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Visual Neuroscience ~2006!, 23, 579582. Printed in the USA. Copyright © 2006 Cambridge University Press 0952-52380 06 $16.00 DOI: 10.10170 S0952523806233091

A whiter shade of pale, a blacker shade of dark: Parameters of spatially induced blackness

DAVID L. BIMLER,1 GALINA V. PARAMEI,2 and CHINGIS A. IZMAILOV
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3

Depar tment of Health and Human Development, Massey University, New Zealand Institute of Psychology, Darmstadt University of Technology, Germany Depar tment of Psychophysiology, Moscow Lomonosov State University, Moscow, Russia

(Received November 8, 2005; Accepted November 29, 2005!

Abstract The sur face-mode proper ty of "blackness" is induced by simultaneous contrast with an adjacent, more luminant surround. As numerous studies have shown, the degree of blackness induced within an achromatic test field is a function of the relative luminance of the adjacent chromatic inducing field, but not of its hue. But in the converse case of chromatic test fields, susceptibility to blackening has been repor ted to vary with wavelength. The present study investigates this possibility, that some wavelengths are more susceptible. We also questioned whether "white" and "black" sensory components function as opposites in blackness appearance. We recorded the appearance of a central monochromatic test field of constant luminance ~10 cd 0 m 2 !, with wavelength ranging across the visible spectrum, while a broadband white annulus was set to six luminance levels ranging across three log steps. Three color-normal observers followed a color-naming technique. All six opponent-hue names and their combinations were response options; blackness and whiteness in the test field could therefore be repor ted independently. Of primary interest were the achromatic responses. When represented within a multidimensional space, these revealed the "white-to-black" dimension but in addition a quality ~dimension! of "desaturation." Compared against chromatic proper ties of the test field, the results provide evidence that blackness is a function of inducing field brightness ~not luminance!. This result is in accord with observations made by Shinomori et al. ~1997! using a different procedure. We conclude that blackness induction occurs at a stage of visual processing subsequent to the origin of the brightness signal from a combination of opponent-process channels. Keywords: Spatially induced blackness, Chromatic light, Color naming, Bidimensional achromatic quality

Introduction In the language of color description, "red" and "green" form the polar extremes of one dimension of color experience; they are not used together to describe the same hue. In the same way, "blue" and "yellow" constitute the poles of a second chromatic dimension. "White" and "black" are a third pair of polar opposites, but their behavior differs in cer tain ways from the previous pairs. First, they can coexist, so that a given shade of gray might be described as containing black and white in equal amounts. Second, "blackness" is not observed in isolation, and cannot be examined in the simplified situation of "aper ture mode." Blackness only exists as par t of an environment, and must be induced by contrast with a lighter color elsewhere in the visual field ~spatial contrast! or immediately preceding the test stimulus ~temporal contrast!.

Address correspondence and reprint requests to: David L. Bimler, Depar tment of Health and Human Development, Massey University, Private Bag 11-222, Palmerston Nor th, New Zealand. E-mail: d.bimler@ massey.ac.nz

A number of studies have examined blackness induction into a white center by a chromatic annulus with wavelength l A . Shinomori et al. ~1994! elicited judgments of blackness and whiteness while varying the relative annulus luminance; the curves of "percentage blackness" followed the same shape at each l A . Other studies elicited the annulus luminance L A required to induce a given level of blackness, as a function of l A . Criteria included "perceptible greyness" ~ Evans, 1967!, just-noticeable blackness ~ Mount & Thomas, 1968!, and complete blackness and the disappearance of any contour ~e.g. Werner et al., 1984!. These are all criteria of decreased subjective lightness. Kulp and Fuld ~1989! found that the variables involved in the phenomenon are the same whichever criterion is used: there is a consensus that blackness induction into an achromatic center depends only on the ratio of luminance between the contrasting elements. Changes in annulus l A influence L A through the luminance function Vl , but they have no effect otherwise. Like Vl , the blackness-induction function for a white center proves to be additive when wavelengths are combined in the annulus ~ Volbrecht et al., 1990!. It is tempting to assume that the same principle governs the opposite situation where blackness is induced into a chromatic 579

580 center ~wavelength l C ! by a white surround. One objective of this study is to investigate the converse possibility, that the role of color in the interaction is not symmetric, with l C as an independent parameter of blackness induction ~ Fuld et al., 1986!. This would have implications for the stage of color processing where contrast is computed. Cicerone et al. ~1986! and Mount and Thomas ~1968! both examined four settings of l C while varying annulus wavelength l A . The published details do not permit comparison among l C settings to see whether l C has any independent role in induction ~e.g. through variations in "chromatic strength"!. However, the efficiency of blackness induction as a function of l A retained the characteristic shape of Vl , ruling out any interaction between l A and l C . Evans and Swenholt ~1967! examined two criteria as a function of l C : the chromatic threshold between complete central blackness and the last vestige of color, and G0 , chromatic strength, defined as the threshold of perceptible desaturation by the first appearance of gray. The two functions were parallel, separated by about a log step in annulus:center luminance ratio. The value G0 depar ted from the luminance function Vl and bore a closer resemblance to the "purity discrimination" function ~or "absolute saturation threshold"!. Shinomori et al. ~1997! obtained strikingly similar results. The annulus:center luminance ratio required for complete central blackness was higher for some wavelengths than others, with the log ratio varying from 2.5 to 4. Plotted against l C , the function closely resembled the brightness function Bl . Like Bl , but unlike Vl , blackness induction depar ted from additive behavior when the center contained combinations of wavelengths. The present study used an extended color-naming procedure to elicit descriptions of the appearance of monochromatic stimuli in the presence of luminance contrast. Observers' responses were analyzed to extract an index of spatially induced blackness. We consider a wider range of intensity ratios than Shinomori et al. ~1997!: the broadband white annulus ~2850 K !, providing the contrast, ranged in luminance in six levels across three orders of magnitude, from 1050 to 20 times the intensity of the central stimulus. Fuld and Otto ~1985! collected color-naming responses for the same situation of a monochromatic central stimulus ~wavelength l C ! darkened by contrast. However, they studied relatively few wavelengths, and did not examine the possibility that l C was a parameter in the spatial induction of blackness. A secondary objective of the present study is to investigate the dimensionality underlying the achromatic responses, that is, how many independent qualities they convey. Clearly the two terms black and white can operate as the opposite extremes of a bipolar continuum of subjective lightness. In the color-naming data of Fuld and Otto ~1985!, subjects hardly ever repor ted both within the same stimulus. However, "black" and "white" both convey a quality of desaturation, and they can be used together to characterize a grayness or lack of hue. Quinn et al. ~1985! and Fuld et al. ~1986! found that the two terms can indeed coexist. Thus it is not clear how far they function as antagonists. Heggelund ~1992! argues that the true opposition is between black and luminous, defining one axis between them, while whiteness is a separate, or thogonal axis. Again, "whiteness" and "blackness" are separate processes in the hyperspherical model of color discrimination ~ Izmailov, 1981; Izmailov & Sokolov, 1991!. It would seem that a color-naming response of "white" can arise for two different reasons. Materials and Method

D.L . Bimler et al.

The experiment was carried out at Moscow Lomonosov State University, Russia. Subjects were three Russian-speaking women aged 21, 22, and 24 years. They were confirmed as normal trichromats using the Rautian anomaloscope ~ Rautian, 1957!. Stimuli: 156 stimuli were presented foveally in Maxwellian view. Each consisted of a monochromatic center of fixed luminance ~ L C 10 cd 0m 2 ! subtending 2 deg, and a contrast-inducing annulus with 2 deg inner and 6 deg outer diameter. The central wavelength l C ranged from 425 to 675 nm, with 25 values provided by inter ference filters ~with 4 to 6 nm half-bandwidth!, plus a broadband tungsten white light ~ca. 2850 K !. Six levels of annulus luminance L A were tested, ranging across three orders of magnitude: 0.2, 2, 10, 20, 100, and 200 cd 0m 2 ~i.e. values of the annulus:center luminance ratio were 0.02, 0.2, 1, 2, 10, 20!. Procedure: Each stimulus was presented 20 times over 10 sessions, in pseudo-random order. Subjects described the appearance of the center with one, two, or three terms, in order of decreasing salience. The six permitted terms were the Russian equivalents of red, yellow, green, blue ~ sinij !, white, and black ~ R, Y, G, B, W, and Bk!. Analysis: A color term scored 10 points if it was used in isolation; two terms received 6 and 4 points in order of salience; three terms received 5, 3, and 2 points. Points for each term were summed over presentations, giving a value ~from 0 to 200! for that color-naming function. Responses across the subjects were sufficiently similar to combine them. The similarity between any pair of stimuli was quantified as the covariance between the corresponding vectors of color-name values, before analyzing the matrix of similarities with nonmetric multidimensional scaling ~ MDS!. MDS represents stimuli as points in an n-dimensional space, arranged so that interpoint distances reflect interitem similarities. A badness-of-fit function Stress1 quantifies the mismatch between distances and similarities. Results and discussion Solutions with two to five dimensions were fitted to the 156-by156 covariance matrix. Respective values of Stress1 were 19.2%, 8.8%, 6.0%, and 4.8%. We argue that the last incremental dimension to provide a substantial improvement in fit is the four th; that is, the solution is four-dimensional ~cf. Izmailov et al., 1999!. Plausible interpretations can be assigned to the four axes ~ labeled as D1, D2, D3, D4! but not to a fifth. The solution consists of 156 points, each located by coordinates $ x i1 , x i 2 , x i 3 , x i 4 % . Fig. 1 plots the coordinates of the points against l C . Here D1 and D2 can be identified as perceptual chromatic axes. They are almost identical to R-G and B-Y difference functions. Two achromatic axes D3 and D4 contain all the achromatic content of the color-naming descriptions. The solution is rotated so that D3 maximizes the dispersal of the six broadband-center stimuli, arranging them along a gradient from lightest to darkest annulus. This prompts an interpretation of D3 as "strength of blackness from contrast induction." Axis D4 is interpreted as "desaturation," since x i 4 values for chromatic stimuli coincide with direct ratings of desaturation ~Gordon & Abramov, 1988!, while the broadband stimuli are all at the positive extreme. Axis D4 fur ther agrees with the desaturation axis found in an earlier MDS analysis of similar data ~ Bimler & Paramei, 2005!. It is clear from Fig. 1c that when the ratio L A 0L C between annulus and center luminance is sufficiently high, induced black-

Parameters of spatially induced blackness

581

Fig. 1. Coordinates of color points in the 4D color space ~ver tical axis, arbitrary units! plotted against central wavelength l C ~nm!: ~a! x i 1 ~"green 0red"!; ~b! x i 2 ~"blue 0 yellow"!; ~c! x i 3 ~"blackness induction"!; ~d! x i 4 ~"desaturation"!. Lines connect stimuli with same annulus luminance ~ L A !, except for white centers at the right. 0.2 cd 0m 2 20 cd 0m 2 2 cd 0m 100 cd 0m
2 2

10 cd 0m 2 200 cd 0m 2

ness dominates the center whatever its wavelength l C . That is, x i 3 reaches a ceiling value. But at lower ratios ~ L A 0L C 1! the impact of a step increase in L A varies across l C . For some wavelengths ~e.g. yellow centers!, x i 3 increases dispropor tionately, and the corresponding line in Fig. 1c is displaced upward. Less-responsive wavelengths catch up as the annulus luminance continues to increase. For a given l C , across the six luminance ratios L A 0L C , x i 3 values approximate a sigmoid function. The primary research question is addressed by finding the inverse to the sigmoid function for each l C . The level of luminance contrast required to produce some chosen value of x i 3--that is, to induce a given criterion of blackness content-- can then be calculated as a function of central wavelength l C . We do this by interpolating within a logistic curve, fitted to the x i 3 values for the six distinct values of L A 0L C . Results are shown in Fig. 2. The MDS solution is still open to arbitrary rotations of the achromatic plane. It might be preferable, for instance, to rotate it through 45 deg and create separate achromatic axes of "brightness" and "darkness," but the alignment used here is most convenient for addressing the research questions. Note that distance from the origin is nearly constant across the points, where this distance is R i ~ x i2 x i22 x i23 x i24 ! . If the solution is rescaled so that 1 mean ~ R i ! 1, then the standard deviation of R i is 0.016. Points do not fill the 4D space, but are roughly confined to a locally

three-dimensional "sur face." The solution is essentially a hyperspherical shell: it remains compatible with Izmailov and Sokolov's ~1991! hyperspherical model of color discrimination, and with their hyperspherical coordinate system.

M

Fig. 2. Luminance ratio L A :L C predicted to produce three par ticular values of x i 3 ~i.e. to induce three specific levels of blackness induction!, as a function of central wavelength l C . Here L A , L C are luminance of annulus and chromatic center. Solid grey, broken, and solid black lines indicate x i 3 0, 2, 4.

582 Conclusions The curves of Fig. 2 are gratifyingly close to previous measurements of blackness induction into monochromatic centers ~e.g. Shinomori et al., 1997, Fig. 3!, and of the visible-grayness or G0 criterion ~ Evans & Swenholt, 1967, Fig. 3!. The 570-nm trough in resistance to blackness induction, the smaller dip at 490 nm, and the peaks at 520 and 650 nm are all familiar features from those counterpar ts. The declines in the curves at the highest and lowest wavelengths could be ar tefacts, but they are also present for some subjects in the results of Shinomori et al. The wavelength dependence of blackness induction ~its efficiency or action spectrum! is very similar to the brightness spectrum Bl , so a parsimonious explanation would involve the latter. The brightness signal is thought to arise from a nonlinear combination of opponent signals. The implication is that the blacknessinduction aspect of contrast is computed subsequently to the origin of Bl , quite late in visual processing. But less-bright wavelengths such as 570 nm are also low in "chrominance" or "chromatic strength": that is, a comparatively high propor tion of 570-nm light is required to produce a perceptible hue when mixed with white light. Thus an alternative explanation for these results is that induced blackness is independent of l C , but the blackness then dilutes or drowns out low-chrominance center wavelengths to the point of invisibility ~complete blackness! more easily than high-chrominance l C . In this explanation, x i 3 is interpreted as the ratio of blackness induction to chrominance, rather than as blackness in isolation. However, that account is excluded by Fuld et al. ~1986!, who used a criterion of "equal induction of black and white," where hue strength and visibility are irrelevant. Their results were similar to our Fig. 2: black and white canceled or balanced when the annulus matched the center for brightness ~not luminance!. This is also visible in our color-naming data for the case L A L C , where the same annulus induced significant Bk-naming for less-bright yellow centers, and significant W-naming for high-brightness blue centers. This can be seen in the L A 10 cd 0m 2 line of Fig. 1c, and in the lowest curve of Fig. 2. We are left with the direct link between blackness induction and brightness. In an earlier study of monochromatic, aper ture-mode stimuli ~ Bimler & Paramei, 2005!, where Bk was not among the response categories in the color-naming data, the third dimension of a MDS solution was identified as "desaturation." It is replicated by the four th axis of the present 4D solution. Thus the or thogonal dimensions D3 and D4 both have plausible interpretations, confirming that neither is an ar tefact. As noted above, "white" can also convey implications of both lightness and desaturation. There is a fur ther implication that Bk is not simply the inverse or absence of W: between them, the two naming functions capture more than a single aspect of color appearance. A number of wavelength 0 luminance-ratio conditions required a combination of black and white for a description. This is not simply the result of summing data across three subjects with different response functions, since it holds true when individual subjects' responses are examined. Acknowledgments

D.L . Bimler et al.

Preparation of the ar ticle by G.V.P. was suppor ted by a fellowship from the Hanse Institute for Advanced Study, Germany. We are grateful to J. Werner for helpful comments on an earlier version of the paper.

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