representation of memory prototype for an object color

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Representation of Memory Prototype for an Object Color* S. N. Yendrikhovskij, 1 F. J. J. Blommaert, 1 H. de Ridder 2 1 IPO, Center for Research on User-System Interaction, Eindhoven, The Netherlands 2 Delft University of Technology, Department of Industrial Design Engineering, Delft, The Netherlands Received 18 September 1997; revised 29 April 1999; accepted 3 June 1999 Abstract: This article presents a general framework for modeling memory colors and provides experimental evi- dence supporting this model for one particular object, i.e., a banana. We propose to characterize memory colors from experimentally determined similarity judgments of apparent object colors with the prototypical color of that object category. The aim of the first experiment was to analyze the memory representation of banana color in the CIELUV color space. To this end, we prepared images imitating different colors of a banana and asked subjects to scale the similarity in color of a banana shown on a CRT display and a typical ripe banana as it is remembered from their past experience. The relationships between the similarity judg- ments and chromaticity coordinates representing the ma- nipulated banana samples can be well described by a biva- riate normal distribution. Another experiment was carried out to gain more insight into the perception process leading to an appearance of the banana stimuli. Additionally, a sample of banana colors from a fruit market was measured and compared with the similarity judgments. © 1999 John Wiley & Sons, Inc. Col Res Appl, 24, 393– 410, 1999 Key words: memory colors; apparent colors; prototypes; similarity; categorization INTRODUCTION The first unification of the terms object, color, and memory was elaborated by Hering, 1 who claimed that all objects known to us from past experience are seen through the “spectacles of memory colors.” Memory colors define the colors that are recalled in association with familiar objects in long-term memory. 2 They should be distinguished from the term color memory, which refers to the ability to re- member color in general. The notion of memory colors has long been of interest in different areas of color research. Several studies have discussed the concept of memory col- ors in reference to color appearance, 3–5 color recognition, 6 color matching, 7 color focality, 8 and color reproduction. 9,10 However, only a few experimental investigations 2,11 have aimed at characterizing the nature of memory colors per se. The following research is an attempt to fill the gap in explicit characteristics of memory colors by adopting the computational notion of representation. Following Marr, 12 representation defines “a formal system for making explicit certain entities … together with a specification of how the system does this.” In general, a computational model is based on the precise specification of the input and output of the process under investigation (semantic specification), and algorithms for the mathematical transformation of the input to the output (algorithmic specification). This article pre- sents a computational model of memory colors and provides experimental evidence supporting this model for one par- ticular object, i.e., a banana. COMPUTATIONAL MODEL OF MEMORY COLORS Semantic Specification Let us consider a specific example of using memory colors in everyday life. Imagine a person searching for his favorite ripe banana in a supermarket. We assume that the process of choosing the desired banana is based on five major subprocesses: sensation, perception, generalization, comparison, and decision (see Fig. 1). * The article was partially presented at the 19th European Conference on Visual Perception, ECVP 1996, in Strasbourg, France. ² Correspondence to: S. N. Yendrikhovskij, IPO, Center for Research on User-System Interaction, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands; e-mail: [email protected] © 1999 John Wiley & Sons, Inc. Volume 24, Number 6, December 1999 CCC 0361-2317/99/060393-18 393

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Representation of MemoryPrototype for an Object Color*

S. N. Yendrikhovskij,1† F. J. J. Blommaert,1H. de Ridder2

1 IPO, Center for Research on User-System Interaction, Eindhoven, The Netherlands

2 Delft University of Technology, Department of Industrial Design Engineering, Delft, The Netherlands

Received 18 September 1997; revised 29 April 1999; accepted 3 June 1999

Abstract: This article presents a general framework formodeling memory colors and provides experimental evi-dence supporting this model for one particular object, i.e.,a banana. We propose to characterize memory colors fromexperimentally determined similarity judgments of apparentobject colors with the prototypical color of that objectcategory. The aim of the first experiment was to analyze thememory representation of banana color in the CIELUVcolor space. To this end, we prepared images imitatingdifferent colors of a banana and asked subjects to scale thesimilarity in color of a banana shown on a CRT display anda typical ripe banana as it is remembered from their pastexperience. The relationships between the similarity judg-ments and chromaticity coordinates representing the ma-nipulated banana samples can be well described by a biva-riate normal distribution. Another experiment was carriedout to gain more insight into the perception process leadingto an appearance of the banana stimuli. Additionally, asample of banana colors from a fruit market was measuredand compared with the similarity judgments.© 1999 John

Wiley & Sons, Inc. Col Res Appl, 24, 393–410, 1999

Key words: memory colors; apparent colors; prototypes;similarity; categorization

INTRODUCTION

The first unification of the termsobject, color, andmemorywas elaborated by Hering,1 who claimed that all objects

known to us from past experience are seen through the“spectacles of memory colors.”Memory colorsdefine thecolors that are recalled in association with familiar objectsin long-term memory.2 They should be distinguished fromthe termcolor memory, which refers to the ability to re-member color in general. The notion of memory colors haslong been of interest in different areas of color research.Several studies have discussed the concept of memory col-ors in reference to color appearance,3–5 color recognition,6

color matching,7 color focality,8 and color reproduction.9,10

However, only a few experimental investigations2,11 haveaimed at characterizing the nature of memory colors per se.

The following research is an attempt to fill the gap inexplicit characteristics of memory colors by adopting thecomputational notion ofrepresentation. Following Marr,12

representation defines “a formal system for making explicitcertain entities … together with a specification of how thesystem does this.” In general, a computational model isbased on the precise specification of the input and output ofthe process under investigation (semanticspecification), andalgorithms for the mathematical transformation of the inputto the output (algorithmic specification). This article pre-sents a computational model of memory colors and providesexperimental evidence supporting this model for one par-ticular object, i.e., a banana.

COMPUTATIONAL MODEL OF MEMORY COLORS

Semantic Specification

Let us consider a specific example of using memorycolors in everyday life. Imagine a person searching for hisfavorite ripe banana in a supermarket. We assume that theprocess of choosing the desired banana is based on fivemajor subprocesses: sensation, perception, generalization,comparison, and decision (see Fig. 1).

* The article was partially presented at the 19th European Conference onVisual Perception, ECVP 1996, in Strasbourg, France.

† Correspondence to: S. N. Yendrikhovskij, IPO, Center for Research onUser-System Interaction, Eindhoven University of Technology, P.O. Box513, 5600 MB Eindhoven, The Netherlands; e-mail: [email protected]© 1999 John Wiley & Sons, Inc.

Volume 24, Number 6, December 1999 CCC 0361-2317/99/060393-18 393

Sensationstarts with a light incident in a person’s eyesfrom an object surface in a certain viewing context. Theviewing context includes the color of a light source, anobject surrounding, and accounts for such perceptual phe-nomena as color constancy, adaptation, induction, etc. An

important question is whether the perceptual phenomenainfluence the observer’s choice. If so, then from the same setof fruits the person might pick out different bananas in thesupermarket compared to outdoors, due to the fact that thefruits appear to be different (e.g., due to incomplete color

FIG. 1. Diagram depicting the judgment process of memory colors. Rectangles: input, output, and intermediate represen-tations. Ellipses: processes that map one representation in the next.

394 COLOR research and application

constancy or simultaneous color contrast). However, if thevisual system disregards the viewing context, then the ob-server’s choice should be independent of the light sourceand the object surrounding. A comparative study13 of mem-ory colors with two different illuminants showed a signifi-cant influence of the light source on subjects’ choice ofcolors associated with some familiar objects. A well-knownproblem in recognizing object colors under mercury vaporstreet lamps is another example indicating that the completedisregard for the viewing context is hardly possible.

Perceptionis considered as a separate process to high-light the importance of assigning a meaning to complexcolor patterns. This assigning is based on the top-downinput from the internalized object knowledge includingmemory colors and object names.6 The influence of theobject knowledge on color appearance was demonstratedfor example in experiments of Bonaiuto,14 where figureswith incongruous object tonality such as blue bread wereperceived by observers to be more saturated than figureswith the same but congruous object tonality such as a bluesea. Although the influence of memory colors on objectcolor appearance is not our focus here (see Beck15 for areview), the postulated coupling leads to an interestingprediction examined in the present research: an unusual, orunnatural, depiction of an object complicates its interpreta-tion. Presumably, the choice of the “right” color for thebanana would be more difficult to make using color patches(i.e., unnatural depiction) than using real fruit (i.e., naturaldepiction). The difficulty may be caused by an obstacle ininterpreting the color patches as object colors.

Generalizationis argued to be an essential process in theformation of memory colors. According to Shepard,16 it isvery unlikely for an object to reappear in exactly the sameviewing context and, thus, it is useful for the organism toestablish general regularity in object appearance. The gen-eralization process is assumed to result in construction of aparticular group, what is called anatural kindor category.Rosch17 argued that categories can be viewed in terms ofprototypes or the “clearest cases of category membership.”The termprototypecan be used at least in two senses. First,the prototype can be considered as an abstract model con-taining the most representative attributes of the category orcorresponding to its central value. There is evidence thatobservers have a tendency to recognize the central value ofa category, even when this central value or prototype hasnever been seen (e.g., see recent experiments with facerecognition in Cabezaet al.18). Second, the prototype can beconsidered as a particular exemplar resembling the abstractmodel best. It was shown that the most prototypical mem-bers of categories are learned and identified more rapidlythan members with a lesser degree of prototypicality.19 Inparticular, prototypical colors tend to be more consistentlyperceived and remembered than nonprototypical colors.20

Therefore, we propose to represent memory color by pro-totypical color, i.e., the most typical color of an objectcategory. In other words, we suggest that memory colors do

not define all colors that are recalled in association withfamiliar objects but mainly the prototypical ones.

Comparison, or similarity judgment, is performed be-tween an apparent object color and a prototypical color ofthe corresponding object category. It should be noted thatthe representation of an object category by its prototype inthe similarity judgments is not without controversy. Forexample, according to Exemplar Models of Categorization(e.g., Nosofsky21), the similarity is computed between thestimulus representation and the memory representation ofall category members. Although the Exemplar Models havesuccessfully accounted for different categorization phenom-ena (especially for categories with a small number of items),it seems unlikely in our example that the global matchingoperation includes all category members: to conclude that agreen banana is not a ripe banana, it is not necessary tocompute its similarity to every banana we have ever seen.The question “What is exactly stored and compared inmemory?” has been one of the major points of discussionbetween different models of categorization (see Ashby22 fora review). In this article, this question has been reformulatedinto a computational question: “How many parameters areneeded to sufficiently describe the similarity judgments?”

Decision is based on the degree of similarity betweenapparent and prototypical object colors. All green andbrown bananas from our example would be judged unac-ceptably dissimilar with an observer’s desired banana, and,therefore, would be rejected. Apparently, an observer estab-lishes a decision bound for the degree of similarity to beacceptable or not; there is no unique typical ripe banana innature, but there are a lot of objects admitted to be withinthe bounds of “ripe banana.”

Algorithmic Specification

The basic representation assumptions of our study, fol-lowing the multidimensional models of categorization,22 arethat (1) any psychological representation is probabilistic,and (2) any perceptual and cognitive effect of a givenstimulus can be represented as a point in a multidimensionalpsychological space. In general, any perceptual or cognitiverepresentation can be described by a multivariate probabil-ity function. This assumption can be viewed as a multidi-mensional generalization of Signal Detection Theory.23 Theexact way object colors and memory colors are representedis no trivial matter. For the present, we consider plausiblealternatives and make the following assumptions.

Color can be represented as a point in some perceptuallyuniform color space. As a suitable approximation, wechoose the CIE 1976L*u*v* (CIELUV) color space. TheCIELUV color space is one of the two approximately uni-form color spaces recommended by the Commission Inter-nationale de l’Eclairage (CIE) for industrial application.The CIELUV color space is widely used in practice forcathode ray tube (CRT) color television. Although thisspace has some shortcomings, we decided to use the CIE-

Volume 24, Number 6, December 1999 395

LUV color space, because it has an associated chromaticitydiagram.

Object colorof any natural category is not a single point.Even homogeneously colored objects like bananas containspots of different colors. To represent object color, i.e.,colorimetric color of object surface, we propose a statisticaldescription and assume that all colors belonging to an objectsurface are distributed around a centroid with a densityfunction. There are at least three ways to specify the cen-troid: (1) the mean or the arithmetic average of the distri-bution, (2) the mode or the most probable value, and (3) themedian or the point exactly midway between the top andbottom halves of the distribution (for more details on themean, mode, and median definitions in statistics see, e.g.,Hays24). As a first choice, we represent object color by themean of its distribution in the CIELUV color space. Wedenote the coordinates of surface colorSi of an objecti inthe CIELUV color space by the vectorsi (see Fig. 2).

Theapparent object colorfor two objects with the samecolorimetric mean might be different due to various color-appearance phenomena, such as chromatic adaptation, in-duction effect, etc. At present, there is no single color-appearance model that is reliable and universally accepted(see, e.g., Fairchild25 for a review). It implies that there is nostandard transformation from colorimetric into apparentcolor values. One of the plausible solutions is to character-ize actual apparent colors by matching them with corre-sponding colorimetric colors in a psychometric space underwell-defined conditions. For example, to model the induc-tion effect, we can represent an apparent object color by a

corresponding colorimetric color in the CIELUV colorspace with relation to the color of itsbackground. Thebackground color can be specified in the same way as theobject color, i.e., by the mean of its distribution in theCIELUV color space. Denote the coordinates of the appar-ent object colorAi and that of the background colorGi inFig. 2 by the vectorsai andgi, respectively. Then

ai 5 si 1 kgi, (1)

wherek is a constant that accounts for the magnitude anddirection of the induction effect.

The color of an object category is modeled as a proba-bility density function around itsprototypical color, whichplays the role of a centroid. The variability of the distribu-tion describes the spread, or the extent of differences,among the category members. The degree of variability canbe represented by the variance of the distributionsc

2, i.e., theaverage of the squared deviations from the mean. Thecategory distribution is proposed to have three sources ofvariability:

sc2 5 ss

2 1 s l2 1 sp

2. (2)

The first source is the variability in surface reflectance ofobjects distributionss

2. One can assume that the variance ofthe probability density function for the category “applecolor” might be bigger than for the category “banana color”because of a greater variability of apple surface colors innature. The second source is the variability in light illumi-nating the objects distributionsl

2. This variability is mostlikely to be similar for various objects. The third source isthe variability caused by perceptual phenomena distributionsp

2, e.g., the variation in appearance of object colors due toobject surroundings, adaptation, etc. This variation is deter-mined by the properties of the visual system and alsoassumed to be approximately equal for different objectcategories. In general, the statistical properties of the den-sity function representing an object category can be derivedfrom the frequency distribution of the apparent object colorsseen in the past. Note that, ifss

2 ! (sl2 1 sp

2), the totalspread of the category distributionsc

2 should beindepen-dentof object category.

The probability density function can be described moreaccurately by increasing the number of parameters. As afirst approximation, we adopt the assumption from GeneralRecognition Theory22 that the structure of natural categoriescan be effectively modeled by a multivariate normal(Gaussian) distribution. This model assumes (1) a very largenumber of exemplars within categories, (2) the dimensionsof categories are continuous-valued, (3) a category containsa few extremely atypical members, (4) the distribution ofexemplars within a category tends to be unimodal andsymmetrical. Apparently, these assumptions are disputable:there are some categories that do not completely possess allthese properties.

For example, in our preliminary experiments we havefound that the category “banana color” actually is not uni-

FIG. 2. Algorithmic aspect of memory colors. Vectors si andgi represent the surface color of image i and its backgroundcolor, respectively. Vector ai is shifted with respect to si due tothe induction effect of the background. hBi is the distancebetween apparent object color ai and prototype mB of categoryB with variance su and sv on u* and v* dimensions.

396 COLOR research and application

modal but has two maxima: “yellow banana” and “greenbanana.” Categories “apple color” and “pepper color” areclearer instances of multimodality. One of the obvious so-lutions is to consider an object as a member of a hierarchyof categories. For example, it is possible to describe thecategory of “banana color” as the conjunction of two sub-categories, namely “ripe banana color” and “unripe bananacolor,” which are both unimodal. Let the categoryB repre-sent the category of “ripe banana color” and its centroid bedenoted bymB. In a normal distribution, the mean, median,and mode are all equal, somB is a good candidate for theprototype. Let the prototypemB of the ripe banana berepresented by a point in theu*v* plane (see Fig. 2).

Similarity is modeled as the likelihood that an apparentobject sample belongs to the category and, therefore, isproportional to the function value of the category distribu-tion. If the category is described by a Gaussian probabilitydensity function, then the similarity is also assumed to beconsistent with a Gaussian distribution. The particular sim-ilarity between the apparent object colorAi and prototypicalcolor mB from Fig. 2 can be characterized by a bivariateGaussian distribution:

hBi 5 expS 2 1

2~1 2 r2! SSuAi 2 mBu

suD 2

2 2rSuAi 2 mBu

suDSvAi 2 mBv

svD 1 SvAi 2 mBv

svD 2DD , (3)

wherehBi is the similarity between apparent object colorAi

and prototypemB; uAi andvAi are correspondingu* and v*coordinates of apparent object colorAi in the CIELUVchromaticity plane;mBu andmBv are correspondingu* andv* color coordinates of prototypemB in the CIELUV chro-maticity plane; s2

Bu and s2Bv are the variances of the

category distribution onu* and v* dimensions; andr is thecorrelation coefficient ofu* and v* values of the categorydistribution in the CIELUV chromaticity plane. If thestrength of the viewing context is not significant, then Eq.(3) is equivalent to

hBi 5 expS 2 1

2~1 2 r2! SSuSi 2 mBu

suD 2

2 2rSuSi 2 mBu

suDSvSi 2 mBv

svD 1 SvSi 2 mBv

svD 2DD , (4)

whereuSi andvSi are correspondingu* andv* coordinates ofobject colorSi in the CIELUV chromaticity plane.

Another way of presenting the category distribution is viathe contours of equal likelihood. All points of the samecontour are associated with the same likelihood. Specifi-cally, the contours of equal likelihood are the set of allu*andv* that satisfy

hBi~u*,v* ! 5 e2d25 constant (5)

for some arbitrary constantd. It follows from Eq. (4) that

d2 51

2~1 2 r2! SSuSi 2 mBu

suD 2

2 2rSuSi 2 mBu

suDSvSi 2 mBv

svD 1 SvSi 2 mBv

svD 2D . (6)

The constantd can be regarded as the distance in theCIELUV chromaticity plane between the prototypemB andpoints of the same likelihood. To represent thedecisionboundfor the degree of similarity acceptable to an observer,we propose to used2 5 1/2. The distanced2 5 1/2 from theprototype to any given point of the category distribution canbe used to represent a “just-acceptable” chromaticity differ-ence. The notion of “just-acceptable” chromaticity differ-ences is comparable to the notion of “just-noticeable” chro-maticity differences studied by MacAdam.26

If values hBi, uSi, andvSi are known, we can derive thegeneral characteristics of the category distribution. How-ever, it is hardly possible to determinehBi directly. One ofthe alternatives is to use scaling methods and estimate theperceived similarityhperceived from the scaled similarityhscaledthat is determined experimentally. As a first choice,let hscaled increase approximately as a linear function ofhperceived. That is,

hscaled5 ahperceived1 b, (7)

wherea andb are scaling coefficients of the mapping fromthe perceptual scale to the response scale. It is important tonote that the response scale might be biased by stimulus setand experimental procedure.27–29

To summarize, we propose to (1) represent memory colorof an object by prototypical color of the correspondingobject category; (2) characterize the prototypical color by itssimilarity with apparent colors of object samples of thatcategory; (3) describe the perceived similarity by a multi-variate probability density function (e.g., Gaussian) in aperceptually uniform color space (e.g., CIELUV); (4) derivethe parameters of the probability density function fromexperimental research.

EXPERIMENTAL RESEARCH OF MEMORY COLORS

Aim of the Experimental Study

The following research was designed to provide experi-mental support for some of the main assumptions made inthe computational model of memory colors as discussedabove (see Fig. 1).

The first part of the research focuses on the comparisonstage of the model and specifies the representation of pro-totypical color of the category “ripe banana” in the CIELUVcolor space. The second part of the research focuses on theperception stage of the model and specifies the representa-tion of apparent colors of few banana samples in an appear-ance space. The third part of the research focuses on thegeneralization stage of the model and determines a samplingof surface colors of ripe bananas from a Dutch fruit market.

Volume 24, Number 6, December 1999 397

In Experiment 1, subjects scaled the similarity in color ofa banana shown on a CRT display and a typical ripe bananaas remembered from their past experience. In Experiment 2,observers scaled the differences in colors of two bananasamples displayed on the screen. In both experiments, threetypes of object depictions were used: (1) fruit, i.e., a bananaamong other fruits; (2) banana, i.e., the same banana againsta homogenous grayish background; and (3) contour, i.e., asilhouette of a banana with its average color against thegrayish background (see Plate 1). Note, that from types

(1)–(3) the amount of texture information and the natural-ness of the object depiction are decreased.

Three questions have been formulated for the first part ofthe research:

● Does the naturalness of object depiction influence thesimilarity judgments?

● How many parameters are needed to sufficiently describethe representation of prototypical color in the CIELUVcolor space?

PLATE 1. Examples of images used in Experiment 1 and Experiment 2. The CIELUV hue-angle values of each pixelrepresenting banana was rotated over (first column) 215 degrees, (second column) 0 degrees, (third column) 15 degrees forthe (upper row) “fruit,” (middle row) “banana,” and (lower row) “contour” images.

398 COLOR research and application

● Does the type of object depiction influence the represen-tation of prototypical color in the CIELUV color space?

Three questions have been formulated for the second partof the research:

● Does the type of object depiction influence the represen-tation of apparent colors in the appearance space?

● How many parameters are needed to sufficiently describethe representation of prototypical color in the appearancespace?

● Does the type of object depiction influence the represen-tation of prototypical color in the appearance space?

One question has been formulated for the third part of theresearch:

● How large is the variability of the surface colors incomparison with the variability of prototypical color?

Experiment 1: Prototypical Object Color

The aim of Experiment 1 is to specify the representationof prototypical color of the category “ripe banana” in theCIELUV color space.

MethodSubjects.Eight subjects, 4 females and 4 males, with normalor corrected-to-normal vision took part in the experiment.All were checked with the H-R-R PseudoisochromaticPlates30 and had no deficiencies in color vision. Their agesvaried between 20–30.

Stimuli.A set of common food items from a supermarketwas used to make a picture composition. The items (banana,potato, carrot, lime, orange, kiwi, tomato, plum, peas, greenand blue grapes, green and red apples, and green, red andyellow pepper) were arranged together with a set of Kodakcolor control patches on a fairly neutral cloth under naturaldaylight (correlated color temperature 5400 K) and werephotographed using a Pentax P30 Professional Photocam-era. The slide used in the experiment was selected fromseveral originals on the basis of object distance, exposurerange, and overall quality impression. Red, green, and bluegray-values for video signals were obtained by scanning theslide and digitizing it with 8 bits per pixel on a grid of5123 512 pixels using a Leaf System Leafscan 35-SCSI. Aregion of interest of 4483 450 pixels was selected forfurther image processing.

The digitized image was described by its color pointdistribution in the CIELUV color space through the sequen-tial transformation ofr, g, b gray values to absoluteR, G, Bluminance values, then to theX, Y, Ztristimulus values, and,eventually, to theL*, u* , and v* color coordinates. Thetransformation into the CIELUV space was made by usingstandard formulae.31 Each color point corresponded to onepixel. Reference white wasD55 with the CIE 1931 chro-maticity coordinates (xw, yw) 5 (0.332, 0.347). The CIE

1931 (x, y) chromaticity coordinates of the green, red, andblue phosphors of our monitor, measured by the Spectrara-diometer SpectraScan PR-650, were: (xr, yr) 5 (0.619,0.349), (xg, yg) 5 (0.308, 0.594), (xb, yb) 5 (0.148, 0.073).

The two types of banana depiction, namely “fruit” and“banana,” were distinguished only by the characteristics oftheir backgrounds. The image of the original scene was usedas the “fruit” depiction. The “banana” depiction was con-structed by cutting out the banana from the other fruits andby filling in a homogenous background in the rest of theimage. To produce the background, the colors of all thepixels belonging to the table cloth were determined andaveraged in terms of theL*, v*, and v* color coordinates.Thus, the background had the average lightness, chroma,and hue of the original surroundings with the exception ofthe fruits. For the third type of depiction, namely “contour”,the silhouette of the banana with its average color againstthe same background as in the “banana” stimuli was used.Photographs of these three scenes are further called masterimages. The color point distributions of the master imagesin the CIELUV chromaticity plane are presented in Fig. 3.

For each master image, a set of new images was preparedby changing the CIELUV chroma and hue-angle values foreach pixel of the banana, while its lightness and the rest ofthe images were kept constant. For the chroma changes, thechroma value of each pixel in the master images was mul-tiplied by the constants 0.7, 0.8, 0.9, 1.0, 1.1, 1.2, 1.3. Forthe hue changes, the hue-angle values were rotated by215,210, 25, 0, 5, 10, 15 degrees. This image processing wasaimed to imitate the different colors of a banana and coverthe main part of its variation in nature. If, during theprocessing of the images, calculated values were out of thepossible range for the gray values of the monitor, the nearestpossible value of the chroma was used without changing thehue (clipping). Plate 1 presents a few examples of theprocessed images. Averaged color coordinates of the whole7*7 set of the “fruit” and “banana” stimuli together with twocorresponding backgrounds in the CIELUV color space areshown in Fig. 4.

The images were displayed by an Image Sequence Pro-cessor ISP500 of a Digital Video System. A high-resolution50 Hz noninterlaced BARCO CCID7351B color monitordriven by a SUN-3/260 workstation was used to present thestimuli. The monitor was colorimetrically characterized andcalibrated by using a Look-Up-Table technique in such away that the total gamma, i.e., the luminance transfer,equals one for the whole chain reality-slide-scanner-moni-tor. Screen luminance measured by the Luminance meterLMT L1003 ranged from 0.01–70 cd/m2.

Because of unavoidable inaccuracies in all stages of animage preparation process, it is not possible to produce aperfect match in chromaticity coordinates between real anddisplayed objects. The magnitude of the mismatches in thecolor reproduction was evaluated by comparing the originalCIE 1931 (x, y) chromaticity coordinates of the Kodak colorcontrol patches at the moment of taking the picture withthose reproduced by the monitor. The absolute values of the

Volume 24, Number 6, December 1999 399

differences were 0.0136 0.007 forx and 0.0106 0.010 fory chromaticity coordinates.

Procedure.The experiments were run in a dark roomwith a white dimly lit 2.5 cd/m2 background behind themonitor. The subjects were seated approximately 1.5 m

from the screen. The images were displayed with flexibletiming until the subjects gave a response. The intervalbetween two image exposures was 4 s, during which a 6.7cd/m2 (i.e., approximately the mean luminance of the wholeset of images) gray adaptation field appeared on the screen.During a 5-min period of adaptation to the room illumina-tion and screen luminance, the subjects studied instructionsand then performed a training series of 10 stimuli to famil-iarize themselves with the experimental procedure and toestablish an internal scale sensitivity.

The instructions stated that the purpose of the experi-ments was to investigate memory colors, namely, “colorsthat are recalled in association with familiar objects.” Thesubjects’ task was to judge the similarity in colors betweenthe banana samples displayed on the screen and a typicalripe banana as they remembered it from their experience,using an 11-point numerical category scale: from 0 (nosimilarity between perceived and remembered colors) to 10(complete similarity between perceived and rememberedcolors). The experiments were divided into six sessions (twosessions per presentation) with a random intra/inter-subjectorder. For each presentation, all 49 images were randomlyshown 2 times in 2 separate sessions. Each experimentalsession lasted approximately 25 min.

ResultsTo minimize the effect of different scaling constants fordifferent subjects, the data obtained for each observer werestandardized viaz-score transformations24 by subtractingthe mean and dividing by the standard deviation of theindividual scales. The comparison of intra-subject scores(among 4 replications per subject) with inter-subject scores

FIG. 4. Averaged u* and v* color coordinates of the(square) “banana” and (circle) “fruit” stimuli used in (smallopen symbols) Experiment 1, (small black symbols) Experi-ment 2, and (large gray symbols) the two backgrounds.

FIG. 3. Color point distribution in the CIELUV color space forthe master (a) “fruit,” (b) “banana,” and (c) “contour” images,projected on the u* v*-plane (every 16th point plotted).

400 COLOR research and application

(among 8 observers per three object depictions) did notreveal systematic differences. Therefore, we combined theindividual z-scores of 32 trials and converted them to acommon scale by adding the mean and multiplying by thestandard deviation of the averaged scales.

Figure 5 presents the averaged similarity-to-prototypical-banana-color judgments for 7 images with a chroma con-stant equal to 1 (left pictures) and for 7 images with hueshift equal to 0 (right pictures) plotted vs. the CIELUV hueand chroma differences with the original. The data areleast-squares fitted by Gaussian curves. The hue and chromadifferences with the original are shown in Fig. 4. Figure 6shows an example of individual differences in the similarityjudgments of “fruit” images.

The averaged similarity judgments were characterized bya bivariate normal distribution [see Eq. (4) and Eq. (7))].The scaling constantb from Eq. (7) was assigned to zero,because in the previous research10 we found that, for thestimulus set containing a large variation of samples,hscaled

increases approximately in proportion tohperceived. Thisimplies the assumption that the judgments were made on

ratio scales. Five parameters were determined by least-squares fitting:mBu andmBv, i.e., correspondingu* and v*coordinates of prototypical colormB in the CIELUV chro-maticity plane;su

2 andsv2, i.e., the variances of the category

distribution onu* and v* dimensions;r, i.e., the correlationcoefficient of theu* and v* values in the category distribu-tion (see Fig. 7). The valuesmBu and mBv specify thelocation of the mean of the distribution,su

2 andsv2 specify

the spread of the distribution, the ratiosu/sv specifies theshape the distribution, the valuer specifies the orientationof the distribution. Figure 8 shows the best-fit of a Gaussiansurface and the contours of equal likelihoodd2 5 1/2(further referred to asd-ellipses) on the grid of stimuli in theCIELUV chromaticity plane.

An analysis of the distribution parameters reveals thefollowing effects. As can be seen in Fig. 9, the threedistributions have similarorientation, which corresponds tothe angle of inclination of the major ellipse axis to the axisof theu*-coordinates. The major ellipse axes approximatelyagree with the chroma direction, and the minor ellipse axeswith the hue direction.

The shape, which corresponds to the ratio of the majorand minor axes, is also similar for the three distributions.Apparently, the variances of the distributions representingthe similarity judgments in the CIELUV color space arebigger in the chroma dimension than in the hue dimension.This implies that subjects were more tolerant to the varia-tion in the banana colors along the chroma direction than tothe variation along the hue direction.

Thespread, which corresponds to the total area within theellipses, of the “banana” and “fruit” distributions is slightlysmaller than that of the “contour” distribution (see also Fig.7). The d-ellipses are proposed to represent the decision

FIG. 6. An example of (dots) individual differences and(circles) averaged scores of the similarity judgments for“fruit” images. The axes are the same as the ones in Fig. 5.

FIG. 5. The averaged similarity-to-prototypical-banana-color judgments vs. the (left) CIELUV hue and (right) chromadifferences with the master image for (top) “fruit,” (middle)“banana,” and (bottom) “contour” images. The data areleast-squares fitted by Gaussian curves. The vertical barsindicate the standard error of the mean.

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bounds for the degree of similarity between perceived andprototypical object colors that is acceptable to an observer.Given this model, the decision bound varies for the threeobject depiction. Although these differences are not big,they are in agreement with the observer’s remarks that thesimilarity judgments were more difficult to make with the“contour” images than with the “fruit” and “banana” im-ages. The difficulty is caused by an obstacle in interpretingthe “contour” colors as object colors. The same obstaclemight produce the differences in the total variance of inter-subject scores (see Fig. 10). In conformity with the predic-tion postulated above, the more natural the objects look, themore easily and consistently they are compared with theprototypical color.

The location, which corresponds to the center of theellipses, of all three distributions in Fig. 9 is close to themaster stimuli, but moved towards a slightly more saturatedpoint. Evidently, there also is a significant shift in locationamong the three distributions. The center of the “banana”distribution is slightly more saturated than that of the “fruit”distribution, and slightly more reddish than that of the“contour” distribution.

To summarize the main results of the experiment, (1) thenaturalness of the banana depiction facilitates the similarityjudgments between the apparent and prototypical colors; (2)the similarity judgments representing the prototypical ba-nana color in the CIELUV space can be sufficiently de-scribed by five parameters of a bivariate normal distribu-tion; (3) the location and spread of the distributionrepresenting the prototypical banana color in the CIELUVspace vary for the three types of object depiction.

DiscussionIt should be noted that the spread and location of thedistribution representing the prototypical banana color

FIG. 7. The statistical parameters of the bivariate normaldistribution representing the similarity judgments in the CIE-LUV color space. The vertical bars indicate 95% confidenceintervals of the fit. The dashed lines indicate the averagevalues.

FIG. 8. The (dots) similarity judgments least-squares fitted by a Gaussian surface and d-contour maps on the grid of stimuli.The hue and chroma differences are the same as in Fig. 5.

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might be biased by the range and centroid of the stimulus setused in the experiment. We studied the impact of the stim-ulus range on the basic parameters of the distribution in apreliminary experiment and found that the orientation,shape, and location of the distributions were not influencedby the stimulus range. The spread of the distribution growsmonotonically with the stimulus range up to a certain de-gree. When the stimulus range (represented by the varianceof the u* and v* values of the stimuli) is sufficiently large,as it is in Experiment 1, its impact on the spread of thedistribution is negligible. For published data of a similarresearch and justification of assumption of ratio scale seeYendrikhovskijet al.10

The impact of the centroid of the stimulus set could berevealed by a tendency of the subjects to scale the sim-ilarity with the mean of the stimulus set rather than theprototypical color held in their memory. We calculatedthe centroids for the three stimulus sets used in Experi-ment 1 and found that they were slightlylesssaturatedthan the originals, i.e., master images. This was due to thepartial clipping of highly saturated values of the bananastimuli. Figure 9 shows that the centroids of the distri-butions representing the similarity judgments for the“fruit”, “banana,” and “contour” stimuli aremore satu-rated than the master images. Therefore, even if thecentroid-effect influenced the subjects’ response, this in-fluence was probably not large. The precise impact of thecentroid-effect requires comparison of the similarityjudgments of stimulus sets with different centroids,which is a subject for future research.

Experiment 2: Apparent Object Colors

The aim of Experiment 2 is to specify the representationof apparent colors of 15 stimuli used in Experiment 1.

MethodSubjects.Eight subjects took part in the experiment, only 4of them participated in Experiment 1. Other subject char-acteristics were similar to those in Experiment 1.

Stimuli. From the same set of stimuli as in the previousexperiment, 15 images (5 for each banana depiction) werechosen to run the study (see Fig. 4). To present two stimulisimultaneously, we deleted an area of 89*450 pixels (i.e.,20%) from the left side of each image.

Procedure. The viewing conditions were identical tothose in Experiment 1. The instructions stated the purposeof the experiment “to investigate the differences in colorappearance of objects.” The subjects’ task was to judge thedifference in apparent color between two bananas presentedsimultaneously on the right- and left-hand side of the mon-itor screen. They were allowed to use the integer numbersfrom 0 (no difference in apparent colors) to 10 (maximumdifference in apparent colors). Before the actual experiment,the subjects estimated a training series of 10 stimuli tofamiliarize themselves with the experimental procedure andto establish an internal scale sensitivity. The stimuli werecombined to form 225 stimulus pairs. These pairs werepresented once in a random order in two sessions, yieldingfour repetitions per pair ignoring the presentation positionon the monitor.

Results: Obtained-Appearance SpaceTwo 15*15 matrices of color differences between the im-ages were obtained for each observer. These matrices werecombined in one averaged lower-half matrix per subjectbefore they were processed by the Symmetrical INDSCAL(SINDSCAL) program (e.g., Schiffmanet al.32; Greenet

FIG. 9. The (solid curves) best-fitting Gaussian d-contourellipses and (dashed curves) 95% confidence intervals rep-resenting the similarity judgments in the CIELUV chromatic-ity plane for (circle) “fruit,” (square) “banana,” and (triangle)“contour” images. Cross denotes the master images.

FIG. 10. The total variance of inter-subject scores for thethree types of object depictions.

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al.33). This program represents data by points in a multidi-mensional Euclidean space, such that the distances betweenthe points are linearly related to the corresponding differ-ence judgments. The advantage of this program is the pos-sibility of finding a common space that holds for all thesubjects as well as individual spaces for each subject. Withan iterative least-squares procedure, the program determinesthe stimulus coordinates and the dimension weights thataccount for the maximum variances in matrices of scalarproducts derived from the experimental data. The correla-tion r between the scalar product and the computed scoresindicates the goodness-of-fit.

An analysis of individual spaces did not reveal consider-able differences and only the common two-dimensionalspace (r 5 0.90) obtained for all subjects is discussed here.This space (further referred to as obtained-appearancespace) is shown in Fig. 11(a). The data demonstrate smallbut systematic differences between locations of the apparentcolors for the three object depiction. The “fruit” stimuli areslightly shifted in the unsaturated-greenish (U-G) direction,and the “contour” stimuli in the unsaturated-reddish (U-R)direction relative to the “banana” stimuli. The differencesbetween the locations of the apparent colors might becaused by two effects: (1) mode-effect in representing ob-ject colors, and (2) induction-effect in representing apparentobject colors, which are discussed in the following section.

Results: Predicted-Appearance SpaceThe differences between the apparent “banana” and “con-tour” stimuli can be explained by the mode-effect. Beforestarting the experiments, we assumed that the object colorcould be represented by the mean of all colors belonging toan object surface. Consequently, the “contour” master im-age was produced with the sameaveragechromaticity asthe “banana” master image. However, the object color canalso be represented by themode, i.e., the most frequentvalue. If the internal-apparent representation of the bananacolor is determined by the mode, then the external-stimulusrepresentation of the banana color of the “contour” imageshould also have been chosen as the mode. The “banana”stimuli in Fig. 11(a) are shifted towards a slightly moregreenish point compared with the “contour” stimuli. Thisshift is approximately in the same direction and has aboutthe same magnitude as the one resulting from applying themode instead of the mean as the representation of thebanana color [see Fig. 11(b)]. The color coordinates of themode were computed from histograms of the pixels repre-senting “banana” stimuli in the CIELUV color space andcorresponded to the value with the highest number of pixelson theu* and v* dimensions.

The differences between the apparent “banana” and“fruit” stimuli can be explained by theinduction-effect. Thebackgrounds of the “banana” and “fruit” stimuli haveslightly different average chromaticities and, therefore, theobservers’ adaptation states in the two conditions are notexactly the same. As a result, the “banana” and “fruit”stimuli might have different apparent colors due to the

influence of chromatic adaptation on color appearance (e.g.,Webster and Mollon34). If this is true, the same induction-effect should also be observed in the previous experiment.

FIG. 11. (a) Obtained-, (b) predicted-, and (c) calculated-appearance spaces of 15 apparent object colors for (circle)“fruit,” (square) “banana,” and (triangle) “contour” images.G, S, R, and U denote greenish, saturated, reddish, andunsaturated directions from the master image, respectively.

404 COLOR research and application

In fact, by means of Eq. (1), it is possible to derive thecoordinates of the apparent “banana” and “fruit” colorsfrom the results of Experiment 1. The only unknown pa-rameter in this equation is a constantk describing themagnitude of the induction effect. This constant was calcu-lated from the distance between coordinates of the centersof the two distributions representing similarity estimates ofthe “banana” and “fruit” stimuli (see Fig. 9). Figure 11(b)shows the location of 5 apparent colors of the “fruit” stimuliobtained by the shiftk from the “banana” stimuli.

In general, Fig. 11(b) can be interpreted as a spaceshowing the location of 15 apparent object colors predictedfrom Experiment 1 on the basis of the mean-mode andinduction effects. This space (further referred to as predict-ed-appearance space) is largely in agreement with the ob-tained-appearance space from Experiment 2 [Fig. 11(a)].Both spaces demonstrate a small but systematic shift of the“fruit” stimuli in the unsaturated-greenish (U-G) direction,and the “contour” stimuli in the unsaturated-reddish (U-R)direction relative to the “banana” stimuli. The only dis-agreement between the predicted-appearance space and theobtained-appearance space is with the chroma values of afew “contour” stimuli.

It is interesting to note that, although the metrical prop-erties of both spaces are very similar, there are two smalldifferences that can be seen in Fig. 11. First, the distancebetween points in the chroma direction (S-U) of the ob-tained-appearance space is slightly smaller than in the huedirection (R-G), while in the predicted-appearance spacethese distances are almost identical. It seems that the sub-jects underestimated the apparent chroma differences incomparison with the apparent hue differences of the dis-played banana stimuli. Second, the distance between satu-rated (S) and reddish (R) points of the obtained-appearancespace is slightly larger than the distance between unsatur-ated (U) and reddish (R) points, while again in the predicted-appearance space these distances are almost identical. Itindicates that there is some small correlation between thechroma and hue values in the obtained-appearance space.

Results: Calculated-Appearance SpaceThe metrical differences between the obtained-appearancespace and predicted-appearance space can be reduced bymeans of a matrix transformation procedure called MAT-FIT.35 Let us consider thex, y coordinates of the stimuli inthe obtained-appearance space as a 2-dimensional orthogo-nal matrix O, and theu* , v* coordinates of stimuli in thepredicted-appearance space as 2-dimensional orthogonalmatrix P. The MATFIT algorithm finds an optimal trans-formation matrixT, such that the correlation betweenO andTP for the given stimulus configuration is maximal. Sincewe do not know the characteristic of the mapping functionfrom the CIELUV to the SINDSCAL metrics, both linearand nonlinear transformations on theu* and v* axes wereapplied. The matrixT derived by the MATFIT procedurewas used to transform the coordinates of the stimuli in thepredicted-appearance space to new coordinates in a calcu-

lated-appearance space [see Fig. 11(c)]. On the one hand,the calculated-appearance space has the advantage over thepredicted-appearance space that it more closely resemblesthe actual appearance of object colors determined in theexperiment. On the other hand, the calculated-appearancespace has the advantage over the obtained-appearance spacethat it can represent not only the 15 stimuli, but the wholeset of images used in Experiment 1.

The averaged similarity judgments of Experiment 1 werecharacterized by a bivariate normal distribution in the cal-culated-appearance space. The agreement between the sim-ilarity judgments derived experimentally and those calcu-lated on the assumption of a normal distribution is good:correlation between the model and experimental data isr 50.957 for the “fruit”, r 5 0.917 for the ”banana,“ andr 50.955 for the “contour” stimuli (see Fig. 12). The statisticalparameters of the density functions are shown in Fig. 13.The differences between the parameters for the three objectdepictions are smaller than the ones obtained in Experiment1 for the CIELUV color space (compare Fig. 13 with Fig.7). The result that the average correlation coefficientr of theu* and v* values in the category distribution is close to 0implies that the number of parameters needed to sufficientlydescribe the similarity judgments in the calculated-appear-ance space is reduced to four: two chromaticity coordinatesof the prototype and two variances of the category distribu-tion. Using the fact that there are only small differencesbetweensu and sv, the number of parameters could bedecreased down to three.

Figure 14 shows the best-fit of Gaussiand-ellipses rep-resenting the similarity judgments in the calculated-appear-

FIG. 12. Scatter diagram of experimentally determineddata and those calculated on the assumption of a normaldistribution for (circle) “fruit,” (square) “banana,” and (trian-gle) “contour” images.

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ance space. One of the remarkable results seen from thisfigure is that the distributions are less elongated and moreoverlapping in comparison with the ones shown in Fig. 9.This implies that the shift between the distributions repre-senting the prototypical color, the tolerance to the chromadifferences, and the correlation between the hue and chromavalues found in Experiment 1 have approximately the samedirection and magnitude as the shift between the apparent

colors, the underestimation of the chroma differences, andthe correlation between the hue and chroma values found inExperiment 2.

To summarize the main findings of the experiment, (1)the location of apparent colors in the obtained-appearancespace vary for the three object depictions, probably due tothe mode-effect and the induction-effect; (2) the similarityjudgments representing the prototypical banana color in the

FIG. 13. The statistical parameters of the bivariate normal distribution representing the similarity judgments of Experiment1 in the calculated-appearance space. The vertical bars indicate 95% confidence intervals of the fit. The dashed lines indicatethe average values.

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calculated-appearance space can be sufficiently describedby three parameters of a bivariate normal distribution; (3)the distribution representing the prototypical banana colorin the calculated-appearance space does not vary much forthe three types of object depiction.

DiscussionThe results of Experiment 2 suggest that the differences inlocation between the distributions representing similarityjudgments for the three object depiction found in Experi-ment 1 can be explained by the difference in appearance ofthe object colors. Siple and Springer11 argued that access tomemory for object color is independent of the object con-text. They compared memory colors of food items with andwithout shape and texture cues, and concluded that thesecues did not produce any differences in location of memorycolor selection. We found small differences in location ofthe prototypical object colors in the CIELUV color space,but come to the same conclusion. The results of Experiment2 demonstrate that these differences might be due to themode-effect and the induction-effect.

The outcomes of the experimental research with the threeobject depictions lead to the discussion whether apparentand prototypical colors are invariant. The location of theprototypical color, derived from the similarity judgments ofExperiment 1, seems to be independent of the object depic-tions in the calculated-appearance space, but not in theCIELUV color space. Therefore, the prototypical colorsmight be invariant on the level of apparent object colors, butnot on the level of colorimetric object colors. The locationof the apparent colors, derived from the difference judg-

ments of Experiment 2, vary for the three object depictionsin the obtained-appearance space. In particular, apparentcolors of exactly the same objects in the “fruit” and “ba-nana” depictions were perceived differently due to the effectof the object surroundings. Although the differences foundin our experiments are rather small, the surroundings effectcan be more impressive (e.g., see Fairchild25 for a recentreview) and affect not only appearance but color name aswell. For example, McFaddenet al.36 shown that somechromaticities were labeled purple with a red surround,whereas with a blue surround they were labeled pink. Itseems that the visual system incorporates the object in acontext-dependent appearance. The context-dependent ap-pearance is also expressed in the phenomenon known ascolor constancy, i.e., the perceived invariance of objectcolors under different illuminants.

One of the main problems of color constancy is thathuman color vision exhibits onlyapproximatecolor con-stancy (see Thompsonet al.37 for ecological reasoning) andits degree depends on the experimental task,38,39 learningand illuminant familiarity,40 and complexity of the scene inview.41 For example, Jin and Shevell41 studied the relation-ship between color memory and color constancy for twoexperimental conditions. In their experiments, a test colorwas surrounded by either a complex pattern composed ofseveral color patches or a simple pattern composed of auniform gray field. They reported that results with thecomplex surround were consistent with a surface-reflec-tance hypothesis, which states that the color recalled frommemory is based on an inferred spectral reflectance of asurface independent of the spectral distribution of the illu-minant; while the results with the simple surround primarilysupport the photoreceptor hypothesis, which states that thecolor recalled from memory is determined by the lightabsorbed by each type of cone. These findings are in agree-ment with computational models implying that color con-stancy increases with the number of distinct chromaticitiesin view.42

Returning to our example of the person searching for hisfavorite ripe banana, we can conclude that perceptual phe-nomena might influence the observer’s choice. From thesame set of fruits, the person might pick out differentbananas in the supermarket compared to outdoors simplydue to the fact that the fruits might appear to be differentunder different illuminating conditions or surroundings.This chance is even bigger, if he participates in an experi-ment with an artificial stimuli when banana colors arerepresented by color patches and the complexity of thescene in view is limited. However, the inconsistency of theobserver’s choice does not necessarily imply the inconsis-tency of memory color, which might be invariant in theobserver’s appearance space.

Population of Object Colors in Nature

The aim of this investigation was to determine the sam-pling of ripe banana colors in the CIEu’v’ chromaticity

FIG. 14. The (solid curves) best-fitting Gaussian d-ellipsesand (dash curves) 95% confidence intervals representing thesimilarity judgments of Experiment 1 in the calculated-ap-pearance space. Symbols are the same as in Fig. 9.

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diagram and compare it with the similarity-to-prototypical-banana judgments derived from Experiment 1.

The sampling was obtained by 100 measurements ofbananas from a Dutch fruit market. The measurements werecarried out using a Spectraradiometer SpectraScan PR-650from eye level. The choice of location, object, and measure-ment areas was random, i.e., the Spectraradiometer was“blindly” pointed towards a branch of bananas. Beforetaking the measurement, we checked whether it was reallypointed towards a banana surface. If not, it was directedtowards the closest surface. For every 10 different locations(10 samples per location), a reference white was also mea-sured.

Figure 15 shows the CIEDu and Dv coordinates of themeasured samples together with the best-fit of 2d- and 3d-ellipses of the Gaussian distribution representing thesesamples, and thed-ellipse of Gaussian distribution repre-senting the similarity judgments of Experiment 1 for the“fruit” stimuli. Both distributions are similar in their shapeand orientation, but not in location and size. The mean ofthe distribution representing the similarity judgments isslightly shifted towards more saturated points than the meanof the object sample distribution. The effect, however, is notlarge, and considerably smaller than the shift in the huedirection. The size of thed-ellipse of the similarity judg-ments is approximately 2.5 times bigger than thed-ellipsefor the measured samples.

The presented measurements of the surface samples isjust a first step in investigating the complex relationshipsbetween memory colors and statistics of the outside world.However, even these preliminary and rather arbitrary mea-surements lead to the following important conclusions.First, the measurements show that the shape and orientationof the distribution representing the prototypical bananacolor correspond well with the shape and orientation of thedistribution representing the population of the banana sur-face colors. As far as we know, this is one of the firstcomparison of these attributes (most of the previous re-search on memory colors was limited by comparison of themean values only). It provides a direct evidence that theformation of memory colors might indeed be determined bythe statistics of object colors seen in the past. Second, themeasurements show that the variability of the surface colorsis approximately 2.5 times smaller than the variability of thedistribution representing the prototypical color. Therefore,the size of the surface variability is most likely to be small,but not negligible. This conclusion indicates that the totalspread of the category distribution probably is dependent onobject’s category [see our discussion with respect to Eq.(2)].

General Discussion and Future Research

This article gives an insight into the phenomenon ofmemory colors and provides the framework for their formalspecification. We present a computational model of memorycolors and propose to characterize them from similarity

judgments, i.e., experimentally determined similarity judg-ments of apparent object colors with the prototypical colorof the corresponding object category. The similarity judg-ments can be described by a multivariate probability densityfunction (e.g., Gaussian) in a perceptually uniform colorspace (e.g., CIELUV). Two aspects have to be emphasizedhere. First, we have considered memory colors within aframework of categorization, which is one of the fundamen-tally important processes for perception and cognition ingeneral (e.g., Ashby22; Rosch17) and for color vision inparticular (e.g., Boynton and Olson43; Uchikawa and Shi-noda44; see Saunders and Brakel45 for discussion). Thecategorical aspectis essential to understand memory colorsand refers to the semantic level of their specification. Sec-ond, we have represented memory colors by a Gaussianprobability density function in the CIELUV color space.The type of the function and the space isnot essential tounderstand memory colors and refers to the algorithmiclevel of their specification. The Gaussian function and theCIELUV space were chosen as a first approximation, butother functions and spaces can also be used. For example,color categories can be modeled employing fuzzy settheory,46,47and the recently proposed CIECAM97’s space48

might be a better choice to model the appearance space.The results of Experiment 2 for the “fruit” and “banana”

stimuli show that apparent colors of exactly the same ob-jects were perceived differently due to the effect of theobject’s surroundings. It seems that the visual system doesnot correct for this effect and incorporates the object in acontext-dependent appearance. Roughly speaking, this leads

FIG. 15. The (dashed lines) best-fitting 2 d- and 3 d-el-lipses of the Gaussian distribution representing the mea-sured samples of banana colors, and the (solid line) d-ellipseof the Gaussian distribution representing the similarity judg-ments for the “fruit” stimuli in the CIE u’v’ chromaticitydiagram.

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to the fact that a banana on a very blue background mightlook slightly more yellow than exactly the same banana ona very yellow background. What are the biological or eco-logical reasons that the visual system works in this manner?What are the advantages and disadvantages of such a pro-cess? So far one can only speculate that despite the obviousdisadvantage in establishing dissimilarity in color appear-ance of identical objects due to their context, the visualsystem apparently gains something from processing infor-mation globally, i.e., over the whole field of view (seeThompsonet al.37; Thompson49 for discussion). The advan-tage of global processing might be related to another in-triguing phenomenon known as approximate color con-stancy, i.e., the relatively stable appearance of object colorsunder various illuminants. It would be interesting to inves-tigate an effect of color categories on color constancy. Someexperiments50–52 have already been started in these impor-tant directions, but more research is needed.

For the present, the relation between outside world sta-tistics and memory representations is also an issue for opendiscussion. We have measured samples of banana colorsand compared the parameters of the distributions describingthese samples with those describing the similarity judg-ments. The closeness of both types of distributions in theirshape and orientation indicates that the formation of mem-ory prototypes for object colors might be determined by thepopulation of object colors seen in the past. But the differ-ences in location and spread of these distributions suggestthat the determination should not be considered straightfor-ward. For example, the fact that the variability of the dis-tribution representing the prototypical color is approxi-mately 2.5 times bigger than the variability of the measuredsamples might be caused by a number of factors. In general,the spread of the category’s distribution can be influencedby (1) variability in the surface reflectance statistic, (2)variability in the illuminant statistic, (3) variability in theperceptual domain [see Eq. (2)]. It would be interesting toinvestigate the impact of these variables on the formation ofprototypical colors in more detail. For example, one cananalyze the representation of memory color of a well-knownobject exhibiting very limited variation in surface reflec-tance, e.g., cash bank-notes. This would give an approxi-mate estimate of variability in the illuminant and perceptualdomain only.

CONCLUSIONS

We introduce a computational model of memory colors,which (1) represents memory color of an object by proto-typical color of the corresponding object category; (2) char-acterizes the prototypical color by its similarity with appar-ent colors of object samples of that category; (3) describesthe perceived similarity by a multivariate probability den-sity function in a perceptually uniform color space.

Experiment 1 specifies the representation of prototypicalcolor of the category ”ripe banana“ in the CIELUV colorspace for the three object depictions and shows that (1) the

naturalness of the banana depiction facilitates the similarityjudgments between the apparent and prototypical colors; (2)the similarity judgments representing the prototypical ba-nana color in the CIELUV space can be sufficiently de-scribed by five parameters of a bivariate normal distribu-tion; (3) the distributions for the three object depictions inthe CIELUV space have similar shape, orientation, but notthe same spread and location.

Experiment 2 specifies the representation of apparentcolors of 15 stimuli used in Experiment 1 and shows that (1)the location of apparent colors in the obtained-appearancespace vary for the three object depictions; (2) the similarityjudgments representing the prototypical banana color in thecalculated-appearance space can be sufficiently describedby three parameters of a bivariate normal distribution; (3)the distributions for the three object depictions in the cal-culated-appearance space have similar shape, orientation,spread, and location.

We also determined the sampling of 100 ripe bananacolors in the CIEu’v’ chromaticity diagram and showed that(1) the shape and orientation of the distribution representingthe prototypical banana color were consistent with the shapeand orientation of the distribution representing the popula-tion of the banana surface colors; (2) the variability of thesurface colors is approximately 2.5 times smaller than thevariability of the distribution representing the prototypicalcolor.

ACKNOWLEDGMENTS

The authors wish to thank Prof. J. A. J. Roufs, Prof. Ch.M. M. de Weert, Dr. E. A. Fedorovskaya, and T. J. W. M.Janssen for their helpful comments and valuable adviceduring the preparation of the manuscript, and G. KleinTeeselink for her contribution in preparing the photographs.

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