lightness and brightness judgments of coplanar retinally...

2442 J. Opt. Soc. Am. A/Vol. 10, No. 12/December 1993

Lightness and brightness judgments of coplanar retinallynoncontiguous surfaces

James A. Schirillo and Steven K. Shevell

Department of Psychology and Department of Ophthalmology and Visual Sciences, University of Chicago,Chicago, Illinois 60637

Received November 16, 1992; revised manuscript received May 24, 1993; accepted June 2, 1993

Several experiments reveal that judgments of lightness and brightness of an achromatic surface depend, in part,on the luminances of other surfaces perceived to share the same depth plane, even if the surfaces are wellseparated on the retina. Two Mondrians, simulated on a CRT, were viewed through a haploscope. The morehighly illuminated Mondrian contained a comparison patch and appeared nearer than the more dimly illumi-nated Mondrian, which contained the test patch. By independently varying the disparity of the test patch, ob-servers could make the test patch appear to be in the depth plane of either the dimly or the highly illuminatedMondrian. Observers set the luminance of the test patch to match that of the comparison patch. The test wasset as high as 15% more luminous when it was perceived in the depth plane of the highly illuminated ratherthan the dimly illuminated Mondrian. Both brightness and lightness judgments were affected by the perceiveddepth of the test, although the lightness judgments of inexperienced observers sometimes were dominated bylocal-contrast matching.

INTRODUCTION

In nature, surfaces sharing a common depth plane oftenshare the same illumination, while regions in differentdepth planes often differ in illumination.'3 Becausecoplanar surfaces may not be retinally adjacent to oneanother, the illumination falling on retinally contiguoussurfaces may differ. Consequently, the brightness of asurface in a three-dimensional scene may depend on morethan local luminance contrast4' 5 and on more than simplyincorporating the luminances of distant regions irrespec-tive of their perceived depth.6'7 If judging the perceivedbrightness of a surface requires an inference about thelight illuminating it, then the three-dimensional relationsamong objects may be an important factor.

If coplanar regions share the same illumination, thenone possible way to assess the illumination falling onto asurface is perceptually to group surfaces that share acommon depth plane, regardless of where light from thesesurfaces strikes the retina. The coplanar illuminationhypothesis specifies that the perceived brightness of asurface may vary with the perceived depth of the surface.For example, imagine judging the brightness of a grayshirt as it hangs in a dimly lit closet surrounded by otherclothes. Then imagine judging its brightness as it ismoved into a well-lit room while it is still "retinally" sur-rounded by the clothes hanging in the closet. In the lat-ter case the luminance of only the shirt, not the clothingthat surrounds it, is increased. Attributing the increasein luminance to additional illumination falling on theshirt will increase the perceived brightness of the shirt.This would make the shirt's perceived brightness corre-late with the illumination of the depth plane in which itlies. If, however, the increased difference in luminance isnot attributed to a higher level of illumination, the per-ceived lightness of the shirt will increase; that is, the shirt

will appear whiter instead of brighter. Lightness andbrightness are separate perceptual dimensions. Light-ness is judged on a relative scale: a surface is perceivedas either lighter or darker than a fixed standard in a scaleof grays. Brightness is judged on an absolute scale: asurface is perceived as brighter or dimmer, more akin toperceived intensity.' 1

The coplanar illumination hypothesis is an under-pinning of other models of lightness and brightness per-ception; it provides essential groundwork for Gilchrist'scoplanar ratio hypothesis.2 Gilchrist argues that the per-ceived lightness of a surface depends on its contrast withapparently coplanar surfaces, while noncoplanar surfaceshave virtually no effect. The coplanar ratio hypothesisprovides a means by which "perceived lightness might bedetermined primarily by ratios within perceived planesrather than by all retinal ratios regardless of perceiveddepth" (Ref. 2, p. 186; see also Ref. 11).

In the current study, observers judged the perceivedbrightness and lightness of an achromatic surface by ad-justing the luminance of a test patch to match a compari-son patch. The test patch was varied in perceived depth.An important feature of the experimental design is thatwe assessed inferred illumination without varying retinalillumination. This is unlike previous studies of adapta-tion and constancy, in which the experimenters varied theilluminating light to determine the degree to which it wasdiscounted.4 "' 2 3 In that we varied only stereo disparity,the significance of altering the three-dimensional repre-sentation was isolated while keeping the two-dimensionalretinal image virtually unchanged.

Overall, lightness and brightness judgments covaried inthe predicted direction with the perceived depth of thetest patch. The lightness judgments were in the directionof constancy However, the magnitude of the light-ness and brightness effects was much smaller than

0740-3232/93/122442-11$06.00 © 1993 Optical Society of America

J. A. Schirillo and S. K. Shevell

Vol. 10, No. 12/December 1993/J. Opt. Soc. Am. A 2443

Fig. 1. Diagram of the stimulus pattern on the CRT screen.The entire upper Mondrian and lower test patch had 34' ofcrossed retinal disparity. Each Mondrian had a 6:1 range ofsimulated surface reflectance. The luminance of each patch inthe lower Mondrians was one fifth that of its corresponding patchin the upper Mondrians.

predicted if only the coplanar illumination was considered.The results indicate that the inferred illuminant dependsonly in part on coplanar surfaces.

METHODS

ObserversThree observers with normal acuity and normal stereo-acuity were tested. Author JS, a 35-year-old male, wasknowledgeable about the experimental paradigm and hadexperience in making brightness and lightness matches,using Mondrians in two-dimensional displays. SG, a 24-year-old female graduate student, had experience withsimple three-dimensional chromatic displays but not withachromatic Mondrians and was naYve regarding the ex-perimental paradigm. BP, a 19-year-old female under-graduate, was an inexperienced observer who was alsonaYve about the purpose of the experiment.

ApparatusGray patterns were generated with a Pixar II image pro-cessor under the control of a Sun 3/150 work station andwere presented on an accurately calibrated Sony 17-in.(43-cm) color monitor. The 1280 X 1024-pixel screen wasset to provide a steady, neutral background with an aver-age luminance of 17.4 cd/m 2 and CIE chromaticity x =0.33 and y = 0.33. The scan rate was 60 Hz noninter-laced. The red, green, and blue guns were linearized byuse of a 9-bit look-up table. A given chromaticity and lu-minance, set by software, did not vary appreciably overthe effective viewing area. The luminance was approxi-mately constant (±31%) within the central region of thescreen that displayed the four Mondrians.

The monitor was viewed haploscopically at a distanceof 40 in. (100 cm) in a dark room. Two 450 mirrors, onedirectly in front of each eye, could be varied in distancefrom the eyes so that the observer always perceived a crispthree-dimensional image. The left-hand half of the CRTscreen projected an image to only the left eye, while theright-hand half of the CRT screen projected an image toonly the right eye.

StimuliThe subjects perceived a three-dimensional image byviewing the CRT screen through the haploscope (Fig. 1).The CRT displayed four Mondrians simultaneously, each50 high x 6.20 wide. Identical Mondrians located in theupper-left-hand and upper-right-hand quadrants of theCRT screen had 34' of crossed retinal disparity. Twoother Mondrians, identical to each other, were located inthe lower-left-hand and lower-right-hand quadrants of theCRT screen and had no retinal disparity. When the leftand right Mondrians binocularly fused with use of thehaploscope, the upper (comparison) Mondrian appeared tobe closer to the observer than the lower (test) Mondrian(Fig. 2).

The entire image was composed of lights covering a30:1 luminance range. The comparison (i.e., upper andnearer) Mondrian was composed of 12 patches that variedin luminance over a 6:1 range. These patches simulateda 6:1 range of surface reflectance. Twelve patches ofidentical shape and location formed the test (i.e., lowerand farther) Mondrian. The luminance of each patch inthe test Mondrian was set at one fifth of the luminance ofits corresponding patch in the comparison Mondrian.This fivefold difference in luminance created an overallappearance of two Mondrians having identical surfacereflectances, with each under a distinct illumination.Grouping surfaces of higher luminance within the com-parison Mondrian made it appear brightly illuminated (werefer to this as 100% illumination). Grouping surfaces oflower luminance within the test Mondrian made it appeardimly illuminated (we refer to this as 20% illumination).

The upper Mondrian contained at its center a 1° X 1°comparison patch, the luminance of which was set by theexperimenter. The simulated reflectance was 36%, 51o,68%o, or 90% (Munsell value v = 6.5/, 7.5/, 8.5/, or 9.5/, re-

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Fig. 2. Schematic of the binocularly fused stimulus pattern.The upper Mondrian appeared to be nearer than the lowerMondrian. The 10 x 1° test is shown with both 0' and 34' ofcrossed retinal disparity. In Experiment 3 the gray (R = 25%)immediate surround (shown here) was black (R = 0%). InExperiment 8 the luminances of selected patches (e.g., A and A)were exchanged while others (e.g., B and B') were not untilthe difference in average luminance across Mondrians wasminimized.


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spectively). The comparison patch was centered within a3 X 3-square area with a simulated reflectance of 25%(Munsell value v = 5.5/). The other patches within eachMondrian ranged in simulated reflectance from 5% to 92%(Munsell value v from 2.5/ to 9.6/). The geometric meanreflectance across the entire display (both dimly andbrightly illuminated Mondrians) was 29.5% (Munsell valuev = 6.0/; 17.4 cd/M2).

The test-patch luminance was varied by the observer.In the no-depth condition a 1 X 1 test patch, centeredwithin a 30 x 3 surround and located at the center of thelower Mondrian, had no disparity. The test patch ap-peared to lie in the same depth plane as its retinally adja-cent surround and the remainder of the test Mondrian.In the depth condition the test patch had 34' of crossedretinal disparity. It appeared to lie in the same depthplane as the upper, nearer, retinally nonadjacent compari-son Mondrian (see Fig. 2). The small shift in retinal dis-parity kept the 1 1 test patch close to the center ofeach eye's 3 x 3 surround. Thus retinal contrast wasvirtually the same in the no-depth and depth conditions.In the depth condition, the "nearer" test was perceived tofall in the center of the "farther" 3 x 3 surround.

ProcedureObservers participated in several practice sessions toensure that they understood the instructions. Head posi-tion was maintained with a chin rest. Observers darkadapted for 3 min and then light adapted for 3 min to auniform field at the average level of the Mondrian lumi-nances. Adaptation was followed by observation of theMondrian images described above. Observers easily andimmediately fused the Mondrians so that they appearedthree dimensional. An experimental session consisted of20 depth trials randomly intermixed with 20 no-depthtrials. The comparison patch was one of four differentluminances selected randomly from trial to trial. On thefirst trial for each comparison luminance, the initial levelof the test was set equal to its immediate surround.

Observers used a method of adjustment to set the testluminance so that the test and comparison patchesmatched perceptually. They controlled the luminance ofthe test patch by pressing separate buttons on a three-button computer mouse. One button incremented test

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luminance; another button decremented test luminance.The third button signaled that a satisfactory match hadbeen achieved, at which point the test level was recordedand the trial ended. Between trials the CRT screen wasuniform gray for 3 s. Then the next trial began. Onsubsequent trials the initial test luminance was randomlyoffset ±10% from the previous setting for the givencomparison-patch luminance. Each session took approxi-mately 1 h.

Instructions to subjects were as follows:Test patch adjustment: "You will be asked to adjust a

single test patch in the lower half of the display so that itmatches its corresponding comparison patch in the upperhalf of the display. Throughout the experiment you are tospend about the same amount of time looking at the upperand lower halves of the display by alternating your gazebetween them about once every two seconds."

Brightness judgments: "Using the mouse in front ofyou, vary the intensity of the lower test patch until it hasthe same brightness as the designated comparison patchin the upper half of the display. Disregard, as much aspossible, all the other patches of the display. In essence,adjust the test so that it appears to be identical in inten-sity to the comparison."

Lightness judgments: "Using the mouse in front ofyou, vary the intensity of the lower test patch until it hasthe same lightness as the designated comparison patch inthe upper half of the display. Utilize, as much as possible,all the other patches of the display. In essence, adjust thetest so that it appears to be the same shade of gray as thecomparison. 15

RESULTS

Tests of a Coplanar Illumination Hypothesis

Experiment 1: Brightness Matches with Gray Surroundingthe Test and the ComparisonThe brightness of a test patch on a dimly illuminatedMondrian was matched to a comparison patch on abrightly illuminated Mondrian. Both the test and thecomparison patches were centered within a gray surroundof the same simulated reflectance.

The test-patch luminance for a brightness match (sym-bols, Fig. 3) was always set below the physical luminance

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COMPARISON LUMINANCE COMPARISON LUMINANCE COMPARISON LUMINANCEFig. 3. Brightness matches (symbols) as a function of comparison luminance. Test and comparison luminance of 1.0 = 58.9 cd/mi2.Squares, no depth (test coplanar with its immediately surrounding Mondrian); circles, in depth (test coplanar with the nearer retinallynonadjacent Mondrian, i.e., out of the depth plane of its immediately surrounding Mondrian). The 450 dashed lines are the physical-luminance matches; the dotted lines are the reflectance matches (i.e., lightness constancy). Each data point is the average of three sepa-rate sessions performed on different days. Error bars indicate the standard error of the mean across days (subjects: JS, SG, and BP).

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Fig. 4. Lightness matches (symbols) as a function of comparison luminance. Squares, no-depth; circles, in-depth (subjects:and BP). Other information is the same as for Fig. 3.

of the comparison patch (dashed lines). Figure 3 showsthat observers judged the test patch within the dimly illu-minated Mondrian to be too bright when it was physicallyequal to the comparison patch within the brightly illumi-nated Mondrian. Observers thus reduced the test lumi-nance away from a physical-luminance match.

This is expected from classical brightness contrast(however, see Experiment 9 below). The more importantresult, however, is that the perceived depth of the testpatch affected the brightness measurements (circles abovesquares, Fig. 3). Observers set the test luminance, onaverage, 16% higher when it was perceived in the near,highly illuminated depth plane than when it was perceivedin the dimly illuminated plane (JS, p < 0.001; SG, p <0.001; BP, p < 0.05). This difference is in the expecteddirection if the observer is inferring that a test coplanarwith the highly illuminated comparison Mondrian is undera higher level of illumination than a test in the plane of adimly illuminated Mondrian. This difference suggestsalso that retinal contrast, which remains constant acrossdepth conditions, is not solely responsible for removing theeffect of varying illumination.

Although information from coplanar surfaces affects thebrightness match in the direction expected for inferredillumination, the effect of moving the test to the near-depth plane is quantitatively much less than of actuallyinferring a fivefold increase in the illumination falling onthe test. If observers had completely accounted for thefivefold difference in luminance between the test andcomparison Mondrians, they would have increased the testlevel by 500% in the near-depth plane.

Experiment 2: Lightness Matches with Gray Surroundingthe Test and the ComparisonIf observers infer a higher illumination when the test isperceived in the plane of the nearer, more highly illumi-nated Mondrian, then lightness judgments also shouldshow an increase in the luminance of the test when thetest appears in depth. Observers made lightness judg-ments (symbols, Fig. 4) using the same stimuli that theyused for brightness judgments. As expected, the lightnessmeasurements differed markedly from the brightness set-tings (symbols, Fig. 3). They show approximate lightnessconstancy (dotted lines) when the test remained within

the depth plane of the dimly illuminated Mondrian(squares, Fig. 4). Only experienced observer JS, however,set the test to a significantly higher luminance when itwas perceived in the highly illuminated depth plane(p < 0.001). Under a higher perceived illumination, anincrease in luminance is required for maintaining an in-depth test of constant reflectance. On the other hand,the perceived depth of the test caused no significant dif-ference in the lightness matches of the other observers(SG, p > 0.25; BP, p > 0.50).

Experiment 3: Black Surrounding the Test and theComparisonThe lightness results in Experiment 2 showed clear differ-ences among observers. We considered whether the in-experienced observers, SG and BP, might have interpretedthe lightness instructions as asking for simple local-contrast matches. If so, luminance contrast at retinallyadjacent edges would dominate the lightness computa-tion.'7 In order to determine whether this was the case,we remeasured the effect of depth on lightness and bright-ness with a 30 x 30 black patch immediately surroundingboth the test and the comparison (simulated reflectance of0.0%; Munsell value v = 0.0/). This made the surround-ing patches in each plane equal to each other and elimi-nated the possibility of judgments based on relative grayscales of adjacent patches (the surround's luminance is notaffected by the level of illumination, because its reflec-tance is 0%). The geometric mean reflectance acrossboth Mondrians was now 13.0% (Munsell value v = 4.2/;7.7 cd/M2).

As in the first experiment, varying the perceived depthof the test caused a luminance difference for brightnessmatches (filled circles above filled squares, Fig. 5). Onaverage, the test was made 8% more luminous when it wasperceived in the highly illuminated depth plane (JS,p < 0.001; SG, p < 0.02; BP, p < 0.05). This is half of themagnitude obtained with the gray surrounds. With blacksurrounds the brightness matches fell closer to a physical-luminance match (filled circles and filled squares arenearer to the dashed line than in Fig. 3). This effect isexpressed by the slope of the brightness results, which in-creases, on average, from 0.64 to 0.82 when the simulatedsurround reflectance is reduced from 25 to 0%.16ls The

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COMPARISON LUMINANCE COMPARISONLUMINANCE COMPARISONLUMINANCEFig. 5. Brightness (filled symbols) and lightness (open symbols) matches as a function of comparison luminance. The area surroundingthe test and comparison patches now is black. Squares, no depth; circles, in depth (subjects: JS, SG, and BP). Dashed lines, physical-luminance matches; dotted lines, reflectance matches.

slope for physical-luminance matching is 1.0 and forperfect-reflectance matching is 0.20.

More important is that the lightness judgments for allthree observers now show a clear effect of varying thedepth plane of the test. On average, the test luminancewas set 17% higher (open circles above open squares;Fig. 5) when it was perceived in the more highly illumi-

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nated depth plane (JS, p < 0.001; SG, p < 0.01; BP, p <0.001). However, as with brightness judgments on eithergray or black surrounds, the magnitude of change inthe lightness settings with test depth falls far short of aphysical-luminance match. This implies that, while ob-servers' brightness and lightness judgments require ahigher test luminance in the depth condition, the illumi-nation of the near, highly illuminated Mondrian is notactually inferred to be the illumination that is falling uponthe test.

Evidence with Test, Surround, or Mondrian Depth-PlaneVariations

... Q,*'...... El.s Experiment 4: Test at Various DepthsI . .- s ;-"'ODMPARIS0NLUMINANCE The above results suggest that the inferred test illumina-,., - - O 036 tion is influenced by its coplanar Mondrian. Next we

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0 50 100 150 200 250 (the previous depth condition) or 200% depth (twiceTESTDEl H(%) the disparity of the previous depth condition) or at(b) 120%, 150%o, or 180% of the disparity of the previous depth

a) Brightness judgments expressed as the percentage condition.test luminance relative to the no-depth condition When the observer was making brightness judgments,

ius no depth, divided by no depth), as a function of test then the observer in asparity), for subject JS. Results are shown for four the test luminance set by the observer increased asrn-luminance levels. Dashed curves are fits of a two- the test depth increased to 100% (coplanar with nearmodel. (b) Same as (a) for subject SG. Mondrian). Figure 6(a) shows for observer JS the per-

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centage change in test luminance that is due to the depthof the test (i.e., luminance with depth minus luminancewith no depth, divided by the luminance with no depth).Each symbol shape represents a different comparisonluminance. Each dashed curve is a two-parameter fitwith a linear increase to 100% disparity and no furtherincrease thereafter. The test at 0% depth (no depth) dif-fers significantly from those at 20% (p < 0.001), 50%(p < 0.001), 80% (p < 0.001) and 100% (p < 0.001).Also, the four nonzero test depths significantly differfrom one another (p < 0.05), except that 80% depth doesnot differ from 100% depth. There is no significant in-crease in test luminance as the test depth is moved closerthan the near Mondrian, i.e., from 100% to 200% (p >0.25). The smallest comparison luminance (0.36) pro-duced the largest relative change in test luminance thatwas due to test depth [diamonds, Fig. 6(a)].

Overall, observer SG's brightness judgments showed asimilar though smaller depth effect [Fig. 6(b)]. The testdepth at 0% (no depth) differs significantly from 50%(p < 0.01), 80% (p < 0.05), and 100% (p < 0.001); and the20% and 50% tests differed significantly from the 80%and 100% tests (p < 0.01). There is no increase in testluminance as the test depth is moved closer than the nearMondrian, i.e., from 100% to 200% (p > 0.50).

Experiment 5: Depth of Test and Surround CovaryWe next considered whether local edge contrast dependson inferred illumination. One possibility is that perceivedlocal contrast depends only on retinal stimulation and noton inferred illumination. On the other hand, if illumina-tion is inferred first, then perceived local contrast willvary when the perceived location of the test is moved tothe near, more highly illuminated depth plane, because thetest's immediate surround remains in the dim, far depthplane. In the current experiment the perceived depthplane of the test and its surround are varied together;thus they are kept under the same inferred illuminationeven as the test varies in depth.

The luminance of the 30 x 30 gray surround contiguouswith the test was held fixed at its previous luminance[reflectance of 25%, Munsell value v = 5.5/, dim (20%) illu-

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mination] but was varied in disparity with the test so thatit could be perceived in the depth plane of the highly ordimly illuminated Mondrian. The disparity of the testand its surround always varied together. When the testand its surround appeared in the depth plane of the near,highly illuminated Mondrian, the observers set brightnessmatches that were 18% more luminous, on average, thanthose made in the depth plane of the far, dimly illuminatedMondrian (symbols, Fig. 7; JS, p < 0.001; SG, p < 0.001).These results are virtually the same as in the first experi-ment, in which only the test patch was varied in depth(symbols from Fig. 3 are replotted as dashed lines inFig. 7). These results demonstrate, again, that the per-ceived brightness of the test patch, with or without a co-planar surround, is not determined solely by a matching ofthe local perceived edge contrast. 21 22

Moreover, moving the surround and the test to a morehighly illuminated depth plane maintained the change inbrightness seen when the test alone was changed in per-ceived depth. This suggests that inferred illuminationaffects brightness at a stage that follows perceived localcontrast.

Experiment 6: Mondrians in Two DimensionsIt has been reported that changes in test disparity modifythe effects of local neural retinal connections, such as lat-eral inhibition, thereby altering lightness and brightnessjudgments.12 2 22 3 We show here that coplanar surfaces,not simply the perceived depth plane of only the test patch,are the critical factors that mediate the depth effect. Todetermine the effect of merely separating in perceiveddepth the test and its surround, we placed both Mondriansof Experiment 1 in the same (far) depth plane, andonly the perceived depth of the test patch was varied.This procedure preserved each Mondrian's separate illu-mination while removing depth as a basis for inferringillumination.

Overall, test depth had no effect on brightness judg-ments (symbols, Fig. 8; JS, p > 0.15; SG, p > 0.35; BP,p > 0.50). There was at most a possible trend at the low-est level of increment (0.36) toward slightly higher lumi-nance levels with increasing depth of test.20 24

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Fig. 7. Brightness matches when test and immediate surround vary together in depth (symbols) as a function of comparison luminance.Squares, no depth (test and immediate surround coplanar with immediately surrounding Mondrian); circles, in depth (test and immediatesurround coplanar with the nearer retinally nonadjacent Mondrian. Brightness matches from Fig. 3 are replotted here as dotted-dashedcurves (subjects: JS and SG). Dashed lines, physical-luminance matches; dotted lines, reflectance matches.

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COMPARISON LUMINANCE COMPARISONLUMINANCE COMPARISON LUMINANCEFig. 8. Brightness matches (symbols) as a function of comparison luminance with Mondrians in two dimensions. Squares, no depth;circles, in depth (subjects: JS, SG, and BP). Dashed lines, physical-luminance matches; dotted lines, reflectance matches.

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COMPARISON LUMINANCE COMPARISONLUMINANCE COMPARISONLUMINANCEFig. 9. Brightness matches (symbols) with test behind far Mondrian (in depth) or in its surrounding Mondrian (no depth). Squares, nodepth; circles, in depth (subjects: JS, SG, and BP). Dashed lines, physical-luminance matches; dotted lines, reflectance matches.

Experiment 7: Test behind Far MondrianIn this experiment the test was positioned in depth behindthe far Mondrian, at a disparity equivalent in magnitudeto that of the test when it had been coplanar with thenearer Mondrian in the original experiment.2 5 Gogel andMershon 2 and Mershon and Gogel2 7 would predict thesame degree of neural uncoupling from the surroundwhether the test is in front of or behind the fartherMondrian. 2"

Observers judged brightness in the current experimentby setting the test to a lower luminance (Fig. 9, filledcircles below filled squares, by 8% on average) when it wasperceived to be behind the far Mondrian (JS, p < 0.001;SG, p < 0.001; BP, p < 0.05).

These findings are in the direction opposite to that ofthose obtained in Experiment 1 (see Fig. 3) and thereforedo not support Gogel and Mershon's hypothesis of correlat-ing perceived stereo depth with neural uncoupling. In-stead, they suggest that observers infer an even lowerilluminant than that of the far Mondrian when the test isperceived to lie behind it. This inference may be due tothe black background of the screen that extends beyondthe Mondrians.

Experiment 8: Comparison behind Near MondrianFrom previous experiments we have argued that thebrightness of a patch is due in part to an illuminant in-

ferred from other surfaces in the same depth plane. Ifthis interpretation is correct, then changing the perceiveddepth plane of the comparison to that of the far Mondrianshould increase the perceived brightness of the compari-son patch (which has a fixed luminance). This hypothe-sis was tested with a test field that remained coplanarwith the far Mondrian. Unlike in the previous experi-ments, the comparison field was varied in depth so that itwas coplanar with either its usual near Mondrian or withthe dimly illuminated (far) Mondrian. This makes thein-depth position of the comparison analogous to the in-depth position of the test patch in the first experiment.

Brightness judgments resembled those obtained in theoriginal experiment (symbols, Fig. 10). Observers set thetest, on average, 10% more luminous when the comparisonwas perceived in depth (i.e., within the dimly illuminatedfar plane) than when the comparison was perceived in nodepth (i.e., the brightly illuminated near plane) (JS,p < 0.01; SG,p < 0.02; BP,p < 0.005).

Evidence with Illumination Variations

Experiment 9: Mondrians with Ungrouped LuminancesIf test depth alone is responsible for the above results,then the illumination in the two depth planes is irrele-vant. According to the coplanar illumination hypothesis,however, the illumination difference in the two depth

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planes is critical. To compare these two possibilities, weswitched the luminances of selected patches that sharedthe same spatial location within each Mondrian so thatthe average luminance in the near Mondrian and the farMondrian was approximately the same. For example, theluminances of patch A and patch A' of Fig. 2 wereswitched, while the luminances of patch B and patch B'were not. To preserve local contrast, we did not alter thepatches immediately surrounding the test and the com-parison. We selected the patches that were switched inorder to retain the original experiment's luminance in-formation while minimizing the difference in averageluminance between the two Mondrians. The resultinggeometric mean reflectance of what had been the highlyilluminated (upper and nearer) Mondrian was 13.7%(Munsell value v = 4.2/), while the dimly illuminated(lower and farther) Mondrian was now 14.5% (Munsellvalue v = 4.4/). Because each Mondrian was composedof patches of different luminances (i.e., patch luminanceswere ungrouped), the entire display appeared as a seriesof reflectances (30:1 range) under a single illuminant.2 9

As predicted by the coplanar illumination hypothesis, thismanipulation eliminated the difference in brightnessjudgments as the perceived depth of the test was varied(Fig. 11, symbols connected by solid lines). There was no

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reliable effect of depth on the observers' settings of thetest-patch luminance (JS, p > 0.50; SG, p > 0.50).

Brightness matches approximated a physical-luminancematch when the luminances of the noncontiguous patcheswere ungrouped. This occurred despite the differencesin the level of light immediately surrounding each patch(i.e., the comparison patch was five times higher). Thedramatic effect of grouping the luminances of only thenoncontiguous patches is demonstrated by the differencebetween the grouped results of Fig. 3 (replotted here asdashed lines) and measurements from this experiment(solid lines). The large effect of grouping the remote non-contiguous patches is further evidence against local edgeinformation as the primary mechanism of brightnessperception.

Experiment 10: Variation of Test SizeThe test size was constant in all previous experiments sothat the test appeared smaller when it was in the nearerdepth plane. A 10 x 10 test in the no-depth condition isperceived to be approximately the same size as a 0.80 X0.8° test in the depth condition. To ensure that perceivedsize did not affect brightness judgments, we comparedmeasurements in the depth condition with use of a 10 X 1°test and a 0.8° X 0.80 test.

1 0.3 0.4 0.5 0.6 0.7 0.8 0.9 I


Fig. 10. Brightness matches (symbols) with the comparison in depthplane). Squares, no depth; circles, in depth (subjects: JS, SG, and BP).tance matches.

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(far plane) or in its usual adjacent Mondrian (no depth, nearDashed lines, physical-luminance matches; dotted lines, reflec-

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COMPARISON LUMINANCE COMPARISON LUMINANCE

Fig. 11. Brightness-lightness matches (symbols) as a function of comparison luminance, with Mondrians with ungrouped luminances.

Solid symbols from Fig. 3 are replotted here as dotted-dashed lines. Squares, no depth; circles, in depth (subjects: JS and SG). Dashedlines, physical-luminance matches; dotted lines, reflectance matches.

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differences in brightness judgments (JS, p > 0.35;SG, p > 0.30). Therefore a difference in apparent testsize cannot account for the findings of the originalexperiment.

DISCUSSION

To Be Inferred, Illumination Differences Must BePerceivedThe process of judging the lightness and brightness of asurface in a three-dimensional scene requires a percep-tual representation of the illuminations that fall withinthat scene.30 Since retinally noncontiguous coplanarsurfaces often share a common illuminant, the coplanarillumination hypothesis makes interpretation of the lumi-nance of any surface less ambiguous. Judging the appear-ance of a surface by using only local retinal luminancecontrast can be misleading when retinally adjacent areasare stimulated by light from surfaces in different depthplanes with different illuminations. Incorporation ofinformation from an inferred coplanar illuminant couldrectify this situation.

The coplanar illumination hypothesis requires a percep-tual representation of at least two different illuminantswithin a scene. Selective grouping of patches with a 30:1range of luminances made two Mondrians appear to beunder different illuminations.31 Spatially ungroupingthese patches eliminated any basis for perceiving a differ-ence in illumination. Consequently, as predicted by thecoplanar illumination hypothesis, ungrouping also elimi-nated a difference in the brightness judgments of the testas perceived depth of the test was varied (see Experi-ment 9, Mondrians with ungrouped illumination). Thisimplies that spatial integration and segregation across theentire visual field contributes to the perceived brightnessof a surface.3 5

An important finding here is that a fivefold differencein luminances between the two Mondrians produced atmost a 15% change in test luminance as the perceiveddepth of the test moved between the depth planes of thetwo Mondrians. This is far less than the 500% change inthe test settings that would be predicted if the illumina-tion of the test were inferred according to the fivefold dif-ference in Mondrian illuminations. This discrepancyindicates that although information about the coplanarilluminant may be inferred, it is not taken as the actualillumination of the test surfaces.

LightnessLightness judgments also do not rely solely on luminance-edge ratios.2 2 An integration step0'3 5 38 must combineratios from various edges to give a spatial distribution ofrelative lightness.3 9 Even so, proper segmentation re-mains a problem since reflectance and illumination edgesremain confounded.3 7 3 8 Coplanarity can be a cue towhether a surface's edge ratio contains a change in illumi-nation and reflectance.

In order for lightness constancy to be maintained, theluminance of an in-depth test should increase so that anincrease in inferred illumination is offset. While themost experienced observer, JS, demonstrated this patternwith use of a gray surround, inexperienced observers SGand BP did not. Their results suggest they made local

ratio matches when the test was in either depth plane.When a black surround replaced the gray one, thus elimi-nating local edge contrast as a cue, lightness judgmentsshowed an expected increase in test luminance when thetest was perceived in the near depth plane (compareFigs. 4 and 5). A black surround forces inexperiencedobservers to use a retinally nonadjacent gray scale; theresult is establishment of a more-global perception of illu-mination differences.40 -42 As with brightness judgments,however, the change in test luminance with depth wasmuch less than was predicted only from the coplanar illu-mination (observed average change of 17%, compared with500% predicted for the coplanar illuminant).

CRT SimulationStereoscopic viewing of a CRT is a method of constructingthree-dimensional scenes designed to simulate naturalviewing of papers under two different illuminants. ACRT offers accuracy,8 and haploscopic viewing enhancesthe screen's realism by producing clearly defined depthplanes. For example, stereoscopic photography has beenreported to produce better lightness constancy than does asingle-lens camera.43 Most important, the stereo displaysensured that the perceived depth information was affect-ing perception at a locus beyond the retina.

Comparison with Previous StudiesIn 1977 Gilchrist2 claimed that the coplanar ratio hypothe-sis determined the lightness of a surface. This hypothe-sis tacitly assumes that the illumination that is fallingacross any particular depth plane is constant. Gilchristconstructed stimuli with a single inferred illuminantacross at least one coplanar retinally adjacent luminanceedge from which observers could derive a lightness ratio(Fig. 1 of Ref. 2). This method differs from that of thecurrent study, in which an in-depth test patch has no reti-nally adjacent coplanar surround.

Lightness judgments obtained with such stimuli suggestthat perceived coplanarity provides some illumination in-formation, while noncoplanar, even nonretinally adjacent,surfaces may establish a gray scale. We can only specu-late on how an observer selects an appropriate gray scalewhen the test's retinally adjacent borders are in a differentdepth plane. The lightness instructions were specificallydesigned to minimize the biasing of observers toward ref-erencing the test to a particular Mondrian or illumination(see instructions to observers, above). Lightness resultssuggest that observers used the gray scale primarily fromthe retinally adjacent, noncoplanar surround. Lightnessjudgments were affected by the coplanar illuminant onlywhen the retinally adjacent surround was extinguished(0% reflectance).

We agree with Gilchrist2 that local contrast alone isinsufficient for determining lightness.212 2 39 However,we suggest that his observers may have inferred the illu-mination that was falling on the test from a retinally ad-jacent coplanar gray scale. This assumption underliesthe hypothesis that surface lightness is determined bycoplanar luminance ratios.1144 45 We propose that, whenthe test does not share a coplanar retinally adjacent edge,the effect of a different illuminant is diminished, andnoncoplanar local contrast may dominate lightness judg-ments.



Table 1. Ratio of the SEM for Log Brightness tothe SEM for Log Lightness for In-Depth, No-Depth,and On-Average Tests for Subjects JS, SG, and BP'

SEM Log Brightness/SEM Log Lightness

Experiment Depth No Depth Average

1. Gray surround 2 1 1 b 2.77c 2.442. Black surround 2.49c 3.19c 2.844. Test and surround covary 2 .0 6 b 2.90C 2.48

5. 2D Mondrians 4.41c 4.67c 4.54

6. Test behind 3.48c 3.91C 3.70

7. Comparison behind 3.29c 3.01c 3.15

ap values were determined with a sign test; bp < 0.05, Cp < 0.01.

VariabilityBrightness settings tend to be significantly more variablethan lightness settings.11 1646 It is noteworthy thatthe standard error of the mean (SEM) was substantiallylarger for brightness measures than for lightness mea-sures in the current study. This was the case for eachobserver across all experiments. Brightness variabilitydecreased when the test was coplanar with the brightlyilluminated Mondrian, except when the perceived depthof the comparison patch was varied (Experiment 8).Table 1 summarizes the brightness log SEM to lightnesslog SEM ratio, averaged over observers, for all relevantexperiments.

The variability in lightness judgments is far less thanthe difference in gray-scale reflectances that might con-strain the upper and lower (lighter and darker) limits ofthe test. The lightness SEM across experiments is ap-proximately 1.0%, while the median difference in surfacereflectance within either Mondrian was 6.0%. This sug-gests that constraints in addition to the upper and lowerlimits of any two patch reflectances restrict lightnessjudgments.

DecrementsPreliminary experiments were done with decrements inthe same three-dimensional scenes in which incrementswere tested. Unfortunately, these findings are not easilyinterpreted with the framework developed here. We re-versed the illumination falling on the depth planes bymaking the near Mondrian dimly illuminated and the farMondrian brightly illuminated. This was done to avoidthe possibility of the observer's setting the test to an in-crement to match a (comparison) decrement when the testwas perceived in the near depth plane. Observers did notvary the luminance of the test with perceived depth whenjudging either brightness or lightness. Likewise, use ofdecrements with Mondrians under the illumination con-ditions of Experiment 1 also showed no effect of depthof test.

The often-noted asymmetries between increments anddecrements4 7 may also apply to the Coplanar Illuminationinformation. For example, Noguchi and Kozaki50 notedthat the appearance of a white surface is strongly affectedby changing illumination, while a black surface tends to beunchanged despite changes in illumination. Likewise,varying either the reflectance or the illumination of a testsurround embedded within a two-dimensional Mondrian

demonstrated a strong effect of local contrast on decre-ments but not on increments.1 ' 22 Additional experimentsare needed for determining whether any of these relatedfindings explains why inferred illumination affects incre-ments differently than it does decrements.

ACKNOWLEDGMENTS

This research was supported in part by National Institutesof Health grants T32 EY-07098, EY-04802, and EY-07390.We thank Sandy Guzman and Becky Powell for serving assubjects, Linda Glennie for computer programming,Cheryl Schirillo for proofreading, and Larry Clarkberg fortechnical assistance.

*Present address, Department of Psychology, Universityof San Francisco, 2130 Fulton Street, San Francisco,California 94117-1080.

REFERENCES AND NOTES

1. E. Hering, Outlines of a Theory of the Light Sense (transl.L. M. Hurvich and D. Jameson) (Harvard U. Press,Cambridge, Mass., 1964).

2. A. Gilchrist, "Perceived lightness depends on perceived spa-tial arrangement," Science 195, 185-187 (1977).

3. A. Jacobsen and A. Gilchrist, "The ratio principle holds overa million-to-one range of illumination," Percept. Psychophys.43, 1-6 (1988).

4. H. Wallach, "Brightness constancy and the nature of achro-matic colors," J. Exp. Psychol. 38, 310-324 (1948).

5. E. Heinemann "Simultaneous brightness induction as a func-tion of inducing- and test-field luminances," J. Exp. Psychol.50, 89-96 (1955).

6. R. C. Reid and R. M. Shapley, "Non-local effects in theperception of brightness: Psychophysics and neurophy-siology," in Seeing Contour and Colour, J. J. Kulikowski, C.M. Dickinson, and I. J. Murray, eds. (Pergamon, Oxford,1989).

7. Perceived brightness and perceived lightness in a three-dimensional scene can be derived from local contrast ofretinally adjacent coplanar surfaces that share an illuminant(see Ref. 8).

8. J. A. Schirillo, A. Reeves, and L. Arend, "Perceived lightness,but not brightness, of achromatic surfaces depends on per-ceived depth information," Percept. Psychophys. 48, 82-90(1990).

9. J. Beck, Surface Color Perception (Cornell U. Press, Ithaca,N.Y., 1972).

10. R. Evans, "Variables of perceived color," J. Opt. Soc. Am. 54,1467-1474 (1964).

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

12. W Gogel and D. Mershon, "Depth adjacency in simultaneouscontrast," Percept. Psychophys. 5, 13-17 (1969).

13. L. Sewall and B. Wooten, "Stimulus determinants of achro-matic constancy," J. Opt. Soc. Am. A 8, 1794-1809 (1991).

14. In a related paradigm, L. Kardos, "Ding und schatten," Z.Psychol. 23, (1934), claimed that surface lightness was deter-mined by the illumination in a given depth plane. He reducedthe illumination falling upon a light-gray test to make theluminance of the test approximately equal to that of a highlyilluminated dark-gray coplanar surround. This caused thetest both to appear dark-gray and to be under the same highillumination as its coplanar surround. Reducing the overallillumination falling upon the light-gray test and the dark-gray surround in a separate depth plane preserved the lightertest. Although Kardos used depth to segment multiple illu-minations within a scene and showed that coplanar surfaceswith equal luminance appear to have both equal reflectanceand equal illumination, he did not derive a coplanar rule.



15. The two displays of Arend and Goldstein' 0 "were identicalpaper arrays illuminated by different sources." Their in-structions to "adjust the test patch to look as if it were cutfrom the same piece of paper" makes explicit to the observerthat the test and comparison patches were under differentilluminants. The current instructions to create the "sameshade of gray" do not demand that the observer infer a dif-ferent level of illumination for the test and comparison.Jacobsen and Gilchrist (Ref. 3 and Ref. 16) also obtainedlightness judgments by having observers match the "shade ofgray."

16. A. Jacobsen and A. Gilchrist, "Hess and Pretori revisited:resolution of some old contradictions," Percept. Psychophys.43, 7-16 (1988).

17. Parenthetically, studies by W Kohler, 'Aus der anthropoiden-station auf teneriffa. II. Optische untersuchungen amschimpansen und am haushuhn," Abh. Preuss Akad. Wiss.Phys.-Math. K. no. 3 (1915); N. Locke, "Color constancyin the rhesus monkey and in man," Arch. Psychol. 135, 5-38(1935); and R. Thouless, "Phenomenal regression to the realobject. I," J. Psychol. 21, 23-43 (1931), have reported thatchildren, animals, and untrained observers favor lightnessmatches over brightness matches.

18. Y. Hsia, "Whiteness constancy as a function of difference inillumination," Arch. Psychol. 284, 5-63 (1943).

19. H. N. Leibowitz, N. A. Myers, and P. Chinetti, "The role ofsimultaneous contrast in brightness constancy," J. Exp. Psy-chol. 50, 15-18 (1955).

20. Gibbs and Lawson23 showed that a small test disparity af-fected brightness judgments by approximately 10%, whereasaddition of disparity to the test did not increase the effect.

21. L. Arend and B. Spehar, "Lightness, brightness, and bright-ness contrast I. Illuminance variation," Percept. Psycho-phys. (to be published).

22. L. Arend and B. Spehar, "Lightness, brightness, and bright-ness contrast II. Reflectance variation," submitted to Per-cept. Psychophys.

23. T. Gibbs and R. Lawson, "Simultaneous brightness contrastin stereoscopic space," Vision Res. 14, 983-987 (1974).

24. Only 40 of Gogel and Mershon's'2 60 observers reported theeffect of depth separation on lightness.

25. Observers did not report that the test appeared in a filmmode of perception (Ref. 26) when it was viewed in a holewithin the far Mondrian.

26. D. Katz, The World of Color (Kegan Paul, Trench, Trubner,London, 1911).

27. D. Mershon and W Gogel, "Effect of stereoscopic cues on per-ceived whiteness," Am. J. Psychol. 83, 55-67 (1970).

28. Mershon and Gogel27 reported a maximum perceived differ-ence of 0.7/ Munsell step when the far disk was 44% fartherthan the near disk. Their hypothesis of increased neuraluncoupling with increasing depth implies that with sufficientseparation, induction effects would disappear altogether. Inthe current experiment the far Mondrian was 19% fartherthan the test patch that was perceived in the near plane.

29. This altered the perceived brightness of the immediate sur-round of the test and comparison. R. Shapley and R. Reid,"Contrast and assimilation in the perception of brightness,"Proc. Natl. Acad. Sci. 82, 5983-5986 (1985).

30. T. Oyama, "Stimulus determinants of brightness constancy

and the perception of illumination," Jpn. Psychol. Res. 10,146-155 (1968).

31. The fact that such a restricted range is sufficient suggeststhat many natural scenes potentially contain multiple levelsof illumination. For example, in more than 100 natural out-door scenes the average contrast is approximately 160: 1,34while luminance ratios greater than 60:1 tend to be per-ceived as changes in illumination instead of as changes inlightness (Refs. 32 and 33 below).

32. H. Helson, "Some factors and implications of color con-stancy," J. Opt. Soc. Am. 33, 555-567 (1943).

33. D. Jameson and L. Hurvich, "Complexities of perceivedbrightness," Science 133, 174-179 (1961).

34. L. Jones and H. Condit, "The brightness scale of exteriorscenes and the computation of correct photographic expo-sure," J. Opt. Soc. Am. 31, 651-678 (1941).

35. G. Buchsbaum, 'A spatial processor model for object colourperception," J. Franklin Inst. 310, 1-26 (1980).

36. E. Land and J. McCann, "Lightness and retinex theory,"J. Opt. Soc. Am. 61, 1-11 (1971).

37. B. Horn, "Determining lightness from an image," Comput.Graphics Image Process. 3, 277-299 (1974).

38. D. Marr and E. Hildereth, "Theory of edge detection," Proc.R. Soc. London Ser. B 207, 187-217 (1980).

39. A. Gilchrist, S. Delman, and A. Jacobsen, "The classificationand integration of edges as critical to the perception of re-flectance and illumination," Percept. Psychophys. 33, 425-436 (1983).

40. A. Gilchrist, "The perception of surface whites and blacks,"Sci. Am. 24, 88-97 (1979).

41. C. Brice and C. Fenneman, "Scene analysis using regions,"Artif. Intell. 1, 205-226 (1970).

42. R. Evans and J. Klute, "Brightness constancy in photographicreproduction," J. Opt. Soc. Am. 34, 540-553 (1944), claimthat illumination differences must be apparent in black-and-white photographs for adequate lightness constancy to beobtained.

43. R. Evans, "Visual processes and color photography," J. Opt.Soc. Am. 33, 579-614 (1943).

44. J. Schirillo and L. Arend, 'An illumination change at a depthedge can reduce lightness constancy," submitted to Percept.Psychophys.

45. A. Laudauer and R. Rodger, "Effect of 'apparent' instructionson brightness judgments," J. Exp. Psychol. 68, 80-84 (1964).

46. P. Whittle, "Increments and decrements: luminance dis-crimination," Vision Res. 26, 1677-1691 (1986).

47. The following sources provide specific incidents of increment-decrement asymmetries: brightness and lightness,' light-ness and illumination,' 8 figure-ground, 48 adaptation, 32

qualities of "pronouncedness" (Ausgepragtheit) and "insis-tence" (Eindringlichkeit),'6 illumination,3 and grouping.49

48. K. Koffka, Principles of Gestalt Psychology (HarcourtBrace, New York, 1935).

49. J. Hochberg and A. Silverstein, 'A quantitative index ofstimulus-similarity proximity vs. differences in brightness,"Am. J. Psychol. 69, 456-458 (1956).

50. K. Noguchi and A. Kozaki, "Perceptual scission of surface-lightness and illumination: an examination of the Gelb ef-fect," Psychol. Res. 47, 19-25 (1985).


lightness and brightness judgments of coplanar retinally...

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