on attributes of achromatic and chromatic object-color perceptions

On Attributes of Achromatic andChromatic Object-ColorPerceptions

Yoshinobu Nayatani*Oomori-cho 12-11, Nishinomiya 663-8023, Japan

Received 3 June 1999; accepted 17 December 1999

Abstract:Adapting luminance dependencies of various colorattributes of object colors (lightness, brightness, whiteness-blackness, whiteness-blackness strength, chroma, and color-fulness) were clarified under white illumination with variousadapting illuminances. The correlation between the percep-tions of lightness and brightness and those of whiteness-black-ness and whiteness-blackness strength is also clarified forachromatic object colors. The difference between the increaseof brightness and that of whiteness-blackness contrast (theeffect studied by Stevens and Jameson—Hurvich) by raisingtheir adapting illuminance is resolved without any contradic-tion. It is also shown that the nonlinear color-appearancemodel developed by the author and his colleagues is able toexplain the complex characteristics of all the above colorattributes of object colors by making minor modifications to it.In addition, two kinds of classifications of various color at-tributes are given; one is based on the similarity of perceptionlevel, and the other on the degree of adapting illuminancedependency.© 2000 John Wiley & Sons, Inc. Col Res Appl, 25, 318–332,

2000

Key words: lightness; brightness; whiteness-blackness;whiteness-blackness strength; chroma; colorfulness; oppo-nent-colors responses; adapting illuminance dependency

INTRODUCTION

The color attributes of object colors are psychologicallycomplex. Furthermore, there are several systems of denot-ing such attributes. For example, Munsell Value andChroma are attributes specific to a color sample. Any Mun-sell color notation has its corresponding color sample irre-spective of illuminant and adapting illuminance. See item(1) of Notes at the end of the article. As correlates of

lightness and chroma attributes, we also have the CIE sys-tem of metric lightness and metric chroma. Their values fora color sample also do not change with change of adaptingilluminance. However, the attributes of lightness andchroma may well be affected by changing the adaptingilluminance for a color sample. For this reason, the formu-lation of all the psychological correlates of color attributesof object colors remains an important problem in colorim-etry and color vision. The purpose of the present article is toclarify the relations between the color attributes of lightness,brightness, chroma, colorfulness, whiteness-blackness, andwhiteness-blackness strength of object colors. The percep-tions on whiteness and blackness rarely have been discussedin the field of colorimetry. The present study applies only towhite illumination (D65 or C) with variable adapting illu-minances.

Even limiting the illumination to white and the stimuli toobject colors, we still have the perceptions of lightness andbrightness for achromatic attributes, and of chroma andcolorfulness (or chromaticness) for chromatic ones. Gener-ally it is believed that lightness relates to chroma, andbrightness to colorfulness at the level of object-color per-ception. The relations are found from their definitions in theInternational Lighting Vocabulary,1 shown in Appendix 1for the reader’s convenience. Throughout the present article,the term “perception” is used for each color attribute ofobject colors rather than “sensation.” The terms are ex-plained in Appendix 1. By raising adapting illuminance butkeeping the same white illuminant for any object colorsample, generally its color perceptions change dependingupon the kinds of color attributes. However, it is verydifficult to distinguish, for example, colorfulness fromchroma in actual observations for naive subjects in anyexperiment using subjective estimation, even when theirCIE definitions are shown to them. The distinction betweenchroma and colorfulness may be difficult even for experts inthis field.

* Correspondence to: Yoshinobu Nayatani (e-mail: [email protected])© 2000 John Wiley & Sons, Inc.

318 COLOR research and application

Limiting color samples to achromatic ones, there is an-other important attribute called “whiteness-blackness.” Tothe general public, the attribute of whiteness-blackness ismore fundamental and familiar than that of lightness inobject-color perception. The whiteness-blackness is also animportant concept in the opponent-colors theory of Hering,2

and it is also used as an important color scale in the SwedishNatural Color System (NCS).3 Furthermore, the degree ofwhiteness-blackness perception is affected by changing theadapting illuminance of a color sample.

In the present article, the following items (1)–(4) arereported, which relate to various color attributes of objectcolors and their mutual relations. In addition, some discus-sions are added to clarify their mutual relations by using thenonlinear color-appearance model developed by the presentauthor and his colleagues.4,5 It should be noted here that thepresent article does not compare the model’s predictionsdirectly with experimental observations.

1. Adapting-illuminance dependencies between lightness,brightness, chroma, and colorfulness. Referring to theCIE definitions in Appendix 1, I feel that the differenceof adapting-illuminance dependencies between light-ness and brightness is the same as that between chromaand colorfulness. Further, I anticipate that adapting-illuminance dependencies are the same between bright-ness and colorfulness, and between lightness andchroma. Is this correct?

2. Relations in adapting-illuminance dependencies be-tween lightness, brightness, whiteness-blackness, andwhiteness-blackness strength. Definitions for white-ness-blackness and whiteness-blackness strength usedin the present study are given in Appendix 2. For anachromatic series of Munsell color samples from N1–N10, we consider the case of changing their adaptingilluminance from 10 lx to 1000 lx. Ordinarily, thebrightness perception of all achromatic color samplesincreases with the increase of adapting illuminance.This has been confirmed experimentally and is gener-ally accepted. However, the situation is quite differentin the perception of whiteness-blackness for the sameachromatic color samples. By raising adapting illumi-nance, the strength of whiteness increases for whitishachromatic-color samples, and conversely those ofblackness also increase for blackish achromatic-colorsamples. We call these combined perceptions “white-ness-blackness strength.” Two famous experimentalstudies on the increase of whiteness-blackness strengthby raising adapting illuminance are called the Stevensand Jameson–Hurvich Effect.6,7 Further, for clarifica-tion, numerical examples of various achromatic colorperceptions are given for lightness, brightness, white-ness-blackness, and whiteness-blackness strength. Theeffects of brightness and whiteness-blackness strengthstated above seemingly contradict each other. Is there arational explanation to correlate both effects?

3. Relations between whiteness-blackness strength andcolorfulness. Whiteness-blackness strength is explained

in item (2). Colorfulness corresponds to the change ofchromatic strength of a chromatic color by changing itsadapting illuminance. For example, by raising theadapting illuminance of an object color with red uniquehue, its colorfulness of redness increases. How does thiscolorfulness effect relate to the increase of whiteness-blackness contrast by increasing adapting illuminance,from the viewpoint of the opponent-color theory?

4. How does the nonlinear color-appearance model4,5 ex-plain the problems raised in items (1)–(3) above? Dur-ing the present study, it was found necessary to modifythe measures predicted by the model, especially white-ness-blackness strength and lightness. By applyingthese slight modifications to the model, it can explainall the items raised above. The modifications are de-scribed in the present study.

ADAPTING ILLUMINANCE DEPENDENCIES ONLIGHTNESS AND BRIGHTNESS

It is expected that the perceptions of lightness and bright-ness change significantly or slightly by changing the adapt-ing illuminance of an object color. These changes are de-scribed in this section.

In the present article, the terms “adapting illuminance,”“adapting luminance,” and “adapting background” are usedto specify the adapting state of observation. Detailed de-scriptions of them are given in Appendix 3, together withthe expected observing conditions.

Function for Adapting-Illuminance Dependencies

The author has previously given the following equationson adapting-luminance dependencyK(La) in the predictionof the Helmholtz–Kohlrasch effect or the brightness-lumi-nance ratio (B/L) effect8,9:

K~La! 5 0.2717z @6.4691 6.362z La0.4495/

@6.4691 La0.4495#, (1-a)

or

K~La! 5 1.729z @La0.44951 1.017#/

@La0.44951 6.469#, (1-b)

whereLa is adapting luminance (cd/m2) used in the exper-iment under study. The adapting luminanceLa is given byYoEo/100p, whereEo corresponds to the adapting illumi-nance andYo to the luminance factor (%) of backgroundused in the experiment under study. (See Appendix 3.) Bothfunctions in Eqs.(1a) and (1b) are completely the sameexcept for their representations. The functionK(La) is thesame as that ofb1(La) on adapting luminance dependenciesin the long- and medium-wavelength responses in the non-linear color-appearance model.4,5 Further,K(La) is also sim-ilar to the physiological response of visual cells to luminousstimuli.10

The functionK(La) is normalized to 1.0 atLaN 5 63.66

Volume 25, Number 5, October 2000 319

cd/m2. This normalized luminanceLaN corresponds to thatof the adapting background with luminance factor (%)Yo 520.0 kept atEo 5 1000 lx. Figure 1shows the relationbetweenLa and K(La). When normalization ofK(La) isnecessary for any other adapting luminanceL9aN differentfrom LaN 5 63.66 cd/m2, the functionK(La)/K(L9aN) must beused instead ofK(La). In the succeeding descriptions, eitherthe term “adapting illuminance” or “adapting luminance” ischosen corresponding to the situation used. However, theyare closely related to each other, as stated in Appendix 3,and have essentially the same meaning.

Adapting-Luminance Dependency on Lightnessand Brightness

Generally it is widely accepted that the lightness con-stancy holds irrespective of the change of adapting lumi-nance. This phenomenon was also observed in the so-calledCSAJ experiment.11,12 The lightness correlateJ(La) at anyadapting luminance is given by the following equation foran achromatic sample with metric lightnessL*:

J~La! 5 L*. (2)

Equation (2) shows that the lightness correlateJ(La) doesnot change irrespective of changing the adapting luminance.

On the other hand, the brightness correlateBr(La) of thesame achromatic sample withL* changes by changing theadapting luminance, and it is given by the following equa-tion:

Br~La! 5 L* z K~La!. (3)

The effectiveness of Eqs. (2) and (3) has already beenreported and confirmed in our previous studies.12,13 Thelightness and the brightness correlates in Eqs. (2) and (3)completely follow their CIE definitions (Appendix 1). ThevaluesJ(La) andBr(La) are scaled to have the same value100 to the white sample with its metric lightnessL*w 5 100

at La 5 LaN 5 63.66 cd/m2. See item (2) of Notes at the endof the article.

Supplement on Lightness Constancy

It should be noted here that the perfect lightness con-stancy given in the last section does not hold in the rigorousanalyses of experiments used in CIE TC1-34 Testing ColourAppearance Models.12,13 In other words, the adapting-lumi-nance dependency of lightness is very small, but still itexists. The lightness correlateJ(La) is given by the follow-ing equation on the basis of the above analyses:

J~La! 5 L* z K~La!0.1. (4)

The effect of the functionK(La)0.1 is estimated below. As

already stated, at the adapting luminanceLa 5 63.66 cd/m2

(Yo 5 20, Eo 5 1000 lx), the relationK(63.66) 5 1.00holds. Now setting the adapting luminance 10 cd/m2 (Yo 520, Eo 5 157 lx), K(La) 5 0.714 for brightness andK(La)

0.1 5 0.967 for lightness. This shows that the decreaseto about 1/6 of adapting luminanceLa gives a decrease ofbrightness correlate of about 30%, but a decrease of light-ness correlate of only about 3%. This decrease of lightnesscorrelate corresponds to only 0.15 Value to the color samplewith Munsell Value 5/. In other words, perfect lightnessconstancy almost holds.

Brightness and Adapting Luminance

As already stated in the last section, lightness constancyalmost holds in the achromatic perception, and it is onlyfound in the object-color mode of appearance.

On the other hand, by raising the adapting illuminance tovarious achromatic color samples, the brightness perceptionin each of them increases. Considering the CIE definition ofbrightness in Appendix 1, the brightness of object-color isthe perception caused by the increase of reflected light byraising its adapting illuminance. In other words, by raisingor decreasing the adapting illuminance to a specific achro-matic color sample, its brightness increases or decreasesfollowing the corresponding change of reflected light fromthe sample.

Figure 2 shows the relations between the brightness andthe adapting luminance of achromatic object colors. Thepredictions are made by the nonlinear color-appearancemodel5 to a series of achromatic color samples from whiteto black presented on a gray background14 with Yo 5 20. InFig. 2, the abscissa corresponds to the logarithmic value ofsample luminance log10L, and the ordinate to the predictedbrightnessBr. The parameters shown on the right-hand sideof the curves in the figure are theYvalue of each achromaticsample, and the parameters shown above the curves are thevalues of adapting illuminances. Figure 2 clearly shows thatall the brightness values of achromatic color samples in-crease by raising their adapting illuminance or luminance.

FIG. 1. Relation between adapting luminance La cd/m2 andthe function K(La) in Eq. (1). The ordinate corresponds toK(La), and the abscissa to log10La.


ADAPTING LUMINANCE DEPENDENCIES ONWHITENESS-BLACKNESS AND WHITENESS-

BLACKNESS STRENGTH

Attribute of Whiteness-Blackness for AchromaticObject-Colors

The most fundamental perception in a series of Munsellcolor samples from N0–N10 is that of whiteness-blackness.This perception is closely related to their Munsell Values.The achromatic color sample N10 corresponds to perfectwhite, N0 to perfect black, and N5 to gray. In the NCSColor Order System, the whitenessw 5 100 corresponds toperfect white N10, and the blacknesss 5 100 to perfectblack N0. These statements are generally accepted withoutany further explanations. Considering these discussions, it iseasy to see that the attributes “whiteness-blackness” and“lightness” are mutually transformable. Both lightness andwhiteness-blackness are the perceptions of the achromaticsamples themselves.

Lightness and whiteness-blackness are the achromaticcolor attributes most closely related to each other. For thisreason, corresponding to lightness constancy with a changeof adapting luminance already described, it is expected thatadapting luminance dependency is also very small in regardto the perception of whiteness-blackness (of the color sam-ple itself). This stability of the whiteness-blackness percep-tion for the adapting luminance change is also illustrated asfollows.

The perception of whiteness-blackness stated above ap-proximately corresponds tow and s in the NCS system,which consists of the whitenessw, blacknesss, and thechromaticnessC. In the system, the normalization is always

made to keep the relationshipw 1 s 1 C 5 100. For anyachromatic colors, the relationshipw 1 s 5 100 alwaysholds. This normalization is expected to give the stableobserved results for the achromatic color samples assessedin any experiment irrespective of the change of its adaptingluminance. In other words, the measuresw ands in the NCSsystem also approximately hold constant in their corre-sponding perceptions for a change of adapting luminance.This normalization using the sum of 100 is similar to thatfor lightness. The lightness of the color sample under illu-mination is derived from its brightness by dividing thebrightness of the white sample under the same illuminationfollowing the CIE definition of “lightness” given in Appen-dix 1.

Attribute of Whiteness-Blackness Strength forAchromatic Object Colors

A certain level of whiteness perception is found by illu-minating a whitish sample, of 100 lx for example. Byraising the illuminance to 1000 lx, the perception of white-ness strength increases. This phenomenon is often observedin our daily experiences, and it may correspond to theincrease of brightness by raising adapting illuminance. Wecall this whiteness perception change by raising adaptingilluminance “whiteness strength,” whose definition is givenin Appendix 2. This is named, because there is no corre-sponding term in the CIE International Lighting Vocabu-lary.1 On the other hand, the perception of blacknessstrength increases by raising adapting illuminance for ablackish sample with N2 from 100 lx to 1000 lx. Theblackness strengths of achromatic color samples with lowMunsell Values (lower than 5/) also increase by increasingtheir adapting illuminance. The phenomena stated above onwhiteness-blackness strength are quite different from thebrightness perception, which increases in all achromaticcolor samples by raising their adapting illuminance.

As found from the discussions so far, there are two kindsof perceptions of achromatic colors: one is “whiteness-blackness” and “whiteness-blackness strength,” and theother “lightness” and “brightness”. Lightness correspondsto whiteness-blackness, and brightness to whiteness-black-ness strength. The former two are stable irrespective ofchanging adapting illuminance, and the latter two are af-fected significantly by changing adapting illuminance,though all the four perceptions change by changing theMunsell Value orY value of the achromatic color sampleunder study.

Summarizing above, the perceptions of whiteness-black-ness on a series of achromatic color samples from white toblack remain constant irrespective of adapting illuminancechange. The perceptions of whiteness-blackness belong tothose of the color samples themselves. However, on white-ness-blackness strength of the series of samples, whitishsamples become whiter and blackish samples becomeblacker by raising their adapting illuminance. These phe-nomena are already well known. Each of the whiteness andthe blackness strengths increase in opposite directions by

FIG. 2. The brightness correlates of achromatic Munsellcolors for different adapting illuminances derived by thenonlinear color-appearance model. The ordinate shows thebrightness correlate, and the abscissa shows the luminanceof the samples. Numerals 1.210–78.66 correspond to the Yvalues of the samples. Numerals 10–10,000 show theadapting illuminance (lx).14


raising adapting illuminance. The predicted results by thenonlinear color-appearance model are shown in Fig. 3 forthe above phenomena.14

In Fig. 3, the ordinate shows theQ function correspond-ing to whiteness-blackness strengths. The valueQ 5 0corresponds to the perception of grayness, which has noperception of whiteness or blackness strength in it. For therangeQ . 0, the perception of whiteness strength is found,and for Q , 0, that of blackness strength exists. Theabscissa and all the other parameters are the same as in Fig.2. Figure 3 shows that the grayness perception is found forthe achromatic color sample of N5 (Y 5 19.77%). In ach-romatic color samples with Munsell Value higher than 5/,the perception of whiteness strength appears, and it in-creases by raising adapting illuminance. On the contrary, inachromatic color samples with Munsell Value lower than 5/,the perception of blackness strength is found, and it alsoincreases by raising adapting illuminance. It should benoted that the state ofQ 5 0 does not mean “null.” Itcorresponds to the existence of grayness perception. Furtherdiscussion occurs in a later section together with chromaticopponent-color perceptions. On the notations of brightnessBr and whiteness-blackness strengthQ in the present article,some explanations are shown in Appendix 4 together withthe corresponding notations used in CIECAM97s.15,16

The phenomena in Fig. 3 have been well known in thefield of color appearance of object-colors. Hering,2 thefounder of the opponent-color theory, introduced the phe-nomenon that white and black color samples were perceivedas dull white and dull black colors within a dark room atmidnight (at low adapting illuminance), and they were per-ceived as clear white and clear black (the increase of white-ness-blackness strength) at dawn (at high adapting illumi-nance). Further, Stevens6 and Jameson–Hurvich7 in 1963reported experimental results similar to Fig. 3. In their

articles, they claimed that their experiments were done onthe basis of brightness evaluations.

However, to illustrate the appropriateness of their exper-imental results similar to Fig. 3, Jameson–Hurvich7 wrotethe following sentence on p. 175 of their article. “Conser-vative skeptics who find the results of Fig. 6 (similar to Fig.3 in this article) difficult to accept are only to observe, say,a bottle of India ink or a standard telephone set under dimillumination, and then note the increasedblacknesswhenthe overhead lights are switched on.” Stevens6 also gave asimilar description in his article, which might show theimportance of blackness strength in his study on the appar-ent brightness evaluation of achromatic object-colors. It isgiven in Appendix 5.

From the above discussion, it now appears that the trendsin Fig. 3 may correspond to the evaluations of adaptingilluminance dependencies of whiteness-blackness strength.

Numerical Examples on Lightness, Whiteness-Blackness, Brightness, and Whiteness-BlacknessStrength

The following numerical examples clarify the relationsbetween lightnessJ, whiteness-blackness [W-Bk], bright-nessBr, and whiteness-blackness strengthQ on a series ofachromatic colors (11 samples from N0–N10 at every 1Munsell Value step ) under white illuminant D65 and adapt-ing illuminance 100 lx for adapting backgroundYo 5 20.The adapting luminance isLa 5 6.366 cd/m2. The normal-ized luminanceLaN is 63.66 cd/m2, which corresponds to1000 lx for Yo 5 20.

The first column in Table I shows the Munsell Values ofthe achromatic samples, and the second column shows theirY values. The third column gives the computed results onmetric lightness of the achromatic colors. The (perceived)lightness correlatesJ are the same as the metric lightnessvalues L*, as long as complete lightness constancy forchanging adapting illuminance holds for those achromaticcolors. In other words, the relationJ 5 L* holds. Further,the fourth column shows the values of whiteness-blacknesscorrelates [W-Bk] 5 L*or 50, when complete lightness

FIG. 3. The correlates of whiteness-blackness strength Qof achromatic Munsell colors for different adapting illumi-nances.14 The ordinate corresponds to Q. See the caption ofFig. 2 for other notations.

TABLE I. The values of metric lightness L* and white-ness-blackness [W-Bk] for achromatic Munsell colors.Metric lightness is the correlate of lightness J.

MunsellValues

Luminancefactor in %.

Y values

CIE metriclightnessL* ( 5 J )

Whiteness-blackness

[W-Bk]

10 100.00 100.00 50.009 78.66 91.08 41.088 59.10 81.35 31.357 43.06 71.60 21.606 30.05 61.70 11.705 19.77 51.58 1.584 12.00 41.22 28.783 6.555 30.77 219.232 3.126 20.54 229.461 1.210 10.63 239.370 0.000 0.00 250.00


constancy holds. The completely white object-color corre-sponds to150, and the complete black one to250. Thelightness and the whiteness-blackness correlates are theattributes of achromatic object-colors themselves.

Now, we derive the functions of brightnessBr and white-ness-blackness strengthQ. They are given by the followingequations based on their definitions in Appendices 1 and 2:

Br 5 L* z K~La!, (5)

Q 5 @W-Bk# z K~La!. (6)

The functionK(La) is the same as Eq. (1). The value ofK(La) is normalized to 1.0 atLaN 5 63.66 cd/m2. The valueof K(La) at La 5 6.366 cd/m2 (adapting illuminance 100 lx)is 0.6538. UsingK(La) 5 0.6538 for Eqs. (5) and (6), thevalues of brightness correlates are shown in the secondcolumn of Table II, and those of whiteness-blacknessstrength in the third column.

The values of brightness correlatesBr become lower thanthose of lightness correlatesJ 5 L* in Table I, because ofthe low adapting luminanceLa 5 6.366 cd/m2 as comparedwith the normalized luminanceLaN 5 63.66 cd/m2. Further,the value ofQ for the white object color (N10) is132.69,that of the gray one (N5) zero, and that of the black one232.69. The strengths of whiteness and blackness decrease,respectively.

As is clear from the above discussion, the followingrelation holds for the adapting illuminance 1000 lx (La 563.66 cd/m2) the same as the normalized adapting illumi-nance (LaN 5 63.66 cd/m2):

Br 5 J, (7)

Q 5 @W-Bk#. (8)

Further, by raising the adapting illuminance from 1000 lx, itfollows that theBr values increase as compared with theJ

values, and the existing range of whiteness-blacknessstrengthQ becomes wider than that found in [W-Bk] inTable I.

Differentiating between Brightness and Whiteness-Blackness Strength

The lightness of an achromatic color sample has a one-to-one correspondence to its whiteness-blackness percep-tion. However, by raising the adapting illuminance for aseries of achromatic color samples from white to black,there is a significant divergence between brightness andwhiteness-blackness strength as already found from Figs. 2and 3. The author wishes to claim that this is rational; inother words, that both sets of trends in Figs. 2 and 3 cancoexist without any contradiction. Further, both brightnessand whiteness-blackness strength belong to the same levelof perception, and they have an adapting illuminance de-pendency similar to each other. On these points, detaileddiscussions occur in later sections together with those onvarious chromatic color attributes.

As in the above discussion and Fig. 3, theQ function inthe nonlinear color-appearance model is the psychologicalcorrelate of the perception of whiteness-blackness strength.Up to the present, theQ function has been directly used toderive the lightness correlate in the nonlinear color-appear-ance model.4,5 However, the lightness correlateJ(La) in thenonlinear color-appearance model is now derived by thefollowing equation, using its brightness functionBr onthe basis of the CIE definition of lightness1 given inAppendix 1:

J~La! 5 @Br~La!/Brw~La!# 3 100, (9)

whereBr(La) is the value of the brightness correlate of anobject-color sample under an adapting luminanceLa, andBrw is that of the white sample withYw 5 100 under thesame adapting luminance.

Simple Observations on the Distraction betweenBrightness and Whiteness-Blackness Strength

The divergence between brightnessBr and whiteness-blackness strengthQ is apparent from Figs. 2 and 3. At firstglance, these results seem contradictory. The following sim-ple experiment shows the coexistence of both perceptionswithout any contradiction.

An observing booth was divided vertically at its centerinto two parts. The background of each divided booth waskept at a white color with N8. On each of the backgrounds,the same blackish sample with N2 was set. One booth waskept at 100 lx, the other at 1000 lx. Due to the difference inadapting illuminance, the perceived colors of the blackishsamples were different for different booths. The subjectswere allowed to see both booths freely, and the followingquestions were asked of them:

1. “Which sample is brighter than the other?”

TABLE II. The values of brightness correlate Br andthose of whiteness-blackness strength Q for achro-matic Munsell colors at adapting luminance La 56.366 cd/m2. The brightness correlate is computed byEq. (5), and the whiteness-blackness strength by Eq.(6). The value of K(La) at La 5 6.366 cd/m2 is 0.6358.

MunsellValues

Brightness atLa 5 6.366 cd/m2

Br (La 5 6.366)

Strength ofwhiteness-

blackness atLa 5 6.366 cd/m2

Q(La 5 6.366)

10 65.38 32.699 59.55 26.868 53.18 20.497 46.81 14.126 40.34 7.655 33.72 1.034 26.95 25.743 20.12 212.572 13.43 219.261 6.95 225.740 0.00 232.69


2. “Which sample is higher in the blackness strength con-sidering the intensity of illumination to it? Please do notassess only the blackness of the blackish sample itself.”

The assessments of five subjects agreed well. They al-ways chose the blackish sample under the high illuminance1000 lx. This confirms that the blackish sample under thehigh illuminance 1000 lx is always higher in brightness, andalso in blackness strength than that under the low illumi-nance100 lx. The former corresponds to the increase ofbrightnessBr for Y 5 3.126 with increasing adapting lumi-nance in Fig. 2, and the latter to the decrease of theQ valuefor Y 5 3.126 with increasing adapting luminance in Fig. 3.In other words, the increase of the negative value (black-ness) in theQ function does not mean the decrease, butinstead the increase of the blackness strength. The relation-ship between Fig. 2’s brightness and Fig. 3’s whiteness-blackness strength is now clarified.

ADAPTING LUMINANCE DEPENDENCIES ONLIGHTNESS, BRIGHTNESS, WHITENESS-BLACKNESS

STRENGTH, CHROMA, AND COLORFULNESS

In the previous sections, the characteristics of adapting-luminance dependencies are described only for achromaticcolor attributes: lightness, brightness, whiteness-blackness,and whiteness- blackness strength. In this section, the adapt-ing luminance dependencies on chroma and colorfulness areclarified, and they are compared with those of the aboveachromatic perceptions. In addition, the following relation-ship is claimed.

The attributes of lightness and chroma and those ofbrightness and colorfulness are found in the same level ofperception, respectively, as found from their CIE definitions(in Appendix 1). However, in each of the combinations[lightness and chroma] and [brightness and colorfulness],the adapting illuminance dependency of the latter chromaticperception is always a specific factorK(La) times higherthan that of the corresponding former achromatic percep-tion. The reasons are discussed in this section.

Comparisons among the four kinds of color attributes aredifficult to conduct using subjective estimation methods.Instead, the comparisons are made here using a simpleprediction equation of the Helmholtz–Kohlrausch (H–K)effect by the author.9 The equation uses the CIELUV for-mula. Its computation is simple and is useful for practicalapplications. It was derived from the earlier prediction equa-tion of the H–K effect in the nonlinear color-appearancemodel.17,18 Both equations predict the effect equally well.

Brief Description of the H–K Effect

Now consider chromatic samples with various chroma-ticities x, y and with the luminance factor (%)Y 5 constant.Their metric lightnessL* is naturally constant, but theirhues and metric chromasC*uv are variable according to thechromatic samples. In spite of having the same values ofYandL*, the chromatic samples do not show the same bright-

ness and lightness. These perceptions change significantlyin a complex manner for the change in hue and metricchroma of the chromatic samples. We call this the H–Keffect, and the effect corresponds to an important defectfound in the present CIE photometric system.

It is difficult to estimate the differences in brightness andlightness among the chromatic samples by using a psycho-logical ratio scale directly. Instead, the following procedurehas generally been used for estimating the H–K effect.Consider the various test chromatic color samples with afixed metric lightnessL*. Setting a chromatic sample se-lected from the test colors and an achromatic sample side byside under the same illumination, the lightness match (alsothe brightness match) is established by changing the achro-matic samples. The metric lightnessL*eq of the achromaticsample determined at the lightness match is then used as theestimate of the equivalent lightness19 of the test chromaticcolor. By repeating the same procedure for all the testchromatic color samples, their equivalent lightness valuesare determined. These equivalent lightness values are usedfor estimatingthe differences in perceived lightnessamongthe test samples.

The author and his colleagues have already clarified thatthere are two experimental methods for estimating the H–Keffect. Further, they showed that the observed results weresignificantly different between the two methods,17,18thoughthey had been thought to give the same estimates of theH–K effect before 1994. The two methods are now calledthe Variable-Achromatic-Color (VAC) and the Variable-Chromatic-Color (VCC) methods. The method of lightnessmatch described above corresponds to the VAC method.

In the VCC method, the lightness match is establishedbetween a fixed achromatic color withL*eq and a chromaticcolor with a fixed chromaticityx, y by changing its metriclightnessL*. The procedure is repeated for all the varioustest chromatic samples. All the test chromatic samples justdetermined with differentL* values havethe same per-ceived lightness, because they have the same fixed equiva-lent lightnessL*eq. In practice, the VCC method is moreuseful than the VAC method.20 As already stated, the VACmethod does not give the test chromatic samples with thesame equivalent lightnessL*eq, but gives differentL*eqvaluesamong the test chromatic samples with the same metriclightness L*. Consequently, this section uses the VCCmethod as follows.

Adapting Luminance Dependencies on Lightnessand Chroma

The simple prediction equation of equivalent lightnessL*eq in the VCC method is summarized in the followingequation for a test chromatic color with metric lightnessL*at an adapting luminanceLa under illuminant C9:

L*eq 5 L* z @1 2 0.8660z q~u ! z Sun#

1 0.0872z K~La! z C*uv, (10)

where q(u) is the function of metric hue angleu in the


CIELUV space.9 The measureSun is the metric saturation ofthe chromatic color, andC*un its metric chroma.

The first term including parentheses on the right-handside of Eq. (10) is related to the achromatic lightness per-ception of the test chromatic color. It should be noted thatthe first term is completely independent of the adaptingluminanceLa. The first term consists of the following twofactors. The first factor shows the contribution of the metriclightnessL* of the chromatic color itself to the equivalentlightnessL*eq. The second factorL*[ 20.8660z q(u) z Sun]gives the contribution of the differences in whiteness-black-ness attribute found between the chromatic colors and theachromatic color with the sameL* value to the equivalentlightnessL*eq.20

The second term [0.0872z K(La) z C*un] on the right-handside of Eq. (10) shows the contribution of chromatic com-ponent or metric chromaC*un of the test chromatic color tothe equivalent lightnessL*eq. It should be noted here that thefunction of adapting luminance dependencyK(La) is foundonly in this second term.

Further considering the lightness constancy given in Eq.(2), the quantitiesL*eq andL* in Eq. (10) correspond to thelightness correlatesJeq(La) andJ(La) at any adapting lumi-nanceLa. However, it is expected that the perceived chromacorrelateC*(La) at La is given byK(La) z C*uv in Eq. (10).These results suggest that the lightness correlate is keptconstant irrespective of the adapting luminanceLa, but thechroma correlateC*(La) increases by increasing the lumi-nanceLa following the functionK(La). From this discus-sion, it is understood that adapting luminance dependenciesare different between the lightness and the chroma corre-lates by a factor ofK(La). These expectations are confirmedfrom the good predictability of Eq. (10) of various H–Keffects, including their adapting luminance dependenciesalready estimated.9 However, if lightness and chroma (alsotheir correlates) have the same adapting luminance depen-dency, the relation of Eq. (10) does not hold. In this case,the adapting luminance dependency of the H–K effect alsodoes not hold. This case, however, contradicts the experi-mental facts reported to date.

Further, Eq. (10) may be justified by the following. Light-ness constancy irrespective of the change of adapting lumi-nance is widely accepted in the color community, but wehave never heard the term “chroma constancy” with adapt-ing luminance change. The level of perception is the samebetween lightness and chroma, but the adapting luminancedependency is different between them by a factor ofK(La).The author feels that this is a very interesting finding.

It should be noted here that the above conclusion onlightness and chroma is irrespective of whether the predic-tion equation for CIELUV or another color space is used,because Eq. (10) was derived from the prediction equationof the H–K effect using the nonlinear color-appearancemodel17,18 as already stated, and both equations have thesame structure and can predict various H–K effects quitenicely.

Adapting Luminance Dependencies on Brightnessand Colorfulness

Now we consider Eq. (10) on the equivalent lightness atthe level of brightness. Referring to Eq. (3), Eq. (11) iseasily derived from Eq. (10):

Breq 5 Br z @1 2 0.8660z q~u ! z Sun#

1 0.0872z M, (11)

where the brightness correlatesBreq and Br correspond tothe following equation:

Breq 5 L*eq z K~La!, (12-a)

Br 5 L* z K~La!, (12-b)

and, where the colorfulness correlateM in Eq. (11) is givenby Eq. (13):

M 5 K~La! z C* ~La!,

5 @K~La!#2 z C*un . (13)

As found from Eqs. (12) and (13), the brightness correlate isK(La) times the size of metric lightness, and the colorfulnesscorrelate isK(La)

2 times the size of metric chroma [or thecolorfulness correlate isK(La) times the size of chroma].Though the level of perception is the same in brightness andcolorfulness (also in their correlates), it is found that theadapting luminance dependencies are quite different be-tween them.

CLASSIFICATION OF COLOR ATTRIBUTES

The discussions in the last sections suggest the existence ofthe two kinds of classifications of achromatic and chromaticcolor attributes. One is the classification based on the levelof perception, and the other is that based on the similarity ofthe adapting luminance dependency.

Table III shows the classification of the level of percep-tion. Two kinds of perception levels are used. The first levelcorresponds mainly to the color perceptions of color sam-ples themselves, though they are affected a little or appre-ciably by changing their adapting luminance. For the ach-romatic color attributes, the perceptions are lightness and

TABLE III. Classification of achromatic and chromaticcolor attributes (psychological correlates) based onthe level of perception.

Perception levelAchromatic color

attributesChromatic color

attributes

Perceptions mainlyrelated to color-objectsthemselves

Lightness

Whiteness-blacknessChroma

Compoundperceptions oncolor-objects andtheir adaptingluminances

Brightness

Strength of whiteness-blackness

Colorfulness


whiteness-blackness; and for the chromatic color attribute,the corresponding perception is chroma (saturation is omit-ted in the table). The second level corresponds to the com-pound perceptions induced by color samples and their illu-mination. For the achromatic attributes, the perceptions arebrightness and whiteness-blackness strength; and for thechromatic color attribute, the corresponding perception iscolorfulness. The perceptions of lightness, whiteness-black-ness, and chroma are the correlate perceptions of brightness,whiteness-blackness strength, and colorfulness, respec-tively, normalized by the brightness of the white sampleunder the same adapting condition.

The above discussion on Table III is supported by the CIEdefinitions1 (Appendix 1) and the definitions in Appendix 2given by the author irrespective of achromatic and chromaticattributes. In them, very good similarities are found betweenbrightness and lightness, whiteness-blackness strength andwhiteness-blackness, and also colorfulness and chroma.

Table IV shows the classification of color attributes basedon the similarity of the adapting luminance dependencies.The first level corresponds to the condition of completeconstancy in perception irrespective of changing adaptingluminance, orK(La)

0.0 5 1.0 holds. Only the achromaticattributes lightness and whiteness-blackness exist at thislevel, which lacks any chromatic color attribute. The secondlevel corresponds to color attributes with adapting lumi-nance dependencyK(La). The attributes at this level arederived by multiplyingK(La) to the corresponding metricquantities, for brightness, whiteness-blackness strength, andchroma. The third level corresponds to color attributes withK(La)2, that is, only the chromatic color attribute colorful-ness.

Though at first glance the classifications in Tables III andIV appear complex, the author believes that these classifi-cations are necessary and important in the study of colorperceptions and color appearance.

WHITENESS AND BLACKNESS STRENGTHS IN THEOPPONENT-COLORS CONCEPT

As already noted, there are two kinds of achromatic object-color perceptions with significant adapting luminance de-

pendencies: brightness and whiteness-blackness strength.Both change their values in different ways, as shown inFigs. 2 and 3, with changes to the adapting illuminance.This makes achromatic color perceptions more complexthan chromatic ones. In the NCS Color Order System,achromatic colors are represented by only NCS whitenesswand NCS blacknessswithout using the grayness perception;the NCS gray is represented byw 5 s 5 50.

In the following sections, the author describes the impor-tance of grayness, and shows that the concept of the oppo-nent-color axis of whiteness-grayness-blackness is similarto the ordinate axes of redness-grayness-greenness, andyellowness-grayness-blueness.

Grayness Perception in the Opponent-Colors Theory

Now we wish to illustrate relations between whiteness-blackness, chroma, and grayness from the point of view ofthe opponent-colors theory. Consider the redness-greennessaxis of the opponent colors with an intermediate lightness.Only by decreasing the chroma component found in ahighly saturated red color along the axis, does the perceivedcolor become less chromatic and reach the perception ofgrayness. Then the greenness in the perceived color starts toappear, and reaches highly saturated green color by increas-ing its chroma.

In the process of the color-appearance change, thechroma perception in the chromatic color series is alwaysassessed only by considering its chromatic component ofredness or greenness, but neglecting its grayness. Althoughthe perception of grayness always exists in any chromaticcolor with intermediate chroma, we do not use the graynesscomponent in the assessment of chroma. Considering thecorrespondence between whiteness-blackness and chromain the level of perception, it seems reasonable that thegrayness can be also neglected in the assessment of white-ness or blackness. The grayness is also important for white-ness-blackness perception. We use the terms of whitishgray, grayish white, blackish gray, and grayish black as thesame as those of reddish gray, grayish red, greenish gray,and grayish green. We never use the term blackish white orwhitish black.

The above discussion indicates the similarity between thethree opponent-colors axes white-black, red-green, and yel-low-blue on the grayness perception. What the authorwishes to propose is a concept of the opponent-colors axisof whiteness-grayness and grayness-blackness. However,Hering did not introduced the perception of “grayness” inthe achromatic axis of his opponent-colors system, asclearly found in Fig. 2 of his book.2

Whiteness-Blackness Strength and Colorfulness

As described in the last section, the achromatic percep-tion of whiteness-blackness is similar to the chroma ofredness-greenness in the opponent-colors concept with thegrayness perception at its center. The similarity also appliesto the chroma of yellowness-blueness. The above similari-

TABLE IV. Classification of achromatic and chro-matic color attributes (psychological correlates) basedon adapting luminance dependency.

Adaptingluminance

dependencyAchromatic color

attributesChromatic color

attributes

K(La)0.0 a-1) Lightness —

a-2) Whiteness-blackness

K(La)1.0 b-1) Brightness c) Chroma

b-2) Strength ofwhiteness-blackness

K(La)2.0 — d) Colorfulness


ties also apply to whiteness-blackness strength and color-fulness of redness-greenness or yellowness-blueness. Theabove discussion shows that perceptions of six primarycolors (whiteness-blackness, chroma of redness-greenness,and that of yellowness-blueness) constitute the opponent-colors responses. Similarly, additional perceptions of sixprimary colors (whiteness-blackness strength, colorfulnessof redness-greenness, and that of yellowness-blueness) alsoconstitute opponent-colors responses. This means that theopponent-colors responses are found in the two levels ofperception. Further discussion is given below in detail to-gether with the merits of introducing the “grayness” per-ception.

On the Coordinate System of the Opponent-Colors Re-sponses.Each of the opponent-colors pairs (whiteness-blackness, redness-greenness, and yellowness-blueness) hasthe grayness perception at its center. By increasing theprimary-color component in each of the six primary colors,finally we expect to have the purest perception in eachprimary color. Without using the “grayness” perception,object-color perceptions in the opponent-colors system aredesignated in an oblique- or triangle-coordinate system. Thefact was already suggested by Hering in Fig. 4 of his book,2

and it is also found in the NCS Color Order System.3 It wasalready reported that the introduction of “grayness” percep-tion to the opponent-colors responses makes the use of theorthogonal-coordinate system for object-color perceptionspossible,21 not only in the NCS Color Order System, butalso in the nonlinear color-appearance model. The orthog-onal-coordinate system is more convenient than the trian-gle-coordinate one for analyzing color perceptions of objectcolors using any color-appearance model.

On the Hunt Effect.Generally, the perception of color-fulness of chromatic object colors increases by raising theiradapting illuminance. In other words, their perceived dif-ference from the grayness increases. This phenomenon iswell known as the Hunt effect, and applies to all hues ratherthan only opponent colors. By raising the adapting lumi-nance to red and green color samples, the colorfulness ofredness and greenness increases in the opposite directionfrom the gray perception along the opponent-colors ordinateof redness-grayness-greenness. Further, the Hunt effect onany hue can be illustrated by using neighboring unique huesin the opponent-colors responses; e.g., the Hunt effect of anorange color is explained by composing the colorfulnessincrease of its primary color perceptions of redness andyellowness from the grayness perception.

On the Relation between the Hunt Effect and the Stevensand Jameson–Hurvich Effect.Similarly to the Hunt Effect,both whiteness strength of a whitish color sample andblackness strength of a blackish one increase by raising theiradapting illuminance, as already shown in Fig. 3. The effectis called the Stevens and Jameson–Hurvich Effect. For awhitish red color sample, its colorfulness increases withincreasing adapting illuminance. This colorfulness increaseis also explained by composing the increase of whitenessstrength and of redness colorfulness in the primary colorperceptions of whiteness and redness. In other words, the

colorfulness increase of the whitish-red color sample isexplained by combining the Hunt Effect and the Stevensand Jameson–Hurvich Effect. Irrespective of achromaticand chromatic color perceptions, it is commonly found thateach perception of the six primary colors increases byraising adapting illuminance. As understood from the HuntEffect and the Stevens and Jameson–Hurvich Effect, anincrease of perception with increasing adapting illuminanceis found for all the primary colors in the opponent-colorsspace with grayness at its center. It is now clear that theHunt Effect and the Stevens and Jameson–Hurvich Effectbelong to the same category in the opponent-colors concept.

Proposal of the Term Colorfulness to Whiteness-Black-ness Response.The above discussion suggests that the termcolorfulness can be used for all six primary colors in thethree opponent-colors responses. Though white and blackare not chromatic, they are colors. The author, therefore,proposes the concept of colorfulness to describe the increaseof the whiteness or blackness component of achromaticcolors by raising their adapting illuminance, which has beencalled whiteness-blackness strength in the present article.The positive value of theQ function corresponds to thecolorfulness of whiteness, and its negative value to thecolorfulness of blackness. These characteristics of theQfunction are the same as those of the colorfulness responsesM(R-G) for redness-greenness andM(Y-B) for yellowness-blueness in the nonlinear color-appearance model.

On the Gray Color and the Six Primary Colors.Further,the following common feature exists for object colors with-out fluorescence on an achromatic background. In the op-ponent six primary colors and the gray at their center, onlythe gray color is actually realized, but all the other six purestcolors of white, black, red, green, yellow, and blue areactually difficult to realize. This is found in the NCS ColorOrder System, in which the gray color sample exists, butcolor samples are not found for NCS whitenessw 5 100,blacknesss 5 100, and chromaticmessC 5 100 for uniqueor near unique hues.

On Color-Appearance Models of the Opponent-ColorsResponses.In models for predicting various colors percep-tions, called the color-appearance models or color-visionones, usually the following representations are used for thechromatic responses of opponent-colors pairs. When red-ness and yellowness responses are represented by positivevalues, those of greenness and blueness are shown by neg-ative values. Naturally grayness perception is set at zero.Even in the case of reversing the signs in the responses, theopponent-colors concept is not affected. The increase in thenegative direction on each of the negative responses (green-ness and blueness) does not mean the decrease, but theincrease in the greenness or the blueness response. Simi-larly, Fig. 3 shows that the negative value of the whiteness-blackness strengthQ shows the existence of blackness, andits further increase in the negative direction corresponds tothe increase of blackness.

On Whiteness-Blackness Strength and Brightness in theNonlinear Color-Appearance Model.Theoretically, theblackness strength of the achromatic response extends end-


lessly in the negative direction with increasing adaptingilluminance. On the other hand, brightness of any realobject-color under illumination always has positive value.Only in the case of no illumination is the brightness of anyobject color reduced to zero. This is the main differencebetween whiteness-blackness strength and brightness. It isnoted here that the nonlinear color-appearance model4,5

contains these three kinds of opponent-colors responses(whiteness-blackness, redness-greenness, and yellowness-blueness) immanently within its model structure, and alsoexplains brightness and lightness.

On Grayness in the Nonlinear Color-Appearance Mod-els. It should be noted here that the zero value in all theopponent-color responses of object colors in the nonlinearcolor-appearance model does not merely mean the no-per-ception, but corresponds to the gray perception. In otherwords, the color perception with the zero value in theopponent-colors responses shows the pure gray without anyof whiteness, blackness, redness, greenness, yellowness,and blueness.

OPPONENT-COLORS MECHANISMS IN LUMINOUSAND OBJECT-COLORS

In addition to the perceptions of lightness and brightness,there are the perceptions of whiteness-blackness, whiteness-blackness strength, chroma, and colorfulness on the threeopponent-colors responses (whiteness-blackness, redness-greenness, and yellowness-blueness). For the achromaticcomponent of luminous colors, whiteness-blackness, white-ness-blackness strength, and lightness disappear, and onlybrightness is found. For the chromatic component, the twoopponent-color responses (redness-greenness and yellow-ness-blueness) still remain. However, the perception ofchroma disappears, and only colorfulness and saturation areleft. The differences between luminous- and object-colorstimuli make relations among the achromatic perceptions oflightness, brightness, whiteness-blackness, and whiteness-blackness strength very complex.

ON THE NONLINEAR COLOR-APPEARANCE MODEL

It has been considered that theQ function in the nonlinearcolor-appearance model is related to the lightness correlatein the model.5 However, as found from the above discus-sions, it can now be said that theQ function is the correlateof whiteness-blackness strength or colorfulness of white-ness-blackness. In this section, some corrections to thenonlinear color-appearance model are given.

Correction of the Nonlinear Color-Appearance Model

Some corrections are necessary to some formulations ofthe nonlinear color-appearance model, as given in the Ap-pendix of the reference5 (called the appendix in this sec-tion). The corrections are based on the discussions above,and are shown below using the notations used in the model.5

1. Exclude Step 10 in the appendix. The Step 10 to beexcluded is briefly shown below for readers’ conve-nience. In the step, lightnessL*p is given byQ 1 50,whereQ is the whiteness-blackness strength defined inthe present article. Instead of using the relation, light-nessL*p is defined in (2) from brightness, following theCIE definitions in Appendix 1.

2. After Step 16 in the appendix, insert the following newStep N.

Step N: Lightness is derived by the following equation:

L*p 5 ~Br/Brw! z 100. (A-N-1)

Note 1. L*p for an achromatic color sample under D65 isgiven by the following equation:

L*p 5 41.69z log10@~Y 1 n!/~20 1 n!#. (A-N-2)

Note 2. To further improve the fitting of the lightnessestimates to the observations, the following coefficientK(Lo) is multiplied to each of Eqs. (A-N-1) and (A-N-2):

K~Lo! 5 @K~Lo!/K~Lor!#0.1, (A-N-3)

whereLo is the adapting luminance of the experiment, andLor the normalized luminance. The postscripts are the sameas those used in the appendix.

Eq. (A-N-3) corresponds to Eq. (4) in the present article,which is used to adapt the predictions to the correspondingobserved data on lightness for various adapting luminancelevelsLo. In Eq. (4), the functionK(LaN) corresponding toK(Lor) in Eq. (A-N-3) is normalized to unity.

On the Corrected Nonlinear Color-Appearance Model

The corrected nonlinear color-appearance model can ex-plain almost all the color appearance phenomena of object-colors under various illuminants and illuminance levels.22

They imply the special effects called by the names ofHelson–Judd, Stevens and Jameson–Hurvich, and Hunt.14,23

Furthermore, by developing the model, the important phe-nomenon known as the Helmholtz–Kohlrausch effect can bepredicted nicely.20

The corrections together with the original model5 can beused for the condition of complete adaptation to the adapt-ing illuminant used. In the case of incomplete adaptation,refer to reference,22 in which the degree of adaptation isspecified from the experimental conditions used. Combin-ing the degree of adaptation with the model, prediction ofthe actual observations is further improved. For the noisecomponent,n 5 1.0 has been used, but at this stage the useof n 5 0.1 is recommended.22,24 The complete formulationof the revised nonlinear color-appearance model and itsreverse computation will be reported in a future article.

Now the values of theQ function on whiteness-blacknessstrength and of the brightnessBr in the nonlinear color-appearance model are computed for the same achromaticcolor samples as those found in Table I for the adaptingluminanceLa 5 6.366 cd/m2. The normalized adapting


luminance is kept atLaN 5 63.66 cd/m2. The results areshown in Table V. The results of Table V are very similarto those already given in Table II, which shows the valuesof Q andBr derived by the abridged computations alreadydescribed. From the numerical examples shown in Tables I,II, and V, it is found that the functionQ in the nonlinearcolor-appearance model is not related to the lightness cor-relateJ, but the correlate of whiteness-blackness strength.

Eccentricity Coefficient of Whiteness and Blackness

Hunt introduced the eccentricity coefficient es (u) on hueangleu in his color-appearance model by attending to theeccentricity of hue in the constant and small chroma con-tours of Munsell colors.25 The author clarified the problemin the coefficient, and proposed a new method for correctingit.4 The introduction of the eccentricity coefficient wasmade by the different chromatic strengths for different hues.The concept of chromatic strengths for various spectrumcolors was proposed by Evans and Swenholt.26 However,the proposal by Hunt is important.

It has already been stated that the whiteness-blacknessperception in the opponent-colors responses resemblesthose of redness-greenness and yellowness-blueness. Forthis reason, it is only to be expected that a difference inchromatic strength or another eccentricity coefficient mightexist between whiteness and blackness.

The specific chromatic strengths of whiteness and black-ness are estimated by a simple computation below. Now,keeping the white background at 100 cd/m2, the black colorcorresponds to about 1 cd/m2, the white to 100 cd/m2, andthe gray to about 20 cd/m2. This means that twenty (20/1)times of luminance are required to change the black to thegray by canceling blackness. On the other hand, only fivetimes of luminance are needed for making the gray to thewhite. This means that the chromatic strength of whitenessis about four times as high as that of blackness. Further

considering the brightness perception is approximately pro-portional to the logarithm of luminance, the whitenessstrength is higher than the blackness strength by about afactor of 1.86 (5 log20/log5), which is the inverse ratio oflog 5 for whiteness and log20 for blackness. In other words,the whiteness strength is 1.86, provided that the blacknessstrength is kept at 1.0.

The ratio between the whiteness and the blacknessstrengths is compared with that used in the nonlinear color-appearance model. Already theQ function for achromaticcolor samples under illuminant D65 is given by the follow-ing equation14:

Q 5 k z b1~La! z e~Y! z log10@~Y 1 n!/~20 1 n!#, (14)

wherek is a normalizing coefficient, andb1(La) the coeffi-cient for adapting luminance dependency the same as Eq.(1). La is the adapting luminance, andY the luminancefactor (%) or theY tristimulus value of the achromaticsample under study. The termn is the noise component, ande(Y) is given by the following equation:

e~Y! 5 1.758 forY ^ 20,

e~Y! 5 1.000 forY , 20.(15)

The whiteness strength in whitish samples is higher thanthe blackness strength in blackish samples. The coefficient1.758 is introduced to compensate for the differences be-tween the whiteness and the blackness strengths. Further,the logarithmic value ofY is used in Eq. (14). The value1.758 is similar to 1.86 approximately estimated above.

CONCLUSIONS

The results obtained in the present article are summarized asfollows:

1. The adapting-luminance dependencies of various ob-ject-color attributes (lightness, brightness, whiteness-blackness, whiteness-blackness strength, chroma, andcolorfulness) were clarified under white illuminationwith various adapting illuminances. Further, two clas-sifications of object-color attributes were shown; one ison the basis of perception levels (Table III), and theother is on the basis of the similarity of the adaptingluminance dependencies (Table IV). On the latter clas-sification, the author believes that it has not been clearlystated in the field of colorimetry to date.

2. Previously, the following two effects were consideredcontradicting to each other: (a) brightness values of allachromatic colors increase by raising their adaptingilluminance, and (b) both whiteness strength of whitishsamples and blackness strength of blackish samplesincrease by raising their adapting illuminance. It wasdemonstrated, with the help of a simple experiment,that both effects coexist without contradiction.

3. Abridged correlates for whiteness-blackness [W-Bk] 5L* 2 50 and whiteness-blackness strengthQ 5 [W-Bk]

TABLE V. The values of brightness correlate Br andthose of whiteness-blackness strength Q for achro-matic Munsell colors at adapting luminance La 56.366 cd/m2, as computed by the nonlinear color-appearance model.

MunsellValues

Brightness per thenonlinear color-

appearance model atLa 5 6.366 cd/m2

Br (La 5 6.366, NCAM)

Strength of whiteness-blackness per the nonlinearcolor-appearance model at

La 5 6.366 cd/m2

Q(La 5 6.366, NCAM)

10 65.37 32.699 60.44 27.758 54.57 21.887 48.11 15.426 40.83 8.145 32.56 20.134 27.01 25.683 20.59 212.102 13.43 219.261 6.04 226.630 23.35 236.04


z K(La) are newly derived by using the CIE metriclightnessL*. They correlate well to the correspondingquantities already derived by the nonlinear color-ap-pearance model.4,5,14Numerical examples are given forconfirmation.

4. The opponent-colors concept in the present study isessentially the same as that established by Hering,2

especially in using the six primary colors in the system.However, the present study demonstrates two kinds ofopponent-colors responses on the basis of differentperception levels (Table III). One is whiteness-black-ness, redness-greenness chroma, and yellowness-blue-ness chroma, and the other is whiteness-blacknessstrength, redness-greenness colorfulness, and yellow-ness-blueness colorfulness. At each perception level,the three responses constitute the fundamental threeaxes (six opponent colors) in the opponent-colors the-ory without any contradiction.

5. A further contribution to the opponent-colors theory isthe recognition of the importance of the grayness per-ception in the opponent-colors responses. The introduc-tion of the grayness perception provides various meritsfor understanding the opponent-colors responses.

6. The proposal of a concept of colorfulness on whiteness-blackness, redness-greenness, and yellowness-bluenessclarifies that the Hunt Effect and the Stevens and Jame-son–Hurvich Effect are now demonstrated to belong tothe same category from the viewpoint of the opponent-colors theory.

7. The nonlinear color-appearance model and its relatedstudies reported previously can explain almost all thecolor attributes of object-colors discussed in the presentarticle. However, some minor corrections to the modelare found advisable, as shown above. Further studiesare expected in the future to confirm the proposals inthe present article by using color-appearance observa-tions from subjective estimation.

NOTES

1. The colorimetric values of a Munsell color samplechange by changing the illuminant for deriving them.However, irrespective of the computed results, the sam-ple itself, for example, with the notation 5R 5/6, isalways fixed. For a specific illuminant, the fixed sam-ple’s colorimetric valuesx, y, Y, metric lightnessL*,and metric chromaC* are easily determined.

2. The relation between the correlates ofBr in Eq. (3) andof J in Eq. (2) is derived by the following equation onthe basis of their CIE definitions:

J(La) 5 [Br(La)/Brw(La)] 3 100 (16)

whereBrw(La) is the brightness correlate of the white sam-ple withYw 5 100 andL*w 5 100. In Eq. (3),Brw(La) 5 100K(La) holds. Introducing this relation to Eq. (16), it is easilyexpected that Eq. (2) holds.

ACKNOWLEDGMENTS

The author thanks the reviewers for their kind suggestionsin improving the present article. The author is also thankfulto Dr. Ralph W. Pridmore for his valuable comments andkind assistance in clarifying the manuscript. Further, theauthor is indebted to his colleagues, Dr. K. Hashimoto, Dr.H. Sobagaki, and Mr. T. Yano, for helpful discussionsconducted during the course of the present study.

APPENDIX 1: CIE DEFINITIONS OF LIGHTNESS,BRIGHTNESS, CHROMA, AND COLORFULNESS

The CIE definitions1 of brightness and colorfulness areshown below:

Brightness: Attribute of visual sensation according to whichan area appears toemit more or less light.

Chromaticness; colorfulness: Attribute of a visual sensationaccording to which theperceived color ofan area appearsto be more or less chromatic.

The different parts in the definitions of both terms areshown in italic script. Most parts of the two definitions arethe same irrespective of achromatic and chromatic at-tributes. It is understood that both attributes belong to thesame level of perception as shown in Table III.

The CIE definitions of lightness and chroma are shownbelow:

Lightness :The brightness of an area judged relative tothebrightness of a similarly illuminated area that appears tobe white or highly transmitting.

Chroma :Chromaticness, colorfulness of an area judged asa proportion ofthe brightness of a similarly illuminatedarea that appears to be white or highly transmitting.

The different parts in the definitions of both terms areagain shown in italic script. Most parts of the two definitionsare the same irrespective of achromatic and chromatic at-tributes. It is understood that both attributes belong to thesame level of perception as shown in Table III.

In the above definitions of color attributes, the term“sensation” is used. However, in the present study, theauthor uses the term “perception” throughout for all thecolor attributes of object-colors, including the terms givenin Appendix 2, for the following reasons. In the presentarticle, we always discuss the color attributes of object-colors. They are a combination of spatial sensation of sur-face object on a background and a sensation of the colorattribute studied, which corresponds as a combination to theterm “perception.”

This article differentiatescolor sensationandcolor per-ceptionas follows, based on explanation in Chapters 2, 4,and 5 of theScience of Color(SC), 1963.27 Sensationis thedirect result in consciousness of the present stimulation ofthe sense organs, whereasperceptionincludes the combi-nation of sensation(s) and past experience (including knowl-


edge) in recognizing the objects or facts from which thepresent stimulation arises. The perception is, thus, morecomplex and specific than a sensation. Actual color expe-riences are rarely simple sensations, but almost alwaysoccur in more complex perceptual forms, i.e., as percep-tions. These occur in different settings or modes of appear-ance, which may involve various temporal or spatial factorsand/or previous learning or conditioning. Color sensationsare the basic psychological attributes of color vision, widelyaccepted to be brightness/lightness, hue, and saturation/colorfulness. These are basic to all modes of appearance,e.g., luminous/aperture/unrelated color and object/relatedcolor (with submodes, e.g., surface and volume color). In aparticular mode of appearance (e.g., object-color), thesebasic attributes or attributes unique to that mode (e.g.,depth, location, shadow, glossiness, etc.) are perceived asdistinct from the attributes of another mode. See p. 151 andTable 1 of SC.27 When a psychological attribute derivesfrom a particular mode (e.g., object-color, as in the presentarticle) it is termed a color perception, as being a combina-tion of sensation(s) and/or experience(s).

APPENDIX 2: DEFINITIONS OF “WHITENESS-BLACKNESS STRENGTH” AND “WHITENESS-

BLACKNESS” USED IN THE PRESENT ARTICLE

The definitions of whiteness strength, blackness strength,and whiteness-blackness strength are shown below:

Whiteness strength: Attribute of visualperceptionaccord-ing to whichthe perceived color ofan area appears tobemore or less whitish.

Blackness strength: Attribute of visualperceptionaccordingto which the perceived color ofan area appears tobemore or less blackish.

The different parts in the definitions between brightnessand the above two terms are shown in italic script. In thecase of combining both concepts, whiteness strength andblackness strength together, the term whiteness-blacknessstrength or strength of whiteness-blackness is used through-out the present article. Both whiteness-blackness strengthand brightness belong to the same level of perception, asshown in Table III, from their definitions.

The definitions of whiteness and blackness are shownbelow:

Whiteness: The whiteness strength of an area judgedas aproportion of the brightness of a similarly illuminatedarea that appears to be white or highly transmitting.

Blackness: The blackness strength of an area judgedas aproportion of the brightness of a similarly illuminatedarea that appears to be white or highly transmitting.

The different parts in the definitions between lightnessand the above two terms are shown in italic script. In thecase of combining both concepts, whiteness and blacknesstogether, the term whiteness-blackness is used throughout

this article. Both whiteness-blackness and lightness belongto the same level of perception, as shown in Table III, fromtheir definitions.

APPENDIX 3: ADAPTING AND OBSERVINGCONDITIONS

The observing condition of the color-appearance modelused in the present study is described in the previous arti-cle.23 For readers’ convenience, it is again introduced herein detail.

A test color sample with a visual angle 2° is placed in thecenter of a large nonselective (achromatic) background withits luminance factorYo (%). The visual field consisting ofboth the color sample and the background is illuminated byan adapting illuminant of illuminanceEo lx. The illumi-nanceEo is called “adapting illuminance” and the back-ground “adapting background” in the present article. For theadapting illuminant, D65 is always used in the presentstudy. The luminanceLa of the background, “adapting lu-minance”, in cd/m2 is determined byLa 5 YoEo/100p. Thesubscript ‘o’ for Y andE corresponds to the adapting back-ground used in the experiment under study.

Color-appearance attributes of a test color sample areassessed by an observer adapted to the visual field. It isassumed that the adapting state of the observer is com-pletely determined by the adapting luminanceLa and thechromaticity of the adapting background, D65 in the presentstudy. In other words, the adapting state of the observer isindependent of the kind of test color sample to be assessed.The phenomenon of the change of color perception bychanging its adapting luminance is called “adapting-lumi-nance dependency” in the present article.

The above situation corresponds to the actual observingconditions, using an observing booth painted on all the innerwalls with an achromatic color with luminance factorYo

(%), and observing test color samples one at a time. Further,observers are instructed always to look at the adaptingbackground, and they are allowed to see a test color sampleonly briefly when necessary for its assessment. These actualobserving conditions satisfy the theoretical requirements foradapting condition stated above.

It has already been shown that the nonlinear color-ap-pearance model by Nayataniet al.4,5 can predict severalexperimental results from color-appearance studies withvarious color sample arrays and modes including a Mon-drian color-sample array and color-monitor display.22 Thegoodness in predictability is partly caused by the fact thatthe effect of the change of adapting luminance is not solarge as found in Fig. 1. In other words, the adaptingluminance dependencies are approximately proportional tothe logarithmic values of adapting luminance.

APPENDIX 4: NOTATIONS USED FOR BRIGHTNESSAND WHITENESS-BLACKNESS STRENGTH

In the nonlinear color-appearance model by the presentauthor, the notationBr is used for brightness, andQ for


whiteness-blackness strength. The notationQ for whiteness-blackness strength has been used in all the previous studieson the nonlinear color-appearance model by the author andhis colleagues.4,5 On the other hand, in the color-appearancemodel CIECAM97s,15,16 the notationQ is used for bright-ness. This notation follows that used in the Hunt model of1982.25 Other notations are almost the same or similarbetween the two models.

APPENDIX 5: BLACKNESS IN THE STUDYBY STEVENS

In relation to Fig. 4 in the Stevens study,6 which is similarto Fig. 3 of the present article, Stevens gave the followingsentences on p. 86 of his article. In spite of the scale ofapparent brightness used in his study, he uses the word“blacker.” The Stevens article6 indicates that a close relationexists between Fig. 4 in his study and whiteness-blacknessstrength.

“What seems startling in Fig. 4 is that for some shades ofgray the apparent brightness is supposed to decrease whenthe illumination is increased. Turn on more light and thetarget looks darker! That is the verdict of the dashed linesthat slope down toward the right. This prediction has beenchecked with six observers who, having spent about 10minutes in adapting to darkness, viewed a dark gray on awhite background. The darkness of the target seen in dimlight grew suddenly deeper when the illumination was sud-denly increased by 10 or 20 decibels. The observers foundit especially interesting to watch the target turn graduallyblackeras the illumination is gradually increased.”

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6. Stevens SS. To honor Fechner and repeal his law. Science 1961;133:80–86.

7. Jameson D, Hurvich LM. Complexities of perceived brightness. Sci-ence 1961;133:174–179.

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9. Nayatani Y. Simple estimation methods for the Helmholtz–Kohlrauscheffect. Col Res Appl 1997;22:385–401.

10. For example: Naka KI, Rushton WAH. S-potentials from luminosityunits in the retina of fish (Cyprinidae). J Physiol 1966;185:587–599.

11. Mori L, Sobagaki H, Komatubara H. Field trials of CIE chromaticadaptation formula. In: CIE Proc 22nd Melbourne. Vienna: CentralBureau of CIE; 1991. Division 1, p 55–58.

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25. Hunt RWG. A model of colour vision for predicting color appearance.Col Res Appl 1982;7:95–112.

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on attributes of achromatic and chromatic object-color perceptions

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