Errata:

1) On page 200, the coefficient on B^1/3 for the j coordinate in Eq. 5.2 should be -9.7, rather than the +9.7 that is published.

2) On page 203, Eq. 5.4, the upper expression for L* should be L* = 116(Y/Yn)^1/3-16. The exponent 1/3 is omitted in the published text. In addition, the leading factor in the expression for b* should be 200 rather than 500.

3) In the expression for "deltaH*_94" just above Eq. 5.8, each term inside the radical should be squared. Color Appearance and Color Difference Specification

David H. Brainard Department of Psychology University of California, Santa Barbara, CA 93106, USA Present address: Department of Psychology University of Pennsylvania, 381 S Walnut Street Philadelphia, PA 19104-6196, USA

5.1 Introduction 192 5.3.1.2 Definition of CI ELAB 202 5.31.3 Underlying experimental data 203 5.2 Color order systems 192 5.3.1.4 Discussion olthe C1ELAB system 203 5.2.1 Example: Munsell color order system 192 5.3.2 Other color difference systems 206 5.2.1.1 Problem - specifying the appearance 5.3.2.1 C1ELUV 206 of surfaces 192 5.3.2.2 Color order systems 206 5.2.1.2 Perceptual ideas 193 5.2.1.3 Geometric representation 193 5.4 Current directions in color specification 206 5.2.1.4 Relating Munsell notations to stimuli 195 5.4.1 Context effects 206 5.2.1.5 Discussion 196 5.4.1.1 Color appearance models 209 5.2.16 Relation to tristimulus coordinates 197 5.4.1.2 C1ECAM97s 209 5.2.2 Other color order systems 198 5.4.1.3 Discussion 210 5.2.2.1 Swedish Natural Colour System 5.42 Metamerism 211 (NC5) 198 5.4.2.1 The problem of metamerism 211 5.2.2.2 OSA Uniform Color Scale 5.4.2.2 Colorant order systems? 21 1 (OSAlUCS) 199 5.4.2.3 Metamerism indices 21 1 5.2.2.3 DIN color system 201 5.4.2.4 Linear models 212 Acknowledgments 213 5.3 Color difference systems 202 5.3.1 Example: CIELAB color space 202 Notes 213 5.3.1.1 Problem - specifying color tolerance 202 References 213

The Science of Color Copyright © 2003 Elsevier Ltd ISBN 0-444-5/2-519 All rights of reproduction in any form reserved I 91 - • THE SCIENCE OF COLOR

5.1 phenomenology of color appearance and describes the psychological attributes of hue, sat­ The physical properties of color stimuli may be uration/chroma, and brightness/lightness. specified using spectral measurements or tristim­ The chapter begins with a discussion of color ulus coordinates. Such specification, however, order systems. A color order system is a type of provides Iinle intuition about how the stimuli color appearance system - that is, a type of system will appear. For applications such as color for specifying color appearance. In a color order selection we would like to specify color using system, the color appearance of a carefully appearance terms and have an automatic method selected set of color samples is specified. The for computing the corresponding tristimulus samples are arranged to make it easy to find a coordinates. To do so we need to understand the desired color and to allow visual interpolation relalion between the physical description of a between samples. To help fix ideas, a detailed color stimulus (e.g. its tristimulus coordinates) review of the popular Munsell color order system and a quantitative description of its color is provided, followed by a brief description of a appearance. few other systems. Next comes an overview of A second topic of practical importance is to color diHerence systems. The overview begins specify the magnitude of diHerences between with a concrete example, the CIELAB uniform colored stimuli. Here we need to understand color space, which is useful for specifying small the relation between changes in the physical color differences. Following the example, a lew description of a color stimulus and corresponding other systems are briefly described. The chapter changes in appearance. In specifying color repro­ closes with discussion of a number of issues and duction tolerances, we are likely to be concerned tOpICS. with small color diHerences: how different must the tristimulus coordinates of two stimuli be before the color diHerence between them is just barely noticeable? For color coding, on the other 5.2 hand, we are more likely to be concerned with whether two colors are sufficiently diHerent to 5.2.1 EXAMPLE: MUNSELL COLOR be easily discriminable. For example, if we are ORDER SYSTEM designing trarfic signals we would like to be sure that the red and green lights are easy to tell 5.2.1.1 Problem - specifying the apart. appearance of surfaces There are a number of systematized methods The Munsell color order system was originally available bOlh for specifying color appearance conceived by A.H. Munsell in 1905 (Munsell, and for specifying color difference. Unfort­ 1992). His goal was to provide a system for spec­ unate
y' no perfect system exists for either ifying colors and for teaching students about the purpose. To use the systems successfully, it is perceptual anributes of color. He devised a necessary to have a firm grasp of the principles symbolic notation for color appearance: this is underlying their design. The purpose of this referred to as Munsell notation. Munsell's system chapter is to provide an introduction to color was operationalized as a collection of color specification systems and some guidance as to samples, so that it was possible to understand their use. A detailed survey of such systems is visually the relation between Munsell color not attempted here, but a number of excellent names and the corresponding color percepts. The reviews are available (Judd and Wyszecki, 1975; Munsell system has been modified several times Robertson, 1984; Billmeyer, 1987; Hunt, 1987b; to improve the correspondence between the Derefeldt, 1991; Fairchild, 1998). This chapter actual samples and the underlying perceptual builds on the material introduced in Chapters 3 organization (Nickerson, 1940; Berns and and 4. Chapter 3 introduces the color matching Billmeyer, 1985). experiment and describes how tristimulus Current collections of samples (see coordinates may be used to represent the spec­ http://munsell.com/) implementing the Munsell tral properties of light. Chapter 4 discusses the system are based on the results of an extensive

192 COLOR APPEARANCE AND COLOR DIFFERENCE SPECIFICATION • study by an Optical Society of America commit­ Samples that differ in Munsell hue or chroma tee in the 1930s and 40s (Newhall, 1940; but that have the same value should be judged Newhall et aI., 1943). This committee conducted to have the same lightness. Equal steps on the scaling experiments on samples from an early value scale are deSigned to represent equal edition of the Munsell Book of Color. It also changes in perceived lightness. made physical measurements of the samples. The notational form used to express Munsell Based on these data, it generated extensive colors begins with the hue, followed by the tables relating Munsell notations to the tristimu­ value and chroma numbers. These latter two Ius coordinates (under standard conditions of are separated by a slash. Thus the notation 2.5R illumination) that a sample of that notation 8/4 refers to a sample with hue 2.5R. value 8, should have. This tabulation now defines the and chroma 4. The letter N is used to denote Munsell system, and is sometimes referred to as neutral samples and the chroma value is omit­ Munsell renotarion. ted. Thus N 8/ is used to indicate a neutral sam­ ple of value 8 and 0 chroma. In the Munsell 5.2.1.2 Perceptual ideas scheme, any stimulus (provided it is seen in The basic idea underlying the Munsell system is surface mode) has a color appearance that may that color appearance may be described in terms be described by the appropriate Munsell nota­ of three attributes: hue, chroma, and lightness tion. See Chapter 4 for a discussion of modes of (see Chapter 4). The system therefore consists of appearance. scales for each of these attributes. Munsell hue is a circular scale based on 10 5.2.1.3 Geometric representation major hues, Red (R), Yellow-Red (YR), Yellow If we hold the attribute of hue constant, it is nat­ (Y), Green-Yellow (GY), Green (G), Blue-Green ural to represent Munsell value and chroma (BG). Blue (B), Purple-Blue (PB), Purple (P), using rectilinear coordinates. A rectilinear repre­ and Red-Purple (RP). In addition, the 10 major sentation makes sense for these two attributes hues are subdivided further into a scale that because each has a well-defined origin (black ranges from I to 10, with 5 denoting the major for value, neutral for chroma) and because hue itself. A digit-letter notation is typically used numerical differences on each scale are related to specify Munsell hue, so that 2.5R would refer monotonically to perceived color difference. to step 2.5 in the major hue category red. Equal The situation is not so simple for Munsell hue. steps on the Munsell hue scale are designed to First. there is no natural origin for hue. Second, represent equal changes in perceived hue. Thus there is no linear scale for hue such that num­ the 10 subdivisions of the 10 major hues form a erical differences on the hue scale are mono­ 100 point scale for hue. tonically related to perceived differences. It is Munsell chroma is specified on a numerical possible, however, to represent hue geometrically scale starting at 0 and extending out to the using a polar coordinate system. It turns out that maximum possible chroma for each hue. A when hue is arranged in a circular fashion, dis­ chroma of zero indicates a black, gray, or tances between points provide a reasonable white. Increasing chroma numbers indicate approximation to their perceptual differences progressively more pure color percepts. Samples (see Chapter 4). that differ in Munsell hue but that have the The rectilinear representation for chroma and same chroma should be judged to differ equally value may be combined with the circular repre­ from an achromatic sample of the same light­ sentation for hue to provide a cylindrical coordi­ ness. Equal steps on the chroma scale are nate system for the Munsell system. In cylindrical meant to represent equal changes in perceived coordinates, the angular coordinate represents chroma. hue, the linear coordinate represents value, and The Munsell scale for lightness is called the radial coordinate represents chroma. Any value. Munsell value is specified on a numerical stimulus seen in surface mode can thus be scale that ranges from 0 for colors judged to have thought of as a point in a three-dimensional the same lightness as black to 10 for colors Munsell space. The geometry of the Munsell sys­ judged to have the same lightness as while. tem is illustrated in Figure 5.1.

193 • THE SCIENCE OF COLOR --

75

65

chroma

value

Figure 5.1 The Munsell color order system.The Munsell hue circle (upper left) is a series of neutral colors that vary in value only (vertical series on right), and a series that varies in chroma at constant hue and value (middle left). As shown at the lower left, the Munsell system may be organized cylindrically, with an angular coordinate representing hue, a linear coordinate representing value, and a radial coordinate representing chroma. (Courtesy of Munsell Color Services, a division of GretagMacbeth.)

194 COLOR APPEARANCE AND COLOR DIFFERENCE SPECIFICATION •

5.2.1.4 Relating Munsell notations to scaled and the numerical scales adjusted so that stimuli equal steps on each scale corresponded to equal Note that the conceptual system described above perceptual differences. Finally, judgments across describes perceptual variables and is independ­ colors of differing value were made, so as to ent of any specification of which stimuli elicit equate the hue and chroma scales across varia­ particular perceptions (e.g. Figure 5.1). Another tions in value. way to say this is that, in principle, one can The current specification of the relation imagine the appearance of any Munsell specifi­ between Munsell notations and physical samples cation without ever having seen a set of Munsell is based on experiments performed on the 1929 samples. Thus we can regard the Munsell system samples by a committee of the Optical Society of as a theory that describes the phenomenology America (Newhall, 1940; Newhall et al., 1943). of color perception. No direct experiments justi­ Observers performed two types of tasks in these fied this theory; it was derived primarily from experiments. In one, they judged whether the Munsell's own introspection. 1929 samples in fact satisfied the requirements The Munsell system would not have much of the Munsell perceptual scheme. In one exper­ practical value if it were only an abstract theory iment, for example, observers viewed a series of of perception. The usefulness of the system arises samples that had the same nominal hue and because there exist a set of samples that exemplify value but that varied in chroma. They then indi­ the system. The original implementation of the cated whether the samples in fact appeared to Munsell scheme was created by A.H. Munsell in have the same hue and scaled the direction and conjunction with an artist who carefully painted magnitude of any deviations. This type of judg­ samples to match Munsell's conception. This led ment was used to identify adjustments required to the production of the Munsell Color Atlas to achieve better lines of constant hue, chroma, in 1915 (Munsell, 1915). Subsequent work and value. In a second type of task, observers (Munsell et al., 1933; Godlove, 1933) focused on judged differences between samples from the refining the value scale for neutral colors. Thresh­ 1929 book. For example, observers were shown olds for detecting just-noticeable-differences two pairs of samples differing in hue but with (JNDs) were measured over a range of stimuli the same value and chroma. They were then that appeared from black to white, and a scale of asked to judge the ratio of the differences equal JND steps was generated from the data. between the two pairs. This type of judgment This scale was validated using a variety of other was used to adjust the spacing of the samples in scaling procedures. The value scale thus created the 1929 judgment to more closely approximate formed the backbone of the 1929 Munsell Book of the even perceptual spacing that is the goal of Color (Berns and Billmeyer, 1985). the Munsell scheme. The exact judgments used to determine the In addition to scaling experiments on the 1929 samples corresponding to other Munsell nota­ samples, the committee also made physical tions are not well documented. Basically, how­ measurements of the samples. By analYZing the ever, the following scheme was used (Berns and relation between perceptual judgments and Billmeyer, 1985). First, judgments were made to physical tristimulus coordinates, the committee equate the lightness of non-neutral colors to generated extensive tables relating Munsell those of neutral colors. The result was an assign­ notations to the tristimulus coordinates that a ment of values to a large number of samples. sample of that notation should have (under Given a collection of samples of equal value, standard conditions of illumination). The actual observers then scaled these according to their analysis was performed graphically by plotting hues and chromas. There were two goals of the the measurements on large pieces of graph paper scalings. The first was to equate the numbers and fitting smooth curves by hand, so that no assigned for one attribute across variations in the analytic expression for the relation between other, so that within a set of samples with equal Munsell notation and tristimulus coordinates value, lines of constant hue and constant exists. The tabulation now defines the primary chroma were defined. Second, the differences implementation of the Munsell system, and is between lines of constant hue and chroma were sometimes referred to as Munsell renotation.

195 • THE SCIENCE OF COLOR

Current implementations of the Munsell system performed. For the Munsell system, these were conform closely to the renotation aim points. viewing under CIE Standard Illuminant C (an approximation to daylight), with the samples 5.2.1.5 Discussion placed against a nonselective background with The Munsell color order system may be thought a reflectance of approximately 18% (Munsell of as consisting of two pans. The first is an abstract sample N 51). The mapping is not necessarily perceptual scheme for specifying colors. The valid for other viewing conditions, but that does second is a large lookup table that defines an not mean that the Munsell perceptual scheme instantiation of the Munsell scheme (see Figure could not be applied generally. Rather, it would 5.2). One side of the table contains tristimulus take another set of scaling experiments or a coordinates of samples. The other side of the table model of the effect of context on color appear­ contains the symbolic description corresponding ance to provide the appropriate implementation. to each sample when it is viewed under standard The lookup table view of the implementation conditions. Typically these conditions are isolated of color order systems is simplistic, as it neglects viewing against a uniform nonselective (gray) the geometric structure that may be imposed on background under a spedfied illuminan!. The the arrangement of the symbolic names. It does exact details of the standard viewing conditions capture the fact that the mapping between tristi­ vary across color order systems and even for dif­ mulus coordinates and symbolic names is com­ ferent implementations of the same color order plex. Indeed, an analytic description of this system. The mapping between tristimulus coordi­ mapping for implementations of the Munsell nates and symbolic descriptions is defined only system has been elusive. Practical translation for the standard conditions. between tristimulus coordinates and Munsell As emphasized by McCamy (McCamy, 1985), it names is accomplished by lookup table search is useful to maintain the distinction between a and interpolation, sometimes with the aid of color order system's perceptual scheme and neural networks (Simon and Frost. 1987; Smith, implementations of this scheme. In evaluating a 1990a; Burns et aI., 1990; Usai et aI., 1992; color order system, we can ask two types of ques­ Tominaga, 1993). The difficulty with these tions. First. does the perceptual system on which methods is that they require large databases the system is built provide a useful characteriza­ specifying either the table entries or summaries tion of color appearance? Second, does a panicu­ thereof. Wyszecki and Stiles (1982) provide tab­ lar instantiation of the system conform to the ulations of tristimulus coordinates and corre­ underlying perceptual ideas? Ole, for example, sponding symbolic descriptions for the Munsell that the mapping between names and tristimulus and other color order systems. A program for values is valid only for one set of viewing condi­ performing the conversion is available free of tions. These are the conditions under which the charge from the GretagMacbeth Corporation scaling experiments that defined the table were (http://munsell.com/).

x Y z Symbolic 33.8 30.0 30.0 5R 6/4 36.6 30.0 27.2 5R 6/6 ...38.2 ...30.0 ...22.7 5R..6/8. • 28.5 30.0 16.5 5Y 6/4 ...... Viewed in standard context ... 51.4...79.0 ...67.2 ... 5G...9110

Figure 5.2 Lookup table view of a color order system implementation. One side ofthe table contains tristimulus coordinates ofsamples.The other side ofthe table contains the symbolic description corresponding to each sample when it is viewed under standard conditions.Typically these conditions are isolated viewing against a uniform non·selective (gray) background under a specified iIIuminant.

196

---~~~~~~~------COLOR APPEARANCE AND COLOR DIFFERENCE SPECIFICATION •

The Munsell system is useful for several pur­ one would expect from its name. If we consider poses. First, it allows us to specify colors in the original Munsell system, based on physical appearance terms. With a little training, observers samples, the color constancy of the human can apparently become proficient at describing visual system will make the specification some­ colors using Munsell terms (Helson, 1938; what robust in the face of changing illumination. Whitfield et al., 1988) so that the Munsell system Color constancy is not perfect, however, so provides a language for talking about color Munsell notation must be treated carefully in appearance. In this capacity, the system has been applications where the illuminant is not standard. used successfully in scaling experiments that If we consider Munsell renotation, an additional studied the effect of context on color appearance difficulty arises. Renotation relates tristimulus (Helson, 1938; Helson and Jeffers, 1940). coordinates of the samples to the Munsell nota­ More important, perhaps, is the fact that there tion. To take changes in illuminationinto account, exist implementations of the Munsell notational it is necessary to calculate how the tristimulus system. Even il a user is unable to name the coordinates of an actual sample would change exact Munsell term for a desired color, he or she with the Uluminant. Some approximations to this can look through the Munsell book of color calculation are possible (Brainard, 1995). This until a close approximation to the desired color issue is discussed further in the section on is found. Because the samples are arranged in an metamerism below. orderly way and are evenly spaced, it is possible Second, the Munsell system does not provide to interpolate visually between the sample a metric for small color differences. Although the points to specify color more precisely than the Munsell renotation is designed so that equal sample spacing (Billmeyer, 1988). Once the steps correspond to color clifferences judged desired Munsell notation is known, the tables equal. it is important to remember that the color defining the Munsell system in terms of tristim­ differences judged were well above threshold. ulus coordinates may be used to find a physical For small color differences, one is concerned specification for the desired color. with visual thresholds, and there is no obvious Inverse mapping is also possible. A test sample relation between threshold data and the supra­ can be compared to the collection of Munsell threshold judgments on which the Munsell samples under the standard viewing condHions. system is based (MacAdam, 1974; Robertson, It is then possible to interpolate between the 1977). In addition, it is useful to bear in mind near matches and assign a Munsell name to the that the Munsell system was based on scaling test sample. differences in one of the three color attributes Because of the manner in which it was devel­ while the others were held fixed. Thus any oped, the Munsell system also provides a metric effects that intrude when all three attributes are for the apparent differences between colors. For covaried are unlikely to be accurately described example, the perceptual difference correspon­ by the Munsell system. ding to one step of Munsell value should be the same, independent of the hue or chroma of the 5.2.1.6 Relation to tristimulus sample. Note that steps on the three Munsell coordinates appearance scales are of different magnitudes. A The Munsell system may be used to illustrate some step of I on the value scale is designed to be per­ of the perceptual effects discussed in Chapter 4. ceptually equivalent to a step of 2 on the chroma Figure 5.3 shows lines of constant Munsell hue scale and a step of 3 on the hue scale (at chroma plotted in the CIE 1931 chromaticity diagram. The 5). Because hue is specified in polar coordinates, left panel of the figure shows the plot for Munsell the perceptual magnitude of a single hue step value 2, while the right panel shows the plot for varies with chroma. Munsell value 8. Note that in each panel the con­ There are things that the Munsell system does stant hue lines curve, illustrating the Abney hue not provide. First, it does not provide any means shift. Also note that the locations of the lines for to take viewing context into account. The same particular hues shift considerably between the two Munsell paper seen in non-standard viewing panels. The factthat the lines for differentvalue do contexts may appear quite different from what not superimpose illustrates the Bezold-Brlike

197 • THE SCIENCE OF COLOR

.65 .65 .60 .60 .55 .55 .50 .50 c- .:5 .45 ro ~40 U-t::A eE .40 -5 .35 -5 .35 ~ ~ .30-f:i;~ .30 .25 .25 .20 .20 .15 .15 .10 .15 .20 .25 .30 .35 .40 .45 .50 .55 .60 .65 .70 .10 .15 .20 .25 .30 .35 .40 .45 .50 .55 .60 .65 .70 x chromaticity x chromaticity

Figure 5.3 (Left) Lines of constant Munsell hue for Munsell value 2, plotted in the CIE 1931 chromaticity diagram. (Right) Lines of constant Munsell hue for Munsell value 8, plotted in the CIE 1931 chromaticity diagram. (From Wyszecki and Stiles, 1982. Copyright © 1982 John Wiley & Sons, Inc., reproduced by permission.) hue shift. Chapter 4 discusses the Abney and Given this general point, it would be possible Bezold-Brlike shifts in more detail. to compare the details of a large number of The fact that the constant hue lines curve and systems. Such detailed comparisons are avail­ are not invariant with changes in value illus­ able elsewhere (Billmeyer and Bencuya, 1987; trates the basic difficulty in specifying color Derefeldr. 1991). It is of interest, however, to rlis­ appearance. Simple models of visual processing cuss some particular color order systems briefly, do not easily predict the shape of the constant both to familiarize the reader with them and to hue lines. The search for models that do is cur­ illustrate how a system might be built on princi­ rently an area of active research (see section on ples other than those that underlie the Munsell color appearance models below). system. Three systems will be discussed: the Swedish NCS, the OSAIUCS, and the DIN color 5.2.2 OTHER COLOR ORDER SYSTEMS system. None of these systems denies the role of perceptual dimensions related to hue, satura­ The MunselJ color order system is not the only tion, and lightness in our perception of color. color order system. Other color order systems The first two differ from the Munsell system include the Swedish Natural Color System primarily in that the judgments used to define (NCS), the Optical Society of America Uniform the system are not direct scalings of such Color Scale (OSAIUCS), the Deutches lnstitut qualities. fur Normung (DIN) system, and the Coloroid system. From the discussion above, one can see 5.2.2.1 Swedish Natural Colour that there are two primary ways a system could System (NCS) differ from the Munsell system. First. the per­ The fundamental scalings underlying the ceptual principles on which a system is based Munsell color order system are judgments of could differ. Second, the implementation of the hue, chroma, and value. These are not the only system could rliffer. For example, a system based judgments upon which a color order system can on the same perceptual principles as the Munsell be based. Indeed, the NCS is based on a different system but with samples defined for different set of scalings. In the NCS, the appearance of a viewing conditions might be considered a rliffer­ color is specified by its resemblance to six ent system. In practice, it is sometimes rlimcult elementary colors: red, green, blue, yelJow, to decide whether the perceptual principles of black, and white. This system was developed two systems rliffer because the only way to from opponent process notions (see Chapter 4), judge what the words mean is to compare the in that it is based on the tenet that in judging the implementations. color appearance of stimuli, we have access to

198 COLOR APPEARANCE AND COLOR DIFFERENCE SPECIFICATION • the outputs of three independent mechanisms: a Although the basic scaling judgments underly­ red-green mechanism. a blue-yellow mecha­ ing the NCS are six resemblances, the final spec­ nism. and a white-black mechanism. (The ification thus ends up in terms of blackness, white-black mechanism is sometimes referred to chromaticness, and hue. These are conceplllal as the luminance mechanism.) If one accepts this relatives of Munsell lightness (inverted), tenet. then judging color in terms related to chroma, and hue. Like the Munsell system, the tbese mechanisms (by asking subjects about NCS system may be displayed geometrically. The resemblances) is a natural choice. Abramov and standard NCS geometry within a particular hue Gordon (1994) review basic research on this is diagrammed triangularly, as shown on tbe left type of judgment. Samples that implement the of Figure 5.4. Vertical lines represent constant NCS system exist as the NCS Colour Atlas, and chromaticness. Diagonal lines represent loci of tristimulus specifications for the NCS notations constant blackness. The arrangement of the NCS are available (Swedish Standards Institution, hue circle is also shown in Figure 5.4. Because of 1982; 1983; 1989; hltp:/Iwww.ncscolour.coml). the fundamental role played by red. blue, green, The detailed description that follows is based and yellow, these four hues are placed equally primarily on Derefeldl's (1991) review. around the circle. Other stimuli are then placed Although the subject is asked to judge six proportionately according to their relative resemblances in the scalings for the NCS system, resemblances to these four cardinal colors. there are some constraints on the judgments Although both the Munsell and NCS systems they are allowed to make. The first restriction is describe color appearance in terms of similar that no color may be judged as resembling both attributes, it is not clear that the two systems red and green, and no color may be judged as represent the same underlying perceplllal resembling both blue and yellow. Thus a stimu­ dimensions. Indeed. direct comparisons suggest lus may be judged to resemble at most two of that Munsell and NCS hue are quite different red, green, blue. and yellow. The NCS hue is from one another (Billmeyer and Bencuya, defined in terms of the relative resemblances of 1987; Smith et aI., 1990b; see Derefeldt, 1991 for the stimulus to these four unique hues. (See an extended bibliography on this topic). Because Chapter 4 for more on unique hues.) The nota­ the systems differ, one can also ask whether tion used to specify NCS hue is first a letter spec­ one is more easily learned than the other. It has ifying one unique hue, then a percentage, and been claimed that the NCS system is superior in then a second letter specifying a second unique this regard (Derefeldt. 1991). but this remains hue. Thus R20B indicates a hue where the ratio controversial (Whitfield et aI., 1988). of the resemblances to red and green are 80 to 20. The sum of the judged resemblances to the 5.2.2.2 OSA Uniform Color Scale four basic chromatic colors (red, green, blue, and (OSAlUCS) yellow) is referred to in the NCS system as The OSA Uniform Color Scale was designed to chromaticness. The second restriction is that the provide a specification of stimuli wbose appear­ sum of chromaticness and the resemblance judg­ ance is equally spaced perceptually. Its design ments to black and white must be 100. Because shares much in common with other color order of these restrictions, the six NCS resemblances systems and we describe it here rather than with may be specified using only three numbers. other uniform color spaces. The goal of the OSA These are the two non-zero hue resemblances committee that designed the system was to pro­ and the blackness. Because the hue notation is duce a set of samples such that the perceptual normalized, however, the overall NCS notation spacing between neighboring samples was equal. for colors is a number for blackness, a number whether the samples differed in hue. saturation, for chromaticness, and an NCS hue specification. lightness, or any combination of the three. Thus For example, 3060 R20B would represent a color the fundamental scaling judgments underlying whose individual resemblances were 10 for the OSA/UCS are perceplllal difference judg­ whiteness, 30 for blackness, 48 for redness, 12 ments. MacAdam (1974) provides the final for blueness, and zero each for greenness and report of the OSA committee and describes the yellowness. history of the creation of the OSA/UCS system.

199 • THE SCIENCE OF COLOR

Figure S.4 (Left) Geometry of constant NCS hueY90R.The sample outlined in black is 2030Y90R. (Right) NCS hue circle. (Published with permission from the Scandinavian Colour Institute AB, Stockholm, Sweden. NCS - NATURAL COLOUR SYSTEM, Copyright © and trademark ®, property of Scandinavian Colour Institute AB, Stockholm, Sweden, 200 I.)

In the OSA/UCS system. every sample is where x and yare CIE chromaticity coordinates defined by its values on three coordinates. L. j. computed from the XYZ tristimulus coordinates. and g. Roughly speaking. variation along the L The formulae for computing j and g are: coordinate corresponds to variation in lightness. variation on the j coordinate to variation in blue­ j = C( 1.7R~ + 8G~ + 9.7B~) (5.2) ness/yellowness. and variation on the g coordi­ g = C(-13.7RY.+ 17.7G~ - 4BY,) nate to variation in redness/greenness. For the with standard viewing conditions under which the scalings were performed (viewing under CIE C=----x illuminant D65 against a nonselective back­ 5.9rY~ - Jl,j (5.3) ground of 30% reflectance). the Ljg coordinates R = 0.7990X + 0.4194Y - 0.1648Z of a sample may be computed from its CIE 1964 G = - 0.4493X + 1.3265Y + 0.0927Z (10°) XYZ tristimulus coordinates. The XYZ coor­ B = - 0.1l49X + 0.3394Y + 0.7170Z dinates of the sample are specified with respect to CIE illuminant D65 scaled so that a perfect The Ljg coordinate dimensions form a rectilinear diffuser has a Y coordinate of 100. The formulae coordinate system. An interesting feature of the for computing L are: I OSA/UCS system. however. is that the coordi­ nates are intended to be sampled using a regular­ L = .0..:(X-'----_1,-,4_.4-"..) (5.1 ) rhombohedral scheme. This sounds complex. 12 but may be accomplished by applying the sim­ ple rule that the L. j. and g coordinates for 5.9[Y~ - JI, + 0.0421Y - 301~J. X= o Yo> 30 any sample are either all even integers or all 5.9rY~ 301~1. - JI, - 0.0421Yo - Y0-<030 odd integers. with zero being considered even (MacAdam. 1974). In the OSA/UCS system. Yo = Y(4.4934x' + 4.3034y' - 4.276xy ­ chips that are equidistant nearest neighbors on 1.3744x - 2.5643y + 1.8103) the sampled lattice are designed to be equally

200 COLOR APPEARANCE AND COLOR DIFFERENCE SPECIFICATION • salient from one another. One of the features of emphasis may have led to a lack of interest in the using this lattice structure is that it may be sub­ system, but one should bear in mind that the sampled by a large number of different planes. committee's conclusion applies not just to their Each plane provides a palette that may be useful own space but to any color difference space. for color selection (Cowan, personal communi­ Note that the OSA/UCS system makes no cation). Figure 5.5 shows such planar sampling explicit use of the concepts of color appearance. from the OSAIUCS space. The scaling judgments used to define the space The size of color steps in the OSA/UCS lattice are entirely those of color difference. Although is about 20 just-noticeable-differences under the this may be a weakness for applications where viewing conditions used by the committee. The intuitive descriptions of color are required, the commiuee concluded, however, that judgments space may still be used for appearance specifica­ of color discriminations are fundamentally non­ tion. Because the arrangement of colors in the Euclidean, so that they did not recommend their space is regular, users may visually locale a system for specification of color differences desired sample in the space and find its generally. That is, the committee recommended OSA/UCS coordinates by interpolation. against using Euclidean distance in the Ljg co­ ordinate space as a general color metric. Indeed, 5.2.2.3 DIN color system they concluded that no such metric could exist The D[N system was developed as a German (MacAdam, 1974; see also Indow, 1980). This standard for color specification; a readable

Figure s.S A plane of regularly spaced colors in the OSAJUCS space.The plane is constrained by the requirement that L = j. All coordinate values are integral. L values run from -5 to 6 (bottom to top) while g values run from -10 to 6 (left to right).

201 • THE SCIENCE OF COLOR description may be found in a historical review 5.3 by Richter and Will (1986). The principles under­ SYSifEMS lying the DIN system are very similar to those of the Munsell system, with the interesting vari.a­ tion that a number of colorimetric constraints 5.3.1 EXAMPLE: CIELAB COLOR SPACE were imposed to make the system more conven­ ient to use (Richter and Will, 1986; Billmeyer, 5.3.1.1 Problem - specifying color 1987; Derefeldt. 1991). As with the Munsell, tolerances NCS, and OSA/DCS systems, the DIN system is In writing contracts for color reproduction, it is implemented in a color atlas (DIN, 1980). important to be able to specify how accurately The three perceptual variables of the DIN a color must be reproduced. To do this, it is system are hue, saturation, and darkness. The necessary to have an objective metric for meas­ DIN hue scale for a single saturation and dark­ uring color differences. There are several levels ness was constructed from scaling data, much at which one might want to specify color tol­ in the same way as Munsell hue. Rather than erances. For precise applications, one might extending the scale to other saturations and want to know how large a measured color dif­ lighmesses through further scaling experiments, ference has to be before observers can reliably however, DIN hue was defined to be constant for detect it. This size of difference is often referred lines of constant dominant and complementary to as a just-noticeable-difference. On the other wavelength (with respect to CIE Illuminant C: hand, if one is worried about reproducing the Richter and Will, 1986; Billmeyer, 1987). This characteristic color associated with, say, a par­ simplification makes the transformation between ticular brand, one might want to know how tristimulus coordinates and DIN hue straightfor­ large a measured color difference has to be ward, at the cost of making DIN hue only an before it is classified differently by customers. approximate measure of perceived hue. A similar Detectable color differences do not necessarily compromise was used to construct the DIN satu­ cause any change in the color name given to a ration scale. Lines of constant saturation were stimulus. measured for a single darkness level. and the The purpose of the CIELAB color space is to scale was then extended under the assumption quantify small color differences. By small is that lines of constant saturation are the same for meant differences typical of color reproduction all darkness degrees (Robertson, 1984; Richter tolerances - larger than a JND under optimal and Will, 1986; Billmeyer. 1987). Thus the DIN viewing conditions, but smaller than the differ­ hue and saturation of a sample may be calcu­ ences typically scaled in color appearance sys­ lated directly from its chromaticiry coordinates. tems. As discussed in Chapter 3. when stimuli DIN darkness degree is an inverse scale for light­ are expressed in tristimulus coordinates, the ness. DIN darkness was determined by scaling distance between the coordinates of tWO col­ for neutral colors. For non-neutral colors, the ored stimuli does not correlate well with their darkness for a sample is determined as a direct discriminability. The CIELAB color space was function of the sample's relative luminance fac­ derived from the CIE 1931 XYZ coordinate sys­ tor relative to CIE Illuminant C. The relative tem in an allempt to provide coordinates for luminance factor is the luminance of a sample colored stimuli so that the distance between divided by the luminance of an optimal color the coordinates of any tWO stimuli is predictive with the same chromaticity of the sample. An of the perceived color difference between optimal color is a theoretical construct. Its sur­ them. face reflectance is such that it has the highest luminance of any physically realizable surface of the same chromaticity (Schrodinger, 1920; 5.3.1.2 Definition of CIELAB Rosch, 1928; MacAdam, 1935; Wyszecki and The CIELAB coordinates of a light are referred to Stiles, 1982; Richter and Will, 1986). Again, this as the CIE 1976 L*a*b* coordinates. These may is a convenient approximation which simplifies be obtained [rom the light's CIE 1931 XYZ co­ the calculation of DIN darkness degree. ordinates according to the equations

202 COLOR APPEARANCE AND COLOR DIFFERENCE SPECIFICATION •

Y plots the CIELAB a*b* coordinates of contours of - > 0.008856 116(;)-16, equal Munsell chroma and lines of constant Y" L* = " Munsell hue. If the two spaces were consistent Y with each other. the contours of constant 903.3(; ), -$ 0.008856 Y" chroma would be circles and the. radial spacing " between lines of constant hue would be constant (5.4) at each chroma. As the figure illustrates, the agree­ a* = 500 [r(:) - f( ;)] ment between the two spaces is only approxi­ n n mate. Another comparison data set is the MacAdam ellipses, which measure the just­ b* = 500 [r(;) - f(: )] n n noticeable color differences (MacAdam, 1942; see Chapter 3). If CIELAB accurately represents where the function f(s) is defined as uniform color differences, these should plot as circles in the CIELAB space. Figure 5.6 also s> 0.008856 shows the MacAdam ellipses plotted in the f(s) = 16 CIELAB space. Clearly these are not circular. As 7.787(s) + , s <: 0.008856 (5.5) 116 Robertson (1977) points out, the lack of agree­ ment between CIELAB and the Munselll In this equation, the quantities X"' Y", and Z" MacAdam data could arise because CIELAB is are the tristimulus coordinates of a white point. designed to handle color differences of a magni­ Little guidance is available as to how to choose tude intermediate between the spacing of an appropriate white point. In the case where Munsell samples and just-noticeable-differences. , the stimuli being judged are illuminated samples, To provide a feel for the scale of AE:b we can the tristimulus coordinates of the illuminant compute the average AE~b value corresponding may be used. In the case where the lights being to measured just-noticeable color differences. judged are displayed on a color monitor, the Wyszecki and Stiles (1982) prOVide the parame­ sum of the tristimulus coordinates of the three ters for color difference ellipses measured monitor phosphors stimulated at their maxi­ around 25 different chromaticities by MacAdam mum intensity may be used. (1942). The ellipses represent variability in The Euclidean distance between the CIELAB observers' color matches. From the ellipse coordinates of two lights provides a rough guide parameters it is possible to compute the value of to their discriminability. The symbol AE~" is used AE~" that corresponds to traversing 1.96 standard to denote distance in the uniform color space deviations along the major and minor axis of and is defined as each ellipse. The average resulting value is 3.6, with a range of 0.9 to 9.9. Consistent with this, AE:" = )(AL*)' + (Aa*)' + (Ab*)' (5.6) Stokes, Fairchild, and Berns (1992) report that when the average (taken over image locations) where the various A quantities on the right rep­ AE~b difference between two images is below resent the differences between the correspon­ about 2.2, the images are not discriminably dif­ ding coordinates of the two stimuli. ferent from each other. To give a visual sense for the scale of AE~b' Figure 5.7 shows several 5.3.1.3 Underlying experimental data series of colors separated by constant CIELAB It is difficult if not impossible to go back through differences. the literature and discover the fundamental data used to derive the CIELAB system. The formula 5.3.1.4 Discussion of the CIELAB is a simplification of the Adams-Nickerson color system difference formula that was used in industrial There is general agreement that using the practice prior to 1976 (McLaren, 1970, 1971). CIELAB system is an improvement over using Robertson (1977) compares the CIELAB formula the Euclidean distance between XYZ tristimulus with two fundamental data sets. The first of these coordinates as a color difference metric. To is the spacing of the Munsell colors. Figure 5.6 emphasize the difference between CIELAB and

203 • THE SCIENCE OF COLOR

lao 150 VALUE 51 L*=50 lao SO R G 50 ~~ b* a b* \) \)\) 0 RP c::::::, ~ 0 BB a c::::::, ~~(J\J" <;::; -so -so ~ ~~ OPTIMAL PB P COLORS -100 - -100 -ISO - lao -50 a 50 lao 150 - 2ao -150 -lao -50 a 50 lao 150 a* a*

Figure 5.6 (Left) Contours showing equal Munsell chroma and iso-hue lines plotted in CIELAB coordinates. (Right) A plot of the CIELAB coordinates of isodiscrimination contours measured by MacAdam.The scale of each ellipse has been expanded to improve the visibility of its shape. (From Robertson, 1977. Copyright © 1984 John Wiley & Sons,lnc., reproduced by permission.)

Figu...e 5.7 Each row shows a series of colors separated by constant CIELAB differences. First row shows CIELAB AE~b = 4 along the a'" dimension, second row shows CIELAB AE~b = 12 along the b'" dimension. CIELAB coordinates were computed with respect to a white point defined by the background of the figure. tristimulus coordinates, Figure 5.8 shows iso­ measurements. These have led to a revision of the discrimination contours calcuJated lIsing equal original system. The CIE has recommended one t.E:, values. The contours are plolled in the of these revisions, CIE94 (CIE, 1995; Hung and equiluminant XZ plane of the CIE XYZ color Berns, 1995). A second revision in widespread space, If the two distances in XYZ and CIELAB use is the CMC formula (Clark ef al., 1984). In the both represented perceptual color differences, CIE94 system, a distance measure t.E~ is substi­ the contours would plot as circles. Clearly, they tuted for t.E:... To understand the computation of do not. t.E;" first note that we can rewrite Eqn. 6 as Since its initial standardization, predictions of the CIELAB system have been compared to new

204 COLOR APPEARANCE AND COLOR DIFFERENCE SPECIFICATION •

1500 be expected and future versions may provide more precise guidance about the choice of the k weighting factors. Although the CIELAB system was designed for specification of color tolerances, it has been used 1000 - to assess color differences in other contexts (Carter and Carter, 1981; Sllverstein and N w Merrifield, 1981). In the absence of better for­ U i "\ mulae, this is a reasonable thing to do_ However, it should be stressed that the formulae are not 500 grounded in empirical data that support these " / other uses. Figure 5.6 gives useful comparisons to keep in mind. As noted above, one of the chief difficulties o ~c-==-)----___,c ) in developing a color difference specification a +- system is to take the viewing conditions into a 500 1000 accounL Color discrimination thresholds depend CIE X heavily on factors other than the differences in Figure S.8 Isodiscrimination contours calculated tristimulus coordinates. These factors include the using equal AE~b values plotted in the XZ plane of the adapted state of the observer (Stiles, 1959), the CIE XYZ color space.The points on each of the five spatial and temporal structure of the stimulus contours were calculated to have a constant &E: b (deLange, 1958a, 1958b; Mullen, 1985; difference of 15 from a base stimulus.The conversion from XYZ coordinates to CIELAB coordinates was Sekiguchi et al., 1993) and the perceptual task done with respect to a white point with the same being performed by the observer (Carter and chromaticity as CIE 065 daylight and a luminance of Carter, 1981; Silverstein and Merrifield, 1985; 1000 cd/m1.The luminance o(the base stimuli was Poirson and Wandell, 1990; Nagy and Sanchez, 2 always taken to be 500 cd/m .The contours were 1990). The basic CIELAB formulae include nor­ computed in the equiluminant XZ plane. If CIELAB and CIE XYZ agreed about color differences, the malization to a white point which is designed to contours would plot as circles. take the first of these factors into accounL At present, however, our understanding of observer adaptation is not sufficiently well developed to where the chroma coordinate C:b is defined make us believe that the CIELAB formulation is by C*all = J(a*)' + (b*)''allwhere L'.C* denotes the satisfactory (see Brainard and Wandell, 1991; difference in the C'b coordinate of the two stim­ Fairchild, 1998). uli, and where the hue difference L'.H;b is defined Zhang and Wandell (1997) have developed an = by L'.H*ab JL'.E*au - L'.L* - L'.C*ab _ The CIE94 extension of CIELAB, called S-CIELAB, which difference measure L'.E;4 is computed as a modi- takes the spatial structure of the stimulus into fication of Eqn. 7: accounL S-ClELAB is based on psychophysical measurements showing that visual sensitivity to spatial gratings falls off more rapidly with grating L'.E* = (5.8) 94 spatial frequency when the gratings are modu­ lated in some color directions (e.g. red-green In eqoation 5.8 the S weighting factors are and blue-yellow gratings) than when they are _, modulated in others (e.g. black/white gratings: defined as, SL = 1, Sc = I + 0_045C:b and = _ Mullen, 1985; Sekiguchi et al., 1993). The S­ SH I + O.OlSC:b s where C:lu is the chroma coordinate of the standard sample [rom which CIELAB metric is computed in two separable differences are being computed_2 The k weight­ stages, based on the data and model of Poirson ing factors are all set to 1 [or the reference and Wandell (Poirson and Wandell, 1996). The viewing conditions' but may be modified at the first stage computes the effect of spatial structure user's discretion for other viewing conditions. on the discriminabiUty of different chromatic Further refinement of CIELAB-based systems can components of an image_ The second stage

205 • THE SCIENCE OF COLOR applies the standard CIELAB metric to the out­ cussed under color order systems above. As with put of the first stage. The S-CIELAB metric does CIELAB and CIELUV, this system is designed to a better job of predicting observers' judgments of handle cases where samples vary in both chro­ the perceptual differences between color images maticity and luminance. Other color order than the unmodified CIELAB metric. but it is systems (e.g. Munsell, DIN) are based at least in clear that further development is required part on scalings of color differences, as when (Zhang and Wandell, 1998). observers are asked to pick a chip whose satura­ The CIELAB system was not designed to be a tion is halfway between that of two reference color appearance system. Although it does samples. These systems are more difficult to define scales for hue, chroma, and lightness, interpret as full color difference systems, how­ these scales are only approximate and are not as ever, because they are not based on data where well grounded in appearance data as most color multiple stimulus attributes are covaried. order systems or color appearance models. Nonetheless, they are sometimes used in this fashion (Richter and Witt, 1986). 5.3.2 OTHER COLOR DIFFERENCE SYSTEMS 5.4 CURRENili DIRECiflONS IN 5.3.2.1 CIELUV COl!OR SP.ECIF.ICATION At the time the CIELAB standard was intro­ duced, the CIE also introduced a second system 5.4.1 CONTEXT EFFECTS for specifying small color differences. This is called the CIELUV system, and coordinates in As illustrated in Figure 5.2, implementations of this system are referred to as the CIE 1976 color order systems may be thought of as lookup L*u*v* coordinates. Like the CIELAB system, the tables that specify the relation between color CIELUV system was derived from systems used appearance and physical samples. As such, these widely in practice prior to the standardization. implementations embody knowledge about the CIELUV coordinates are derived from tristimulus psychology of color appearance. The implemen­ coordinates as well. The formulae for computing tations, however, depend on scaling experiments CIELUV coordinates may be found in numerous conducted using a well-specified vieWing con­ publications (Wyszecki and Stiles, 1982; CIE, text. This is emphasized in Figure 5.2 by the fact 1986). At the time of standardization, the CIE that the viewing conditions are specified along recognized that it was difficult to choose the arrow linking the two sides of the table. between the two systems, as each worked bet­ Clearly, it would be useful to be able to specify ter on different validation data sets and each had color appearance for conditions other than the its proponents. Indeed, the general feeling in the standard. Of particular interest is the prediction color community was that no color difference of the appearance of images, where the stimulus system explained more that about 80% of the at each location is viewed in the complex sur­ variance in color discrimination data, and that round definedby the restofthe image. Because the each system explained a different 80% (Cowan, effects of context can be quite large (Figure 5.9), personal communication). More recently, opin­ neglecting them can lead to large prediction ion has tended to favor the CIELAB system errors. and its successor CIE94, and the CIELUV system In general. both the appearance and discrim­ is no longer widely recommended (Fairchild, inability of colored stimuli depend on the con­ 1998). text in which the stimuli are viewed (see Chapters 3 and 4). Because our understanding of 5.3.2.2 Color order systems context effects is incomplete, it is not yet possi­ The OSAIUCS color order system may be ble to incorporate precisely the effects of context thought of as a color difference system. This into color specification systems. It is possible to system was designed to apply larger color differ­ layout a general framework that allows us to ences than either CIELAB or CIELUV. It is dis- incorporate what is known about the effect of

206 COLOR APPEARANCE AND COLOR DIFFERENCE SPECIFICATION •

Figure S.9 Illustration of context effects.The x-shaped intersections on the two sides of the figure appear quite different.The light reaching the eye from these two regions is the same, however.This can be seen by tracing from one x-shaped region to the other. (From Albers, 1975. Copyright © 1975 Yale University Press, reproduced with permission.) context into current color order and discrimina­ appearance. The two contexts may be separated tion systems. This framework provides the foun­ spatially or in time, but in either case the dation for current work towards developing observer need only judge identity of color color appearance models. The key to this frame­ appearance; the complex structure o[ appear­ work is asymmetric color matching. ance scaling judgments does not intrude into the Asymmetric color matching is an experimen­ experiment. tal procedure that may be used to establish pairs Let us use the term standard context to refer of stimuli that match across changes in viewing to a set of viewing conditions for which we have context (von Kries, 1902; Burnham et al., 1957; implemented a color order system. Typically, the Stiles, 1967; Krantz, 1968; Brainard and standard context consists of viewing a single Wandell, 1992; Poirson and Wandell, 1993; sample at a time against a uniform gray back­ Webster and Mallon, 1995). In an asymmetric ground, under a well-specified illuminant. Let us matching experiment, the observer adjusts the use the term test context to refer to some other color of one stimulus, seen in some arbitrary set of viewing conditions for which we would context, to match the appearance of a standard like to specily color appearance. Suppose that we stimulus seen in a standard context. By selling are able to develop a descriptive model that pte­ such matches, the observer establishes pairs of dicts observers' asymmetric matches between stimuli that, across contexts, have the same any two contexts. In particular, this model

-- 207 • THE SCIENCE OF COLOR should allow us to relate the tristimulus coordi­ experiments may be conducted without refer­ nates of any stimulus seen in the test context to ence to color names and hence results from the tristimulus coordinates of a stimulus that has them may be used to generalize any color order the same appearance when seen in the standard system. On the other hand, color order systems context. Such a model then allows us to apply may be developed carefully for single context the implementation of the color order system for with the knowledge that they may be general­ the standard context to stimuli viewed in the test ized once an acceptable theory of asymmetric context. This idea is illustrated in Figure 5.10. matching is developed. The left side of the figure illustrates the role of The approach outlined above relies on the asymmetric matching. The asymmetric matching assumption that the effect of context measured model would allow us to map the tristimulus by asymmetric matching correctly predicts the coordinates of a test stimulus seen in a test con­ effect of context on color appearance for other text to the tristimulus coordinates of a matching measures (e.g. color scaling and naming). Recent stimulus with the same appearance when seen empirical work by Speigle and Brainard (Speigle in the standard context. These matching tristim­ and Brainard, 1996; Speigle, 1997; Speigle and ulus coordinates could then be used in conjunc­ Brainard, 1999) lends support to this assumption. tion with an implementation of a color order At present, no general theory of asymmetric system for the standard context to determine a matching exists. Most current theories attempt symbolic description of the colorappearance of the to explain asymmetric matching by developing a test stimulus in the test context. The role of model of how color signals originating in the the color order system is shown on the right of the cone photoreceptors are processed by subse­ figure. Note that this general scheme could also quent visual mechanisms and of how this pro­ be used in reverse to map between symbolic cessing varies with viewing context (von Kries, descriptions of color appearance and tristimulus 1902; Burnham et al., 1957; Hurvich and coordinates in the test context. Jameson, 1957; Stiles, 1967; Krantz, 1968; The advantage of using asymmetric matching Brainard and Wandell, 1992; Fairchild and Berns, to extend color order system implementations to 1993; Poirson and Wandell, 1993; Webster and general viewing contexts is that it separates the Mallon, 1995; Delahunt and Brainard, 2000). problem of understanding context from the The simplest model goes back to von Kries, who problem of implementing a color order system. suggested that the effect of context was simply to On the one hand, the asymmetric matching scale the cone signals independently for each

Aysmmetric matching Color order system

x y z Symbolic 33.8 30.0 30.0 SR 6/4 36,6 30.0 27.2 SR 6/6 x y Z x y z 38.2 30.0 22.7 SR 6/8 40.8 25.0 32.0 ----. I 338 30.0 30.0 I/ ...... • ... 28.5 30.0 16.5 Standard 5Y 6/4 Test stimulus seen Matching stimulus ...... context ... in test context seen in standard 51.4 79.0 67.2 SG 9110 context ......

Figu.re 5.10 Schematic of how asymmetric matching can be used to extend a color order system to other contexts.The left side of the figure illustrates the role of asymmetric matching. A general characterization of asymmetric matching would allow us to map the tristimulus coordinates of a test stimulus seen in a test context to the tristimulus coordinates of a matching stimulus with the same appearance when seen in the standard context.These matching tristimulus coordinates could then be used in conjunction with an implementation of a color order system for the standard context to determine a symbolic description ofthe color appearance of the test stimulus in the test context.The role ofthe color order system is shown on the right ofthe figure.

208 "----- COLOR APPEARANCE AND COLOR DIFFERENCE SPECIFICATION • cone type (von Kries, 1905). This class of model Sobagaki, 1981; Nayatani, Sobagaki, and accounts well for a subset of color context effects Takahama, 1986; Nayatani et aI., 1987; Nayatani (Brainard and Wandell, 1992; Chichilnisky and et al., 1990). More recently, several other color Wandell, 1997) and Land's well-known retinex appearance models have been developed, and theory of context vision is a special case of the the CIE has recently standardized an interim general von Kries scheme (Land and McCann, color appearance model, ClECAM97s, recom­ 1971; Land, 1986; Brainard and Wandell, 1986), mended for use at the current time (ClE, 1998; A von Kries type of transform cannot account Fairchild, 1998). For illustrative purposes, we for all color context effects, however (Krauskopf provide an overview of the CIECAM97s model. et aI., 1982; Poirson and Wandell, 1993; Webster Although this model is likely to be further and Mollon, 1995). Chapter 4 discusses basic refined, its design synthesizes a great deal of our research on this topic in more detail. current knowledge about color appearance, Fairchild (1998) provides a thorough review of 5.4.1.1 Color appearance models recent color appearance models. The goal of color appearance models is to pro­ vide an analytic relation between a specification 5.4.1.2 CIECAM97s of a stimulus and the context in which it is The CIECAM97s model is illustrated in Figure viewed and its color appearance (in terms of 5.11. The initial stage of the model (shown on numerical correlates of appearance attributes). the top of the figure) starts with the encoding of As such, color appearance models must contain a test stimulus (called the source in the CIE doc­ components for both sides of Figure 5.10. One uments) by the visual system. This is accom­ component of the model must account for the plished in the model by computing the CIE XYZ effect of context on appearance, while a second tristimulus coordinates of the test. These coordi­ must provide an analytic description of the map­ nates are indicated in the figure by the grouped ping between tristimulus coordinates and sym­ rectangles. The next step is to take the viewing bolic names for a standard context. context into account. This is done by transform­ An early attempt at developing a color appear­ ing the tristimulus coordinates to coordinates ance model was made by Judd (Judd, 1940). that represent the adapted cone responses of a Second generation models were developed by stimulus that would match the source, when it Hunt (Hunt, 1982; Hunt and Pointer, 1985; was seen under standardized reference viewing Hunt, 1987a, 1987b, 1991) and by Nayatani and conditions. The transformation takes context his coworkers (NayatanL Takahama, and into account and results in a representation of

,------,, , ~ ,

• • ••

H

A • • ------~ J - Q • • RIG • • C - • • • Y/B -----... S M

Figure 5.1 I Schematic illustration of the CIECAM97s color appearance model. See description in the text.

209 • THE SCIENCE OF COLOR the test in terms of the L, M, and S cone pho­ (indicated by A in the figure) is formed as the toreceptor responses. The actual calculation of weighted sum of the three adapted cone signals. the adapted cone responses is somewhat The red/green signal (R/G) is obtained by oppos­ involved and depends on the context in which ing signals from adapted Land S cones with sig­ the test is seen. It is illustrated in the figure by nals from adapted M cones. The yellow/blue the sigmoidal nonlinearity. The arrow from the signal (Y/B) is obtained by opposing signals from context to the nonlinearity indicates that the adapted Land M cones with signals from transformation depends on the context. To apply adapted Scones. the model in practice involves a certain degree of To produce color appearance descriptions, the art, as the user must set a number of parameters model provides a set of transformations between that specify the completeness of adaptation to A R/G, and Y/B and scales for appearance attrib­ the viewing context. The adapted cone responses utes. Included are scales for hue (H), lightness are the output of the first stage of the model and (h brightness (Q), chroma (C), saturation (S), are shown schematically in the figure by the and colorfulness (M). grouped cones. The second stage of the CIECAM97s model is The first stage of the CIECAM97s model is analogous to the second stage of the asymmetric analogous to the first stage in the asymmetric matching framework described above. Note, matching framework described above. The only however, that the lookup table description has difference is that rather than mapping the tris­ been replaced by an analytic characterization timulus coordinates of the test to those of a between the adapted cone responses and the matching stimulus, it maps the tristimulus coor­ appearance scales. A second difference, neg­ dinates of the test to adapted cone responses. lected above, is that in CIECAM97s the relation The adapted cone responses can, however. be between adapted cone responses and the appear­ associated with the tristimulus coordinates of a ance scales does contain a dependence on view­ matching stimulus in the reference context by ing context. For example, the scale for lightness applying the inverse of the first stage with the depends on a comparison of the achromatic sig­ parameters set for the reference context. nal of the test and the achromatic signal for an The purpose of the second stage of image region designated by the user as white. CIECAM97s is to provide an analytic description This dependence means that in CIECAM97s, of how the adapted cone coordinates relate to there is not complete separation between the color appearance attributes. It is based on an effect of context and the transformation between opponent process model of how subsequent adapted cone signals and appearance scales. This visual mechanisms process the adapted cone sig­ separation could be restored if the model of nals. The key idea is that signals originating in asymmetric matching accurately predicts the the three classes of cones are recombined to match to a white sample, since then the adapted form a non-opponent achromatic signal and cone signals for a white seen in the reference opponent chromatic signals. The opponent context could be substituted for the adapted process model was articulated in the modern lit­ cone signals of an image region designated by erature by Hurvich and Jameson (Hurvich and the user as white. Jameson, 1957; Jameson and Hurvich, 1955, 1964), who used it to explain a large number of 5.4.1.3 Discussion color appearance phenomena. It is lent credence CIECAM97s is interesting in that it attempts to by the fact that observers can make judgments bridge basic research on the nature of visual pro­ that may be interpreted as tapping solely the cessing with applied research on color order sys­ chromatic mechanisms (Jameson and Hurvich, tems. The greatest difficulty for testing and 1955,1964; Larimer et aI., 1974, 1975; Krantz, developing this (or any other) color appearance 1975; Walraven, 1976; Shevell. 1978; Werner model is the huge array of possible viewing con­ and Walraven, 1982; Shevell and Wesner, 1989). texts that must be studied. Contextual factors In the model. each of the opponent signals is that influence color appearance include both the formed as a weighted combination of the size and shape of the stimulus itself, its local and adapted cone signals. The achromatic signal global surround, and the adapted state of the

210 COLOR APPEARANCE AND COLOR DIFFERENCE SPECIFICATION • observer. Our current understanding is based stability of the color appearance will depend on primarily on experiments where isolated test which reflectance function is chosen initially. stimuli are viewed against uniform backgrounds How should the designer make this choice? This of varying chromaticities and luminances. The is the problem of metamerism. difficulty is that it is not clear how to generalize from these experiments to more complicated 5.4.2.2 Colorant order systems? viewing situations. Overcoming this difficulty is A brute force approach is provided by colorant a prerequisite for a complete color appearance order systems (Judd and Wyszecki, 1975). These model and research on methods for doing so is are systems that are in many ways like color ongoing (see Chapter 4). Note that if a color order systems. The difference is that these sys­ appearance model contains a successful model of tems are not implemented in terms of tristimu­ context effects, this model could be used Ius coordinates. Rather. their implementation is together with the asymmetric matching frame­ provided directly in terms of amounts of particu­ work described above to extend color order lar pigments, dyes, or inks. The advantage of a systems to multiple contexts. colorant order system is that a designer may A particularly important area of application for choose a sample from it and be guaranteed that color appearance models is to describe the the final production will behave under different appearance of stimuli presented on CRT displays. illuminants exactly as the sample. Thus the A great deal of image previewing and manipula­ designer is restricted a priori to choosing among tion is now done using such displays, with the a set of producible samples, rather than choosing ultimate goal of printing a hard copy of the from a set of specifications that have multiple image. Ideally, it would be possible to make a possible implementations. By investigating how reproduction of the CRT image that had exactly various samples appear under different ilIumi­ the same appearance as the original. This goal nants, the designer may use samples from col­ will probably not become easily achievable, orant order systems to produce acceptable however, until it is possible to describe both orig­ results. inal and reproduced images in color appearance The disadvantage of colorant order systems is terms. As color appearance models are refined, that their use is confined to the output medium they are likely to play increasing roles in auto­ for which they were implemented. This limits mated color reproduction. (See Chapter 8 for a the amount of effort that can go into their discussion of color reproduction.) implementations and tends to make each such system idiosyncratic. 5.4.2 METAMERISM 5.4.2.3 Metamerism indices The goal of a metamerism index is to help 5.4.2.1 The problem of metamerism designers reproduce a target sample so that the An important issue that arises in using color behavior of the reproduction under changes of specification systems is the following. Current illumination closely matches that of the target color specification systems are based on tristim­ (Wyszecki and Stiles, 1982). A metamerism ulus coordinates. This presents no difficulties if index is always based on a metric that defines one's goal is to use the system to produce a sam­ how different two stimuli appear (e.g. CIELAB). ple that will be viewed only under a single illu­ To compute the metamerism index between two minant. One designs the sample to produce the samples that have identical tristimulus coordi­ desired tristimulus coordinates under the desired nates under a reference ilIuminant, one chooses ilIuminant and the actual reflectance function of a test illuminant. Often the reference illuminant the sample is irrelevant (see Chapters 3 and 4). is cm D65 and the test illuminant is cm But what if the sample is to be viewed under Illuminant A. One then computes or measures more than one illuminant? For example, what if the tristimulus coordinates of the two samples the specification is for the color of a car, which under the test illuminant and computes the color will be seen under a variety of daylights (and difference between these using the chosen color perhaps under artificial lighting at night)? The metric. The smaller the difference, the more

21 I • THE SCIENCE OF COLOR

similarly the two samples appear under the Surface Basis Functions change of illumination. Wyszecki and Stiles ,• (1982) provide discussion and an example calcu­ • ~/~ ./f"'\. lation. • ...... ,01...", (.....) 5.4.2.4 Linear models Another approach to the problem of metamer­ 0.8 ism is to specify colors in terms of their physical properties rather than in terms of their uistimu­ Ius coordinates. This seems at first like a radical 00 proposal, as it suggests neglecting the economy w u of specification offered by the color matching c ~ experiment. However, as the problem of meta­ ~ 0.4 merism itself makes clear, there is sometimes a 'm need to preserve more information about sam­ '" ples than their tristimulus coordinates under a particular iIluminanr. A promising theoretical development that 0.L,.---~---~------, might allow such specification is the notIon that 400 500 600 700 small-dimensional lineat models may be used to Wavelength (nm) describe many surface reflectance functions to a high degree of accuracy. Linear models approxi­ Figure S.12 The open squares in the figure show a mate speerral data as weighted sums of a small measured surface reflectance function.The solid line number of fixed basis functions (see Chapter 4; shows an approximation to this function obtained using a three-dimensional linear model.The insert Brainard, 1995). shows the reflectance spectra of the linear model's The number of basis functions used in a linear basis functions. (From Brainard et 01., 1993. Copyright model is called the dimension of the model. This © J993 American Psychological Society, reproduced by nomenclature emphasizes the fact that basis permission of Blackwell Publishers.) functions may be interpreted as describing the dimensions along which specrra may vary. The insert in Figure 5.12 shows the basis functions The basis functions shown in Figure 5.12 were for a three-dimensional linear model for sur­ obtained by performing a principal components faces. The first basis function reflects fairly analysis of the reflectance functions of a large evenly across the visible spectrum. By varying set of colored papers (Cohen, 1964). Similar the weight aSSigned to this basis function, we can analyses have been performed for other collec­ capture variation in overall reflectance from one tions of surfaces and for measured daylight surface to another. The second basis function spectral power distributions (Judd et aI., 1964; reflects positively at the long wavelength end of Maloney, 1986; Jaaskelainen, Parkkinen, and the spectrum and negatively at the short wave­ Toyooka, 1990; Marimont and Wandell, 1992). length end. By assigning a positIve weight to this The results indicate that linear models with a basis function, we capture the fact that some sur­ small number of basis functions provide an faces (e.g. ones that tend to appear red) reflect excellent description of naturally occurring spec­ best at longer wavelengrhs. By assigning a nega­ tra. The main portIon of Figure 5.12 shows a typ­ tive weight to this basis function, on the other ical surface reflectance functjon and its linear hand, we capture the fact that some surfaces (e.g. model approximation. ones that tend to appear green) refleer best at the Linear models provide an efficient description middle and short wavelengths. The third basis for surface reflectance functions, since specifying function, which reflects positively in the middle the weights on each basis functIon provides region of the spectrum and negatively at either enough informatIon to reconstruct a close end, shows another dimension along which approximation to the full reflectance function. surface reflectances within the model can vary. Brainard and Wandell (Wandell and Brainard,

212 COLOR APPEARANCE AND COLOR DIFFERENCE SPECIFICATION •

1989; Brainard and Wandell, 1990) have out­ introduced by MacAdam (1974), the formulae pro­ lined schemes to incorporate linear model speci­ vided in the widely used reference by Wyszecki and fications into color reproduction systems. The Stiles (1982) contain additional errors: they do not incorporate the transformation between :£ and L, basic idea as it applies to color order systems is and the definitions of j and g are reversed. very simple, however. Rather than defining a 2 In many applications there is no a priori reason to color order system in terms of the relation designate either of the two stimuli being compared between sample tristimulus coordinates and as the standard. The effect of arbitrarily choosing symbolic descriptors, the system could be one or the other as standard is small as long as small color differences are being evaluated. An alternative defined in terms of the relation between linear is to use the geometric mean of the chroma coordi­ model weights and the same descriptors. Since it nate: C:b_~ = )C:1UC:b] This issue is discussed in is always possible to compute sample tristimulus more detail in the CIE technical report (ClE, 1995). coordinates from reflectance spectra (under the 3 The reference viewing conditions specify, among standard viewing conditions for which the color other things, viewing samples under erE iliumi­ nam 065 against a nonselective background with order system is defined), the linear model for­ L* = 50. A complete description of the reference mulation loses no information. The formulation conditions is available in severa] sources (CIE, 1995; provides extra information, however, since the Hung and Berns, 1995; Fairchild, 1998). full spectrum of each sample is available. As methods for accurately controlling sample spec­ tra become available, color order systems using spectral sample specification could provide reproduction whose appearance changes with Abramov, 1. and Gordon, J. (1994) Color appearance: illumination were well defined. Moreover, with on seeing red - or yellow, or green, or blue. Annual such a scheme, the system's sample spectra Review ofPsychology, 45, 451-85. Albers, J. (1975) Interaction of Color. New Haven, CT: might even be designed to have roughly con­ Yale University Press. stant appearance across common changes in Berns, R.S. and Billmeyer, F.w., Jr (1985) Develop­ illumination (Berns et aI., 1985). ment of the 1929 Munsell Book of Color: a historical review. Color Research and Application, 10,246-50. Berns, R.S., Billmeyer, F.w., Jr, and Sacher, R.S. (1985) Methods for generating spectral reflectance functions leading to color-constant properties. Color Research and Application, 10, 73-83. I thank P. Alessi, R. Berns, W. Cowan, M. Billmeyer, F.W., Jr (1987) Survey of color order Fairchild, D. Post, S. Shevell, L. Silverstein, W. systems. Color Research and Application, 12, 173-86. Swanson" and B. Wandell for useful discussions Billmeyer, F. W.. Jr (1988) Quantifying color appear­ or comments on the manuscript. ance visually and instrumentally. Color Research and Application, 13, 140-5. Billmeyer, F.w., Jr and Bencuya, A.K. (1987) Interrelation of the Natural Color System and the Munsell color order system. Color Research and Application, 12,243-55. I Formulae for the conversion are provided by Brainard, D.H. (1995) Colorimetry. In M. Bass (ed.), MacAdam (MacAdam, 1974). The published formu­ Handbook of Optics: Volume I. Fundamentals, Tech­ lae, however, contain an error. MacAdam's niques, and Design. New York: McGraW-Hill, pp. Equation I for the computation of:£ works only for 26.1-26.54. stimuli with values of Yo >30. The formulae pub­ Brainard, D.H. and Wandell, B.A. (1986) Analysis of lished here correct for this problem and work for the retinex theory of color vision. Journal of the all values of Yo' They were inferred by examining Optical Society ofAmerica A, 3, 1651-61. Semmel roth (1970) whose Equation 3 provides the Brainard, D.H. and Wandell, B.A. (1990) Calibrated basis for MacAdam's Equation I. The formulae processing of image color. Color Research and published here were checked by implemenring Application, 15,266-71. them as MATLAB functions and verifying that they Brainard, D.H. and Wandell, B.A. (1991) Evaluation correctly reproduce tabulated values (MacAdam, of CIE Luv and CIE Lab as perceptual image repre­ 1978). The implementation is available as part of sentations. Society for Information Display International the freely distributed Psychophysics Toolbox Symposium Technical Digest, 22, 799-80I. (http://psychtoolbox.org/, release 2.45 and later). Brainard, D.H. and Wandell, B.A. (1992) Asymmetric Note also that in addition to propagating the error color-matching: how color appearance depends on

213 • THE SCIENCE OF COLOR

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