unasserted colormight be closer to constancy if there were larger luminancedifferences among the color patches.

We report here extensions of our experiments to simulat-ed patterns of colored papers spanning a wide range of lumi-nous reflectances. As in the earlier experiments we usedboth simple and complex patterns, and we asked for sepa-rate matches of unasserted color and perceived surface color.

We also report a control experiment in which we present-ed the patterns in brief flashes. A comparison with theprevious experiments provides a measure of the effective-ness of the voluntary-eye-movement control of adaptationused in those experiments.

METHODS

EquipmentThe equipment was that used in the previous two experi-ments. Details of the equipment are reported elsewhere.' 9

All patterns were presented on a carefully calibrated Tek-tronix 690SR high-resolution color monitor under the con-trol of an Adage 3000 image processor and a VAX 11/750minicomputer. Chromaticities were based on measure-ments of the spectral radiances of the phosphors. Chroma-ticity and luminance did not vary appreciably over the effec-tive viewing area. Nonlinearity of the relationship betweendigital data and luminance was measured in each color chan-nel individually and linearized by means of 10-bit lookuptables.

Subjects controlled the color of the test patch with a high-resolution graphics tablet. The position of the bit-padpointer was interpreted by the computer as a position withinan RGB color triangle, and the test-patch chromaticity wasset accordingly. Vertical cursor movement controlled yel-low-blue content and horizontal movement controlled red-green content. The luminance of the test patch increased ata constant logarithmic rate when the subject held down oneof two buttons on the bit-pad pointer and decreased whenanother was depressed. Between trials the computer ran-domly offset the luminance and the horizontal and verticalpositions of the color mapping on the bit pad within a rangeof d10% in order to prevent position cues from influencingthe matches. The spatial resolution of the bit pad exceededthe 10-bit resolution of the image processor's digital-to-ana-log convertors.

StimuliThe stimuli were simulations of arrays of uniformly illumi-nated, flat, matte Munsell papers; i.e., there were no high-lights or shadows, and the stimulus appeared flat. Chroma-ticities and luminances of the 32 papers used, under threedaylight illuminants (4000-, 6500-, and 10,000-K correlatedcolor temperatures), were based on the published tables ofKelly et al.2 0 The 4OOO and 1OOOOK illuminantg reprecentthe reddish and bluish extremes of daylight, and 6500 Krepresents average sunlight.

Arend et al.


Since the tables did not include entries for the desireddaylights, we obtained the required chromaticities by meansof an interpolation algorithm. The logic of the simulation isbased on superposition of lights: Conceptually, the 4000-and 6500-K correlated color temperature white lights wereobtained by mixing appropriate amounts of illuminants Aand C used by Kelly et al. and the 10,000-K light by mixingtheir sources S and D. The light reflected from each of the32 papers under, for example, the 4000-K light is just thesum of the reflected lights from the A and C illuminantcomponents of the 4000-K source. In practice, tristimulusvalues for the simulated paper-illuminant combinationswere obtained by linear interpolation between the tabledtristimulus values for illuminants A, C, D, and S. The re-quired ratios for the mixtures of the sources were obtainedby using correlated color temperature lines.21 The resultingchromaticities were produced on our monitor and will here-

Standard

3 01

1±7.1

Ilium. Fixed6500 K

after be referred to by the names of the simulated papers(Munsell notation2 2) and daylight illuminants.

The disk-annulus stimuli are illustrated in Fig. 1(a) andthe Mondrian stimuli in Fig. 1(b). The left-hand display(standard) was given a simulated illumination of 6500 K onall trials, the right-hand display (test) either 4000 or 10,000K. The papers were chosen to provide as large and as uni-form coverage of the Munsell set as possible, given the con-straint that the color gamut of our monitor must simulate allthe selected papers under all illuminants. The hue andchroma composition of the patterns [Fig. 2(a)] was the sameas in our constant-value experiment,' with the exception of afew patches that were made black in order to span the entirerange of physical luminous reflectances.

Figure 2(b) gives the pattern luminances. Two lumi-nance-contrast conditions were run for each pattern com-plexity, one in which the test-patch luminance exceeded the

Test

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(b) Mondrian stimulus diagram.

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(a) Mondrian Munsell designations, (b) Mondrian lumin-

pattern mean luminance and one in which it was less thanthe mean luminance. In the disk-annulus condition theannulus luminance was either a factor of 4.4 greater or afactor of 4.4 less than the test-disk luminance. In the Mon-drian condition two arrangements of test-patch luminanceswere used. In one condition (luminance arrangement 1) thered- and yellow-test-patch luminances were greater than theMondrian mean luminance and the blue- and green-patchluminances were less than the mean luminance. In theother (luminance arrangement 2) the luminance relationswere reversed, with the blue and green patches above themean luminance, the red and yellow below the mean lumi-nance. All other patch luminances were the same in the twoconditions. In the second condition the yellow test patchhad the expected yellow-brown appearance.

Our three illuminants were simulated at the same illumi-nance. Thus the only effect on test-patch luminance ofchanging the illuminant was that resulting from interactionof the illuminant spectral distribution and the paper spec-

tral reflectance distribution. As can be seen from the valuesin Fig. 2(b), these were small because of the broad spectraldistributions of the papers and lights simulated.

ProcedureAt the beginning of the first session the method of control-ling chromaticity and luminance was explained to the ob-servers, who were then given approximately 1 min of prac-tice with the controls and asked whether they understoodhow they were used.

Observers initially adapted to a spatially uniform field,6500 K, 20-cd/M2 white, for 3 min. They then viewed thecontinuously presented test and standard arrays and variedthe chromaticity and luminance of the test patch in order tomatch the corresponding standard patch. Observers wererequested to spend approximately the same amount of timelooking at each display and to alternate between the displaysapproximately once per second. Trials for the five differenttest patches, red (Munsell R 5/8), yellow (Y 5/4), green (G 5/4), blue (B 5/4), and gray (N 5/), occurred in pseudorandomorder, once under 4000 K and once under 10,000 K, in each ofthe five blocks of trials.

TaskIn the unasserted-color condition, observers were instructedto match the hue, saturation, and brightness of the testpatch to those of the standard patch. They were told todisregard, as much as possible, other areas of the screen.

In the perceived-surface-color condition, observers weretold that the two displays were a simulation of identicalpaper arrays illuminated by different lights. They wereinstructed to make the test patch "look as if it were cut fromthe same piece of paper" as the corresponding patch in thestandard array. It was pointed out that other patches in theMondrians had similar colors (there were no patches identi-cal to the test patch) and that the relations among suchgroups might be useful. Hence, they could (for example)match the standard red at 6500 K with the correspondingtest patch at 10,000 K by comparing the standard patch withother reds (or oranges or violets) within the 6500-K standardand then transposing the relevant relations to the 10,000-Kdisplay.

Since three of our four observers (LA, AR, JS) were theauthors, they were familiar with the tasks. For them, theinstructions merely served as reminders for the fixation pro-cedures and use of relations among patches. The fourthobserver (DA) was unaware of the hypotheses and had noprior experience with chromatic adjustments (he had experi-ence as a subject in achromatic matching experiments). Afifth subject, also naive, was run in one session each of theunasserted-color and apparent-surface-color tasks. Herdata are not reported here as they were not complete andclosely resembled the data of three of the other subjects.Both of the naive subjects found the instructions sufficientfor performing the tasks. With no prior training they bothproduced data with differences between tasks comparablewith those of the most experienced observers, LA and AR.

Data Analysis

Plotting MethodBefore presenting the data, let us consider our plottingmethod and the meaning of various data patterns. Figure 3

Arend et al.


u'v' of R 5/8under10,000 K

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Mean x,y of S'sMatches

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task would be roughly equivalent to color matching twopatches on a dark surround. The subject would set the testpatch to approximately the chromaticity of the standardpatch, i.e., R 5/8 under 6500 K, in both illuminant conditions[Fig. 3(a)]. In doing so, he would not be setting the patch inthe test illuminant to the R 5/8 reflectance of the standardpatch which gives the chromaticity indicated by the opentriangle. Instead he would set the test patch to the reflec-tance that, under the test illuminant, gives the same chroma-ticity as R 5/8 under the 6500-K standard illuminant. Inother words, there would be no constancy of surface color.

If the subject had perfect surface-color constancy, on theother hand, he would set the test-patch chromaticity to thatof R 5/8 under the 4000-K test illuminant, the open triangle,or, for the 10,000-K test illuminant, to the open square [Fig.2(b)].

Mean u',v' of S'sMatches

(b)

a

b

Constancy IndexIn achromatic surface-color constancy there are severalwidely accepted, unidimensional indices of constancy, forexample, the Brunswik ratio. We have attempted to devel-op a comparable index of chromatic constancy in order tofacilitate comparisons across different experimental condi-tions. We decided to restrict the index to (primarily) chro-matic dimensions and ignore, for the moment, the lumi-nance dimension. Our achromatic constancy experiments9

indicated that there should be no complications due to light-ness variation. Nevertheless we decided to analyze light-ness separately in order to eliminate any possibility of lumi-nance matches influencing our chromatic index. Our indexis not, therefore, closely related to color difference formulasdeveloped for other purposes." We emphasize that thisindex is for comparative purposes and is not necessarilyoptimal from a theoretical standpoint. It is difficult tojustify any single scalar index as it requires collapsing a two-dimensional quantity into a single number. Under theseconditions we decided in favor of simplicity.

We employed the 1976 CIE u', v' color space, which pro-vides a crude approximation to equal, just-noticeable differ-ences in the region of our primaries. The deviation fromcolor constancy can be represented by the Euclidean dis-tance b from the match point Po to the chromaticity P2, atwhich color constancy would be perfect [Fig. 3(c)]. That is,

(c)Fig. 3. Diagram of logic of data graphs: (a) appearance of data incase of almost no color constancy, (b) appearance of data in case ofnearly perfect color constancy, (c) distances used in calculation ofconstancy index (= 1 - b/a).

represents a small piece of the 1976 CIE u', v' chromaticitydiagram around the locus of our red test paper, R 5/8. Theopen circles, triangles, and squares are the chromaticities ofR 5/8 under the 6500-, 4000-, and 10,000-K illuminants,respectively. The open circles are therefore the chromatic-ity of the R 5/8 in the standard array. Closed triangles andsquares are (hypothetical) settings of the test patch underthe 4000- and 10,000-K illuminants, respectively.

If the visual system were such that the stimulus patternsurrounding the test patch had no effect on the appearancesof the test and the standard patches, the two test-illuminantconditions would produce identical matching data. The

b = [(u - u'2)2 + (O - '2 )2 ]1/2 . (1)

The different test patches may be made comparable by di-viding each b by the Euclidean distance a between the chro-maticity P, of the test patch when illuminated by the 6500-Kstandard and the chromaticity P2 of the same patch underthe comparison illuminant:

a = [(u'l U'2)2 + (v' - v' 2)2 ]' 2 (2)

Our chromatic constancy index is then

I = 1 - b/a, (3)

the distance from constancy relative to the colorimetric shiftof the test patch, averaged over the five test patches. Per-fect constancy is indicated by I = 1, and a chromaticitymatch between test and standard patches (no constancy) isindicated by I = 0.

Alrend et al.


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Fig. 4. Mean-chromaticity settings for Mondrian patterns, first luminance arrangement: open symbols, theoretical chromaticities; closedsymbols, mean-chromaticity data. The left-hand column shows unasserted-color matches; the right-hand column shows surface-colormatches. The rows present data by observer. Error bars represent -1 standard error.

RESULTS

Five-trial mean-chromaticity settings for the Mondrian pat-terns (luminance arrangement 1) are plotted in Fig. 4. Thematches in the unasserted-color condition (left-hand pan-els) were closer to the 6500-K theoretical points than to thetest-illuminant theoretical points. Thus, when the testpatch was at the correct simulated chromaticity under thetest illuminant (open squares or triangles), its unassertedcolor did not match that of the standard patch. To producea match, the observer required a chromaticity closer to thatof the standard patch. Moreover, the illumination differ-ence between the two displays was always quite visible.

On the other hand, for three of our four subjects theapparent surface-color matches (right-hand panels) weresignificantly closer to surface-color constancy. Even thoughthe patches in the test displays had different unassertedcolors from their counterparts in the standard display, the

subjects knew approximately what sensory appearance thestandard paper would have under the test illuminant andcould set the test patch chromaticity in order to produce it.

This qualitative description is supported by our constancyindex (Fig. 5). The unasserted-color matches were closer toa chromaticity match (I = 0) than to constancy (I = 1). Bycomparison, the surface color matches were closer to con-stancy. Indices calculated by using data from our equal-value experiments' are plotted for comparison.

Means from luminance arrangement 2 Mondrians areplotted in Fig. 6. The pattern of the data is much the sameas for luminance arrangement 1, even for the yellow patchwith its different appearances in the two conditions (yellowin 1, brown in 2). The constancy indices are similar for thetwo luminance arrangements (Fig. 7).

Means from both luminance ratios of the disk-annuluspatterns are shown in Fig. 8. For all but observer JS'ssurface-color matches, the constancy index was higher when

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the annulus luminance was greater than that of the disk (Fig.9). On the other hand, the effect of the task was inconsis-tent from subject to subject. For observer AR the differencebetween the unasserted-color matches and the apparent-surface-color matches was smaller for disk-annulus patternsthan that for Mondrian patterns. For LA there was littledifference between the two stimulus conditions, and theMondrian data from our equal-value experiment were nomore constant than the disk-annulus data. We tentativelyconclude that pattern complexity had little effect on eithertask.

6500-K-6500-K MATCHES

For analysis of the perceptual meaning of our data the theo-retical points described above are the correct referencepoints; they describe the physical reality. The vectors fromthe data to the 6500-K point might be slightly misleading asempirical descriptions, however. Matches of a 6500-K illu-

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minated test field to the 6500-K illuminated standard fieldmight not fall exactly on the theoretical 6500-K point. Sub-jects often introduce biases into matches, based on spatialposition or based on which field is fixed and which variable.

To examine this issue, we reran the unasserted-color-match condition, using test Mondrian illuminants of 4000,6500, and 10,000 K. Trials with the three test illuminantsappeared once each, in random sequence, in each of fiveblocks of trials. All other procedures were the same as in theabove experiment.

Mean-chromaticity settings are shown in Fig. 10. Thematches for the 4000- and 10,000-K illuminants were similarto those in Fig. 4. For all four subjects there were somebiases present in the 6500-K-6500-K matches but not for allcolors. The R, G, and N matches for all four subjects wereclose to the chromaticity matches. Two of the subjects' Ymatches also showed little bias, but LA and AR both showedbiases toward higher purity (relative to the N 6500-K theo-

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retical point). All four observers showed higher-purity bias-es for the B patch.

The tendency to set the patch to higher purity makessense in terms of the observers' introspections. The observ-ers had to be reminded each session to resist the urge tomatch the hue precisely, at the expense of accurate satura-tion matching. This bias probably explains a portion of thevectors in Figs. 4 and 5. The problem is clearest in AR's Ypoint. His vectors to the 6500-K point are misleadingly longwith respect to differences among the appearances of thetest illuminants. Had we always included the 6500-K testilluminant, we might have often gotten this configuration.Nevertheless, the longer vectors are perceptually correct inthe sense that he was actually selecting surface colors thatwere discrepant from identical surface color.

FLASHED MONDRIAN EXPERIMENT

The above experiment and our previous constancy experi-ments all involved continuously presented displays. In

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The subjects adjusted the test patches as in the aboveexperiments, according to the unasserted-color-match in-structions.

Results and ConclusionsMean chromaticities from five trials are plotted in Fig. 12.The data closely resemble those from the continuous-pre-sentation experiments. Figure 13 shows the constancy indi-ces for these flashed data compared with the unasserted-

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0. 40, ~~~~~~~. . .. . . . . . .. . . . . . . . . . . .,, ...a e

,, , , ,, - ~~. ..... E ... .. I~~~~~~~~~... ... .-... . . : , .. .

Fig. 11. Timing sequence in flashed-exposure experiment.0. 35

0. 10 0. 15 0.20 0.25 0. 30 0. 35 0. 40

U.

those experiments we attempted to isolate rapid processesfrom slow ones by ensuring that the stimulus for slow mecha-nisms was approximately constant over the experiment.This required that retinal exposure, integrated over times ofthe order of 1 min or more, had constant chromaticity. Theobservers were preadapted for 3 min to a uniform field of thestandard 6500-K illuminant. Then the 4000- and 10,000-Ktest-illuminant trials were presented in pseudorandom or-der. To minimize drifts of slow adaptation in the directionof the current test illuminant, the observers were instructedto make frequent eye movements (approximately once persecond) between the test pattern and the 6500-K standardpattern.

There were several reasons for preferring continuous pre-sentation to more controlled flash procedures for most of ourexperiments. Continuous presentation provided more nat-ural viewing conditions, with temporal changes confined tothose due to eye movements. With the Mondrian patterns,for flashed exposures the observers required a good deal oftime and effort to locate the critical patches. However, as aseparate control experiment to test the effectiveness of ourcontinuous-presentation procedures, our observers madeunasserted color matches in briefly exposed Mondrians, al-ternated with a uniform 6500-K gray field.

MethodsThe spatial patterns were the Mondrians of our equal-valueexperiment.' All the papers were simulated at Munsell val-ue 5/, making their luminances approximately equal (_20cd/m 2 ).

The subjects were preadapted for 3 min to a 6500-K white,spatially uniform field. The test and the standard patternswere then simultaneously presented in 1-sec exposures, inalternation with 5-sec exposures of the 6500-K homogeneousfield (Fig. 11). This sequence was continued until the sub-

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O. 10

0. 15 0. 20 0. 25 0. 30 0. 35 0. 40

UI

/ ., iS 0. 5 0.20 0.25 0.30 0. 35 0.40

UI

Fig. 12. Mean-chromaticity settings of flashed Mondrian testpatches, unasserted color criterion. Symbols and rows as in Fig. 4.Error bars represent - 1 standard error.

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0.6-

0.5 -

0.4-

0.3

0.2-

0.1 1

0.0LA AR Js

Subjact

Fig. 13. Mean-constancy index for unasserted-color matches, con-tinuously presented, equal-value Mondrians (Continuous) versusflashed equal-value Mondrians (Flashed). Continuously presentedequal-value data were previously published.' Error bars represent+1 standard error.

color-match data from the equal-value Mondrian experi-ment. We conclude that the observers' voluntary eyemovements in the previous experiments were sufficient toprevent important slow-adaptation effects.

DISCUSSION

The Mondrian data from the current experiment are sub-stantially the same as those from our previous equal-valueexperiments, and we conclude that relations among appar-ent surface colors and unasserted colors in complex patternsare largely independent of the luminance contrast of thescene.

For both experiments our data show that rapid processesalone (e.g., simultaneous color contrast) are insufficient toproduce invariance of unasserted color over the range ofdaylight illuminants. Accordingly, our overall conclusion isthat there is little constancy of unasserted color from oneilluminant to another within the same scene, provided thatthe observer scans the scene sufficiently rapidly that slowadaptation is uniform over the retina.

The paper-match data, on the other hand, show that theunasserted-color differences perceived between test andstandard Mondrians are systematic. The illumination dif-ference is always visible as a pattern of correlated shifts ofunasserted color. Our subjects' attempts to produce theappearance of the standard paper under the test illuminantwere often of approximately the correct magnitude and di-rection, though seldom exactly color constant. Thus thevisual system has rapid processes that can distinguish be-tween reflectance and illumination gradients, computing apercept that represents both. This multivalued perceptualrepresentation has been previously noted and systematicallystudied in achromatic vision. 914

The small effects of stimulus complexity require com-ment. These results are misleading with respect to theimportance of pattern complexity. Disk-annulus patternsare too impoverished to support monostable perception ofsurfaces and illuminations. The bluish hue of our MunsellN test annulus under the 10,000-K illuminant is just as likely

to be the result of a 6500-K illuminant falling on a bluish-gray surface as it is to be due to a bluish illuminant falling ona gray surface. In the Mondrians the situation is less ambig-uous perceptually. The chromaticity shifts between patch-es in the standard Mondrian and the test Mondrian arecorrelated. The simplest perceptual explanation (i.e., theone requiring the fewest convenient environmental coinci-dences) for this covariance is that the test illuminant is abluer (in the 10,000-K case) color than the standard illumi-nant. It is difficult or impossible to perceive our Mondrians'hues as being caused by two different populations of reflec-tances under a single illuminant, even though the chromati-cities all lie within the gamut of Munsell papers under 6500K. The corresponding shapes and spatial positions in ourMondrians no doubt contribute to the stability of this per-cept, but random rearrangement of the chromaticities in thetest Mondrian does not destroy the perception of two illumi-nants. With the disk-annulus pattern, on the other hand, itwas only our instruction, that observers consider the testannulus to be the same gray surface-color under a differentilluminant, that permitted the apparent-surface-color datato resemble those from the Mondrians. Had we described itas a bluish-gray paper under the same 6500-K illuminationas the standard annulus, the apparent-surface-color datawould presumably have been much closer to chromaticitymatches to the standard disks.

There remain at least two conditions for which theremight be large, rapid unasserted-color shifts: single illumi-nant scenes and scenes with gradual spatial changes of illu-minant. None of our experiments would have revealed asimultaneous mechanism normalizing unasserted color overthe entire visual field.

ACKNOWLEDGMENTS

This research was supported by U.S. Air Force grantsAFOSR-89-0377 to L. Arend, AFOSR-84-NL-044 to A.Reeves, and AFOSR-F49620-87-C-0018.

L. Arend and R. Goldstein are also with the Department ofOphthalmology, Harvard Medical School, Boston, Mass.

REFERENCES AND NOTES

1. L. Arend and A. Reeves, "Simultaneous color constancy," J.Opt. Soc. Am. A 3, 1743-1751 (1986).

2. P. Sallstr6m, "Some remarks concerning the physical aspect ofcolour vision," Rep. 73-09 (Institute of Physics, University ofStockholm, Stockholm, 1973).

3. L. T. Maloney and B. A. Wandell, "Color constancy: a methodfor recovering surface spectral reflectance," J. Opt. Soc. Am. A3, 29-33 (1986).

4. M. Brill and G. West, "Contributions to the theory of invarianceof color under the conditions of varying illumination," J. Math.Biol. 11, 337-350 (1981).

5. J. A. Worthey, "Limitations of color constancy," J. Opt. Soc.Am. A 2, 1014-1026 (1985).

6. E. H. Land, "The retinex," Am. Sci. 52, 247-264 (1964); "Theretinex theory of color vision," Sci. Am. 237, 108-128 (1977);"Recent advances in retinex theory and some implications forcortical computations: color vision and the natural image,"Proc. Natl. Acad. Sci. USA 80, 5163-5169 (1983).

7. M. D'Zmura and P. Lennie, "Mechanisms color constancy," J.Opt. Soc. Am. A 3, 1662-1672 (1986).

8. H.-C. Lee, "Method for computing the scene-illuminant chro-maticity from specular highlights," J. Opt. Soc. Am. A 3, 1694-1699 (1986).

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9. L. E. Arend and R. Goldstein, "Simultaneous constancy, light-ness and brightness," J. Opt. Soc. Am. A 4, 2281-2285 (1987).

10. A number of terms have been previously used for similar con-cepts. To our knowledge, all carry unwanted additional mean-ings. One will not go far wrong replacing our term with "senso-ry color," but only the definition here is intended. In particu-lar, we wish to avoid unproductive arguments concerning themeanings of "sensation" and "perception."

11. G. Wyszecki and W. S. Stiles, Color Science (Wiley, New York,1967).

12. G. Wyszecki, "Color appearance," in Handbook of Perceptionand Human Performance, K. R. Boff, L. Kaufman, and J. P.Thomas, eds. (Wiley, New York, 1986), pp. 9-1-9-57.

13. V. V. Maximov, Transformation of Colors by IlluminantChange (Nauka, Moscow, 1984).

14. R. M. Evans, The Perception of Color (Wiley, New York, 1974);A. Kozaki, "Perception of lightness and brightness of achromat-ic surface color and impression of illumination," Jpn. Psychol.Res. 15, 194-203 (1973); A. Gilchrist, S. Delman, and A. Jacob-sen, "The classification and integration of edges as critical tothe perception of reflectance and illumination," Percept. Psy-chophys. 33, 425-436; K. Koffka, "Some remarks on the theoryof colour constancy," Psychol. Forsch. 16, 329-345 (1931); J.Beck, Surface Color Perception (Cornell U. Press, Ithaca, N.Y.,1972); S. S. Bergstrom, "Common and relative components ofreflected light as information about the illumination, colour,and three-dimensional form of objects," Scand. J. Psychol. 18,180-186 (1977); I. Lie, "Perception of illumination," Scand. J.Psychol. 18, 251-255 (1977).

15. This result was stated as Kirschmann's third law of color con-trast: A. Kirschmann, "Uber die quantitativen Verhaltnissedes simultanen Heligkeits- and Farben-Contrastes," Philos.Stud. (Wundt) 6,417-491 (1890).

16. J. S. Kinney, "Factors affecting induced color," Vision Res. 2,503-525 (1962).

17. S. S. Bergstrom and G. Derefeldt, "Effects of surround/test fieldluminance ratio on induced colour," Scand. J. Psychol. 16, 31-38 (1975). This reference includes a literature review.

18. S. S. Bergstrom, G. Derefeldt, and S. Holmgren, "Chromaticinduction as a function of luminance relations," Scand. J. Psy-chol. 19, 265-276 (1978).

19. A. Valberg, "Color induction: dependence on luminance, puri-ty, and dominant or complementary wavelength of inducingstimuli," J. Opt. Soc. Am. 64, 1531-1540 (1974).

20. K. L. Kelly, K. S. Gibson, and D. Nickerson, "Tristimulus speci-fication of the Munsell Book of Color from spectrophotometricmeasurements," J. Opt. Soc. Am. 33, 355-376 (1943).

21. Y. Le Grand, Light, Colour and Vision (Chapman & Hall, Lon-don, 1968).

22. Data from Kelly et al.2 0 refer to the original Munsell notation,

and our simulated papers are described in those same terms.Both hue and chroma are somewhat different in the two sys-tems. Our test stimuli, R, G, Y, B, and N, correspond closely torenotation hues 5R, 5G, 5Y, 5B, and N, respectively. The reno-tation chromas closest to the chromas of our test patches areapproximately /2 chroma steps greater than our reported val-ues, e.g., 5R 5/10 for our R 5/8.

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