The role of spatial frequency in color induction

Vision Research 41 (2001) 1007– 1021 www.elsevier.com/locate/visres

The role of spatial frequency in color induction Vivianne C. Smith *, Phil Q. Jin, Joel Pokorny Visual Sciences Center, The Uni6ersity of Chicago, Chicago, IL 60637, USA Received 26 June 2000; received in revised form 9 January 2001

Abstract Color induction was measured for test and inducing chromaticities presented in spatial square-wave alternation, with spatial frequencies of 0.7, 4.0, 6.0 and 9.0 cpd. Observers matched the test chromaticities to a rectangular matching field using haploscopic presentation. Data were collected and analyzed within the framework of a cone chromaticity space, allowing analysis of spatial frequency effects on post-receptoral spectral opponent pathways. Assimilation, a shift of chromaticity toward the inducing chromaticity, was found at the highest spatial frequency (9.0 cpd). Contrast, a shift of chromaticity away from the inducing chromaticity, occurred at the lowest spatial frequency (0.7 cpd). The spatial frequency at the transition point from assimilation to contrast was near 4 cpd, independent of the cone axis. Assimilation was unaffected by the presence of a neutral surround and could be described by a spread light model. Contrast was reduced in the presence of a neutral surround. The data suggested that retinal contrast signals are important determinants in the perception of chromatic contrast. © 2001 Elsevier Science Ltd. All rights reserved. Keywords: Assimilation; Color contrast; Induction; Spatial frequency

1. Introduction Chromatic induction refers to a change in the chromatic appearance of a test stimulus under the influence of other nearby chromatic stimuli, inducing stimuli, in the field of view (Wyszecki, 1986). Chromatic induction includes both chromatic contrast and chromatic assimilation. Chromatic contrast occurs when the chromaticity of the test color changes away from the chromaticity of the inducing color, e.g. a test field of white shifts toward red when viewed with a green inducing field (see reviews by Ware and Cowan, 1982 and Chichilnisky and Wandell, 1995). Chromatic assimilation occurs when the chromaticity of the test stimulus changes toward the chromaticity of the inducing stimulus, e.g. a test field of white shifts toward green when viewed with a green inducing field. The geometry of the stimulus display is the most important factor in determining the induction direction (Helson & Joy, 1962; Helson, 1963; Schober & Munker, 1967; Walker, 1978; Fach & Sharpe, 1986). Contrast occurs for simple displays, test * Corresponding author. Fax: +1-773-702-0939. E-mail address: [email protected] (V.C. Smith).

stimuli in larger surrounds or with abutting inducing fields. Assimilation is found for complex displays, especially those with repetitive patterns (Wyszecki, 1986). There are a diversity of assimilation effects, suggesting that no single explanation will suffice for all. A simple display, the square wave grating, can exhibit either contrast or assimilation depending on its spatial frequency. This study concerns assimilation and contrast using a square wave grating display. Despite the historical and substantial numbers of studies of induction, few have examined a wide range of inducers and test colors, and none have been designed to allow systematic analysis in a modern framework dictated by advances in retinal physiology.

1.1. Assimilation For a square-wave periodic pattern, the transition from chromatic contrast to chromatic assimilation occurs at 4–6.7 cpd (Fach & Sharpe, 1986). There is a parallel result for brightness induction, which shows both assimilation and contrast depending on the spatial frequency of the display (Helson & Joy, 1962; Helson, 1963). For a square-wave periodic pattern, the transi-

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tion from brightness assimilation to brightness contrast occurs near 4 cpd (Walker, 1978). For some stimulus displays, assimilation can result from optical aberration and scatter in the eye. This indeed was an early explanation. Assimilation may also be of neural origin (Hurvich & Jameson, 1974; DeValois & DeValois, 1975; Reid & Shapley, 1988; Jameson & Hurvich, 1989; Moulden, Kingdom, & Wink, 1993). Hurvich and Jameson (1958, 1974) and Jameson and Hurvich (1989), for example, proposed a post-receptoral model that postulated parallel processing at multiple size scales. When a grating pattern is imaged on the retina, neurons with large receptive fields will integrate over a number of bars and will respond as if the light were actually mixed on the retina, whereas neurons with small receptive fields, at the same patch of the retina, will respond to individual bars. At a higher level that combines outputs of many neurons, both blending of hue and brightness (assimilation), and a preservation of spatial pattern may occur. According to this explanation, assimilation might occur at differing spatial frequencies for different post-receptoral channels due to the spatial sampling properties of the retinal mosaic. The post-receptoral retinal channels coding spectral information include the parvocellular (L/M) channels that show receptive field opponency between LWS and MWS cones and the koniocellular (S) channel that shows receptive field opponency between SWS and the sum of (LWS + MWS) cones. Equiluminant chromaticity planes consistent with retinal physiology include those of MacLeod and Boynton (1979) and Derrington, Krauskopf, and Lennie (1984). The maximal visual acuity for equiluminant chromatic gratings with correction for chromatic aberration was studied by Mullen (1985) using a pair of monochrome monitors with interference filters. A 526 – 602 nm pair produced a ‘‘red –green’’ grating, and a 470 – 577 nm produced a ‘‘blue –yellow’’ grating. These choices provide predominant stimulation to the Parvocellular and Koniocellular pathways respectively. The maximal acuity was estimated at 11–14 cpd. Similar values have been obtained by others, as reviewed by Williams, Collier, and Thompson (1983). Using an interference technique, Sekiguchi, Williams, and Brainard (1993a) and Sekiguchi, Williams and Brainard (1993b) obtained resolution to 20–27 cpd for a 514.5 – 632.8 nm pair and for a 441.6 nm grating on a 580 nm background. The maximal visual acuity for achromatic gratings is much higher; the interference technique yields a high frequency cut-off almost twice as high for achromatic gratings (Sekiguchi et al., 1993b). It is possible that grating perception may be maintained by achromatic percepts, while assimilation occurs for chromatic percepts. Further, since the SWS cone is presumed to have a coarse spatial mosaic, assimilation for SWS mediated percepts may occur at

lower spatial frequencies than for LWS/MWS mediated percepts, as suggested by Sekiguchi et al. (1993b). One way to examine Hurvich and Jameson’s (1974) and Jameson and Hurvich’s (1989) hypothesis is to assess assimilation using stimuli that confine stimulation to the desired retinal spectral opponent channels. The first goal of this study was to establish if the transition from assimilation to contrast occurred at different spatial frequencies for different post-receptoral pathways.

1.2. Contrast Chromatic contrast has been accounted for by the two-process model of chromatic adaptation (Hurvich & Jameson, 1958; Shevell, 1980, 1987). This model proposes that the inducing chromaticity affects test appearance in two ways (Jameson & Hurvich, 1972; Shevell, 1978): (1) it determines the gain of the receptor signals encoding the inducer; (2) it causes an incremental (or decremental) shift to chromatic opponent neural systems. The differing roles of multiplicative versus additive effects have been emphasized in several papers (Walraven, 1976, 1979; Shevell, 1987; Chichilnisky & Wandell, 1995; Smith & Pokorny, 1996a). Although some studies have emphasized the multiplicative effect (Walraven, 1976, 1979; Chichilnisky & Wandell, 1995), others emphasized the need for an additive effect (Shevell, 1980, 1987). The alternating bar pattern used by Ware and Cowan (1982) was not consistent with a pure multiplicative effect, and the two-process model was superior in accounting for the data. An alternative approach to explaining color contrast is to phrase the induction in terms of retinal contrast signals as opposed to the perceptual contrast signals of the Jameson and Hurvich (1955) model. The equiluminant cone excitation space, exemplified by MacLeod and Boynton (1979) or Derrington et al. (1984), has a major axis rotated from those of the equiluminant chromatic opponent space of Jameson and Hurvich (1955). A yellow –green or violet light metameric to the equal energy spectrum for a tritan would induce activity on two axes in the chromatic opponent space but activity on only one axis in the cone chromaticity space. The second goal of this study was to evaluate the hypothesis that the retinally based cone chromaticity space provides an economic metric for perceived color contrast. The purpose of this study was to investigate the mechanisms of chromatic induction in the framework of an equiluminant cone chromaticity space. The use of a cone chromaticity space allowed analysis of the spatial frequency effects on post-receptoral retinal opponent pathways. Further, the use of equiluminant space ensured that the percept of the spatial content of our stimuli was limited to the same post-receptoral retinal opponent pathways mediating the induction effects. We measured induction for different stimulus

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spatial frequencies (0.7, 4.0, 6.0, and 9.0 cpd) that included the transitional spatial frequencies between assimilation and contrast. We chose adapting and test chromaticities to evaluate the viability of a retinal version of the two-process model for chromatic contrast.

energy spectrum. These lines correspond to the cardinal axes of cone chromaticity spaces used both for physiological (Derrington et al., 1984) and for psychophysical studies (Krauskopf, Williams, & Heeley, 1982; Zaidi, Shapiro, & Hood, 1992; Miyahara et al., 1993; Smith & Pokorny, 1996a).

2. Methods

2.4. Inducing chromaticities

2.1. Apparatus

Nine inducing colors were chosen to span chromaticity space. Fig. 1 shows the chromaticities of the test stimuli (solid diamonds) and the inducing stimuli (open circles) and the phosphor gamut (triangle) in the relative cone troland chromaticity space. As a mnemonic device in the paper, we have coded the inducers with a letter indicating the predominant color percept associated with the inducer as noted on Fig. 1. Five inducing colors were placed on the l- and s-cardinal axes. They gave constant stimulation to one axis but varied stimulation on the other. These inducers intersected at equal energy spectrum (inducer W that appeared white). On the l-axis inducer, G appeared green and gave a low stimulation to the l-axis; inducer R appeared red and gave a high stimulation to the l-axis. On the s-axis, inducer Y appeared yellow and gave a low stimulation to the s-axis; inducer V appeared violet and gave a high stimulation to the s-axis. Four inducers were chosen to combine low or high stimulation on both axes, within the color gamut. Inducer YG appeared yellow –green and gave a low stimulation on both axes; inducer O appeared orange and combined low stimulation of the s-axis with high stimulation of the l-axis. Inducer BG appeared blue –green and combined a high stimulation

The stimuli were generated by a Pixar II image processor controlled by a Sun 3 workstation (Miyahara, Smith, & Pokorny, 1993) and were presented on a high-resolution RGB monitor (Nanao T560i). The chromaticities of the phosphors were calculated in a cone chromaticity space (l, s, YJ), (MacLeod & Boynton, 1979) and normalized to relative cone trolands (Boynton & Kambe, 1980; Smith & Pokorny, 1996b). The experiment was performed at a constant luminance level of 12 cd/m2, corresponding to about 115 effective trolands (Le Grand, 1968). A chin rest helped stabilize head position. The screen was viewed through a 1 m haploscope (Smith & Pokorny, 1996a). A −1.0 diopter ophthalmic lens placed before each eye allowed the observers to accommodate freely to the stimulus array.

2.2. Stimulus display The stimulus display consisted of test and comparison fields arranged side by side, separated by 1.0° (Smith, Jin, & Pokorny, 1998). The comparison field was 2.0° wide by 5.0° high. The test field was a horizontal grating 5.0° high, in which test stripes alternated with inducing stripes. The width of the test stimuli (1.75° in visual angle) was slightly shorter than the width of the inducing stimuli (2° in visual angle) so that the observer could easily distinguish the test from the inducing stimuli. The spatial frequencies of the test and inducing gratings were 0.7, 4.0, 6.0 and 9.0 cpd. There were two surround conditions, a dark surround and a surround metameric to the equal energy spectrum (l= 0.665, s=0.997) at a luminance level slightly below (YS = 9.5 cd/m2; 90 effective td) that of the test and comparison fields. The surround filled the monitor screen, encompassing both test and comparison fields and extending 8°× 12°, centered at the binocular fixation point as viewed in the haploscope.

2.3. Test chromaticities There were 10 test colors, five parallel to the l-axis and five parallel to the s-axis of the relative cone troland chromaticity space (Smith & Pokorny, 1996b), intersecting at a chromaticity metameric to the equal

Fig. 1. Coordinates of the test stimuli (solid diamonds) and the inducing stimuli (open circles) plotted in the relative cone troland chromaticity space. The phosphor gamut at equiluminance is shown by the triangle. The solid line on the left and bottom identifies a portion of the spectrum locus; the solid line on the right identifies a portion of the locus of extra-spectral purples.

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of the s-axis with a low stimulation of the l-axis; inducer P appeared purple and gave a high stimulation on both axes.

2.5. Obser6ers Three observers took part in the experiments; N.W. (male) and Y.Z. (female) were naı¨ve as to the purpose of the experiments. Q.J. (male, one of the authors) was an experienced psychophysical observer. The observer ages were between 26 and 32 years. All three observers had normal color vision as evaluated by the Ishihara Pseudoisochromatic Plates, Farnsworth – Munsell 100Hue Test and the Rayleigh equation on the Neitz-OT anomaloscope.

2.6. Use of indi6idual lines in cone chromaticity space The inducing and test stimuli were presented at the personal photometric matches for each observer. On the s-line, inducing and test stimuli were presented on each observer’s personal tritan line. Fig. 1 shows the nominal stimuli for the Judd (1951) observer; actual chromaticities varied slightly among observers. We used minimum motion photometry (Anstis & Cavanagh, 1983) to equate the luminances of the three phosphors and a minimally distinct border technique (Tansley & Boynton, 1978) to estimate the individual tritan lines for each observer. In the cone chromaticity space, the tritan line for the Judd standard observer is vertical (90°). Each individual observer’s tritan line deviated slightly from vertical. The tritan lines for observers N.W., Q.J., and Y.Z. were 90.55, 90.27, and 90.20°. The expected upper limit of tritan rotation using monitor primaries and population values for individual variability in photoreceptor spectral sensitivity, lens and macular pigment is 90.38° (Smith & Pokorny, 1995). Observer N.W. has a more extreme value, but the other observers are within the estimate of normal limits.

2.7. Procedure Induction was measured using the method of asymmetric matching. The observer was instructed to match the test and match stimuli in hue and saturation. A luminance adjustment was available to compensate for brightness differences, but the observers did not alter the luminance settings. A control box used three bi-directional switches, two for the adjustment of chromaticity along an individual observer’s s-axis and l-axis lines, and one for adjustment of luminance. A response button signaled that the match was made and presented the next trial. Only Q.J. knew the theoretical significance of the response box. The cone axes provide an intuitive color space and matches are made with ease.

The test stimuli were presented in random order. The observer adjusted the matching stimulus to achieve a hue and saturation match. At the beginning of each trial, the initial chromaticity of the match stimulus was slightly perturbed from the chromaticity of the test stimulus so to ensure that the observer made some adjustment on both axes. The mean chromaticity of three matches was taken as the estimate of the chromaticity of the induced color. Depending on the inducer, some test stimuli could not be matched within the available chromaticity gamut, e.g. a red-biased inducer with a green test color. In this event, no match was recorded. Two control tests were performed; one was to check for interocular differences, the other to evaluate the effect of spatial frequency per se. For the interocular test, the inducing and test bars of the test stimulus were of identical chromaticity to give a uniform chromaticity test field. None of the observers showed an interocular difference. Observers N.W. and Y.Z. showed desaturation at the highest (9.0 cpd) spatial frequency; Q.J. did not. The induction data were corrected for the spatial frequency effect. The scatter of the matches was low.

3. Results

3.1. O6er6iew of the data The experiment entailed 64 conditions per observer. Figs. 2 and 3 show matches of observer Y.Z. plotted in cone troland chromaticity space for the four spatial frequencies (columns) and four inducing colors (rows) with a dark surround. Fig. 2 shows data for four inducers on the l-axis: G, R, and the s-axis: Y, V from top to bottom. Fig. 3 shows data for the four inducers with energy on both l- and s-axes: Y–G, O, B–G, and P from top to bottom. The spatial frequency decreases from left to right. Matches are shown as vectors connecting the test and match stimuli, with the tails of the vectors representing the test stimuli. Each arrowhead indicates the match made with the inducing stimulus present. The filled circle shows the chromaticity of the inducing stimulus. The data show assimilation (arrows point toward the inducer) with a high spatial frequency grating (9.0 cpd) and contrast (arrows point away from the inducer) with the low spatial frequency grating (0.7 cpd). The data obtained at intermediate spatial frequencies (4.0 or 6.0 cpd) show a mixture of contrast, assimilation or no effect. The data collected with a 90 td surround exhibited a closely similar assimilation but less contrast. To evaluate the transition from assimilation to contrast, we coded each inducer and spatial frequency according to whether the data revealed assimilation, contrast or no effect. To evaluate whether the transition

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Fig. 2. Raw data for observer Y.Z. plotted in relative cone troland space for four inducers on cardinal axes. The vectors show the chromaticities of the test (tail) and the match (arrowhead). Data for the four spatial frequencies (columns) and four inducing chromaticities (rows) are shown. The spatial frequency of the stimulus decreases rightward. Chromaticities of the inducers are G, R, Y and V from top to bottom.

developed at differing spatial frequencies on the l- and s-axes, we performed this coding for each axis independently; good agreement was obtained between two of the authors who coded the data independently. At 9.0 cpd, all nine inducers revealed assimilation. The 6 cpd data primarily showed assimilation. For observer Q.J., at 6 cpd, eight inducers showed assimilation and one showed contrast on the l-axis line; all nine inducers showed assimilation on the s-axis line. For observer N.W., seven inducers showed assimilation, and two showed contrast on the l-axis line; all nine showed assimilation on the s-axis line. For observer Y.Z., all nine inducers showed assimilation on the l-axis line; seven inducers showed assimilation, and one showed contrast on the s-axis line. At 4 cpd, the effects were small and variable. Many inducers produced no systematic effect. For observer Q.J., at 4 cpd, four inducers showed assimilation and three showed contrast on the l-axis line; four inducers showed assimilation on the

s-axis line. For observer N.W., four inducers showed assimilation, and two showed contrast on the l-axis line; six inducers showed assimilation on the s-axis line. For observer Y.Z., five inducers showed contrast on the l-axis line; three inducers showed assimilation and three showed contrast on the s-axis line. At 0.7 cpd, there was no assimilation. The transition from assimilation to contrast occurred near 4.0 cpd, approximately a 7.5% bar width. There was no systematic difference in the spatial frequency of transition for the l- and s-axes. For the retinal illuminance level produced by the CRT, we measured visual acuity mediated by SWS cones under long-wavelength adaptation, using methods described previously (Wilson, Blake, & Pokorny, 1988; Swanson, 1989). The estimate is a lower SWS cone mediated acuity limit. A square wave grating using only the B phosphor was presented on the monitor with a superimposed longwavelength adapting field of variable luminance. Cor-

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rect identification of vertical or horizontal orientation was assessed in a staircase procedure. As the luminance of the background field increased, visual acuity decreased and reached a plateau above 1000 td. This plateau corresponds to that used to isolate SWS cones in an increment detection task. The limiting visual acuity was 5 cpd for Y.Z. and 6 cpd for Q.J. and N.W., higher than the spatial frequency at the transition from assimilation to contrast. It should be emphasized that a grating percept was observed for all conditions of the induction experiments, including s-axis tests with s-axis inducers.

3.2. Assimilation At a spatial frequency of 9 cpd, the data vectors pointed to the chromaticity coordinate of the inducer. We could thus ask whether the perceived color appeared simply as a physical mixture color of test and inducer. Calculation of mixture colors is simple in the equiluminant cone chromaticity diagram. The l-chromaticity of the mixture color is given by: lmatch = klinducer +(1−k)ltest

(1)

where lmatch, linducer and ltest are the l-chromaticities of the match, the inducer and the test stimulus, and the constant k represents the proportion of inducer in the mixture. It is convenient to rewrite the equation as: lmatch = ltest + k(linducer − ltest).

(2)

A plot of lmatch versus ltest will yield data falling on a straight line of slope less than unity and passing through the chromaticity of the inducer. A similar equation is written for the s-axis. Fits were made independently for the l- and s-axes and separately for each inducer and surround, using a least-squares method with the slope k as a free parameter. The data and fits with the surround are shown in Fig. 4 for Y.Z. comparing the surround and no-surround conditions and in Fig. 5 for Q.J. and N.W. for the surround condition. In both figures, the left panels show data for the l-axis, and the right panels show data for the s-axis. Matches are shown as open circles, the inducer as a closed square; the thin solid line represents the diagonal (no effect), and the dashed line represents the fit. Data for different inducers are displaced vertically for clarity. The data uniformly showed a shallower slope than the diagonal, consistent with assimilation. Fits were per-

Fig. 3. Raw data for observer Y.Z. plotted in relative cone troland space for four inducers with mixed l-axis and s-axis chromaticity. The plot follows the format of Fig. 2. Chromaticities of the inducers are Y – G, O, B – G, and P from top to bottom.

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Fig. 4. Induction data for the 9 cpd spatial frequency for Y.Z. The upper panels show data and fits with the surround, and the lower panels show the no surround data. The abscissa shows the test chromaticity and the ordinate shows the matching chromaticity. Data for different inducers are displaced by vertical adjustment for clarity. The solid squares show the position of the inducers; the thin diagonal lines indicate no effect. The open circles show data, and the dashed lines are best fits of an additive light model.

formed for three observers (Q.J., N.W. and Y.Z.) and both surrounds. In general, the quality of the fits was good. The values of k did not vary appreciably as a function of the inducer or the axis, and k was averaged across inducer and axis. Mean values (plus/minus one s.d.) for k in the 90 td surround were 0.18 (9 0.07) for N.W., 0.30 (9 0.13) for Q.J. and 0.39 (9 0.06) for Y.Z.

The mean values for k in the dark surround were 0.22 (9 0.07) for N.W., 0.25 (9 0.06) for Q.J. and 0.36 (9 0.05) for Y.Z. Thus, the difference between the surround and no-surround conditions was less than one standard deviation for each observer (shown graphically for Y.Z. in Fig. 4). At 6 cpd, there was still evidence of assimilation for most inducers viewed in the

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white surround and fewer in the dark surround. We fit the 6 cpd data showing assimilation with Eq. (2). The mean values for k were reduced, ranging from 0.10 ( 9 0.05) for N.W., 0.20 (90.12) for Q.J. and 0.18 ( 9 0.12) for Y.Z.

3.3. Contrast At a spatial frequency of 0.7 cpd, the matches pointed away from the inducing chromaticity, indicating contrast. These data can be replotted for the l- and

Fig. 5. Induction data for the 9 cpd spatial frequency for Y.Z. The upper panels are induction data for the 9 cpd spatial frequency for observers Q.J. and the lower panels are induction data for N.W. The left panels are data for the l-axis, and the right panels show data for the s-axis. The format is as for Fig. 4.

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s-axes separately. In evaluating contrast, we prefer to renormalize the l- and s-axes at the equal energy spectrum (Smith & Pokorny, 1996a,b). For the l-axis, we plot (l− lw)match versus (l− lw)test; for the s-axis, we plot (s −sw)match versus (s − sw)test. This normalization is similar to that of Jameson and Hurvich. If there is no contrast effect, the matches will fall on a 45° line passing through the origin. Contrast effects may affect either the slope of the line or the horizontal position of the line. Any interaction of the l- and s-axes is noted by plotting (s− sw)match versus (l −lw)match for the l-axis and (l−lw)match versus (s −sw)test for the s-axis. Within the framework of color theory, the W inducer has no chromatic content and therefore cannot induce a chromatic percept. Ware and Cowan (1982) showed, however, that matches in their experiment revealed that the test bars in the grating pattern appeared more saturated than the large comparison field. In a chromaticity diagram such as Fig. 2, the vectors diverged from the white point. We observed a similar result for the W inducer, analyzed separately (Smith et al., 1998). For an inducer on a cardinal axis, induction should be confined to that axis. The R and G inducers should not induce percepts of blue and yellow according either to the relative cone troland space or to the Jameson and Hurvich (1955) chromatic opponent space. This means that the data for these inducers should be parallel to the horizontal axis. However, for these inducers, a small effect of increasing saturation was noted (Fig. 2). The V and Y inducers are on cardinal axes of the cone troland chromaticity space but not on a cardinal axis of color appearance space. According to the Jameson and Hurvich model (Jameson & Hurvich, 1955), the V inducer should induce greenness, and the Y inducer should induce redness. This result was not noted in the match data, which were consistent with a small saturation effect (Smith et al., 1998) (see Fig. 2). We suggested that the saturation effect occurred because the grating pattern maintained chromatic contrast in the test field compared with the uniform comparison field. The phenomenon may be related to the observation that a uniform field fades under continuous view (Vimal, Pokorny, & Smith, 1987). Our goal was to evaluate chromatic contrast in terms of a retinal spectral opponency. The two-process model for the l-axis can be adapted from the formulation for chromatic opponent valences of Jameson and Hurvich (1955) to an equation for retinal spectral opponency of the form, involving only LWS and MWS cones. Studies of equiluminant chromatic contrast discrimination using chromatic adaptation (Smith, Pokorny, & Sun, 2000) have postulated a retinal model with two sources of adaptation. First, there is a stage of cone-specific multiplicative gain followed by spectral opponency. Second, a subtractive gain subtracts the residual signal

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at the chromatic adaptation point from the spectral opponent signal. (l −lw)match = (g1Dl − g2 Dmt)− a(l −lw)inducer

(3)

where g1Dl and g2Dm represent the spectral opponent responses to the test light incorporating both subtractive gain at the opponent stage and multiplicative gain, g1 and g2 at the receptor stage. The two-process model for induction then allows a subtractive term, a, that depends only on the inducer. A similar equation can be written for the s-axis (Zaidi et al., 1992). (s− sw)match = (g3Ds −g1Dl − g2Dmt)− a(s − sw)inducer. (4) The factors determining the gain terms are unspecified in the Jameson and Hurvich model. They could be the gain of the test field alone, the gain of the inducer alone, or some combination. According to Shevell (1980), all three terms are determined only by the inducing chromaticity. In this event, the predicted effect of the inducing surround does not distinguish between the gain and additive effects at a single adapting chromaticity, as we used. If matching chromaticity is plotted as a function of test chromaticity, the matches will be shifted horizontally toward the chromaticity of the inducer but will maintain a 45° slope (Smith & Pokorny, 1996a). If the test chromaticity were to play a role in receptor gain, then we would expect an interaction of test chromaticity and inducing chromaticity and slopes other than unity. The data were first examined to see if a slope factor was needed, implying an interaction between the inducing and the test chromaticity. The data did not reveal slopes other than 45°. We therefore fit our data with linear equations: (l− lw)match = (l −lw)test − k(l −lw)inducer

(5)

where (l− lw)match, (l− lw)inducer and (l− lw)test are the chromaticities of the match, the inducer and the test stimulus, and the constant k represents the value of the contrast effect. The data and fits with the dark surround are shown in Fig. 6 for Y.Z. comparing the surround and no surround conditions, and in Fig. 7 for Q.J. and N.W. with no surround. In both figures, the left panels show data for the l-axis inducers and matches and the right panels show data for the s-axis inducers and matches. Matches are shown as open circles, the inducer as a closed square; the thin solid line represents the diagonal (no effect), and the dashed line represents the fit. Data for different inducers are displaced vertically for clarity. For the l-axis (left panels of Figs. 4 and 5), the data are displaced vertically in order of increasing l-chromaticity of the inducing stripes. The three lower data sets are for ‘‘green’’ biased inducers, and the matches are displaced above the diagonal (less green). The three

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Fig. 6. Induction data for the 0.7 cpd spatial frequency Y.Z. The upper panels show data and fits with the surround, and the lower panels show the no-surround data. The left panels are data for the l-axis expressed as (l− lw)test, and the right panels show data for the s-axis, expressed as (s −sw)test. Data for different inducers are displaced by vertical adjustment for clarity. The solid squares show the position of the inducers; the thin diagonal lines indicate no effect. The open symbols show the data. For the (l −lw) matches, the symbols are: inverted triangles, G; squares Y–G and B – G [matched in (l − lw)]; circles P and O [matched in (l −lw)]; upright triangles R. For the (s −sw) matches the symbols are: inverted triangles, Y; squares Y – G and O [matched in (s− sw)]; circles P and B – G [matched in (s −sw)]; upright triangles V. The dashed lines are best fits of the two-process model with neutral adaptation.

upper data sets are for ‘‘red’’ biased inducers, and the matches are displaced below the diagonal (less red). The Y – G and B–G inducers differed only in S-chromaticity as did the O and P inducers. There was no interaction effect for the observers in either surround between the amount of induction for the l-axis and the level of

s-chromaticity in the inducer. The (s− sw)match was independent of the (l− lw)test chromaticity. Fits were performed for three observers (Q.J., N.W. and Y.Z.) and both surrounds. In an initial set of fits, k was allowed to vary with the inducer. There was only a scattered variation in k. Therefore, we fixed k and fit

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all six data sets with one parameter. The mean squared residual was less than twofold higher despite the reduction in parameters from six to one. The values of k with a dark surround were 0.47 for Q.J., 0.29 for N.W. and 0.25 for Y.Z. The surround reduced the amount of induction, as noted in Fig. 5. The values of k with a 90 td surround were 0.18 for Q.J., 0.08 for N.W. and 0.18 for Y.Z. In general, the quality of the fits was good, although occasional deviant data points can be noted. For the s-axis (right panels of Figs. 4 and 5), the data

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are displaced vertically in order of increasing s-chromaticity of the inducing stripes. The three lower data sets are for ‘‘yellow’’ biased inducers, and the matches are on or displaced above the diagonal (less yellow). The three upper data sets are for ‘‘blue’’ biased inducers, and the matches are on or displaced below the diagonal (less blue). For these matches, the Y–G and O inducers differed only in l-chromaticity, as was the case for the B–G and P inducers. Again, there was no indication of an interaction between the amount of induction for the

Fig. 7. Induction data for the 0.7 cpd spatial frequency for Q.J. (upper panels) and N.W. (lower panels) with a dark surround. The format is as for Fig. 6.

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s-axis and the level of l-chromaticity in the inducer. The (l – lw)match was independent of the (s – sw)test chromaticity. The s-axis data can be fit with an equation parallel to that of Eq. (4) (s − sw)match = (s− sw)test −k(s −sw)inducer.

(6)

We first fit the data allowing k to optimize for each inducer. We noted that the values of k for the three ‘‘yellow’’ inducers did not differ systematically from each other but were different from the values of k for the three ‘‘blue’’ inducers. We therefore reduced the parameters to two without reduction in quality of the fits. The values of k with a dark surround for ‘‘yellow’’ inducers were 1.73 for Q.J., 0.63 for N.W. and 0.78 for Y.Z., and for ‘‘blue’’ inducers 0.17 for Q.J., 0.08 for N.W. and 0.10 for Y.Z. Again, the surround reduced the amount of induction, as noted in Fig. 5. The values of k with a 90 td surround for ‘‘yellow’’ inducers were 0.65 for Q.J., 0.24 for N.W. and 0.63 for Y.Z., and for ‘‘blue’’ inducers were 0.10 for Q.J., 0.01 for N.W. and 0.05 for Y.Z. The quality of the fits was generally good for N.W. and Y.Z. but data for Q.J. were more scattered. In particular, the V and O inducers showed an interaction of the match with the test chromaticity.

4. Discussion The data confirm previous studies (Helson & Joy, 1962; Helson, 1963; Schober & Munker, 1967; Walker, 1978; Fach & Sharpe, 1986) in showing that spatial frequency is the major factor affecting the transition from assimilation to contrast in simple grating stimuli. By employing stimuli along physiologically important axes in chromaticity space, we found no consistent difference in the spatial frequency of the assimilation/contrast transition between the l- and s-axes. Further, the amount of assimilation at 9.0 cpd was similar for the l- and s-axes. Assimilation was independent of the chromaticity of the inducer, and the presence or absence of a surround. Assimilation could be described as a color match of test and inducer, demanding a constant proportion of the inducing chromaticity. The proportion varied from 0.18 to 0.39 among observers. Finally, all observers saw the 9.0 cpd display as a series of color stripes even when inducers and tests stimuli lay on the same lines in cone chromaticity space. These results strongly suggest that optical factors rather than spatial resolution were the major determinants of the assimilation effect for equiluminant grating stimuli. In the following section, we calculate the expected effect.

4.1. Calculation of the spread light Optical factors including optical aberrations and scattered light affect the spread light in the image. We

calculated the amount of spread light using the linespread function derived by Williams, Brainard, McMahon, and Navarro (1994). We computed the amount of light that spread into the test stimulus region by summing the amount of spread light produced from all lines in the inducing stimulus region to a horizontal line within the test stimulus region and the inducing stimulus region. For the calculation, light spread was calculated for 0.1% width lines. The calculation was repeated for many horizontal lines in the inducing and the test area, a method similar to that employed by Shevell and Burroughs (1988) when they computed the spread light from an annular source. The fraction of spread light from the inducing areas more than two cycles away from the test line was less than 0.03% for the highest spatial frequency stimulus (9.0 cpd) and was therefore not calculated in the results. The relative amounts of light for spatial frequencies of 9.0, 6.0, 4.0 and 0.7 cpd were computed across two cycles of the gratings. The amount of spread light was least in the middle of the test stimulus region and increased towards the edge of the test stimulus region. The light-distribution curve for the stimulus with the spatial frequency of 0.7 cpd showed that an insignificant amount of spread light reached the test stimulus region except in the area near the inducer-test border. With increase in spatial frequency, the minimum fraction of spread light, which was in the center of the test stimulus region, increased. The minimum fractions of spread light were calculated as 0.04, 0.14, and 0.27 for spatial frequencies of 4.0, 6.0, and 9.0 cpd. For 9.0 cpd, the fraction of spread light agrees with the fraction of inducer calculated by Eq. (2). Observer data at 9 cpd ranged from 0.18 to 0.38 with an average of 0.28. Further, the calculations indicate that the spread light should be reduced by 50% when the spatial frequency is reduced to 6.0 cpd and would be negligible at 4 cpd. This result too is consistent with our observer data. Thus, our data are compatible with assimilation for these simple grating stimuli being determined by spread light.

4.2. Does chromatic aberration play a role in assimilation? The spread-light calculation was based on a linespread function calculated with monochromatic light. Chromatic aberration is another potential source of spread light. For the stimuli used in this study, the retinal image of a stimulus can be treated as approximating the sum of the phosphors, each of a different contrast (Kruger, Mathews, Aggarwala, & Sanchez, 1993). Evaluation of the possible contribution of chromatic aberration to assimilation can be made, based on the defocus of the retinal image. Since the difference in focus between the blue phosphor (465 nm) and the red phosphor (607 nm) is about 1.0 D, there is a point between 465 and 607 nm at which the defocus of the

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blue and the red phosphor light is about 0.5 D. Assuming this state of accommodation, we used the analysis developed by Flitcroft (1990) to calculate the modulation transfer of the red and blue phosphor components. Even for the 9.0 cpd grating, the calculated effect of chromatic aberration was small. This result was consistent with our data. The P inducer, which combined light from both red and blue phosphors, should produce more assimilation than the other inducers if chromatic aberration were an important contributor to assimilation in this study. However, the R inducer, with negligible light from the B phosphor, showed a similar amount of assimilation as the P inducer (high activation of both R and B phosphors). For the CRT-generated stimuli of these experiments, chromatic aberration did not appear to be a major source of assimilation.

4.3. Assimilation The spread-light analysis revealed that a 9 cpd equiluminant grating is a potent source of spread light, perhaps because we used equiluminant test and inducing lights. Although our data, and probably those of Fach and Sharpe (1986), are compatible with assimilation caused by spread light, assimilation measured under other stimulus situations has other explanations. Many demonstrations of assimilation combine chromatic and luminance contrast in complex spatial displays (e.g. Ware, 1980; De Weert & van Kruysbergen, 1997) where spread light is an unlikely cause of assimilation. As an example, chromatic grid phenomena (Gindy, 1963) demonstrating assimilation cannot be attributed to spread light (Shevell, Marcangelo, & Barnes, 1999). De Weert and Spillmann (1995) have shown a ‘‘pincushion’’ display that produces assimilation for achromatic contrast but no effect for equiluminant chromatic contrast.

4.4. Contrast The amount of contrast induction could be described by lines of 45° slope, displaced from the diagonal. This result is consistent with the interpretation that adaptation to the test bars was not a factor in contrast induction. The size of the contrast effect was small, with values of k for the l-axis varying from 0.25 to 0.47. The variation among observers was almost twofold higher for Q.J. than for N.W. and Y.Z. on both the land s-axes. The presence of the 90 td neutral surround decreased the values of k to 50.18 for all three observers. In comparison, a previous study using a 1° center in a 3° by 6° surround, cone-axis stimuli and a haploscopic matching procedure (Smith & Pokorny, 1996a) noted quite different results. A red inducer (l− lw)] 0 removed the redness content of all test chromaticities. A percept of green, however, occurred only for test

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chromaticities (l −lw)5 0. There was an area between white and the inducer for which test lights appeared neither reddish nor greenish, termed the hiatus. For stimuli of higher chromatic content than the inducer, there was pronounced induction with k-values of 0.66 – 0.93, consistent with adaptation to the inducer. In comparison, the amount of greenness induction for chromaticities (l− lw)5 0 was small with k-values of 0.04 –0.16. Parallel data were obtained for green inducers and for data on the s-axis. In a second study, Miyahara, Smith, and Pokorny (in press) noted that surround widths of 30% or more generated similar matching data. Reduction in surround width to 15% or 3% reduced the amount of induction and the width of the hiatus. The current study did not reveal a hiatus. There was a major difference in the spatial format of the displays. In the current study, there were multiple abutting test and inducing bars. This format may lead to eye movements across the bars as the observer tries to match the test bars to the larger comparison field. Owing to eye movements, cells along edges continually sweep across the borders. With a grating pattern, spectral opponent cells will generate continual contrast signals but will not adapt to the chromaticity of either side. Chromatic discrimination for the l-axis suggests that spectral opponent cells have an intrinsic normalization near equalenergy white (Boynton & Kambe, 1980; Miyahara et al., 1993; Yeh, Pokorny, & Smith, 1993; Smith et al., 2000). The results suggest that adaptation to the test and inducing stimuli did not play a significant role in our experiment. Our data were consistent with the interpretation that the adaptation state was neutral, and the contrast effects were generated only by an additive effect present at the level of opponency of either retinal or cortical origin. A second consequence of the grating display is that the vertical edges of the test and inducing bars abutted the dark or neutral surround. This neutral surround may have contributed to the failure to achieve adaptation to either test or inducing bar. Previous data have suggested that contrast is greatest when the test field is embedded within the surround (e.g. Jameson & Hurvich 1961). The l-axis matches were well described within the L–M spectral opponency of the primate retina. The Hurvich & Jameson chromatic opponent for red –green includes a contribution to redness from SWS cones (Hurvich & Jameson, 1958; Jameson, 1972). This contribution was not evident in the l-axis matches. In particular, the Y and V inducers did not have a consistent contrast effect on the l-axis matches (Fig. 2) (Smith et al., 1998). Chromatic contrast discrimination is symmetrical for increment and decrements in l-chromaticity (Smith et al., 2000). Thus, retinal contrast signals are equal for increments and decrements in l-chromaticity, and these contrast signals may generate equivalent size contrast effects at higher levels.

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For the s-axis, as for the l-axis, adaptation was neutral giving a pure ‘‘additive’’ effect. The value of k differed for the ‘‘yellow’’ and ‘‘blue’’ inducers. Induction by ‘‘yellow’’ lights was stronger than induction by ‘‘blue’’ lights. One possible factor is that the S-cone pathway is not strongly opponent in dark surrounds (Le Grand, 1949; Boynton & Kambe, 1980; Miyahara et al., 1993; Yeh et al., 1993). However, the asymmetry was present in both the dark surround and the 90 td surround. A dim surround does induce spectral opponency to the chromaticity of the surround (Miyahara et al., 1993). Even in a dim surround, chromatic contrast discrimination for SWS cone signals is not symmetrical about the adapting chromaticity. Chromatic contrast discrimination is better for decrements than for increments in s-chromaticity (Zaidi et al., 1992; Miyahara et al., 1993). This result suggests that retinal contrast signals are much greater for increments in s-chromaticity than for decrements in s-chromaticity, and may generate asymmetric-sized contrast effects at higher levels. In summary, our studies have revealed that chromatic contrast can be formulated within a retinal spectral opponent space. The strength of chromatic contrast may be related to the strength of retinal contrast signals generated by cells as they sweep across chromatic borders.

Acknowledgements NEI Research Grants EY00901 (Pokorny) and EY 07390 (Smith) supported this research. The authors thank observers N.W. and Y.Z. for their time and patience. Publication was supported by Research to Prevent Blindness.

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