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UNIVERSITY OF CALIFORNIA

Santa Barbara

"The Role of Illumination Perception in Color Constancy"

This Dissertation submitted in partial satisfaction of the requirements for the degreeof

Doctorate of Philosophy

in

Psychology

by

Melissa Drake Rutherford

Committee in charge:

Professor David H. Brainard, Chairperson

Professor John M. Foley

Professor Jack M. Loomis

Professor Russell Revlin

August 2000

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The dissertation of Melissa Drake Rutherford is approved

________________________________________________Professor John M. Foley

________________________________________________Professor Jack M. Loomis

________________________________________________Professor Russell Revlin

________________________________________________Professor David H. BrainardCommittee Chairperson

July 2000

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August, 2000

Copyright by


2000

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VITA

December 20, 1968 — Born—Portland, Oregon

1992 — B.A., Yale College

1997-1998 — Fulbright Scholar — University of Cambridge, England

1998-1999 — Assistant Professor — Reed College, Portland, Oregon

1999-2000 — Research Assistant — University of California at Santa Barbara

PUBLICATIONS

Rutherford, M.D. & Brainard, D.H. (2000). The Role of Illumination Perceptionin Color Constancy. Investigative Opthamology & Visual Science, 41, S525.

Baron-Cohen, S., Wheelwright, S., Stone, V., & Rutherford, M. (1999). Amathematician, a physicist, and a computer scientist with Asperger Syndrome:performance on folk psychology and folk physics tests. Neurocase, vol 5, pp.475-483.

Brainard, D.H., Rutherford, M.D. & Kraft, J.M. (1997). Color constancycompared: Experiments with real images and color monitors. InvestigativeOpthamology & Visual Science, 38, S476.

Rutherford, M.D., Tooby, J., & Cosmides, L. (1997). The effects of power onsocial reasoning. In M.G. Shafto & P. Langley (Ed.), Proceedings of theNineteenth Annual Conference of the Cognitive Science Society, p.1029.

FIELDS OF STUDY

Major Field: Psychology

Studies in Perception and Color Constancy.Professor David H. Brainard

Studies in Theory of Mind and Social Cognitive Development.Dr. Simon Baron-Cohen

Studies in Evolutionary Psychology and Social Reasoning.Professor Leda Cosmides

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ABSTRACT

"The Role of Illumination Perception in Color Constancy"

by


According to the albedo hypothesis, the visual system estimates the illuminant of ascene and uses this estimate and the luminance reflected from surfaces to determinethe color appearance of those surfaces. This hypothesis is common to many models ofcolor constancy. In the eight experiments reported here, observers viewed a standardand experimental scene in alternation. The illumination for each scene was underindependent computer control. Each scene contained a test region that consisted of acomputer-controlled display, masked so that it appeared to be an illuminated surface.On each trial of the experiments, observers made two adjustments: they adjusted theillumination in the experimental scene so that it appeared the same as the illuminationin the standard scene, and adjusted the test region in the experimental scene so that itappeared to have the same lightness as the test region in the standard scene. Thealbedo hypothesis predicts that when both the illuminant and the test regions in thetwo scenes appear the same, the physical luminance of the test patch will be the same.However, the experiment yielded different results. When the surfaces in theexperimental scene were chosen to be systematically less reflective than those in theother, the illumination matches set were not veridical matches. This bias inillumination matches was accompanied by a bias in the reflectance matches, aspredicted by the albedo hypothesis. The two biases, however, were not completelycomplementary, and the luminance measurements falsify the albedo hypothesis. Inaddition, manipulating the immediate surround of the test patch affected the matchedsurface lightness without affecting the matched illuminant. Together, these eightexperiments rule out the possibility that the perceived illuminant, as measured bymatching, is the only variable that governs the relation between physical luminanceand perceived surface reflectance.

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TABLE OF CONTENTS

Chapter 1 7The problem of color constancy; theoretical background 7Lightness constancy 11Methodologies in lightness constancy 11Illumination perception 15The relationship between surface color and illumination perception 17Tests and demonstrations of the proposed relationship 19

Egde Classification 21Quantitative Tests 23Oyama, 1968 27Logvenenko & Menshikova, 1994 31Kozaki & Noguchi, 1976 33Noguchi & Kozaki, 1985 34

Chapter 2 36The logic of the current experiments 36General Methods 38Experiment 1A: Symmetric Matches 43Experiment 1B: Symmetric Matches over a Range of Reflectances 52Experiment 2A: Asymmetric Matching 60Experiment 2B: Asymmetric Matching with Change in Surround 81

Chapter 3 91General Discussion 91Conclusion 93

References 95

Appendix 1 99

Appendix 2 108

Appendix 3 110

Appendix 4 112

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Chapter 1

The purpose of this project was to investigate the perception of illumination and toconsider the role of illumination perception in surface color constancy. There are tworeasons why illumination perception may be interesting. First, the perception ofillumination might itself be functional: one may need to estimate the relative warmthor visibility of two possible paths, predict the weather, or to estimate the time of day(Zaidi, 1998; Jameson & Hurvich, 1989). The second possible reason for illuminationperception, the primary focus of this project, is that it may be necessary to estimatethe illuminant in order to see surfaces as having constant colors. Indeed, manycomputational models of surface color perception assume that the perceivedilluminant plays a central role.

Color constancy: theoretical background

Color may be an important clue in object recognition. Human vision allows theobserver to create a stable perceptual mapping between a particular surface and agiven color, even as the proximal stimulus1 changes from context to context. This isremarkable, given that color perception involves the parsing of an inherentlyambiguous proximal stimulus. The light reaching the eye from an object is a productof the object’s surface reflectance function (the reflectance at each wavelength) andthe intensity and spectral distribution (light energy at each wavelength) of the lightsource. Figure 1 illustrates the inherent ambiguity of color perception. Notice thatboth the illuminant and the surface reflectance contribute at each wavelength to thelight reaching the eye.

Because more than one factor influences the proximal stimulus, it is possible for thesame object to give rise to a very different proximal stimulus as the lighting changes,for example at mid-day compared to at sunset. This effect can be so extreme that theproximal stimulus resulting from a blue color chip in a tungsten light can be the sameas that from a yellow color chip in sunlight (Jameson, 1985). Figure 2 shows anexample of the physical difference between two scenes that would appear very similarto an observer who was immersed in either scene.

1 The proximal stimulus is the stimulus on the retina: the exact pattern of excitation of the retina. Itmust somehow be transformed into a perception of something in the world. The proximal stimulus isoften contrasted with the distal stimulus: the physical objects and illuminants in the world that give riseto the proximal stimulus.

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Figure 1: The light reaching the eye from a surface is the product of both the surface reflectance and thespectral power of the illumination at each wavelength. In this figure, the rows depict surface reflectancefunction (left), and illuminant spectral power distribution (center) and the product. Notice that one cannotdetermine either the surface reflectance or the illuminant given the product.

Reflectance Spectral Power Spectral Power

Wavelength

a1i1 e1

a2 i2 e2

x

x

=

=

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[This color plate not included in the electronic version. See Evans’ book for theoriginal.]

Figure 2: These two pictures show the same scene under different illuminations. Although the two pictureslook very different when shown together, they would look almost the same to a viewer of the upper pictureadapted to daylight, and a viewer of the lower picture adapted to an ordinary tungsten light. Photos fromEvans, 1948, plate X.

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Even with these different proximal stimuli, however, a human observer sees theobject as being roughly the same color, that is, humans show a great deal of colorconstancy (e.g. Burzlaff, 1931; Arend and Reeves, 1986; Brainard & Wandell, 1992;Brainard, Brunt & Speigle, 1997; Brainard, 1998). This means that across a range ofconditions, the visual system produces a color representation that is better predictedby the distal stimulus (the surface reflectance) than the proximal stimulus (the lightreaching the eye). Thus, the observer is able to maintain a mapping between an objectand a perceived color, which is exactly what is needed given the assumption thatcolor perception is important in object recognition. How can an observer perceive thesurface of an object as a given color through changes in the proximal stimulus whichresult from changes in illumination? How can an observer maintain a constantrepresentation of an object’s color across a change in background color? These arethe central problems in color constancy.

Human color constancy is not perfect, and there are both biological and physicalsources of its limitation. There are biological limitations in cell response ranges: Onecould not represent colors that are too bright or too dark for the nervous system’srange. (More generally, there are neural limits to the perception of chromaticity aswell as limits in resolution caused by the limited density of the neurons.)Furthermore, the human eye (and any other natural eye) has a limited number of typesof photoreceptor, each maximally sensitive at a particular wavelength. Thesebiological limits might prevent the visual system from maintaining a stable mappingbetween reflectance and color appearance, and thus interfere with color constancy.

Physical limitations in color constancy (limitations inherent to the problem) includethe inherent ambiguity in the distal stimulus. Since there are an infinite number ofpossible reflectance functions of a surface that could give rise to the same proximalstimulus, it is not possible to resolve the exact reflectance function with any finitenumber of photoreceptors. For example, if one wanted to represent a particular colorusing paint or a CRT screen, that percept could be created in a number of differentways, mutually indistinguishable to the human visual system.

Another physical limit to color constancy is the spectral power distribution of theilluminant itself. In normal situations, the illuminant provides a wide enoughspectrum to test the reflectance of a surface at each wavelength. However, it ispossible to create an artificial illumination that is too narrow to reveal the fullreflectance spectrum of the surface. For example, the artificial light of the parkinggarage may make it difficult for you to recognize your blue car because it appears tobe yellow; there may be no part of the illuminant that tests the right part of the visiblespectrum to reveal a blue color.

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Lightness constancyColor constancy applies to both chromatic and achromatic color perception. Lightnessconstancy is a special case of color constancy. It is the stable representation oflightness across illumination and background changes, without reference to spectraldistribution or hue. The question is: how do observers judge “white” or “black” orintermediate shades of gray, as the intensity of the illuminant varies? Lightnessconstancy is illustrated by Figure 3. In this figure, the visual system perceives thecheckbox in the shadow as being similar in lightness to the checkbox in the topcorner, even though they are in fact physically different, as illustrated by the colorchips. The chip on the right is physically the same as the checkbox in the shadow, andthe chip on the left is the same as the checkbox in the top corner. The visual systemprocesses the light reaching the eye from inside and outside the shadow differentlywith the effect of stabilizing perceived surface lightness against changes inillumination.

Although lightness constancy is a special case of color constancy, it shares the samecentral feature: an infinite number of combinations of surface and illuminant canproduce identical proximal stimuli. There are also some differences between the twocases: in the case of achromatic color constancy one is interested in how the stimulusvaries in one dimension, whereas in tri-chromatic color constancy, one is interested inthe independent intensities for at least three different wavelengths. The experimentsdescribed in this project all deal with lightness constancy.

Methodologies in lightness constancy

According to Koffka (1935), Katz published the first work in the field of colorconstancy in 1911. Hering introduced the name “memory color” to describe thephenomenon in 1920. One of the earliest experimental demonstrations of lightnessconstancy was that of Burzlaff (1931). In this experiment, there were two displays of48 shades of gray. One display was placed near the window and the other was placeddeep in the interior of the room where it only got 5% as much illumination. Theobserver, who was next to the window, sequentially matched a square of a particularlightness on the near display (called the test patch) to a square on the far display thatappeared to be the best lightness match (see Figure 4). The results showed striking(though imperfect) lightness constancy.

Katz (1935) measured color constancy using a matching paradigm in which observershad to set the black to white ratio of a spinning color wheel to match a gray paper,when the color wheel was well illuminated and the standard patch was in shadow (seeFigure 5). He found that it was impossible for an observer to exactly perceptuallyequate the color of the light gray paper with the spinning wheel (represented by acircle on the back wall of the apparatus in Figure 5). The observer was never satisfiedthat the two looked alike, even once the match had been made.

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Figure 3: This figure illustrates lightness constancy. The checkbox in the shadow looks similar inlightness to the checkbox in the top corner, even though the lighter chip on the left is physically thesame as the checkbox in the shadow, and the chip on the right is the same as the checkbox in the topcorner. The visual system processes the light reaching the eye from inside and outside the shadowdifferently to create lightness constancy. Image courtesy of Ted Adelson, http://www-bcs.mit.edu/people/adelson/adelson.html

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Figure 4: An example of the matching method. Burzlaff (1931) had two displays, one placed near thewindow and the other was placed deep the room where it was darker. The observer sat next to the windowand selected a color chip to match the test patch. Adapted from Gilchrist et. al, 1999.

These two early experiments both test lightness constancy across two differentcontexts. In this general method, called asymmetric matching, observers must matchone aspect of the visual scene in one context (say the surface color or the illuminationof the scene) with the same aspect in a different scene. These two scenes can be sideby side boxes, like the Katz example, or they can be near and far displays, like in theBurzlaff example. As Katz found, this matching method does not always yieldperceptually satisfying results.

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Figure 5: Katz (1935) had observers match perceived color in a side by side display where one side wasilluminated and the other one shaded. Adapted from Gilchrist et. al, 1999.

As an alternative to the matching paradigm, it is possible to have observers rate,scale, or name colors in one or more contexts (see the descriptions of Kozaki &Noguchi (1976) and Logvenenko & Menshikova (1994) below). These methods areslightly more difficult to interpret because they introduce additional cognitive andlinguistic elements, and rely on the observer to accurately describe the percept.Scaling data is also difficult to interpret because one does not know whether thedifference between two adjacent points on the scale, for example, “dark gray” and“very dark gray” is equal to the difference between another pair of adjacent points,for example “gray” and “light gray.” (See Speigle, 1998 for a discussion andcomparison of different methods for assessing appearance.)

Quantitatively, there have been several proposed measures of achromatic colorconstancy, starting with Katz (1911, 1935). Today, a measure of color constancyproposed by Brunswik in 1933 is widely employed (e.g. Brainard, Brunt & Speigle,1997; Brainard, 1998; Arend, & Reeves, 1986).

For the purposes of the current experimental series, it is important to note that the vastmajority of color constancy studies to date have focused on the manipulation andperception of the surface color. The perception of surface color has been of interestlargely because of the functional role it plays in object recognition. This interest in

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surface colors as opposed to illuminant color is illustrated by a quote from Helmholtzwho suggested “In visual observation we constantly aim to reach a judgment on theobject colors and to eliminate differences of illumination.” (1962/1866 p. 408).Relatively few studies have focused on (or even addressed) the perception of theilluminant. Those few studies that have are described below (see also Beck, 1959).

Illumination perception

There are a number of reasons to believe that humans can perceive illumination. Earlysupport for this idea stems mainly from theoretical arguments or informalobservations (but see the experimental work reviewed in the next section). First, anumber of authors have suggested, based on informal observations, that one’s senseof an environment or scene includes some sense of the illuminant (e.g. Katz, 1935;Woodworth, 1938; Adelson & Pentland, 1991). Second, the ability to judgeilluminant properties could itself be perceptually important (e.g. Zaidi, 1998, seebelow; Jameson & Hurvich, 1989). Third, estimation of the illumination may be animportant step in achieving surface color constancy (e.g. Helmholtz, 1962/1866;Koffka, 1935; Beck, 1972; Epstein, 1973). This third possibility is the central ideathroughout this project. Finally, the perception of illumination has been of greatinterest to artists (e.g. Caravaggio, Rembrant, Pissaro, Monet), suggesting that itsrepresentation is an important part of visually comprehending a scene.

It is worth noting that there may be a difference between perceiving the overallillumination in a visual scene and perceiving the illuminant at a single scene location.Certainly, one could have a sense of an overall illumination in a room, for example,but still be able to perceive that some recesses in the scene are shadowed such that theilluminant at various surfaces differs. Of the experiments described here, the earlierfour ask observers to assess the overall illumination, while the later four explicitlyinstruct observers to focus on the amount of light falling on a given point. For thediffusely illuminated scenes used here, the two judgements do not seem to differ.

The first author to propose that we have some ability to perceive illumination mayhave been Katz (1935). Katz asserted on subjective grounds that empty spaces appearto the observer to be illuminated. He further claimed that the impression ofillumination is stronger even than the impression of surface colors. Katz alsoobserved that the illumination of any given empty space does not need to be uniformbut can contain areas of different distinct perceptible illumination. In other words, ascene can contain multiple frameworks. (Here “framework” in used in the Gilchrist etal. (1999) sense, meaning an area that is “grouped” together and seen as having thesame illuminant.) Such differences in illumination in a visual scene can be side byside or can be one behind the other, as when the observer looks down a dark hallwayinto a well-lit room.

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Woodworth (1938) also thought that the visual system was sensitive to informationregarding the illuminant, but suggested that we use the term “registering” rather than“perceiving” the illumination, since, he suggested, there was not necessarily anexplicit representation of the illumination. He felt that only an explicit representationshould be called a perception. 2 There can be an explicit perception according toWoodworth, as when a light is turned off or the sun goes behind a cloud, but such anexplicit representation is not necessary in order for illumination to play a role in colorconstancy. As to the question of whether illumination can be seen as different indifferent parts of the visual field, Woodworth assures us that “nothing is morecertain,” offering as an example the obvious flecks of direct sunlight under a shadytree (1938, p.432).

Adelson & Pentland (1991) oppose restricting the investigation of lightnessperception to 2D images, arguing that perception of lightness is dependent on theperceived 3D structure of the scene. Their suggestion (consistent with Gilchrist’searly models described below) emphasizes the importance of seeing each change inluminance as either a change in shape, a change in lighting or a change in shading.3

Adelson & Pentland propose a computer model with three “specialists”: the setbuilder (who determines shape), the painter (who determines color), and the lightingexpert (who determines illumination). Their model involves making a Bayesianestimation of the 3D structure, the color and the illumination, given the retinal image,where the Bayesian “cost” is represented as the inverse of probability. In short, theirmodel agrees with others that illumination perception is important and necessarilyrelated to color perception.

Zaidi (1998) proposed that observers are able to encode both the surface colors andthe illuminant. He suggests that the problem for the visual system to solve is not tobring about stable color appearance under different illuminants by discounting theilluminant, but to recognize that objects are indeed being viewed under differentilluminants and to discover what the illuminant properties are. He opposes recentmodels that propose that the illuminant is “discounted” via adaptation or otherprocesses early in perception, suggesting instead that failures in color constancy areby design, and are evidence that observers can extract information about theilluminant. Thus people can and do perceive differences in illumination, for examplebetween a sunny and a shaded path, and such information is important, for examplefor the hiker who seeks warmer or cooler trails. According to Zaidi, perceived objectcolors do change with illuminants and this change in color can be used to extract

2 In spite of my appreciation for Woodworth’s suggestion, I will use the more familiar term “perceive”throughout, but do not intend it to necessarily imply a conscious awareness or the ability to describethe percept. The percept may be explicitly represented, as it is in the current project, or it may not be.3 In Gilchrist and colleague’s discussion of color constancy, the changes in shape and illumination arenot distinguished, since the shading is produced by an “attached illumination edge” in the object.

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information about illuminants. Zaidi also points out that various painters such asMonet and Corot exploit this relationship to provide information about the illuminant.

One might question, however, whether “discounting” the illuminant (or taking it intoaccount in the process of color perception) truly precludes illumination perception. Infact, illumination perception or registration might be necessary in order to calculatesurface color. Perhaps failures in color constancy reflect failures of accurateillumination estimation rather than revealing illumination perception, as Zaidisuggests.

The relationship between surface color and illumination perception

Does illumination perception have a role in the perception of surface color? The factthat human observers have (some degree of) color constancy suggests that differentproximal stimuli can give rise to the perception of (approximately) the same color.For example, imagine the same gray paper in first dim then bright light. It is seen asthe same middle gray in both cases. One suggestion is that in order for this process towork, the illumination difference (which accounts for the difference in the proximalstimuli) must be a factor in the calculation of the color. In order to be a factor, theillumination must be perceived (or at least registered) by the visual system. Anotherway to say this is that when the observer looks at a gray sheet of paper in a givenlight, the retinal stimulus gives rise to two (not necessarily conscious) percepts: thesurface color and the illumination. The exact mathematical relationship between thesetwo percepts could take one of a number of different forms, as discussed below.

Helmholtz (1962/1866) proposed that the judgments of color (or lightness) andillumination must be psychologically coupled, in the sense that the perception of one(lightness) is based on perceiving and taking the other (illumination) into account. “Invisual observation we constantly aim to reach a judgment on the object colors and toeliminate differences of illumination.” (1962/1866 p. 408). He suggested that theluminance of a particular test field was compared with the perceived illumination ofthe overall framework (which may or may not have been the complete visual scene).The surface reflectance, he suggested, was calculated by dividing the luminance ofthe retinal image by the perceived illumination. (This is the classic form of the albedohypothesis as discussed below.) This particular operation was chosen because if onewere dealing strictly with the physics of reflectance, the luminance would be equal tothe surface reflectance times the illumination. Whether this is the actual psychologicalrelationship is an empirical question, tested in this project.

Hering (1907/1920) raised an objection to any proposal (such as that of Helmholtz)suggesting that from a single known quantity (the light reflected to the eye) we couldreliably derive two different perceived quantities. He suggested that it would be

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logically impossible to know which factor was contributing more: was the luminancehigh because of a high reflectance or because of a high illumination? Indeed, this is amajor puzzle in color constancy. This general problem, the problem of anchoring, isdiscussed further by Gilchrist et al. (1999).

Perhaps this seeming paradox can be solved by one or more of the following: First,under natural viewing conditions, the visual field has multiple objects, each of whichprovides some cue to the illumination (Kardos, 1929). Second, the “field of indirectvision” or the periphery may provide information about the illuminant (Woodworth,1938). Third, the visual system may simply make a guess (although the data seem tosuggest somewhat more accuracy than guessing would predict.) Finally, thecomputational approach to color constancy suggests that one can make a principledestimate of the illuminant based on certain regularities in the world (see, e.g. Maloney& Wandell, 1986; D’Zmura, 1992; Brainard & Freeman, 1997; Buchsbaum 1980).

Earlier this century, Koffka (1935) also suggested that there was an invariantrelationship between perceived lightness and perceived illumination in any casewhere there is color constancy. He believed that there would be no other logical waythat color constancy would be possible. He did not firmly advocate any particularrelationship between perceived lightness and perceived illumination, but did assertthat there must be some invariant relationship. Specifically, he suggested “acombination of whiteness and brightness, possibly their product, is an invariant for agiven local stimulation under a definite set of total conditions.” (p.244).

Woodworth (1938) also proposed that there was an invariant causal relationshipbetween perceived color and perceived illumination. According to him, the visualsystem somehow inferred the illumination, based on various cues in the visual field,and then judged lightness based on this “registration” of the illumination.

In the late 1960’s and 1970’s there was a revival of the idea that an observer used anestimate of the illumination to perceive lightness. This was called the albedohypothesis (Beck, 1972). Epstein (1973) called it the “taking-into-accounthypothesis,” a term which is no longer used. Beck formalized the hypothesis,describing it as “the view that an observer discounts the intensity of the illuminationin perceiving lightness.” (1972, p.99). As the term is used in the literature today, thealbedo hypothesis suggests that the visual system first estimates the illuminant, andthen uses that estimate to calculate the surface reflectance for a given surfaceluminance.4 Beck suggested that the albedo hypothesis required a strictly invariantrelationship between the perceived lightness and perceived illumination. One possiblerelationship is that the light reaching the eye, or luminance (e) equals the perceivedlightness or albedo (â) times the perceived illumination (î).

4 Albedo is here used as a synonym for reflectance.

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e = â * î

(He later tested and rejected this hypothesis.) According to the albedo hypothesisthere is a causal relationship between the two percepts: the perceived illumination hasa causal role in the perception of lightness. Thus, a change in the perceivedillumination is a sufficient condition for a change in perceived lightness provided thatthe luminance remains unchanged. The above formulation is the classical form of thealbedo hypothesis, but in principle there are a number of possible formal relationshipsdescribing an invariant relationship between perceived illumination and perceivedalbedo. The important requirement is that there be a regular and causal relationshipbetween the two, such that for a given luminance, the perceptual system is able touniquely determine the albedo, given the perceived illumination. Variations of thispossible equation are discussed below (see the subsection entitled “Quantitativetests.”)

Tests and demonstrations of the proposed relationship

If it is the case that perceived surface color depends on both the surface luminanceand the perceived illuminant, then a prediction would be that by manipulating cues tothe illuminant, one could influence perceived color. One very simple demonstrationof the relationship between perceived illumination and perceived surface color isHering’s (1907/1920) ringed-shadow demonstration: place an object on a white sheetof paper in a room with a single light source. Take a thick felt pen and trace thepenumbra (the lighter gray area) of the shadow on the paper, so that it no longerappears to be a penumbra. Without a penumbra the shadow will not appear to be ashadow, and the paper will appear stained; the perceived color will have beenchanged by a manipulation of the perceived illuminant.5

A second more well known demonstration of deceptive illumination influencingperceived color is the “Gelb effect” (Gelb, 1929). In this demonstration, the room wasdimly lit and the walls were covered with an assortment of objects. The experimenterpresented a black disk suspended from the ceiling, which was illuminated by a hiddenlight source. In this arrangement, the observer was unaware of the light source, andthere was no penumbra. Thus, the disk was not seen as highly illuminated but wasseen as white. Importantly, being told about the light source did not change thepercept; the observer still saw the black paper as white.

The exact inverse of this demonstration has been shown (Kardos, 1934). In this case,the room was very well lit and contained a variety of objects. A disk of white paper

5 Notice however, that this demonstration alone does not require an invariant relationship between theilluminant and the surface color, since other aspects of the retinal image, like the “crispness” of theedge have necessarily changed as well (see also Beck, 1971, described below.) It is, however,consistent with there being such a relationship, and thus may be a suggestive demonstration.

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was suspended from the ceiling and a concealed shadow caster prevented light fromfalling directly on the disk. Observers reported seeing a black disk. As before,subsequent manipulations reveal that the effect is not cognitively penetrable: knowingthat the shadow caster was there did not change the percept. Only cues of shading inthe visual field changed the perceived color. Again, this suggests that it is possible tomanipulate perceived color by manipulating perceived illumination alone.

Beck (1971) offered a more recent replication and improvement on this demonstrativeparadigm. He noticed that it was not logically possible to distinguish between theeffect of illumination perception and the effect of simultaneous contrast (or lateralinhibition) in the above demonstrations. (Indeed, it was Woodworth and Schlosberg(1954), not Gelb, who suggested that the original demonstration revealed the effect ofillumination perception.) Beck projected a bright beam of light onto a whitebackground such that it fell halfway onto a black surface in the foreground. Becauseof the angle of observation, it was in one case possible to see the shadow (an obviouscue to illumination) and in the other case not (see Figure 6). In these two cases thecontrast effect was held constant since the reflectance and perimeter of the edge wereequated. The results were in agreement with the earlier demonstrations: the majorityof the observers rated the target (the illuminated area of the black foreground surface)as darker in the shadow condition than in the non-shadow condition. Thus, even withadjacent contrast equated, a visible cue to illumination affected the perceived surfacecolor.

Figure 6: Experimental set up from Beck (1971). A bright beam of light shines on a white background and fallshalfway onto a black surface in the foreground. In one case (shown on the left) it was possible to see the shadow(an obvious cue to illumination) and in the other case (shown on the right) it was not. The contrast effect was heldconstant. Adapted from Beck, 1971.

White Background

Black Surfaces

Illuminated Area

Shadow

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Edge Classification

Gilchrist and his colleagues (e.g. Gilchrist, 1988; Gilchrist & Jacobsen, 1984)organized and explained these observations using the important concept of edgeclassification. According to this perspective, another way to characterize the“deceptive illumination” in the above demonstrations is to say that the observer has(perceptually) misclassified an abrupt change in luminance. Gilchrist and colleaguesproposed that the perceptual system automatically classifies any abrupt change inluminance as one of two types of edges. A “reflectance edge” is a change in colorcaused by a change in surface reflectance, e.g. by a stripe of paint or a change inmaterial. An “illumination edge,” is a change in the amount of light reaching thesurface, either because of shadowing or because of a bend in the surface. In the caseof Hering’s ringed shadow, the edge is seen as a reflectance edge, a change in thecolor of the paper, rather than as an illuminant edge or a shadow.

Gilchrist and Jacobsen (1984) measured observers’ ability to judge color andillumination in two achromatic scenes. Gilchrist and Jacobsen constructed twoidentical miniature rooms that differed only in the reflectance of their surfaces. Eachroom contained the same objects: a milk carton, two paint cans, a wooden cube, andan egg carton. Each room was painted uniformly such that all the surfaces, includingthe walls and the objects, were of the same reflectance. One was matte black (with areflectance of 4.6%) and the other a matte white (with a reflectance of 84%). Eachchamber was illuminated with a bulb that was hidden by a baffle, such that it was notvisible to the observer.

In one condition the rooms were equally illuminated. Here the luminance level wasmuch higher in the white room than in the black room, but the authors argue that thisalone should not change the appearance of the room, unless one expected that everyillumination change would also change the lightness appearance of the room. Inanother condition, the illumination in the white room was adjusted so that the lightreaching the eye was actually less in the white room than in the black room (both intotal and at every measured point).

Observers were first asked to describe what they saw and were then asked whetherthe illumination appeared to be the same everywhere and whether the surfaces allappeared to be the same shade. Next, observers were asked to make 8 illuminationmatches: they were asked to adjust the illumination on a Munsell chart until itmatched the illumination they saw at 8 different points in each room. In a secondexperiment, the experimenters asked for a Munsell match of the reflectance at each ofthe 8 test points.

By this method, Gilchrist and Jacobsen hoped to answer the following questions:First, will the different surfaces within a single-reflectance room look different? This

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first question is a test of the current contrast account of color constancy, whichsuggests that the perceived color of a surface is influenced by the color of its adjacentsurfaces. Second, what is the perceived illumination at the different test spots in aroom with uniform illumination? Third, will the two single-reflectance rooms lookdifferent from one another?

The results suggested that the various surfaces within each room had roughly thesame apparent reflectance or color. The within observer differences in color judgmentwere very small compared to the differences in illumination judgments. Results alsoshowed that the differences in illumination levels throughout the array wereperceived, and the illumination judgments closely paralleled the true illuminationlevels. The exact match was not always veridical (the matches in the white roomshowed a consistent error), but the ratios between the 8 test spots were perceivedveridically. Finally, results showed that the two rooms appeared to the observers to bedifferent from each other. Even the brightly lit black room was seen as darker(Munsell match 5.5) than the dimly lit white room (Munsell match 7.5), although onemight have predicted the opposite based on the intensity of the light reaching the eye.

They drew two conclusions: First observers were judging color differently, and moreaccurately, than simultaneous contrast theory would predict. Second, observers wereremarkably good at judging the illumination at eight different points in the visualscene. The authors intend the experiment as a demonstration that observers are able toclassify edges as either reflectance edges or illumination edges, and take these resultsto support this view. They point out that sensory theories of color constancy ignoreillumination perception, or assume that illumination is poorly perceived.

Given these results, the authors concluded that contrast theories could not entirelyaccount for color constancy, nor was the “photometer metaphor”6 accurate indescribing human color vision. They offer as an alternative the view that what thevisual system needs to do is to categorize edges. Contrast theories would suggest thatan area of higher luminance would always appear to be whiter than an adjacent areaof lower luminance. Gilchrist and Jacobson suggest that this is only the case if theborder between the areas is seen as a reflectance edge; the same inference cannot bemade if the edge is an illumination edge.

Subsequently, Gilchrist (1988) proposed that edges are categorized by whether theratio or luminance difference remains the same at an intersection. Based on this view,he was able to experimentally manipulate whether the observer saw a luminance

6 The photometer metaphor suggests the photometer as a model of human lightness perception. Aphotometer measures luminance, which is the product of illumination and reflectance, and has no wayto disambiguate the two. This metaphor has previously been discredited by the work Helmoltz, Hering,and the contrast effects literature.

23

gradient as a reflectance edge or an illumination edge, thus manipulating theperceived color.

Gilchrist had the observer look into a small room. On the back wall of this room wasa piece of white (90% reflectance) paper. Illumination came from a hidden point lightsource, and the paper was half shaded by a shadow caster. The target piece of graypaper was attached to the shaded side of the white background, and a Munsell chart,from which observers were asked to chose the matching chip, hung in the illuminatedregion. In one condition, the observers’ view was unobstructed, such that they couldsee the context of the room, the paper, and the shadow. In another condition,observers viewed the room through a hole in a sheet of black paper, such that theycould only see the target, the Munsell grid, and part of the background. According toGilchrist, the case in which the observers could see the context unobscured was anexperiment on color constancy, and the case in which the observer’s view wasobscured by the baffle, such that the illumination difference was not apparent and theshaded area appeared to be darker paper, was an experiment on the contrast effect.

Results clearly show a difference between the two conditions: when the observerscould see the context, they judged the target paper to be much lighter than when theycould not see the context. This is a very important effect, given that observers arelooking at the same target; the retinal stimuli would have been exactly the same in thetwo conditions, at least in the center of the field of view. These results suggest thatperceived illumination can have an effect on perceived color, given the sameproximal (and distal) stimulus.

In addition, Gilchrist also concluded that constancy effects are far greater (six timeslarger) than contrast effects. Based on these data, Gilchrist suggests that contrasteffects represent failures of constancy, contrary to some current authors who havesuggested that constancy and contrast are examples of the same phenomenon.

Quantitative tests

The previous section provides a review of the evidence that humans perceiveillumination and some demonstrations suggesting a relationship between perceivedillumination and perceived surface color. Next it would be interesting to knowwhether there is a consistent, quantifiable relationship. Below is a review of someattempts to quantitatively test the relationship between perceived illumination andperceived reflectance. In addition to the original formulation of the albedo hypothesis,there is another, more general possible quantitative relationships that will beconsidered and tested in this experimental project, as well as an even more specifichypothesis.

24

The most specific hypothesis suggests that the percept is a function of and uniquelydetermined by the physical stimulus:

î = f (i)â = g (a)

According to this hypothesis, the perceived illuminant intensity (î) at any point isdetermined by the physical illuminant intensity (i) at that point, and the perceivedalbedo (â) of any surface is determined by the physical albedo (a) or reflectance ofthat surface. It is known that this form of the albedo hypothesis is not always true(e.g. Hering, 1907/1920; Gelb, 1929; Kardos, 1934; Beck, 1971; Logvenenko &Menshikova, 1994).

In its classic form (Helmholtz, 1866; Koffka, 1935; Beck, 1972), the albedohypothesis is7:

â = e / î

Here e is the amount of light energy reaching the eye (or the luminance) from the testpatch, â is the perceived albedo of the test patch, and î is the perceived illuminantintensity at the test patch. According to this model, color perception involves thefollowing steps: 1) The retinal image is formed as the light is reflected from surfaces2) the visual system calculates the illuminant based on information available in theentire scene, and 3) The perceived reflectance is calculated according to this equation.This original form is the most commonly tested form of the albedo hypothesis.

A more general formulation of the albedo hypothesis is

â = f(e, î)

where f() is a function that is unknown but which is consistent across surfacereflectances and contexts. This general form is similar to and not mutually exclusiveof the classic one. Here the perceived albedo (â) is determined by the light reachingthe eye in a manner that depends on the perceived illumination (î). Again, this is amulti-stage model involving 1) the formation of the retinal image based on theluminance 2) an estimation of the illuminant based on the entire scene and 3) thecalculation of the reflectance by some hypothetical reflectance calculation function 7 This notation may strike the reader as odd, since it is equating a physical measurement with apsychological representation. This makes sense mathematically only if one assumes that the functions fand g mentioned above are identity functions, that is that i = î and a = â. Note that even if thisassumption fails, the following experimental predictions are the same. In that case, call the registered,inaccessible percepts î’ and â’, and the consciously accessible explicit representations î and â. Now aslong as î and â are some fixed functions of î’ and â’ and each function has a one to one relationship, theexperimental predictions in the matching experiments that follow will be the same.

25

based on the luminance and the estimated illuminant. Notice that this function takesas input only the perceived illuminant and the actual physical luminance reflectedfrom the surface of interest according to this model. The output is the perceivedsurface reflectance as illustrated in the top panel of Figure 7.

This suggestion is appealing, because it relaxes the requirement that thepsychological relationship parallel the laws of physics, i.e. that

luminance intensity (e) = albedo (a) * illuminant intensity (i)

This form of the albedo hypothesis is also the most general formulation of the three-stage model of surface perception described above. It is (nearly) universal amongcomputational models of surface color perception. Furthermore, this variant isconsistent with some extant data (e.g. Oyama, 1968; Logvenenko & Menshikova,1994).

Alternatively, it is possible that none of these forms of the albedo hypothesis iscorrect. In this case, there are at least two alternative possibilities. First, it is possiblethat perceived illumination affects perceived reflectance, but does not uniquelydetermine it. Perhaps it is one of multiple factors that is used by the hypotheticalalbedo calculation function to mediate the relationship between luminance andperceived reflectance

â = f(e, î, x).

Here, the variable x represents an unknown factor used in the calculation of theperceived surface reflectance. As seen below, this factor could be the reflectance ofthe immediate surround of the test patch or the ratio between the luminance of the testpatch and that of the surround, for example. The second panel of Figure 7 illustratesthe first alternative to the albedo hypothesis. The luminance and the perceivedilluminant are factors in the calculation of the perceived reflectance, but so is someother factor.

As a second alternative, it is possible that both perceived illumination and perceivedalbedo are represented, but that there is no relationship between the two.

$ â

$ î

26

Figure 7: This figure illustrates the three alternatives: the top panel illustrates a model consistent with thealbedo hypothesis: the stimulus yields an estimate of the illuminant (î), which is available for computing thealbedo (â) given the stimulus. The perceived illuminant (î) governs the relationship between stimulus andperceived surface. The second panel shows this same model, but with additional factors influencing therelationship between physical luminance and perceived reflectance. The third panel shows the perception ofboth î and â with no fixed relationship between the two.

îi

r

reflectance calculation function

î

aa

i

e

reflectance calculation function

î

aa

i

e

â

â

other factor(s)

i î

âa

27

This alternative is the proposal that Beck (1959; 1961; 1971; 1972) promotes. Thethird panel shows the perception of both î and â with no fixed relationship betweenthe two. The experiments described below were designed to select between the albedohypothesis and these two alternatives to it.

The quantitative relationship between perceived surface color and perceivedillumination (given a particular retinal image) has been investigated, for example, byBeck (1959, 1961), Kozaki (1973) and Oyama (1968) and Kozaki & Noguchi (1976;Noguchi & Kozaki, 1985) as reviewed below. Many of these studies reject the mostspecific hypothesis and the classic form of the albedo hypothesis, and some of thedata may reject even the more general form of the albedo hypothesis for certaincontexts. Nevertheless, another, more rigorous test of the albedo hypothesis isjustified, since all of these tests used simple, poorly articulated scenes, which mayhave an effect on color perception.

Oyama, 1968

One experimental test of the hypothesis that perceived albedo is inferred by dividingthe luminance by the perceived illumination (a re-arrangement of the classic form ofthe albedo hypothesis: â = e / î) was conducted by Oyama (1968). In this experiment,there were three boxes, the standard box, comparison box I and comparison box II,each with a rectangular aperture cut in the front of it. Each box was illuminated by alight source from the top front of the box. The standard box was lined with graypaper, and had a hole in the back of the box beyond which there was a very lowreflectance surface. A standard disk (one of 5) was presented in isolation by hangingit down in this opening for the observer to see. Both the illuminant and the reflectanceof the standard disk could be set experimentally. Comparison box I was lined withblack paper on all sides and had a comparison disk on the back wall with anadjustable white-black ratio. The illuminant in this box was set near the upper rangeof those used in the standard box. Comparison box II was lined with white paper, andon the back wall was a white square (the target) mounted on a black disk.

An observer adjusted the white-black ratio of the disk in comparison box I to matchthe surface color of the standard disk in the standard box. Then she adjusted theillumination in Comparison box II to match that in the standard box. Notice that thesurface color match and the illumination match were made in different boxes withdifferent wall colors, so the most general form of the albedo hypothesis could not betested with these methods.

From the matching of the surface color of Comparison box I to the test disk in thestandard, the main empirical result is that the illuminant in the standard box as well asthe surface color in the standard box influenced the matched surface in comparison

28

box I. The fact that the illuminant had an effect on matched surface color indicates adeviation from perfect surface color constancy.

Perhaps more pertinent to the current question are the illumination matches incomparison box II. One important finding is that observers were able to match theillumination between the two boxes rather well. That is, there was a linearrelationship between standard illuminant and matched illuminant with each standarddisk. The matched illuminant, however, depended not only on the standard illuminantbut also on the standard surface. The dependence on the test surface indicates adeviation from perfect illumination color constancy: the surfaces in the standard boxaffect the illuminant matches, but this deviation is quite small.

Of interest from this study is not only the question of whether observers can matchthe illuminant intensity, but also whether Oyama’s data can be used to test any formof the albedo hypothesis. In fact, these data can be used to test the classic form of thealbedo hypothesis: e = â * î. As the step by step analysis below will show, this formof the albedo hypothesis predicts a linear relationship between the luminance of thetest patch in the standard box (e1) and the test box (e2).

The logic is as follows: If the albedo hypothesis were correct in each of the twocontexts, then

e1 = â1 * î1

ande2 = â2 * î2

which gives use1 / î1= â1

ande2 / î2= â2.

Observers matched the surface reflectance of the test disk to the standard disk, so

â1 = â2.

From this, one can derive the prediction that the light from the surface at the twomatched test patches should have a linear relationship. Given the matchedreflectances, one can derive an equality in the previous two equations, yielding

e1 / î1 = e2 / î2

which can be stated:e2 = e1 * î1 / î2

29

ore2 = e1 * c

where c is a scalar constant, which represents the relationship between the perceivedillumination in the two contexts. In other words, the classic form of the albedohypothesis says that when the surface reflectance of the test patches in the twochambers are subjectively matched, there should be a linear relationship between theluminances, measured at the two test patches. Notice that the two perceivedilluminants, î1 and î2 do not have to be the same, they just have to have a consistentrelationship during the test.

Data from the surface color matching part of this experiment do not show this result,and thus falsify the classic form of the albedo hypothesis for Oyama’s context. A plot(see Figure 8) of the log standard reflectance against log matched reflectance shows aslope of greater than one (as opposed to the predicted 1) which falsifies the albedohypothesis in its classic form.

Notice that although the two perceived illuminants do not have to be equal, they maybe. If so,

î1 = î2

then î1 / î2= 1 so

e1 = e2

In other words, according to the classic form of the albedo hypothesis, if â1 = â2 and î1

= î2 then it must be the case that e1 = e2. This will also be true of the more generalform of the albedo hypothesis, f(e, î) = â. This prediction is crucial to the logic of theexperiments in the current project, especially experiment 2A, described below.

With Oyama’s data it is not possible to test the general form of the albedo hypothesis.The illumination matches were not set in the same box as the surface matches, so onecannot test the hypothesis that there is some invariant relationship between â, î and e.One cannot test the idea that the perceived reflectance is determined by the surfacelight reaching the eye, taking perceived illumination into account via some as yetunspecified relationship.

30

Figure 8: a) Schematic representation of the major finding from Oyama (1968) in log coordinates. Thereflectance of the matched surface depends both on the surface color and the luminance at the standard disk.(Each line represents a different standard disk.) That the illuminant has an effect on perceived surface coloris a deviation from color constancy. b) The second panel, based on Oyama’s Figure 4, shows the luminanceof the matched disk as a function of the luminance of the standard disk, both plotted in log coordinates. Itprovides a critical test of form 2 of the albedo hypothesis. The hypothesis predicts a slope of 1 for thisgraph; thus the data clearly challenge the hypothesis.

The relationship between Standard and Matched Luminance

.9

.47

.245

.123predicted

Standard Reflectance

Standard Luminance (mL)

Mat

ched

Lum

inan

ce (

mL)

Effect of luminance and reflectance on matched reflectance

88%46%24%12%5.80%

Standard Luminance (e)

Mat

ched

Ref

lect

ance

(%

)


31

In considering Oyama’s data, it may be relevant to consider some factors in thedisplay. This display was very simple and not very well articulated. The test patchwas large (11° diameter) and was seen against a large (40° by 30°) black background.Gilchrist et al (1999) would thus predict that the test patch itself would have a largeinfluence on anchoring. The brighter the test patch, the bigger this self-adaptationeffect might be, and thus lightness of the test patch would grow less rapidly inresponse to physical reflectance than if it were viewed in a scene where other factorsdominated the state of adaptation.

Logvenenko & Menshikova, 1994

More recently, Logvenenko & Menshikova (1994) tested and claimed to havefalsified the classic form of the albedo hypothesis. Their data are inconsistent with theidea that the retinal image is exactly equal to the perceived illuminant times perceivedsurface reflectance. However, they suggest that there is an invariant relationshipbetween perception of illumination and perception of surface reflectance, but not thesimple relationship of the classic albedo hypothesis. Thus, their data is consistent withthe most general form of the albedo hypothesis, (f(e, î)= â).

Logvenenko & Menshikova started by developing a methodology that would allowthem to compare perceptions of shaded regions to perceptions of painted regions.They used a bisection task (after Torgerson 1958; Pfanzagl, 1968) to develop scalesrelating physical and perceived qualities: one scale related perceived lightness tosurface reflectance and another scale related perceived illumination to illuminantintensity. Observers saw one black chip and one white chip and had to set a third chipto be of a mid-level lightness, exactly equally different from the white chip and theblack chip. Then a chip that was equal to their midpoint judgment (actually themedian of nine trials) was shown with first the white, then the black chip, and theobserver again had to choose the midpoint between the two. Thus, a scale ofperceptual increments was created. An analogous procedure was used to create ascale for an illuminant. These first two experiments yield a relationship between theperceived and the physical quantities such that one can compute one as a (non-linear)function of the other. These functions would, however, only be valid in the context inwhich the original experiment was conducted.

At this point, it would be possible to test a relationship between perceived surfacelightness and perceived illumination by asking whether the two functions have thesame form. The authors did not do this comparison, but the graphs of the twofunctions (see Figure 9) reveal a similar shape. The psychophysical functions betweenphysical illumination and perceived illumination, and between physical lightness andperceived lightness, were both non-linear, and were similar in shape.

32

The authors interpret this non-linearity as evidence against the classic form of thealbedo hypothesis. That is, if human color perception were like a photometer, thenthere would be a perfectly linear relationship between physical illumination andperceived illumination, and this would determine a linear relationship betweensurface lightness and perceived surface lightness. However, it may not be necessaryto make this inference from these data: These are scaling data, and one could imaginethat the result of scaling captures the true perceived lightness or illuminant only aftera non-linear output transformation (see Foley, 1977; Philbeck & Loomis, 1997). It isstill possible that there are inaccessible variables, perceived lightness andillumination, that have a linear relationship to their real world analogs.

In their third experiment, the authors manipulated whether the observers wereperceiving a shadow or a colored region by having them look through a pseudoscope.Originally, observers saw a cone on a white sheet of paper, which cast a shadow.Through the pseudoscope, the cone appeared as a hole in the paper, so the shadowlooked like a stain. While looking at this inverted scene, observers were asked tomatch the “colored surface” to a chip. When the scene was then seen in normal depththe observers were asked to match the shadow to a real shadow. The authors used thescales created in the first two experiments to relate the matches to perceived lightnessand perceived illumination.

The authors used this third experiment to consider the general form of the albedohypothesis, that perceived surface lightness is a function of the light reflected to theeye and perceived illumination (rather than the physical analogs of these percepts). Ifthis were true, the authors argue, then a plot of perceived illumination versusperceived surface lightness should be linear. In fact, Logvinenko and Menshikova’sdata seem to show this linearity. Unfortunately, the authors failed to measure colorand perceived illumination in the same condition. Thus, in order to draw thisconclusion, one must assume that when judging the illumination at different shadowintensities, the perceived lightness at that location (perceived surface reflectance)does not change, and vice-versa when judging the perceived lightness. The authorsassure us that this assumption is valid. Ultimately, Logvenenko & Menshikova (1994)do not reject the general form of the albedo hypothesis.

33

Figure 9: This sketch of Logvenenko & Menshikova’s (1994) data show a non-linear relationship betweena) surface reflectance (a) and perceived surface reflectance (â) and between b) illumination (i) and perceivedillumination (î). Notice, however, that the shapes of the curves are similar.

Kozaki & Noguchi, 1976

Another pair of studies which may provide evidence against the albedo hypothesis inits classic form is that of Kozaki and Noguchi (1976; Noguchi & Kozaki, 1985). Inthe first of these studies, observers made categorical judgments of both lightness and

Per

ceiv

ed "

gray

ness

" �

Reflectance averaged over two observers

Per

ceiv

ed i

llum

inat

ion

�

Illumination averaged over two observers

34

illumination, choosing one of nine category labels for each (e.g. very blackish gray,blackish gray, rather blackish gray, etc.). Illumination and lightness were judged inindependent sessions. In each session, observers made judgments for a number ofdifferent experimentally set test patches, backgrounds and illuminations, for a total of376 judgments for each session.

The data that these sessions yielded can be used to test the various forms of thealbedo hypothesis. The experimenters measured, for each trial, the luminance of thetest patch. Thus, one can compare judgments of illumination and lightness since thelight reaching the eye was held constant. All three forms of the albedo hypothesiswould predict that if the light reaching the eye is the same, and the illumination isjudged to be the same, then perceived albedo must also be the same. This predictionis falsified, and the albedo hypothesis rejected, given Kozaki and Noguchi’s data.

One should be cautious about interpreting data given the fact that the dependentmeasure was scaling data. Furthermore, it should be noted that even if it was the casethat the albedo hypothesis could be rejected in this study, it could only be rejected forthese particular stimulus conditions. The stimulus conditions used in this study wererather simple and not well articulated, which may be important (see Gilchrist et al.,1999).

Noguchi & Kozaki, 1985

The same authors later replicated the experiment, this time testing to see whetherthere was any effect of the test patch being seen as background, in two conditions:one in which small black squares were attached to the test patch, and one in whichsmall white squares were attached to the test patch. Again, results from this studycontradict predictions of all three forms of the albedo hypothesis. Although there is areciprocal relationship between lightness and perceived illumination (specific to eachcondition), judgments of illumination were influenced by the co-existence of higherluminance regions. The albedo of the foreground patches affected the relationshipbetween i and î and the relationship between a and â. Since illumination judgmentswere influenced by the albedo of the test field and its interaction with the albedo ofthe patches, there was no simple relationship between perceived lightness andperceived illumination, according to the authors. The authors conclude that althoughthe visual system can use the equation e = î * â, it only does so for a particular, fixede, and the relationship changes across context.

In sum, the studies described in this section attempted to test the albedo hypothesis,and some (e.g. Logvenenko & Menshikova 1994; Kozaki & Noguchi, 1976; see alsoBeck, 1961) disprove the albedo hypothesis in its classic form. That is, it is not thecase that both lightness and illumination judgments have a linear relationship to theirphysical analogs, and that these have an unchanging multiplicative relationship to

35

light reaching the eye. The eye is not a light meter. Some of the above authors evenreject the most general form of the albedo hypothesis, but relying on scaling data, andonly for poorly articulated scenes.

Chapter 2

The logic of the current experiments

In this chapter 4 experiments presented designed to examine the role of illuminationperception in color constancy. Four more control experiments are included inappendix 1, and essentially replicate the findings in this chapter. These experimentsemployed a matching paradigm; the observer sat between two experimental chamberswhile a computer controlled motorized mirror rotated between the two chambers tochange the view. In each chamber there was a mirror reversed complex scene thatincluded an LCD panel on the back wall that served as the test patch.

The illumination in each chamber was controlled by a bank of diffused overheadlights. The intensity in the match chamber was controlled by the observer via thecomputer. The observer's first task was to match the illuminant in the match chamberto the illuminant in the standard chamber. The observer's second task was to matchthe surface reflectance of the test patch on the back wall of each chamber. Observersmatched the surface reflectance in the same trial as they matched the illuminant. Thatis, once the observer had completed the two tasks, both the perceived illuminant andthe perceived surface reflectance matched for that observer, before they went on tothe next trial.

The first two experiments measured the veridicality of illuminant and surfacematching in this paradigm, and the efficacy of this method. The next two tested thealbedo hypothesis in both its classic, and most general forms. Experiment 2A did soby creating a bias in illuminant matching; the albedo hypothesis suggests that theperceived illuminant determines the perceived reflectance given the physicalluminance. Although the judgment of illumination can be “incorrect” (i.e. notdetermined solely by the actual illumination) whatever that perception is shoulddetermine how the surface lightness is perceived. In Experiment 2B, the stimuli weredesigned to manipulated the surface reflectance matches without any change in theilluminant match. If one can be manipulated independent of the other, than the albedohypothesis in its most general form is false. Experiments 3A and 3B are replicationsand control experiments that are designed to ensure that the relationship betweenilluminant and surface reflectance is localized to the test patch. Experiments 4A and4B are also replications; they control for the possibility that the causal relationshipbetween illuminant perception and reflectance perception might be in the oppositedirection than commonly supposed.

36

The experiments, particularly the last 6 (including the 4 replications in Appendix 1),were designed to provide a rigorous test of the most general form of the albedohypothesis. The logic of how Experiment 2A might falsify the classic form of thealbedo hypothesis is as follows:

Assume that the albedo hypothesis is true in both chamber 1 and chamber 2

e1 = î1 * â1

ande2 = î2 * â 2

then

e1 / â1 = î1

ande2 / â 2 = î2.

Then, since after the illumination match

î1=î2

then

e1 / â1 = e2 / â 2

and, since after the surface reflectance match

â1 = â 2

then

e1 = e2

In other words, the albedo hypothesis makes a prediction about the physicalluminance of the regions that appear to match.

Furthermore, the most general form of the albedo hypothesis also predicts that thephysical luminance must match after the perceived illuminant and the perceivedsurface reflectance are matched. Remember that the most general form of the albedohypothesis, the assumption of most computational models of color perception, is thatthere is a reflectance calculation function that takes as input only the physical

37

luminance of the test patch and the perceived illuminant, calculated across the entirescene.

If the albedo hypothesis is correct, then there is an important prediction for ourmatching paradigm: Once the perceived illuminant is matched in the two chambers,and the perceived surface reflectance is matched in the two chambers, the physicalluminance, or the light coming off the test patch, must match in the two chambers.Again, assume that the hypothesis, (f(e, î)= â), is true in each of our two experimentalchambers. Only e and î influence the calculation of â. After the two matches, î will bethe same in the two chamber and â will be the same in the two chambers. Thus, itmust be the case that e, the only other factor that influences the calculation â, must bethe same in the two chambers. The general form of the albedo hypothesis makes ameasurable prediction for these experiments.

Notice that this prediction is true no matter what the exact form of the reflectancecalculation function is. These experiments can test the hypothesis that the only waythat context affects perceived surface reflectance is by a change in the perceivedilluminant.

This set of experiments can also test whether illuminant matching is possible, andwhether there is more reliability in surface lightness matching or illuminant matching.As mentioned earlier, little is known about illumination perception relative to surfacecolor perception, so any preliminary measurement of illumination perception is ofinterest.

General Methods

The general paradigm employed in these experiments was a matching paradigm inwhich observers were asked to adjust one display until they saw some particularaspect of it (e.g. illumination intensity) as perceptually indistinguishable from thesame aspect in another display. This matching method has often been used in colorconstancy research. In surface color constancy experiments, the extent to which thechange in the illuminants (or in some cases backgrounds) perturbs the matchedsurface color is measured. Illuminant matching is analogous; one can quantify theveridicality of the matches and manipulate the reflectance of the surfaces in the scene.

In the following experiments, observers saw two scenes, each in a separateexperimental chamber as illustrated in Figure 10. The independent variable was theilluminant or the test patch reflectance in the “standard” chamber, and the dependentvariable was the illuminant or test patch reflectance in the "match" chamber after theobserver made a match. Observers were asked to match the illuminant and thereflectance of the test patch in the two chambers. The surface reflectances of the walls

38

and objects in the chambers could be manipulated between experiments. Since boththe illuminants and the surface reflectance of the test patch were matched by theobserver, so both illuminant and surface color constancy were tested in theseexperiments.

Figure 10: Overhead schematic shows the two experimental chambers, motorized mirror, and observer.

Apparatus

There were two identical side by side chambers, either of which could be used as thestandard or the match chamber. The chambers were built out of plywood, and thefloor of each was 36" deep by 31" wide. The ceiling, which was out of view of theobserver, was 35.5" above the floor, and was made of two layers of diffuser paper(Rosco 3026) separated by 1.5".

The interiors of the two chambers were identical to each other except for one beingmirror reversed, and for the surface reflectances of the walls and objects, whichvaried across experiments. In the rear third of each chamber (that is, what appears tothe observer to be the rear after mirror reflection) was an array of objects painted inshades of monochromatic paint, creating a rich, naturalistic viewing environment,identical in the two chambers. The objects were a 1/2 gallon milk carton, a largeStyrofoam cup, a small paper cup, a roll of toilet paper, a mason jar, a cardboard cupholder, a plastic cup lid, a cardboard box measuring 4 1/4" cubed, an egg carton, anda cardboard cylindrical container measuring 5 1/4" high and 5" in diameter. Figure 11shows what the view looked like in one experiment from the observers’ point of view.

39

The observer sat between the two chambers and was able to view the interior of eachvia a rotating mirror. The observer could only see one chamber at a time, and ashutter in the viewing screen occluded the observer's view while the mirror rotated.The mirror measured 16" by 16" and sat beyond and between the two chambers seenin Figure 10. The opening in the chamber through which the observers looked was24" wide by 17" tall. The aperture in the viewing screen through which observerslooked was 4 1/2" by 3 1/2" and was 14 1/4 " in front of the observer's right eye.Observers used a chin rest to restrict movement, and viewing was monocular (righteye for every observer). The chin rest was adjusted for each observer before eachsession to standardize the position of the right eye and thus the view.

Figure 11: One experimental chamber from the observers’ point of view. The test patch is visible on theback wall.

Directly above the diffuser paper in each chamber was a bank of 6 stage lamps (SLDLighting 6" Fresnel #3053, with BTL 500 watt bulbs) arranged in concentrictriangles. Each lamp was covered in a red (Rosco 6100 "flame red"), green (Rosco1959, "light green") or blue (Rosco 4600 "blue") 6.3" round filters. There were threeblue lamps, two green lamps, and one red lamp in each chamber. Using the threeprimaries made it possible to maintain an achromatic illuminant by adjusting the

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intensity of each. The number of lamps for each primary was chosen because itallowed the maximum range of luminances given the requirement that theillumination be achromatic (approximately x= .31, y= .34 in CIExyY coordinates).Each lamp could be controlled individually by a Power Macintosh 7200/120. Thelamp intensities were controlled by varying the RMS voltage across the bulbs (NSI5600 Dimmer Packs, NSI OPT-232 interface card, 256 quantization levels.)

Each chamber also had a flat vertical monitor placed in the back wall of the chamberwhich was visible through a 1 3/8" by 2 3/8" rectangular opening cut in thecardboard. The monitor was a High Resolution Active Matrix Color LCD Panel(Marshall, product number V-LCD5V), and was under the control of the PowerMacintosh computer. The monitor appears as the rectangular test patch in Figure11.This monitor served as a test patch for surface matching. Each panel was coveredby a gray gel (the exact gel varied across the experiments) and a layer of translucentplastic, which was added to reduce the angular dependence and make the patch looklike a piece of paper. Each patch could be computer-adjusted as needed. The monitorsand the software controlling them were identical, so either monitor could serve asstandard or match surface.

Calibration

Both the screens and the bank of overhead lamps were calibrated so that the computercould accurately control the intensity levels and chromaticities. For the monitors, theprocedure involved measuring each of the three primaries (red, green and blue) at 35intensity levels, and then creating a model fit that predicts chromaticity andluminance of the monitors with the three primaries acting in concert. For the overheadlamps, the procedure was similar: Each primary (the one red lamp, the two greenlamps or the three blue lamps) was measured at 25 levels of intensity and thecomputer calculated what intensity would be needed from each primary to produce anachromatic light of any given intensity. For a more complete discussion of calibrationprocedures, see Brainard et al. (1997).

Because of building-wide fluctuations in the power supply, a standardizedillumination measurement was taken before each experiment, once the lamps werewarmed up. The calibration data was then scaled to match the current power level sothat intensities would more closely approximate the desired levels.

Ultimately, the independent variables were the measurements taken at the end of theexperiment, rather than the nominal intensity so any failure in these proceduresshould not affect the conclusions one can draw from this study.

During the matching experiment, as the illumination changed in the match chamber,care had to be taken to keep the simulated reflectance of the test patch perceptually

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the same. The surface luminance (e) of the test patch was a result of two independentcomponents: 1) the actual reflectance of the surface of the unit times the illuminant inthe chamber, and 2) the light generated by the LCD panel. In order to create theappearance of a constant reflectance as the illuminant changed, the LCD’s surfacereflectance (when off) was measured independently during the calibration, so that thetwo independent components could be summed to produce the appropriate surfaceluminance. Then, for each step that the observer took to increase or decrease theilluminant, the computer was programmed to take six interleaved steps. That is, theilluminant would change one sixth of the total adjustment, then the reflectance wouldchange one sixth of the total adjustment until the entire adjustment had been made.This process happened in less than a second, and created the appearance of agradually changing illuminant with little or no perceptual change of the surfacereflectance.

Procedure

First observers were led into the viewing booth and the chair and chin rest wereadjusted for comfort and to standardize the eye position. Observers had to align asmall thread hanging from the near aperture with a specific point in the viewing sceneby adjusting the chin rest, in order to standardize the view. Next observers were giveninstructions orally (see appendix 1 for complete instructions). They were told thatthere would be a series of 16 trials each consisting of an illumination match followedby a surface reflectance match. They were told not to worry about whether the surfacecolors looked the same during the illumination match. Conversely, observers weretold that during the surface matches, they should not worry about whether theillumination levels matched, but that they should make the 2 test patches look likethey were cut out of the same piece of paper. They were given the details about howto adjust illuminations and surface levels and how to accept or reject the matchesusing a Gravis Game Pad.

The Game Pad had a joystick on the left side and a set of four buttons on the rightside. The observers moved the joystick up to increase the illumination or reflectanceand down to decrease the illumination or reflectance. In order to accept a match,observers had to push a blue button on the right side of the Game Pad. If observerscould not make a satisfying match, they could push the yellow button to reject thematch and move on to the next trial. Observers were encouraged to reject a match ifthey were unable to adjust conditions in the match chamber to the point where therewas a perceptual match. A computerized speech simulator cued observers with thewords "Do an illumination match" or "Do a surface match," to help them rememberwhich match to do.

The intensity of illumination and the surface reflectance in the standard chamber werepre-programmed and set by computer. Intensities and reflectances were equally

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spaced within the range of possible intensities that could be produced achromaticallyin the chamber and matched in the match chamber, and the range varied acrossexperiments (see below). The starting points for the illuminant and the reflectance inthe match chamber were selected randomly by the computer from any point in thepossible achromatic range.

Illumination was physically measured in the standard and the match chamber after theobserver had completed the entire session. The illuminant level was measured with aPhoto Research PR-650 spectrometer measuring light off a highly reflective standard,which was placed immediately in front of the test patch. Once the observer left, thecomputer replayed the settings of both the standard chamber and the match chamberat the end of each trial and took the measurements. Similarly, reflectance data camefrom measurements taken after the observer had completed the entire session. Thespectrometer measured light energy from the test patch as the illuminant and testpatch settings were replayed by the computer. The reflectance, represented as aproportion, was derived from these measurements.

Experiment 1A: Symmetric Matches

Experiment 1A was designed to measure illumination matching under very simpleconditions. It was also intended as a baseline experiment using a new methodology,to make sure that the observers could do the task, that apparatus and the procedureworked as expected, and that there was no bias between the two chambers. Thesurface reflectances in the two chambers were identical and monochromatic. Thus,this was a symmetric matching experiment. It is possible that this experiment mightfalsify the albedo hypothesis if matching is not veridical or luminance does not matchin the two chambers, after the two matches, but such an outcome is not expected forsymmetric matching. This experiment was not designed as a test of the albedohypothesis.

Apparatus: 1A

In this experiment, the walls and floor of each chamber were lined with cardboard ofthe same mid level reflectance. The objects in each chamber were painted with thesame middle-reflectance paint. The gel on the LCD panels was a dark gray (Rosco98) in each chamber. Thus, the two chambers were identical in surface reflectance,size, lighting hardware, and the array of objects inside. The array of objects and the"views" of the chambers were mirror images of each other, so that the retinal stimuliwould not be spatially identical, and observers would know unambiguously whichchamber they were looking in.

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Observers: 1A

There were 8 observers. They included two females in their early 20s, one female inher early 30s, and five males in their early 20s. All observers were naïve except forthe author. Observers were paid $10 for each session, except for the author.

Procedure: 1A

Each chamber served as the standard chamber in half of the sessions, but the standardchamber did not change during a particular session. The illumination in the standardchamber was set at the beginning of each trial to one of four different standardstarting points by the computer (15, 35, 55, and 74 cd/m2). Observers were told that inorder to make an illumination match, they should match the amount of light hittingany two corresponding points in the two chambers, for example the amount of lighthitting the test patches. The surface reflectance was also set to one of fourpredetermined levels, and the four illuminant levels were crossed with the foursurface levels (.13, .24, .37, and .50), such that each of the 16 trials was a uniquecombination of illuminant level and reflectance. Each observer completed twoindependent sessions on different days.

Results: 1A

Were illuminant matches veridical? The maximum number of illuminant matchesaccepted by each observer was 32, 16 each for two sessions. (There were few rejectedmatches during this experiment.) Figure 12 shows all illuminant matches for oneobserver. The standard illuminants were plotted on the X-axis and the matchedilluminants on the Y-axis. Notice that for this observer, illuminant matching wasnearly veridical, and the data fall along the diagonal.

The relationship between the illumination in the standard chamber and theillumination in the match chamber may be characterized by the slope of theregression line when the two are plotted against each other. For each observer, datafrom both sessions was used to calculate a slope, with the intercept constrained tozero. Veridical matching would produce a slope of one, since the physical illuminantin the match chamber would be the same as the physical illuminant in the standardchamber. Figure 13 shows the slopes for all observers. The average slope for all 8observers was .95. A paired two-tailed t test on the individual matches showed asignificant difference between standard illuminant and matched illuminant for oneobserver (SIM: t(31) = 4.45, p = .0001). The difference was not significant for anyother observer. Another comparison uses difference scores, calculated by subtractingthe matched value from the standard value, and averaging the differences, giving each

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observer a difference score. A one sample t test for all observers’ average differencescores showed that these scores could not be distinguished from zero (t(7)=1.73, n.s.).

Figure 12: All illuminant matches for one observer for experiment 1A. The data points lie roughlyalong the diagonal, indicating that the illuminant in the match box was approximately equal to theilluminant in the standard box. Matching was veridical.

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Figure 13: Illuminant match slopes for all observers for experiment 1A. Slopes are close to one for all observers,indicating that matches were approximately veridical for all observers.

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Are surface matches veridical? Reflectance matches are also of interest. Themaximum number of data points for each observer was again 32. Figure 14 shows thereflectance matches for one observer. The standard reflectances are plotted on the X-axis and the matched reflectances on the Y-axis. Veridical matching would mean thatthe data fall along the diagonal. Notice that for this observer, reflectance matchingwas nearly veridical, and the data close to the diagonal.

Figure 14: All reflectance matches for one observer for experiment 1A. The data points lie roughly alongthe diagonal, indicating that the simulated reflectance in the match box was approximately equal to thesimulated reflectance in the standard box. Matching was veridical.

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As with the illuminants, the relationship between the reflectances in the standardchamber and the match chamber were plotted, a regression line calculated, and theslope taken for each observer. Figure 15 shows the reflectance slopes for eachobserver. The average slope for all 8 observers was 1.02. A paired two-tailed showeda significant difference between standard reflectances (mean .24) and matchedreflectances (mean .27) for one observer (SIM: t(31) = .4.35, p = .0001). Thedifference was not significant for any other observer. A one sample t test for allobservers’ average difference scores showed that these scores could not bedistinguished from zero (t(7)=1.14, n.s.).

Figure 15: Reflectance match slopes for all observers for experiment 1A. Slopes are close to one for allobservers, indicating that matches were approximately veridical for all observers.

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Does the albedo hypothesis hold for these stimuli? These data are qualitativelyconsistent with the albedo hypothesis. However, remember that in order to test eitherthe classic or the more general form of the albedo hypothesis, the relationshipbetween the physical luminance in the two chambers (measured at the two testpatches after both matches were made) is of interest. Any form of the albedohypothesis predicts that once the perceived illuminant and the perceived reflectance

Figure 16: All Surface luminance data for one observer for experiment 1A. The data points lie roughlyalong the diagonal, indicating that the physical luminance measured at the test patch in the match box wasapproximately that in the standard box.

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Figure 17: Surface luminance slopes for all observers for experiment 1A. Slopes are close to one for allobservers. Physical luminance at the test patch was approximately the same in the standard chamber and thematch chamber after the illuminant match and reflectance match were both made.

are matched in the two chambers, the physical luminance will match as well.Luminance was measured directly from the test patches, as described above. Figure16 shows the luminance data for one observer. Notice that the data lie along thediagonal, on average. Generally, the luminance of the test patch in the match chamberwas close to the luminance of the test patch in the standard chamber for this observer.This is consistent with the albedo hypothesis.

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Figure 17 shows the luminance slopes for all observers. The average slope for all 8observers was .97. A paired two-tailed t test showed no significant difference betweenluminance of the standard test patch and luminance of the match test patch for anyobserver. A one sample t test for all observers’ average difference scores showed thatthese scores could not be distinguished from zero (t(7)=1.02, n.s.). This is consistentwith the albedo hypothesis. Although one cannot reject the albedo hypothesis withthese data, this symmetric matching experiment was not intended as a strong test ofthe hypothesis.

Are the two chambers the same? In order to test whether there was any physicaldifference between the two chambers, a two-tailed paired t test was performedbetween slopes from sessions in which chamber 1 was the standard, and sessions inwhich chamber 2 was the standard, paired by observer. The average of the illuminantslopes were .98 and .94 respectively, and a paired two-sample t test showed that theywere not significantly different (t(7)= .90, n.s.). The average of the reflectance slopeswere 1.00 and 1.00 respectively, and a paired two-sample t test showed that they werenot significantly different (t(7)= .09, n.s.).

Discussion: 1A

One of the most important conclusions from this study is that our observers were ableto understand and perform the tasks of illumination matching and surface reflectancematching in this apparatus. All observers found the task reasonable. The fact that theslope of the illuminant matches was close to 1 suggests that for these very simpleconditions, illuminant matching is nearly veridical.

One may doubt that the data truly show veridical illuminant and surface matches.Indeed, there is an unexpected bias that reaches significance for one observer. Theslopes of the illuminant matches may have been slightly less that one, on average. Infact, one may not need to explain any bias in order to test the albedo hypothesis. Themagnitude of the bias should simply be taken as a baseline to compare biases that willbe induced in future experiments.

Nonetheless, one possible explanation for the bias is the following: If one assumesthat there is more variance in matching for higher standard illuminations than lower(consistent with both Weber's law and the data), then the fact that the starting point inthe match chamber is chosen randomly (rather than constrained by the illuminant inthe standard chamber) might be relevant. The starting illuminant in the matchchamber is more likely to be lower than the veridical point for the higher illuminants.It is known that the starting point of the match stimuli can bias the match slightly(Brainard, 1998). Perhaps this is an error that the observer can overcome for lowerilluminants, but not for higher illuminants, since lower illuminants are easier toaccurately match.

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Another practically, if not theoretically, important result is that there is no measurabledifference in matching when either chamber is used as the standard. This is importantbecause this method of illuminant matching is new, and it is important to ensure thatthere are not any artificial biases in the hardware or the software.

This experiment was not designed to be as strong test of the albedo hypothesis, andwith these results one cannot reject either the classic or the general form of the albedohypothesis (e = î * â) or (f(e, î)= â). These data are consistent with even the strongestform of the hypothesis, i = î and a = â.

Experiment 1B: Symmetric Matches over a Range of Reflectances

Experiment 1B was designed to measure accuracy and reliability of illuminationmatching in the context of a range of surface colors. The two chambers were identicalto each other, but in this experiment, objects and wall reflectances ranged from highto medium to low. The back wall was split vertically in reflectance such that 1/2 ofthe visible wall was covered with white cardboard and 1/2 with black cardboard. Asin experiment 1A, the matches were symmetrical.

Apparatus: 1B

The walls ranged in reflectances from high to medium to low, perceptually white,gray and black. The floor of each chamber was gray. The side wall that was visible tothe observer was black and the side wall opposite (out of view of the observer) waswhite. The visible portion of the back wall was split in half such that the immediatesurround of the LCD panel was white and the other half of the back wall was black.Each LCD panel had a light gray gel (Rosco 97). The objects that were painted blackwere the Java holder, the small Dixie cup, the cup top, and the cylindrical container.The objects that were painted gray were the Mason jar, the toilet paper roll, and theegg carton. The objects that were painted white were the milk carton, the box and theStyrofoam cup. The object positions were mirror images of each other in the twochambers. Figure 18 shows each chamber from the observer’s point of view.

Observers: 1B

Observers were the same 7 of the 8 observers from experiment 1A. They includedtwo females in their early 20s, one female in her early 30s, and four males in theirearly 20s. Observers were paid $10 for each session, except for the author.

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Procedure: 1B

The procedure for this experiment was identical to that for experiment 1A. Again, theillumination in the standard chamber was set at the beginning of each trial to one offour different standard starting points, this time (8, 27, 45 and 64 cd/m2). The surfacereflectance was also set to one of four levels (.28, .41, .54, and .67), and the fourilluminant levels were crossed with the four surface levels, such that each of the 16trials was a unique combination of illuminant level and reflectance.

Figure 18: Stimuli for experiment 1B. There was a range of reflectances in each box, from high reflectanceto medium reflectance to low reflectance. Each object was painted with the same paint as the correspondingobject in the other chamber. Thus, this experiment involved essentially symmetric matches.

Results: 1B

Are illuminant matches veridical? Again, for each observer, a slope was calculatedusing data from both sessions. The maximum number of data points for each observerwas therefore 32. (There were few rejected matches during this experiment.) Figure19 shows the illuminant matches for one observer. The standard illuminants wereplotted on the X-axis and the matched illuminants on the Y-axis. Notice that for thisobserver, illuminant matching was nearly veridical, and the data fall along thediagonal.

Figure 20 shows the slopes for each observer. The average slope for all 7 observerswas .96. Paired two-tailed t tests revealed a significant difference between standardilluminants (mean 40.01 cd/m2) and matched illuminants (mean 32.98 cd/m2) for SIM(t(31)= 7.09, p = 5.7E-8) but not for any other observers. A one sample t test showedthat the average difference scores (standard minus match) for the 7 observers werenot different from zero (t(6)=1.73, n.s.).

Were surface matches veridical? The maximum number of data points for eachobserver was therefore 32. (There were few rejected matches during this experiment.)

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Figure 21 shows the reflectance matches for one observer. Again, for each observer, aslope was calculated by using surface reflectance matches from both sessions. Thestandard reflectances were plotted on the X-axis and the matched reflectances on theY-axis. Notice that for this observer, illuminant matching was nearly veridical, andthe data fall along the diagonal.

Figure 19: All illuminant matches for one observer for experiment 1B. The data points lie roughly along thediagonal, indicating that the illuminant in the match box was approximately equal to the illuminant in thestandard box. Matching was veridical.

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Figure 20: Illuminant match slopes for all observers for experiment 1B. Slopes are close to one for allobservers, indicating that matches were approximately veridical for all observers.

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Figure 21: All reflectance matches for one observer for experiment 1B. The data points lie roughly along thediagonal, indicating that the simulated reflectance in the match box was approximately equal to the simulatedreflectance in the standard box. Matching was veridical.

Figure 22 shows the slopes for each observer. The average slope for all 7 observerswas .97. Paired two-tailed t tests revealed a significant difference between standardreflectance (mean .345) and matched reflectance (mean .366) for SIM (t(28)= 3.33, p= .002) but not for any other observers. A one sample t test showed that the averagedifference scores (standard minus match) for the 7 observers were not different fromzero (t(6)=8*E-17, n.s.).

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Figure 22: Reflectance match slopes for all observers for experiment 1B. Slopes are close to one for all observers,indicating that matches were approximately veridical for all observers.

Does the albedo hypothesis hold for these stimuli? In order to test the albedohypothesis, the relationship between the luminance of the two test patches is ofinterest. The albedo hypothesis predicts that the surface luminance in the standardchamber and the surface luminance in the match chamber should be the same after theilluminant match and reflectance match are completed. Figure 23 shows thereflectance matches for one observer. Notice that the data lie along the diagonal, onaverage. Generally, the luminance of the test patch in the match chamber was close tothe luminance of the test patch in the standard chamber for this observer. This isconsistent with the albedo hypothesis.

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Figure 23: All surface luminance data for one observer for experiment 1B. The data points lie roughly alongthe diagonal, indicating that the physical luminance measured at the test patch in the match box wasapproximately that in the standard box.

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Figure 24: Surface luminance slopes for all observers for experiment 1B. Slopes are close to one for allobservers. Physical luminance at the test patch was approximately the same in the standard chamber and thematch chamber after the illuminant match and reflectance match were both made.

Figure 24 shows the slopes for all 7 observers. If the surface luminance slopes are not1, then the albedo hypothesis is false. The average slope for all 7 observers was .94.Paired two-tailed t tests revealed a significant difference between standard chamberluminance (mean 11.30 cd/m2) and matched chamber luminance (mean 9.88 cd/m2)for SIM (t(28)= 4.03, p = .0004) and for JXK (mean 12.77 cd/m2 standard comparedto mean 11.04 cd/m2 match) (t(20) = 2.40, p = .03), but not for any other observers. Aone sample t test showed that the average difference scores (standard minus match)for the 7 observers were not different from zero (t(6)=1.22, n.s.). Although the albedohypothesis does not hold for two observers, notice that the effect size is quite small

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(see Figure 24) and should be regarded as a baseline effect size for comparison withfuture experiments.

Are the two chambers the same? In order to test whether there was any physicaldifference between the two chambers, a two-tailed independent samples t test wasperformed between slopes from session in which chamber 1 was the standard, andsessions in which chamber 2 was the standard. The illuminant slopes were .95 and .99respectively, and were not significantly different (t(14)= .61, n.s.). The reflectanceslopes were .98 and .97 respectively, and were not significantly different (t(14)= .11,n.s.).

Discussion: 1B

Again, illuminant matching is near veridical in this situation where the surfaces in thetwo chambers have the same (mirror reversed) reflectance across chambers. Overall,these results do not reject any form of the albedo hypothesis, including the strongestform. Notice, however, that since these were symmetric matches, this experiment wasnot a strong test of any form of the albedo hypothesis. This experiment could havefalsified some form of the albedo hypothesis, but was not expected to.

Again, these data suggest that there are no measurable differences between thehardware and software in the two chambers. Hence forth, it will be assumed that thetwo chambers are interchangeable, and they are not counterbalanced in the rest of theexperiments.

Experiment 2A: Asymmetric Matching

In experiments 2A and 2B, the constancy of illuminant matching across scenescomposed of different surface reflectances was measured. In the standard chamber(light chamber), all surfaces were either high reflectance (perceptually white) ormedium reflectance (perceptually gray). In the match chamber (dark chamber), allsurfaces were either medium reflectance (perceptually gray) or low reflectance(perceptually black). These surfaces were spatially arranged so that there was anisomorphism between the two chambers. That is, objects that were middle reflectancein the light chamber were low reflectance in the dark chamber, and objects that werehigh reflectance in the light chamber were middle reflectance in the dark chamber.

Although results from experiments 1A and 1B suggest that observers are able tomatch illuminants, the design of those experiments still leaves open the possibilitythat the matches were made based on a low-level cue (e.g. matching the retinalstimulus) rather than on a perception of the illuminant. Because in Experiment 1 thesurface reflectances in the two chambers were the same, when the illuminantsmatched, the retinal images matched as well. Experiments 2A and 2B can extend the

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test to cases where luminance and thus the retinal image in the two chambers differs.Experiments 2A and 2B were designed to provide a stronger test of the albedohypothesis than experiments 1A and 1B.

Pilot testing suggested that matching across chambers with different reflectanceranges would bias the perception of the illuminant. Thus, it was expected that peoplewould set the illumination in the dark chamber higher than veridical. If these stimulican induce a bias in illumination judgments, then illuminant color constancy isimperfect. Furthermore, inducing a bias in perceived illumination would make itpossible to test whether perceived illumination alone influences matched surfacereflectances. Thus, any form of the albedo hypothesis in which perceived illuminationmediates the relationship between physical luminance and perceived surfacereflectance can be tested by this experiment.

Apparatus: 2A

In the standard chamber, the floor was covered with gray cardboard, and the backwall was split vertically, such that the cardboard around the test patch was gray, andthe other half was white. The side walls were covered with white cardboard. Theobjects that were painted white were the cup top, the egg carton, the cardboard box,the toilet paper roll, and the Mason jar. The objects that were painted gray were thecylindrical container, the small Dixie cup, the Styrofoam cup, the Java holder, and themilk carton. The gel on the LCD panel was light gray (Rosco 97). In the matchchamber, the floor was covered with black cardboard, and the back wall was splitvertically, such that the cardboard around the test patch was black, and the other halfwas gray. The side walls were covered with gray cardboard. The objects that werepainted gray were the cup top, the egg carton, the cardboard box, the toilet paper roll,and the Mason jar. The objects that were painted black were the cylindrical container,the small Dixie cup, the Styrofoam cup, the Java holder, and the milk carton. The gelon the LCD panel in the dark chamber was dark gray (Rosco 98). The gels in the twochambers were different in order to bring the perceptual ranges closer together andallow most of the standard reflectances to be perceptually matched. The objectpositions were mirror reversed in the two chambers. Figure 25 shows the standard andmatch chambers under equal illumination from the observer’s point of view.

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Figure 25: Stimuli for Experiment 2A under equal illumination The surfaces in the standard chamber wereall high or medium reflectance. The surfaces in the match chamber were all medium or low reflectance.These stimuli were intended to create a bias in illuminant matching.

Observers: 2A

The same 7 observers from the previous experiment served in this experiment.

Procedure: 2A

The procedure for this experiment was the same as for previous experiments. Again,the illumination in the standard chamber was set at the beginning of each trial to oneof four different standard starting points, this time (8, 19, 30, and 40 cd/m2). Thesurface reflectance was also set to one of four predetermined levels (.38, .46, .53 and.60). The illuminant levels were low to compensate for the bias so the perceptualmatch would be possible. The highest levels of illuminants and lowest reflectanceswere determined by multiplying the highest possible achromatic level in the matchchamber by the slope of the standard versus the match levels in the pilot data. Thisshould have allowed the average observer to make a perceptually satisfying match forany standard, while still taking advantage of the range of possible standards. The fourilluminant levels were crossed with the four surface levels, such that each of the 16trials was a unique combination of illuminant level and reflectance.

Results: 2A

Did observers show illuminant color constancy? Illumination constancy is analogousto surface color constancy, described in the introduction. Perfect constancy wouldmean that observers see two physically identical illuminants as the same, in spite ofchanges in the surface reflectances in the scene. Complete lack of constancy wouldmean that the matched illuminant was entirely determined by the total luminance in

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the whole scene, rather than determined by the physical illuminant in the standardchamber.

Figure 26: All illuminant matches for one observer for experiment 2A. You can see that the slopeis greater than 1 for this observer. For any given data point, the illuminant in the match chamber is muchhigher than the illuminant in the standard chamber.

The stimuli in this experiment were designed to induce a bias in illuminant matching.All data for one observer are shown in Figure 26. The dashed line indicates thediagonal, on which the data would lie if the illuminant in the match chamber wasphysically the same as the illuminant in the standard chamber at the end of each trial.

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Notice that the data clearly lie above the line; this observer does not show perfectilluminant color constancy.

Figure 27: Illuminant match slopes for all observers for experiment 2A. The average slope forthe illuminant match was 1.84. The fact that the illuminant slopes are not 1 demonstrates a failure ofilluminant color constancy, induced by the manipulation of the stimuli in the scene.

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Again, the data are summarized for each observer with a slope, derived from the datafrom all accepted matches in two sessions. The slopes for all 7 observers are shown inFigure 27. The average slope for all observers was 1.84. In other words, on theaverage trial, an observer would set the illumination in the darker match chamber to1.84 times the lighter standard chamber illuminant level. The slopes are not 1, onaverage, so illuminant matching is not always veridical; these observers did not showperfect illuminant color constancy. Paired two-tailed t tests showed that the differencebetween standard illuminants and matched illuminants was significant for eachobserver. A one sample t test showed that the average differences between thestandard and the matched illuminant for the 7 observers were significantly differentfrom zero (t(6)=10.16, p,.0001, two-tailed).

It is possible that the average slope of the illuminant matches can be explained by theobservers making some physical match. Observers might be matching the luminanceof a medium reflectance object in each chamber. They might be matching theluminance of a medium reflectance object in the standard chamber to that of a lowreflectance object in the match chamber, or matching the luminance of a highreflectance object in the standard chamber to that of a medium reflectance object inthe match chamber. Or, observers might be matching the total light energy passingthrough the aperture from each chamber.

In fact, the following tests revealed no physically measurable quantity that subjectswere matching. That is to say, no physical measurement predicted the observers’performance. One possibility was that observers were matching the physicalluminance of objects of like reflectance. If this had been the case, illuminationmatches would have fallen along the diagonal, so this possibility can be rejected bydata already presented. To formally test this, however, luminance measurements weretaken with the illumination in the standard chamber set at the four standard levelsused in experiment 2A. The illumination in the match box was set at thecorresponding standard times the average slope. Luminance measurements weretaken at two corresponding points of medium luminance (the back wall), but theluminance was not matched in the two chambers. The average across the four levelswas 7.83 cd/m2 in the standard chamber and 13.55 cd/m2 in the match chamber. Thisseems reasonable, given that the two walls had the same reflectance and theillumination was higher in the match chamber. The surface in the match chambermust show a higher luminance.

More revealing comparisons might be between a medium reflectance surface in thestandard chamber and a low reflectance surface in the match chamber. Is it possiblethat a match of physical luminance of these objects predicts observers’ performance?Figure 28 shows the slope that would be predicted if this were the case (11.72), as asolid line, the diagonal representing veridical performance as a broken line, four dotsrepresenting the average matches for the four standard illuminants (average slope

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1.84), and the shaded area representing the area between the highest slope (2.16) andthe lowest slope (1.53) for the 7 observers. Performance was not predicted by aluminance match between medium reflectance surfaces in the standard chamber andlow reflectance surfaces in the match chamber. After setting the illuminant in thestandard chamber to each of the four standards and the illuminant in the matchchamber to the corresponding average match, the luminance was measured at themilk carton in each chamber. The medium reflectance milk carton in the standardchamber measured 8.38 cd/m2 averaged over the four levels, compared to the lowreflectance milk carton in the match chamber, which measured 1.06 cd/m2.

Figure 28: The solid line shows where the data are predicted to fall if observers were matching theluminance of the low reflectance objects in the match chamber to the medium reflectance objects in thestandard chamber. The broken line shows the prediction if the illuminant matching were veridical. Thecircles show the observers’ average matches at the four standards, and the shaded area represents the areabetween the highest and lowest observers’ slopes.

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Similarly, one could compare a high reflectance surface in the standard chamber to amedium reflectance surface in the match chamber. Is it possible that a match ofphysical luminance of these objects predicts observers’ performance? This is what thehighest luminance rule would predict (see, e.g., Gilchrist et al., 1999). Figure 29shows the slope that would be predicted if this were the case, as a solid line with aslope of 4.22. The diagonal representing veridical performance is a broken line, andfour dots represent the average matches for the four standard illuminants.Performance was not predicted by a luminance match between high reflectancesurfaces in the standard chamber and medium reflectance surfaces in the matchchamber. After setting the illuminant in the standard chamber to each of the fourstandards and the illuminant in the match chamber to the corresponding averagematch, the luminance was measured at the toilet paper roll in each chamber. Again,there was no physical match: the luminance of the high reflectance toilet paper roll inthe standard chamber was 14.1 cd/m2 on average, compared to the mediumreflectance toilet paper roll in the match chamber, which measured 5.97 cd/m2.

Finally, one might ask whether the luminance averaged across the whole scenepredicts the matches of the observers. In order to measure the average luminance ineach scene at each of the four standard and match illuminations, a digital photographof the open aperture was taken at each setting. These images were taken with a highquality monochrome CCD camera (Photometrics PXL) with a linear intensity-response function. Three images were taken for each scene measured, one each with500 nm, 550 nm, and 600 nm interference filters placed in the optical path of thecamera. Each image was corrected by subtracting a dark image (taken withoutopening the shutter) of the same exposure duration. The images were then scaled sothat the image data at three chosen locations matched direct luminance measurementsof the same three locations. The scaled image data were then averaged over theviewing aperture, but excluding the area of the test patch. This provided an estimateof the average luminance of the scene. Estimates from the three separatemonochromatic images were then averaged to produce the final estimate used.Although some error in the estimates is introduced by not measuring the full spectrumof the scene at every pixel, this error should be small as the scenes used wereapproximately isochromatic.

Figure 30 shows what a match of the total scene luminance would predict as a solidline. This line does not predict observers’ data, shown as averages for each of the fourmatches. Incidentally, the highest possible achromatic setting in the match chamberwas close to 70 cd/m2, so using this strategy would have allowed a satisfying matchon only the lowest standard illuminant trials. Remember that the standard illuminantswere decided upon based on pilot data and were intended to allow the averageobserver to make a satisfying match.

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Figure 29: The solid line shows where the data are predicted to fall if observers were matching theluminance of the medium reflectance objects in the match chamber to the high reflectance objects in thestandard chamber. The broken line shows the prediction if the illuminant matching were veridical. Thecircles show the observers’ average matches at the four standards, and the shaded area represents the areabetween the highest and lowest observers’ slopes.

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Figure 30: The solid line shows where the data are predicted to fall if observers were matching the total sceneluminance of the match chamber to total scene luminance of the standard chamber. The broken line shows theprediction if the illuminant matching were veridical. The circles show the observers’ average matches at the fourstandards, and the shaded area represents the area between the highest and lowest observers’ slopes.

Did observers show surface color constancy? All data for one observer are shown inFigure 31. The dashed line indicates the diagonal, on which the data would lie if thesimulated surface reflectance in the match chamber was the same as the simulatedsurface reflectance in the standard chamber at the end of each trial. Notice that thedata clearly lie below the line; this observer does not show surface color constancy.

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Figure 31: All reflectance matches for one observer for experiment 2A. You can see that the slope is lessthan 1 for this observer. For any given data point, the surface reflectance in the match chamber is lower thanthe surface reflectance in the standard chamber.

The reflectance match slopes were again calculated using all accepted matches. Themaximum number of data points for any observer is the number of illuminantmatches accepted, although the number could be lower if an observer accepted anilluminant match but rejected the surface match in a given trial. All reflectance matchslopes for the 7 observers are shown in Figure 32. The average slope for all observerswas .39. In other words, on the average trial, an observer would set the reflectance in

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the match chamber to less than half the reflectance of the standard chamber test patch.The slopes are not 1, indicating that surface matching is not veridical; these observersdid not show perfect surface color constancy. The difference between standardreflectances and matched reflectances was significant for each observer. A onesample t test showed that the average differences between the standard and the matchreflectance for the 7 observers was significantly different from zero (t(6)=24.88,p<.0001, two-tailed).

Figure 32: Reflectance match slopes for all observers for experiment 2A. For this experiment the averageslope for the surface reflectance matches was .38 for 7 observers. The fact that these slopes were not 1demonstrates a failure of surface color constancy. Setting the surface reflectance low is what you mightexpect given the albedo hypothesis, but see below for a quantitative test.

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As with the illumination matches, we can ask whether the surface matches weredetermined by any obvious physical measurement. The surface reflectance in thematch chamber might vary, for example, with the highest luminance surface in thescene, the luminance of a medium reflectance surface, the lowest luminance surfacein the scene, or with the average luminance coming from the scene.

First, there is the possibility that the surface reflectance was determined by thehighest luminance surface in each scene. In order to compare this hypothesis with thedata, four measurements were taken of the highest luminance surface in each boxwith the illuminant in the standard chamber set at the four standards and theilluminant in the match chamber set at the average match (that is, the standard timesthe average slope). Then a slope was calculated representing the relationship betweenthe highest luminance surface in the standard chamber and the highest luminancesurface in the match chamber. This slope was .42. One can compare this to thesurface match slopes for this experiment, which ranged between .30 and .44. Thepredicted slope does not fall outside the range of data for these observers, so onecannot reject the hypothesis that surface reflectance in the match chamber isdetermined by the highest luminance surface. Figure 33 illustrates these relationships;the solid line represents the predicted slope, the broken line represents veridicalmatching and the dots represent average data for the four standard reflectances.

Second, consider the possibility that the surface reflectance matches were determinedby the lowest luminance in scene. As above, four measurements were taken of thelowest luminance surface in each box with the illuminant in the standard chamber setat the four standards and the illuminant in the match chamber set at the averagematch. Then a slope was calculated representing the relationship between the highestluminance surface in the standard chamber and the highest luminance surface in thematch chamber. This slope was .128. One can compare this to the surface matchslopes for this experiment, which ranged between .30 and .44. The hypothetical slopefalls outside the range of data for these observers, so one can reject the hypothesisthat surface reflectance in the match chamber is determined by the lowest luminancesurface. Figure 34 illustrates these relationship; the solid line represents the predictedslope, the broken line represents veridical matching and the dots represent averagedata for the four standard reflectances.

Third, consider the possibility that the surface matches are determined by therelationship between the luminances of the same middle reflectance surface in the twochambers once the illumination match has been made. This possibility seemsunlikely, since they would have different luminances after the illuminant match, but itwas formally tested in the same way as described above. The slope between amedium reflectance surface under the standard illuminant and the correspondingmedium reflectance surface under the matched illuminant was 1.74. (Note that the

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slope used here was based on actual measurements of these surfaces, rather than thenominal slope.)This is out of range of the actual data, as illustrated in Figure 35.

Figure 33: The solid line shows where the data are predicted to fall if the highest luminance surface in thescene determined surface matching. The broken line shows the prediction if the reflectance matching wereveridical. The circles show the observers’ average matches at the four standards, and the shaded arearepresents the area between the highest and lowest observers’ slopes. Notice that the predicted slope fallswithin the range of actual data.

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Figure 34: The solid line shows where the data are predicted to fall if the lowest luminance surface in the scenedetermined surface matching. The broken line shows the prediction if the reflectance matching were veridical. Thecircles show the observers’ average matches at the four standards, and the shaded area represents the area betweenthe highest and lowest observers’ slopes. The prediction does not fall within the range of actual data.

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Figure 35:The solid line shows where the data are predicted to fall if the luminance of two middlereflectance surfaces in the two chambers determined surface matching. The broken line shows the predictionif the reflectance matching were veridical. The circles show the observers’ average matches at the fourstandards, and the shaded area represents the area between the highest and lowest observers’ slopes. Theprediction does not fall within the range of actual data.

Finally, one could consider the possibility that the reflectance of the matched surfaceis determined by the average luminance in the whole scene. The average luminancewas calculated as described above in the discussion of illumination constancy. Theslope between the total luminance in the standard chamber under standard illuminantand the total luminance in the matched chamber under the matched

illuminant was .44. One can compare this to the surface match slopes for thisexperiment, which ranged between .30 and .44. The hypothetical slope does not fall

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outside the range of data for these observers, so one cannot reject the hypothesis thatsurface reflectance in the match chamber is determined by the average luminance inthe entire scene. Figure 36 illustrates these relationships.

Figure 36: The solid line shows where the data are predicted to fall if the average luminance in the entirescene determined surface matching. The broken line shows the prediction if the reflectance matching wereveridical. The circles show the observers’ average matches at the four standards, and the shaded arearepresents the area between the highest and lowest observers’ slopes. Notice that the predicted slope fallswithin the range of actual data.

Does the albedo hypothesis hold for these stimuli? Finally, remember that the criticaltest of the albedo hypothesis is whether the measured physical luminance in the two

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chambers match after both the illuminant and the surface reflectance are perceptuallymatched. Even the most general form of the albedo hypothesis predicts a slope of one.All luminance data for one observer are shown in Figure 37. On the average trial,once the illuminant and the surface reflectance were perceptually matched in the twochambers, the luminance was not equal; it was lower in the match chamber. Thedashed line indicates the diagonal, on which the data would lie if the physicalluminance measured at the test patch in the match chamber was the same as theluminance of the test patch in the standard chamber at the end of each trial. Noticethat most of the data clearly lie below the line. A paired two-tailed t test revealed asignificant difference between the standard and matched luminance levels for thisobserver (t(30)=4.31, p=.00016). The data for this observer falsify the albedohypothesis .

All luminance slopes for the 7 observers are shown in Figure 38. The average slopefor all observers was .67. For 6 out of 7 of the observers, a paired two-tailed t testshowed that the measured luminance in the match chamber was significantly differentfrom the measured luminance in the standard chamber, (see table 1 for t tests). A onesample t test revealed that the average difference between the match and standardilluminant for each observer was significantly different from zero (t(6)=4.82, p=.003,two tailed).

Since the relevant question is whether the luminance data fall on the diagonal (i.e.whether the slope between the luminance of the two test patches is 1), all luminancedata for all observers is plotted in Figure 39 for easy reference.

Observer T value, paired t test fordifference betweenstandard and matchedluminance

p value, Two-tailed paired ttest

MDR t(31) = 9.24 2.01498E-10SIM t(31) = 9.36 1.48565E-10MBG t(31) = 4.30 0.00016125ISH t(27) = 5.09 2.39029E-05JAB t(25) = 6.76 6.8041E-07BGS t(20) = 1.18 0.250075254 n.s.JXK t(18) = 3.86 0.001134842

Table 1: Experiment 2A table of surface luminances

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Figure 37: All surface luminance data for one observer for experiment 2A. The quantitative test of thealbedo hypothesis is the relationship between the luminance in the standard chamber and the luminance inthe match chamber. Once the observer has perceptually matched the illuminants and the surface reflectancesin the two chambers, even if each is non-veridical, the albedo hypothesis predicts that the physicalluminance will match. Notice that for this one observer, the slope of the regression line is less than one.

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Figure 38: Surface luminance slopes for all observers for experiment 2A. For this experiment the averageslope was .68. The expected value for each of the slopes would be 1, if the albedo hypothesis were true.These data falsify the albedo hypothesis.

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Figure 39: These are all of the accepted matches from all for experiment 2A. Compare the data with thedashed line, which represents the prediction of the albedo hypothesis. These data differ from the prediction,and thus falsify the albedo hypothesis.

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Discussion: 2A

The most striking and important result from this experiment is that the albedohypothesis, even in its most general form is false. The classic form (e = î * â) and thegeneral form (f(e, î)= â) of the albedo hypothesis both predict that the surfaceluminance (e) must match after the illuminant and the surface reflectance have beenperceptually matched.

Notice that according to the general form of the albedo hypothesis, the function thatcalculates the perceived reflectance takes as input the perceived illuminant and theactual physical luminance from the test patch. If the perceived illuminant were theonly variable mediating the relationship between the physical luminance and theperceived reflectance, then once the perceived reflectance and the perceivedilluminant were both matched, the physical luminance would have to match. It doesnot. Therefore, even the most general form of the albedo hypothesis is false.Perceived illuminant does not uniquely determine perceived surface reflectance for agiven luminance level.

These results also falsify the hypothesis, that i= î and that a=â. If this were true, thephysically measured illuminants would have to match in the standard and the matchchambers, and the physically measured surface reflectances would have to match inthe standard and the match chambers once the perceptual matches were made. Thisdesign, with the "light" chamber as the standard and the "dark" chamber as the matchchamber, induced a bias in the illuminant matches. If the illuminant matching wereveridical, the illuminant matching slope for the average observer would be 1, yet itwas 1.84. This falsifies the hypothesis that i = î. These observers did not showilluminant color constancy; the difference between standard illuminants and matchedilluminants was significant for each observer. The illuminant match data are inbetween veridical matches and true luminance matches for the whole scene, soobservers show neither perfect illuminant color constancy nor a complete lack of it.Notice that one could not, infact, make the dark chamber look exactly like the lightchmaber by adjusting the illumination, because of inter-reflecting. The difference insurface inter-reflectance within the scene, as well as a difference in ratios between thepaints in the dark chamber and the paints in the light chamber, made it impossible tomake an exact retinal match.

The reflectance matches were not veridical either, and the average slope forreflectance matches was not 1. This falsifies the hypothesis that a=â. These observersdid not show perfect surface color constancy; the difference between standardreflectances and matched reflectances was significant for each observer.

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Experiment 2B: Asymmetric Matching with Change in Surround

Results from experiment 2A suggest that that the albedo hypothesis fails for at leastthe conditions created for that experiment. Experiment 2B is designed to furtherchallenge the most general form of the albedo hypothesis by testing whetherreflectance matches can be manipulated while illuminant matches stay constant.Consider the general form of the hypothesis: f(e, î)= â. If there are experimentalconditions which affect perceived surface reflectance (â) without affecting perceivedillumination (î), then it cannot be the case that perceived illumination uniquelydetermines perceived surface reflectance for a given proximal stimulus. In experiment2B, the surfaces are nearly all the same as in experiment 2A, and the averagereflectance in the view is approximately the same so the illuminant matches areexpected to be about the same. The difference between this and the previousexperiment is that the two halves of the back wall have switched positions in thematch chamber. The standard chamber was identical to that in experiment 2A. Thus,experiment 2B, the immediate surround of the test patch is the middle reflectance(gray) cardboard in each chamber.

With this design, the albedo hypothesis can be further challenged. If it is possible tomanipulate the luminance slope (e.g. by changing the reflectance of the immediatesurround), this would falsify the albedo hypothesis. According to the hypothesis, theslope should be 1. Matched illumination is likely to be unaffected by themanipulation, since mean reflectance of all surfaces is unchanged. Any manipulationthat has an effect on surface color matching but little or no effect on illuminationmatching would disprove the albedo hypothesis.

Apparatus: 2B

The apparatus here was identical to that of experiment 2A, with one exception. Thetwo cardboard halves of the back wall were reversed in the match chamber only. Inthe match chamber, half of the visible wall was low reflectance (black) and the otherhalf medium reflectance (gray), with the immediate surround of the test patch beingmedium reflectance. See Figure 40 for a view of the chambers.

Observers: 2B

Observers were the same 7 observers from experiment 2A.

Procedure: 2B

The procedure was identical to the previous experiment. The illuminant levels in thestandard chamber were again 8, 19, 30 and 40 cd/m2. The reflectance levels of the testsurface in the standard chamber were .17, .31, .46, and .60. As before, the highest

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levels of illuminants and lowest reflectances were determined by multiplying thepossible achromatic levels in the match chamber by the slope of the standard versusthe match levels in the pilot data. Again, the four illuminant levels were crossed withthe four surface levels, such that each of the 16 trials was a unique combination ofilluminant level and reflectance.

Figure 40: Standard and Match chamber for experiment 2B. The Standard chamber, shown on the left, wasidentical to that in the previous experiment. In the match chamber, shown on the right, the only differencewas in the placement of the cardboard on the back wall: now the medium reflectance rather than the lowreflectance cardboard immediately surrounded the test patch.

Results: 2B

Were illuminant matches different from experiment 2A?All illuminant match slopes for the 7 observers are shown in Figure 41. The averageslope for all observers was 1.86, compared to 1.84 for experiment 2A. As inexperiment 2A, observers did not show illuminant color constancy. A paired two-tailed t test revealed that the slopes for the seven observers were not significantlydifferent from the slopes from experiment 2A (t(6)= .146, n.s.). There was nosignificant difference in difference scores across the two experiments, either (t(6)=.902,n.s.). Thus, there was no significant difference between illuminant matchingslopes in experiment 2A and experiment 2B.

Were surface reflectance matches different from experiment 2A?All surface reflectance match slopes for the 7 observers are shown in Figure 42. Theaverage slope for all observers was .55, compared to .38 for experiment 2A. As inexperiment 2A, observers did not show perfect surface color constancy. However, apaired two-tailed t test revealed that the slopes for the seven observers weresignificantly different from the slopes from experiment 2A (t(6)= 6.79, p=.0005,).

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There was a difference between surface reflectance matching slopes in experiment 2Aand experiment 2B. Average difference scores were also different across the twoexperiments (t(6)= 7.52, p=.0003).

Figure 41: The black bars show illuminant match slopes for all observers for experiment 2B. The averageslope was 1.86, compared to 1.84 in experiment 2A, represented by gray bars. The changing the immediatesurround of the test patch did not affect the illuminant matches.

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Figure 42: The black bars show reflectance match slopes for all observers for experiment 2B. The average slopewas .55, compared to .38 in the previous experiment, represented by gray bars. Changing the immediate surroundof the test patch did have an effect on the surface reflectance matches. Since perceived illumination and perceivedsurface reflectance can be manipulated independently, perceived illumination cannot uniquely determineperceived surface reflectance.Were surface luminance slopes different from experiment 2A?The interesting question addressed by this experiment is whether one can manipulatethe surface luminance slope simply by changing the immediate surround of the testpatch. Thus, it is important to note that the relationship between the surfaceluminance measured at the test patch in the two chambers in experiment 2B was

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different from that relationship in experiment 2A. The average slope for all observerswas 1.03 in experiment 2B, compared to .68 in the previous experiment, as illustratedby Figure 43.

Figure 43: The black bars show luminance slopes for all observers for experiment 2B. The average slope was1.03, compared to .69 in the previous experiment, represented by gray bars. Changing the immediate surround ofthe test patch had an effect on the luminance slopes, whereas the albedo hypothesis predicts a constant.

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A paired two tailed t test revealed that the surface luminance slopes was differentbetween these two experiments (t(6)= 5.87, p=.001). Average difference scores werealso different across the two experiments (t(6)= 5.81, p=.001). This difference is bestillustrated by Figure 44, which shows all of the luminance data from these twoexperiments, plotted in different colors.

Figure 44: These are all of the accepted matches from all observers for experiment 2A andexperiment 2B. The albedo hypothesis predicts that after illuminant and surface matches, the slope ofthe relationship between luminance in the standard chamber and that in the match chamber should be aconstant, and should be 1. These experiments show that the slope is not always 1, and is not even aconstant; it can be experimentally manipulated.

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Discussion: 2B

The novel conclusion that can be drawn from the above experiment is that changingthe reflectance of the surface surrounding the test patch can change the slope of themeasured luminance while the perceived illuminant and perceived reflectance match.Remember that the prediction of the most general form of the albedo hypothesis wasthat after the two perceptual matches, the luminance slope should be 1. Data from theexperiment 2A suggested that in general the slope is not always 1, and data fromthese two experiments suggest that it is not even a constant.

The difference in results between experiment 2A and experiment 2B suggest that it ispossible to manipulate the relationship between luminance, perceived illumination,and perceived reflectance. With this information, it is theoretically possible to createconditions in which the albedo hypothesis in its general form holds true, and it islikewise possible to create conditions in which the relationship is strongly violated.

Other conclusions from this experiment are in agreement with conclusions fromexperiment 2A. Again, the strongest form of the albedo hypothesis (i = î and a = â) isfalsified by these results, since neither the illuminant matching slopes nor the surfacematching slopes were 1. In addition, the classic form of the albedo hypothesis,e = î * â, and the weaker form of the albedo hypothesis, f(e, î) = â, are falsified bythese results. If perceived illuminant and perceived surface lightness can bemanipulated independently, then it cannot be the case that perceived illuminationuniquely determines the relationship between physical luminance and perceivedsurface lightness.

Are observers better at illuminant matching or surface reflectance matching?One question that can be addressed by this matching paradigm is whether observersperform more consistently during illuminant matching or surface reflectancematching. The slopes of the regression line, discussed above, give a quantitativeestimate of the veridicality of the matches. Likewise, the standard deviations can giveus an estimate of the consistency of the matches. Each observer completed twosessions for each of the above experiments. Each trial in each experiment was unique,but one can compare the two corresponding trials in the two sessions. The standarddeviation of the two like trials across the two sessions for a given observer gives anestimate of consistency.

The proper comparison is between the illuminant measurements and surfaceluminance measurements, since both are measured in candelas per meter squared.However, the average illuminant measurements are on the order 4 times greater thansurface luminance measurements, so Weber’s law suggests that a direct comparisonof the standard deviations would likely lead to the conclusion that illuminantmatching was more variable, even if that were not true. A better estimate of the

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consistency of the matches would be the slopes of the best fitting line fitted to thestandard deviation plotted against mean illuminant or mean luminance (in candelasper meter squared), for each trial pair. Notice, however, that the measures of surfaceluminance include differences in illumination matching as a source of error. In orderto correct for this confound and get a better estimate of the variance in reflectancematching alone, the luminance of the two trials in a pair was calculated bymultiplying the reflectance by the average illumination match set in that pair of trials.This removes the effect of variability in illuminant matching from the surfacematching standard deviations.

See Table 2 for these data for each of the four experiments described above. Theaggregate slope of the regression line when the (two trial) illuminant mean wasplotted against the (two trial) standard deviation for illuminant matches was .118 andfor surface matches was .151. These differences are not big enough to conclude thathuman observers are measurably better at either illuminant matching or surfacelightness matching. Figure 45 shows the matched measurements in cd/m2 on the x-axis and the standard deviation on the y-axis; data from all four experiments arecombined, and surface data and illuminant data are plotted in different colors forcomparison.

Experiment Standard Deviation vIlluminant Slope

Standard Deviation v.Reflectance Slope

1A .0785 .05221B .1300 .18692A .1129 .20162B .1631 .2277

Table 2: Standard deviation slopes for illuminant and surface reflectance matches calculated by takingthe slope of the regression line when mean matches were plotted on the x-axis and standard deviationsplotted on the y-axis, and correcting for variance in illumination matches, as described in the text

This analysis was of interest since there has been very little experimental work doneon illuminant perception or illuminant matching, compared to the work done onsurface color perception and matching. Although any difference found was smallenough to be inconclusive, it does not seem that illuminant matching is lessconsistent.

Appendix 1 shows two pairs of control experiments that were conductedsubsequently. These experiments ensure that the results are the same when observersare instructed to match the illuminant just at the point of the test patch, and when

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observers adjust the illuminant and the surface reflectance simultaneously. The resultsand conclusions from these replications are consistent with experiments 2A and 2B(see Appendix 1).

Figure 45: Standard deviation of matched trials plotted against the mean match for the same trial.Illuminant matches are plotted in green, and surface matches plotted in red. The difference between thetwo is not big, but illuminant matching at least no less consistent than surface matching.

0

2

4

6

8

1 0

1 2

1 4

1 6

0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0

Illumination

Surface

Sta

ndar

d D

evia

tion

(cd/

m2)

Matched Luminance (cd/m2)

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Chapter 3

General Discussion

The primary purpose of this project was to test the albedo hypothesis, in its classicand more general forms. Other important aims were to provide one of the first tests ofobservers’ ability to match illuminations, to compare consistency in illuminationmatching to that in surface color matching, and to explore illumination colorconstancy. The main conclusions that can be drawn from the results of this project areas follows: The albedo hypothesis does not hold, even in its most general form.Perceived illumination does not uniquely determine perceived surface lightness for agiven luminance. People are able to make illumination matches. These matches are(nearly) veridical in the case of symmetric matching, but can be biased bymanipulating the stimuli. People do not always show illumination color constancy.These data do not show conclusively whether people are more consistent whenmatching illuminants or surface colors.

The conclusion that the albedo hypothesis is false rests on results from experiments2A and 2B, and on the replications of these experiments. In experiment 2A, once theperceived illuminant and the perceived surface reflectance were matched, the physicalluminance was not equal when measured at the two test patches. Thus, the perceivedilluminant cannot uniquely determine the perceived reflectance for a givenluminance, as the albedo hypothesis suggests. Results from experiment 2B suggestthat it is possible to manipulate surface reflectance matches without affectingilluminant matches. Again, this would not be possible if there were a consistentrelationship between the three variables across contexts.

The question of whether the albedo hypothesis is correct is of broad theoreticalinterest. Many current models of color perception and color constancy rely on theassumption that we can understand surface color perception as driven entirely by thevisual system's estimate of the illuminant. The hypothesis was important to test,because if it had held, then one could have usefully linked human visual performanceto physics-based computational models of vision (e.g. Landy and Movshon, 1991;Gilchrist & Jacobsen, 1984; Knill and Richards, 1996). These data suggest that adifferent approach is required.

In the introduction, two alternatives to the albedo hypothesis were discussed. The firstwas that perceived surface reflectance is a function of perceived illuminant andphysical luminance, but there are other factors that influence perceived reflectance.The second alternative is that there is no relationship between perceived illuminationand perceived surface reflectance. These experiments were not designed to test these

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two alternatives, and the current data do not require favoring one alternative over theother. Certainly, these data do not reject the idea that perceived illuminationinfluences perceived reflectance. Notice that in experiment 2A, the illuminantmatches are higher and the surface reflectance matches are lower, which isqualitatively consistent with there being some compensation. Furthermore, theliterature reviewed in the introduction (see especially Gilchrist, 1988) suggests arelationship between these two percepts. One cannot reject the idea that î influences â.Although the current study rules out the possibility that it is the only factor thatinfluence perceive reflectance, perceived illumination may be one factor.

Other factors that may influence perceived surface reflectance apparently have to dowith the immediate surround. Experiment 2B, (see also 3B and 4B in Appendix 1)shows that changing the immediate surround changes the relationship between theperceived illuminant and the physical luminance. It may be that the perceivedreflectance of the immediate surround or the ratio of the luminance between theimmediate surround and the test patch are taken as input by the reflectancecalculation function.

Surface color constancy was imperfect in these experiments. In some cases, surfacereflectance in the match chamber was set to less than half what it was in the standardchamber. This seems striking in light of the large literature on the human visualsystem’s high degree of color constancy. Notice, however, that human colorconstancy can be challenged in contrived situations. The Gelb effect, for example (seealso Gilchrist, 1988; Logvenenko & Menshikova, 1994) shows an experimentalsituations in which color constancy fails. It is also possible to make color constancybased optical illusions that rely on simultaneous contrast. The fact that colorconstancy failed in the above experiments is not new or unique, what is interesting isthe stimulus correlates of its failure.

The standard deviation was used in this study as an estimate of the consistency ofmatches. Just comparing standard deviations across trial type would have made itappear that illuminant matches were noisier, since the absolute values of thesemeasurements was higher than surface luminance measurements. The standarddeviation was plotted against the matched illuminant or surface luminance, so that themagnitude of the mean measurement (in cd/m2) would be taken into account. Therewas no remarkable difference in consistency between illuminant and surface matches.However, for each experiment, the illuminant matches are (qualitatively) moreconsistent than surface matches, so one can conclude that illuminant matching is noless consistent than surface reflectance matching. This is interesting, since illuminantperception has not been widely studied in the past. Illuminant perception andilluminant matching are reasonable tasks for human observers. If observers werebetter at illumination matching than surface matching, this would be consistent withKatz’s suggesting that an observer’s impression of illumination is stronger than the

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impression of surface colors (Katz, 1935). It would be inconsistent with Gilchrist andJacobsen’s (1984) finding that within observer difference in color judgments weresmall compared to the differences in illumination judgments.

The albedo hypothesis, as described in the literature, is very clearly a hypothesisabout a causal relationship. The model suggests that the illuminant is estimated first,and then the surface reflectance is calculated based on this estimate. Although thiscausal relationship was what these experiments were designed to test, notice that it ispossible to eliminate a “correspondence” relationship as well. Even models thatpropose that the causal relationship goes the other way (i.e. the perceived surfacereflectance determines the perceived illuminant) or that the two percepts mutuallyinfluence each other in a consistent way are falsified by these results. Experiment 2A(and 3A and 4A, see Appendix 1) shows that î, â and e do not have any consistentrelationship, and in experiment 4A this was tested without relying on assumptionsabout the causal relationship between the factors.

Perhaps a few caveats are in order while considering the conclusions one can drawfrom this project. First, one may be tempted to draw conclusions from these dataabout the precise nature of the perceived variables, î and â. In fact, it would beimpossible, based on this study, to make any strong claims about theserepresentations. It could be the case that any relationship that one could calculatebetween the matched reflectance and the matched illuminant captures the trueperceived lightness (or brightness) only after a non-linear output transformation (seeFoley, 1977; Philbeck & Loomis, 1997). It is still possible that there are inaccessiblevariables, î and â, that have a non-linear relationship to the matched illuminant andmatched surface lightness that the observers produced. Nonetheless, with thismatching paradigm it is possible to falsify certain hypotheses about î and â, and to testthe albedo hypothesis in general. Specifically, Experiments 2 through 4 falsify thehypotheses that i = î and that a = â, and show that perceived illumination does notuniquely determine the relationship between luminance and perceived albedo. Thismatching paradigm is the best current methodology for testing the albedo hypothesis.

A second question to consider when drawing conclusions from these data is: Is thisreally about constancy? One of the major themes of this work (indeed, the title) is therole of illumination perception in color constancy. However, the phenomena observedhere may or may not be about color constancy. Color constancy, or any perceptualconstancy, deals with the invariant relationship between a real world attribute and apercept representing that attribute. Thus, one might suggest that the albedo hypothesisis not necessarily about a perceptual constancy, since if the perceived illumination iswrong, then the perceived surface color will be wrong as well. Still, the albedohypothesis is about constancy in the sense that to the extent that people are colorconstant, the perception of the illuminant is supposed to play a role in producing thatconstancy. The fact that a non-veridical percept at one stage of the process predicts a

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non-veridicality in a later stage does not mean that these models and hypotheses maynot play a role in real world perception. In the real world perceived reflectance doeshave a fairly consistent and regular relationship to actual physical reflectance.

Conclusion

According to the albedo hypothesis, surface color perception is accomplished whenthe visual system first estimates the illuminant of a scene and then uses this estimateto determine the color of a particular surface given the luminance reflected from thesurface. Results from these matching experiments falsify this hypothesis. On eachtrial, observers matched the illumination in the scene and the color of the test patch.The albedo hypothesis predicts that when both the illuminant and the color of the testpatch in the two scenes appear the same, the physical luminance of the two testpatches will be the same. It was not, at least with stimuli that induced a bias inillumination matching. Manipulating the immediate surround of the test patchaffected the matched surface lightness without affecting matched illuminant, whichalso rules out the possibility that the perceived illuminant is the only variable thatgoverns the relation between physical luminance and perceived surface reflectance.

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Gilchrist, A., Kossyfidis, C., Bonato, F., Agostini, T., Cataliotti, J., Li, X., Spehar, B.,Szura, J., Annan, V., & Economou, E. (1999). An anchoring theory of lightnessperception. Psychological Review, 106 (n4):795-834.

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Appendix 1

Experiment 3A: Asymmetric Matching and Location Specific Instructions

The following four experiments were replications of and control experiments forexperiments 2A and 2B. The purpose of experiments 3A and 3B, was to replicateexperiments 2A and 2B using instructions that localized the point of illuminantmatching to the test patch. The purpose of this entire project is to test the relationshipbetween illumination perception and surface color perception, at the point of a givensurface of interest. In the previous experiments. If observers are matching theillumination in the chamber as a whole, but matching the surface reflectances of justthe test patches, the method may not be testing the intended relationship. These twoexperiments thus replicate 2A and 2B, but now observers are specifically instructed tomatch the illuminants at the test patches.

Apparatus: 3A

The apparatus for experiment 3A was identical to that in experiment 2A.

Observers: 3A

There were 4 naïve observers, none of whom had participated in any of the previousexperiments. They included 1 female in her early 20s and three males in their early20s. Observers were paid $10 for each session.

Procedure: 3A

The procedure for this experiment was the same as for experiment 2A. The onlydifference between this and experiment 2A was the wording of the instructionsobservers were given. For illuminant matches, observers were told

Your job is to match the amount of light that is falling on the two testpatches. When you do illuminant matching, it would be possible tothink about matching the illuminant in the whole scene or matchingthe illuminant at a particular point in the scene. We want you to do thelatter, and in particular to match the illuminant at the test patch.

All other instructions were essentially the same, except for reminders of this specifictask. The complete instructions can be found in appendix 3.

Results: 3A

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Again, the data are summarized for each observer with a slope, using the data from allaccepted matches in the two sessions. For illuminant match slopes for all 4 observers,see table 3. The average slope for all observers was 2.03. Paired two-tailed t testshowed that the standard and matched illuminants were different for each observer. Aone sample t test on the average differences scores (standard illuminant minus matchilluminant) for the four observers revealed that the differences were different fromzero (t(3)=14.52, p<.0001, two-tailed). An unmatched t test between illuminant slopesfrom in experiment 2A and 3A showed no difference between two experiments(t(9)=.923, n.s.).

All reflectance match slopes are also shown in table 3. The average slope for allobservers was . 37. Paired two-tailed t test showed that the standard and matchedreflectances were different for each observer. A one sample t test on the averagedifferences scores (standard illuminant minus match illuminant) for the four observersrevealed that the differences were different from zero (t(3)=31.91, p<.0001, two-tailed). An unmatched t test between reflectance slopes from in experiment 2A and3A showed no difference between two experiments (t(9)=.912, n.s.).

Finally, the average luminance slopes for all observers was .76 (shown in table 3).Paired two-tailed t test showed that the luminance measurements in the standard andthe luminance measurements in the match chamber were different for three of thefour observers (see table 4). A one sample t test on the average differences scores(standard luminance minus match luminance) for the four observers revealed that thedifferences were different from zero (t(3)=3.92, p=.03, two-tailed). As in experiment2A, on the average trial, once the illuminant and the surface reflectance wereperceptually matched in the two chambers, the luminance was not equal, and waslower in the match chamber.

Experiment 3A Illuminant slopes Reflectance slopes Luminanceslopes

DCB 1.63 .41 .76JLM 2.70 .35 .92MJH 1.91 .34 .66LVK 1.89 .39 .71

Average 2.035 .37 .76Experiment 3B

DCB 1.65 .53 .91JLM 2.20 .52 1.17MJH 2.08 .50 1.06LVK 1.48 .61 1.00

Average 1.85 .54 1.03

Table 3: Illuminant, reflectance, and luminance slopes for each observer in experiments 3A and 3B

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p value, One tailed paired ttest

DCB t(30) = 2.56 .0159JLM t(12) = 1.39 .191 n.s.MJH t(27) = 7.05 1.41E-07LKV t(25) = 4.00 .0005


Discussion: 3A

These results essentially replicate experiment 2A. These data show both a failure ofilluminant color constancy and surface color constancy, as in experiment 2A. Neitheraverage illuminant slopes nor average surface reflectance slopes were 1, which theywould be if the matches were veridical.

Because the luminance slope (the relationship between luminance measured at thetest patch in the standard chamber and the test patch in the match chamber) is not 1,the albedo hypothesis is false. The logic is outlined in experiment 2A. Thisreplication is important given the new instructions. Because observers were instructedto match the illuminants specifically at the test patch, one can have more confidencethat this experiment tests the relationship between surface reflectance andillumination at the location of the surface.

Experiment 3B Surround Change with Location Specific Instructions

Again, this experiment is a replication of experiment 2B, with the new, more specificinstructions, to ensure that the method tests the relationship between perceivedsurface color and the perceived illumination at the point of the surface in question.

Apparatus: 3B

The apparatus here was identical to that of experiment 2B.

Observers: 3B

Observers were the same four observers from experiment 3A.

Procedure: 3B

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The procedure was identical to the previous experiment. Again observers wereinstructed to match the illuminant at the point of the test patch; instructions were thesame as for experiment 3A.

Results: 3B

Were illuminant matches different from experiment 3A?For illuminant match slopes for all 4 observers, see table 3. The average slope for allobservers was 1.85, compared to 2.03 for experiment 3A. Again, observers did notshow illuminant color constancy, and their deviation from perfect constancy is, onaverage, about the same as that in experiments 2A and 2B. A paired two-tailed t testrevealed that the slopes for the 4 observers were not significantly different from theslopes from experiment 3A (t(3)= 1.11, p=.35, n.s.), nor were the difference scores(t(3)= .84, p=.46, n.s.). Thus, there was no measurable difference between illuminantmatching slopes in experiment 3A and experiment 3B. An unmatched t test betweenilluminant slopes from in experiment 2B and 3B showed no difference between twoexperiments (t(9)=.15, n.s.).

Were surface reflectance matches different from experiment 3A?All reflectance match slopes are also shown in table 3. The average slope for allobservers was . 54, compared to .37 for experiment 3A. As in experiment 3A, theobservers did not show surface color constancy. A paired two-tailed t test revealedthat the slopes for the 4 observers were significantly different from the slopes fromexperiment 3A (t(3)= 8.03, p=.004) as were the difference scores (t(3)= 15.54,p=.0006,). Thus, there was a significant difference between surface reflectancematching slopes in experiment 3A and experiment 3B, just as there was betweenexperiments 2A and 2B. An unmatched t test between reflectance slopes from inexperiment 2B and 3B showed no difference between two experiments (t(9)=.124,n.s.).

Were surface luminance slopes different from experiment 3A?As in experiments 2A and 2B, the interesting question is whether it is possible tomanipulate the luminance slope simply by changing the immediate surround of thetest patch. Again, the relationship between the surface luminance measured at the testpatch in the two chambers in experiment 3B was different from that relationship inexperiment 3A. The average slope for all observers was 1.03 (shown in table 3),compared to .76 in the experiment 3A. A paired two tailed t test revealed that thesurface luminance slopes were different between these two experiments. (t(3)= 5.25,p=.01) as were the difference scores (t(3)= 7.34, p=.005,).

Discussion: 3B

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Results from experiments 3A and 3B are in complete agreement with results fromexperiments 2A and 2B. Changing the reflectance of the surface surrounding the testpatch can independently change the slope of the measured luminance after perceptualilluminant and reflectance matches. The albedo hypothesis predicts that after the twoperceptual matches, the luminance slope should be 1. The slope is not always 1, andagain these data suggest that it is possible to manipulate the relationship betweenluminance, perceived illumination, and perceived reflectance.

Again, changing the reflectance of the surface surrounding the test patch canindependently change the slope of the measured luminance after perceptual illuminantand reflectance matches. Importantly, this is true even in the case when observers arespecifically instructed to match the illumination at the point of the same point wherethey are matching the surface reflectance. This replication is important given the newinstructions: Because observers were instructed to match the illuminants specificallyat the test patch, one can have more confidence that this experiment tests therelationship between illumination and surface reflectance.

Other conclusions from this experiment are also in agreement with conclusions fromprevious experiments. Again, the strongest form of the albedo hypothesis, that i = îand a = â are falsified by these results, since neither the illuminant matching slopesnor the surface matching slopes were 1.

Experiment 4A: Alternating Illuminant and Surface Matches

Experiments 4A and 4B, were additional replications and control experiments for 2Aand 2B. In 4A and 4B, observers were able to adjust both the illuminant and thesurface reflectance simultaneously. They did not have to first accept the illuminantmatch before doing the surface match. Instead, they could make adjustments to one,then the other, and then the first again. They did not accept the match until both theilluminant and the surface reflectance were perceptually matched. This methodensures that any influence of perceived surface reflectance on perceived illuminant istaken into account in the test of the albedo hypothesis. It relaxes the assumption of thealbedo hypothesis that there is a one way causal relationship.

Apparatus: 4A

The apparatus for experiment 4A was identical to that in experiment 2A.

Observers: 4A

There were 4 observers, all of whom had participated in the first four experiments.They included 1 female in her early 20s, 1 female in her early 30s, and two males intheir early 20s. Observers were paid $10 for each session.

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Procedure: 4A

The procedure for this experiment was largely the same as for experiment 2A, exceptobservers had two Game Pads, and could adjust both the illuminant and the surfacereflectance before going on to the next trial. Observers were told

Unlike the experiment you did before, you will be able to adjust theillumination and the surface lightness at the same time. We would likeyou to try to adjust both the illuminant and the surface lightness a littlebit each time the mirror moves, to get both into the right ballparkbefore you start making your final adjustments. As you make yourfinal adjustments, continue to alternate between the two judgements.…Remember, you won't accept the matches until you have adjustedboth the illuminant and the surface lightness.

The rest of the instructions were essentially the same. The complete instructions canbe found in appendix 4.

Results: 4A

Again, the data are summarized for each observer with a slope, using the data from allaccepted matches in the two sessions. For illuminant match slopes for all 4 observers,see table 6. The average slope for all observers was 1.39. Paired two-tailed t testshowed that the standard and matched illuminants were different for three of the fourobservers. A one sample t test on the average differences scores (standard illuminantminus match illuminant) for the four observers revealed that the differences weredifferent from zero (t(3)=3.20, p=.049, two-tailed). A paired two-tailed t testincluding just those observers included in both experiments 2A and 4A showed nodifference in illuminant slopes between those two experiments (t(3) = 2.11, n.s.).

All reflectance match slopes are also shown in table 6. The average slope for allobservers was .38. Paired two-tailed t test showed that the standard and matchedreflectances were different for each observer. A one sample t test on the averagedifferences scores for the four observers revealed that the differences were differentfrom zero (t(3)=23.98, p<.0001, two-tailed). A paired two-tailed t test including justthose observers included in both experiments 2A and 4A showed no difference inreflectance slopes between those two experiments (t(3) = .11, n.s.).

Finally, the average luminance slopes for all observers was .51. Paired two-tailed ttest showed that the standard and matched illuminants were different for each of thefour observers (see table 6). A one sample t test on the average differences scores forthe four observers revealed that the differences were different from zero (t(3)=8.57,

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p=.003, two-tailed). As in experiment 2A, on the average trial, once the illuminantand the surface reflectance were perceptually matched in the two chambers, theluminance was not equal, and was lower in the match chamber. In this replication, theresults again reject the albedo hypothesis.

Discussion: 4A

These results essentially replicate experiment 2A. These data show both a failure ofilluminant color constancy and surface color constancy and falsify the albedohypothesis, as in experiment 2A. Neither average illuminant slopes nor averagesurface reflectance slopes were 1, which they would be if the matches were veridical.Because the luminance slope is not 1, the albedo hypothesis is false. (The logic isoutlined in experiment 2A.)

Experiment 4A Illuminant slopes Reflectance slopes Luminanceslopes

MDR 1.45 .42 .57SIM 1.40 .29 .41MBG 1.67 .39 .63ISH 1.04 .42 .44

Average 1.39 .38 .51Experiment 4B

MDR 1.54 0.688 1.13SIM 1.47 0.544 0.86MBG 2.00 0.568 1.17ISH 1.35 0.587 0.76

Average 1.59 .597 .98

Table 5: Illuminant, reflectance, and luminance slopes for each observer in experiments 4A and 4B


p value, One tailed paired ttest

MDR t(31) = 10.56 8.57 E-12SIM t(31) = 11.22 1.92 E-12

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MBG t(31) = 9.64 7.55 E-11ISH t(31) = 11.33 1.48 E-12


Experiment 4B: Alternating Illuminant and Surface Matches

Again, this experiment is a replication of experiment 2B, but now the observersadjusted both the illuminant and the surface reflectance before going on to the nexttrial, as in experiment 4A.

Apparatus: 4B

The apparatus here was identical to that of experiment 2B.

Observers: 4B

Observers were the same four observers from experiment 4A.

Procedure: 4B

The procedure is identical to the experiment 4A.

Results: 4B

Are illuminant matches different from experiment 4A?For illuminant match slopes for all 4 observers, see table 6. The average slope for allobservers was 1.59, compared to 1.51 for experiment 4A. Again, observers did notshow illuminant color constancy, and their deviation from perfect constancy is, onaverage, about the same as that in experiments 2A and 2B. A paired two-tailed t testrevealed that the slopes for the 4 observers were not significantly different from theslopes from experiment 4A (t(3)= 2.73, n.s.), nor were the difference scores (t(3)=3.01, n.s.). Thus, there was no significant difference between illuminant matchingslopes in experiment 4A and experiment 4B. An unmatched t test between allobservers in experiment 2B and the four in 4B showed no difference between theilluminant slopes in the two experiments (t(9)=1.87, n.s.).

Are surface reflectance matches different from experiment 4A?All reflectance match slopes are also shown in table 6. The average slope for allobservers was .60, compared to .37 for experiment 4A. As in experiment 4A, theobservers did not show surface color constancy. A paired two-tailed t test revealedthat the slopes for the seven observers were significantly different from the slopesfrom experiment 4A (t(3)= 8.24, p=.004), as were the difference scores (t(3)= 11.04,

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p=.002.). Thus, there was a significant difference between surface reflectancematching slopes in experiment 4A and experiment 4B, just as there was betweenexperiments 2A and 2B. An unmatched t test between all observers in experiment 2Band the four in 4B showed no difference between the reflectance slopes in the twoexperiments (t(9)=1.20, n.s.).

Are surface luminance slopes different from experiment 4A?As in experiments 2A and 2B, the interesting question is whether it is possible tomanipulate the luminance slope simply by changing the immediate surround of thetest patch. Again, the relationship between the surface luminance measured at the testpatch in the two chambers in experiment 4B was different from that relationship inexperiment 4A. The average slope for all observers was .98 (shown in table 6),compared to .53 in the experiment 4A. A paired two tailed t test revealed that thesurface luminance slopes were different between these two experiments. (t(3)= 8.49,p=.003) as were the difference scores (t(3)= 32.30, p=.00007.).

Discussion: 4B

These results replicate findings from experiment 2A. It is possible to manipulate therelationship between the luminance of the standard test patch and the luminance ofthe match test patch after both illumination and reflectance are perceptually matched.Since the reflectance matches changed (relative to experiment 4A) and illuminantmatches did not, perceived illumination cannot be the only factor determiningperceived reflectance. Even when one relaxes the assumption about the causalrelationship between perceived illuminant and perceived reflectance, there is not aconsistent relationship.

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Appendix 2 : Instructions used in 1A, 1B, 2A and 2B.

Thank you for participating in this experiment. There will be a total of sixteen trials.In each trial you will first do an illuminant match, and then a surface lightness match.A computer voice will tell you when to do an illumination match and when to do asurface match, and will tell you which trial you are on. The surfaces you will matchare the little patches you see on the back wall of each chamber. You will be able tocontrol the illuminant in one of the two boxes during the illuminant match, and youwill be able to control the surface lightness when you are doing the surface match.

When you are doing an illuminant match, do not worry about how any of the surfacesof the walls or objects look. They may look the same or they may look different whenthe illuminations match. Just try to match the amount of light that is falling at any twopoints in the two boxes, for example, think about how much light is falling on the testpatch, or how much light is falling on the egg carton or the milk carton.

Likewise, when you are matching the surfaces in the two boxes, don’t worry abouthow the illumination levels look. Just try to make the two test patches look like theywere made out of the same piece of paper.

To match the illumination, you will use this GamePad. Move the joystick up toincrease the illumination, and down to decrease the illumination. Each trial will startwith the biggest changes, so when you think that your are in the right ballpark, andwant to decrease the change in illumination with each movement of the joystick, youcan move the joystick to the left. That will decrease the increment size. There arethree different increments, and they cycle through, so once you get beyond thesmallest increment, you’ll be back to the largest. You will hear a beep each time youchange the size of the increment.

Finally, when you want to accept the match, that is, when it looks like theillumination in the two boxes is the same, press the blue button and you'll go on to thesurface match. If you get to the top or the bottom of the range, you’ll hear a beep, andyou won’t be able to adjust the illumination any farther. If this happens, you caneither accept the match by pressing the blue button, or reject the match by pressingthe yellow button. You should reject the match if you don't think the illumination inthe two boxes looks the same. In either case, the surface match will start.

To match the surfaces, you will again use this GamePad. Just like in the illuminationmatch, you will move the joystick up to increase the lightness, and down to decreaseit. When you think that you are in the right ballpark, and want to decrease the changein lightness with each movement of the joystick, you can move the joystick to the left,and again you’ll hear a beep as the increments change. Finally, when you want to

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accept the match, if you think that the lightness of the test patch is the same in the twoboxes, press the blue button. If you reach the end of the range, you’ll hear a beep andyou can either accept the match by pressing the blue button, or reject the match bypressing the yellow button. In either case, you will go on to the next trial.

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Appendix 3: Instructions used in 3A and 3B.

Thank you for participating in this experiment. There will be a total of sixteen trials.In each trial you will first do an illuminant match, and then a surface lightness match.A computer voice will tell you when to do an illumination match and when to do asurface match, and will tell you which trial you are on. The surfaces you will matchare the little patches you see on the back wall of each chamber. You will be able tocontrol the illuminant in one of the two boxes during the illuminant match, and youwill be able to control the surface lightness when you are doing the surface match.

When you are doing an illuminant match, do not worry about how any of the surfacesof the walls or objects look. They may look the same or they may look different whenthe illuminations match. Your job is to try to match the amount of light that is fallingon the two test patches. When you do illuminant matching, it would be possible tothink about matching the illuminant in the whole scene or matching the illuminant ata particular point in the scene. We want you to do the latter, and in particular to matchthe illuminant at the test patch.


To match the illumination, you will use this GamePad. Move the joystick up toincrease the illumination, and down to decrease the illumination. Each trial will startwith the biggest changes, so when you think that your are in the right ballpark, andwant to decrease the change in illumination with each movement of the joystick, youcan move the joystick to the left. That will decrease the increment size. There arethree different increments, and they cycle through, so once you get beyond thesmallest increment, you’ll be back to the largest. You will hear a beep each time youchange the size of the increment.

Finally, when you want to accept the match, that is, when it looks like theillumination is the same at the two test patches, press the blue button and you'll go onto the surface match. If you get to the top or the bottom of the range, you’ll hear abeep, and you won’t be able to adjust the illumination any further. If this happens,you can either accept the match by pressing the blue button, or reject the match bypressing the yellow button. You should reject the match if you don't think theillumination is the same at the two test patches. In either case, the surface match willthen start.

To match the surfaces, you will again use this GamePad. Just like in the illuminationmatch, you will move the joystick up to increase the lightness, and down to decrease

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it. When you think that you are in the right ballpark, and want to decrease the changein lightness with each movement of the joystick, you can move the joystick to the left,and again you’ll hear a beep as the increments change. Finally, when you want toaccept the match, if you think that the two test patches look like they are cut from thesame piece of paper, press the blue button. If you reach the end of the range, you’llhear a beep and you can either accept the match by pressing the blue button, or rejectthe match by pressing the yellow button. In either case, you will go on to the nexttrial.

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Appendix 4: Instructions used in 4A and 4B.

Thank you for participating in this experiment. There will be a total of sixteen trials.In each trial you will do an illuminant match and a surface lightness matchsimultaneously. Unlike the experiment you did before, you will be able to adjust theillumination and the surface lightness at the same time. We would like you to try toadjust both the illuminant and the surface lightness a little bit each time the mirrormoves, to get both into the right ballpark before you start making your finaladjustments. As you make your final adjustments, continue to alternate between thetwo judgements. You will be able to control the illuminant and the surface lightnessin the match box using separate joysticks.

When you are doing an illuminant match, do not worry about how any of the surfacesof the walls or objects look. They may look the same or they may look different whenthe illuminations match. Your job is to try to match the amount of light that is fallingon the two test patches. When you do illuminant matching, it would be possible tothink about matching the illuminant in the whole scene or matching the illuminant ata particular point in the scene. This time, we want you to do the later, and inparticular to match the illuminant at the test patch.


To match the illumination, you will use this GamePad on the left. Move the joystickup to increase the illumination, and down to decrease the illumination. Each trial willstart with the biggest changes, so when you think that your are in the right ballpark,and want to decrease the change in illumination with each movement of the joystick,you can move the joystick to the left. That will decrease the increment size. There arethree different increments, and they cycle through, so once you get beyond thesmallest increment, you’ll be back to the largest. You will hear a beep each time youchange the size of the increment.

To match the surfaces, you will use this GamePad on the right. Again, you will movethe joystick up to increase the lightness, and down to decrease it. When you think thatyou are in the right ballpark, and want to decrease the change in lightness with eachmovement of the joystick, you can move the joystick to the left, and again you’ll heara beep as the increments change.

Remember, you won't accept the matches until you have adjusted both the illuminantand the surface lightness. When you want to accept the match, that is, when it lookslike the illumination and the surface lightness in the two boxes are the same, press theblue button on either GamePad and you will go on to the next trial. If you get to the

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top or the bottom of the range, you’ll hear a beep, and you won’t be able to adjust theillumination any farther. If this happens, you can either accept the matches bypressing the blue button, or reject the matches by pressing the yellow button on eitherGamePad. You should reject the match if you don't think the illumination in the twoboxes looks the same or if the test patches don't look like they are cut out of the samepiece of paper. In either case, you will go on to the next trial.

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