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Abstract
Brown is a contrast color that depends on complex combinations of chromatic and achromatic signals. We measured brown perception with variations in chromaticity and luminance in center-surround configurations. In Experiment 1, the dominant wavelength and saturation in terms of ${S}$-cone stimulation were tested with five observers in a fixed surround luminance (${60}\;{{\rm cd/m}^2}$). A paired-comparison task required the observer to select the better exemplar of brown in one of two, simultaneously presented, stimuli (1.0° center diameter; annulus of 9.48° outer-diameter). In Experiment 2, the same task was tested with five observers in which surround luminance was varied (from 13.1 to ${99.6}\;{{\rm cd/m}^2}$) for two center chromaticities. The results were a set of win–loss ratios for each stimulus combination and converted to ${Z}$-scores. An ANOVA did not reveal a significant main effect of the observer factor but revealed a significant interaction with red/green ($a^*$) [but not with the dominant wavelength and the ${S}$-cone stimulation (or $b^*$)]. Experiment 2 revealed observer variation in interactions with surround luminance and ${S}$-cone stimulation. The averaged data plotted in 1976 $L^*a^*b^*$ color space indicate that high ${Z}$-score values widely distribute in the area of $a^*$ from 5 to 28 and $b^*$ over 6. The balance of the strength between yellowness and blackness differs among observers owing to the amount of induced blackness required for the best brown.
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1. INTRODUCTION
Contrast colors are ubiquitous in natural scenes, and the contrast colors, brown, gray, and black are considered among 11 basic colors [1]. However, these colors are different in production and reproduction from other basic colors because they cannot be perceived in a single light in a completely dark surround. In the opponent color theory of Hering [2] white–black is a color-opponent process similar to red–green and blue–yellow; but with the proviso that spatial and/or temporal contrast is required [3–5]. Brown may be treated as a combined response of yellow and (moderate) black.
Bartleson [6] reported that brown perception is constrained in three dimensions, requiring a certain combination of hue, saturation (chroma), and lightness (value). Using Munsell color chips presented on a gray background, the lightness of the test color is a variable to the fixed lightness of the background gray. In terms of a mechanism of brown perception, it is suggested that the luminance contrast between the test and background is a key factor for brown perception. Fuld et al. [7] reported that the luminance contrast in brown perception should be moderate since very high or low luminance contrasts produce complete black or yellow, respectively; the perception of the center field changed from yellow, brown to black expressed by the relative ratio of each basic color in the color-naming method when the surround luminance increased. Brown perception has also been investigated in terms of color categories, and color chips categorized as “brown” are known [8–10]. However, how the chromatic conditions of the center field change the perception of brown is not entirely clear.
Differences between observers can add difficulty in understanding brown perception. Since the brown perception is influenced by all three factors, hue, saturation, and luminance (lightness) contrast, the possible observer variation on each factor would be compounded, leading to relatively large observer variation. It was reported that the blackness induced in the center field by the increment of surround luminance differs between observers not only in the amount of blackness but also in the slope of the increment function [3,4]. When the center field is chromatic, the amount of blackness induced also depends on the luminance of the center [5].
Quinn et al. [11] used the continuous judgmental color-naming technique to test uniqueness of brown [12]. Some colors described as brown might be decomposed into yellow and black for some observers, but Fuld et al. [7] found it was a required term for other observers.
In addition, Buck and DeLawyer [13] showed that weightings of M- and L-cone stimulation at red–green equilibria are different between yellow and brown; this could be caused by a non-linear influence by the inducing surround field. Although there is a gradual darkening of a central yellow field with increasing surround luminance, Buck [14] suggested that the perception of brown can be separated into the induced brown mixed with yellow which he called “butterscotch” with the induced brown replacing yellow completely as “pure brown.” In this scheme, the darker brown is treated as “pure brown” and the lighter brown is treated as the mixed color of darkness and yellow [15]. If a naïve observer would partly hold this concept consciously or unconsciously, only the brown in high luminance contrast would be called brown, and the brown in relatively low luminance contrast would be treated as dark yellow.
We investigated the relations between brown perception and chromatic conditions of the center field surrounded by a white annulus to characterize possible differences in observer’s judgement of brown. We employed a paired-comparison method in which the observer selected one of two center-surround stimulus sets based on a criterion of “better brown.” The better brown criterion in the paired comparisons means that both of the center fields would not necessarily look like the “best brown” or “pure brown.” We expected that the results of the most frequently selected center-surround stimulus would identify not only the best chromatic and luminance conditions for brown but also the observer’s criterion or definition of brown. In addition, in order to avoid complex arguments about the definition of the perceived saturation since it would be changed by the bright annulus, we defined the amount of saturation in the chromatic centers by the S-cone stimulation. Regardless of the amount of the perceived saturation, this definition is stable for color stimuli in all luminance contrasts. Two experiments were conducted. In Experiment 1 (Exp. 1), the chromatic center was changed in a fixed luminance (contrast) in terms of dominant wavelength and log ${S}$-cone stimulation. In Experiment 2 (Exp. 2), two different chromatic center fields were selected based on the results of Exp. 1 and the luminance of the surround annulus was changed.
2. METHODS
A. Observers
Five observers (Obs#1–Obs#5; two female and three male) participated in Exp. 1 and two of them along with three additional observers (Obs#1, Obs#4, Obs#6–Obs#8; two female and three male) participated in Exp. 2. Obs#8 was one of the experimenters. The other observers were paid volunteers who were naïve about the purpose of the experiments. The observers were 23 to 55 years old; but the difference in retinal illuminance is minor over this age range [16]. All participants had best-corrected visual acuity ${\gt}{20/25}$, with clinically normal retinae and visual fields. All were normal trichromats according to the panel D-15 test, the F2 and HRR plates, the Neitz anomaloscope (Model: OT), and the Cambridge Colour Test.
The procedures and experiments conformed to the principles expressed in the Declaration of Helsinki and were approved by the UC Davis Medical Center’s Institutional Review Board. Written informed consent was obtained from each observer prior to testing.
B. Stimulus
Center-surround stimuli were presented on a 21 in. cathode-ray tube monitor (GDM-F520, Sony Corporation) at a ${1024}\;{\times}\;{768}\;{\rm pixel}$ resolution with a refresh rate of 140 Hz, controlled by a video board with 15-bit resolution in each phosphor’s intensity (VSG 2/4, Cambridge Research Systems). The monitor frame was covered by a black cardboard. The monitor was placed in a dark room and the viewing distance was 100.8 cm. The observers’ responses were registered with a keypad. The monitor was calibrated using a luminance and color meter (CS-100, Konica-Minolta) and custom-made software with the gamma calibration system provided by the manufacturer of the VSG card (OptiCal and control software, Cambridge Research Systems).
To avoid unexpected bias of estimating the magnitude of the brownness perceived in the center field, we employed the paired-comparison method. Two white annuli [${\rm CIE}\;(x,y) = {0.313}$, 0.329] of fixed luminance were presented side-by-side in ${21.8}^\circ \;{\times}\;{16.4}^\circ$ screen as illustrated by Fig. 1, with their centers at 5.53° left and right from the horizontal center. In all experiments, the diameter of the center field subtended 1.00° with inner- and outer-diameters of the annulus of 1.04° and 9.4°, respectively. In Exp. 1, we changed the chromaticity coordinates of the center field in terms of dominant wavelength and saturation to obtain the chromaticity coordinates that define the best brown area of the center color. The luminance of the center and the annulus were ${5}\;{{\rm cd/m}^2}$ and ${60}\;{{\rm cd/m}^2}$, respectively. The background was black $({\rm R,G,B})=(0,0,0)$, with a luminance of ${0.103}\;{{\rm cd/m}^2}$. The saturation was operationally defined by the amount of ${S}$-cone stimulation. The transformation between cone responses and tristimulus values was performed using Smith–Pokorny estimates of the cone photopigment spectral sensitivities [17] with the cone matrix by Kaiser and Boynton [18]. The ${S}$-cone stimulation was defined in the luminance unit base in which the sum of ${L}$- and ${M}$-cone stimulations is the luminance value in [${\rm cd/m}^2$].
Fig. 1. Visual stimuli and time course of one trial for Exp. 1. After the last black screen, the observer pressed a left or right button to select one center-annulus pattern for better brown. The size of the mask pattern and black screen were reduced for better presentation. See text for details.
Figure 2 shows the chromaticity coordinates of chromatic center fields calculated using CIE 1931 standard color-matching functions [19]. In Exp. 1, we changed the dominant wavelength and ${S}$-cone stimulation of the center field. Here, the dominant wavelengths were obtained by a line from D65 to the spectrum locus (denoted by black circles in Fig. 2). We used three logarithmic ${S}$-cone stimulation settings (${-}{1.83},\;- {1.41}$, and ${-}{1.20}$) for the main stimuli and two log ${S}$-cone stimulation settings for red and green [${-}{1.06}$; the same with D65 at equal luminance (${5}\;{{\rm cd/m}^2}$)] and for blue (${-}{0.42}$). The blue and yellow were on the tritan line passing through D65. In the first three sessions of the first two observers, we used 14 center colors with variation in dominant wavelength from 560 nm–595 nm and four control colors [red, green, yellow (566.3 nm), and blue]. The results of the first three sessions indicated that center chromaticities of longer dominant wavelength would be needed so in the second three sessions we added seven additional center chromaticities (denoted by yellow circles in Fig. 2). For three more observers we picked up 18 center colors and three control colors (denoted by circles surrounded by large red circles in Fig. 2). In Exp. 2, we changed the luminance of the white annulus from 13.1 to ${99.6}\;{{\rm cd/m}^2}$ with two colors in each center, 590 nm at ${-}{1.83}$ log ${S}$-cone stimulation, and 595 nm at ${-}{1.20}$ log ${S}$-cone stimulation, while the luminance of the center field was fixed to ${5}\;{{\rm cd/m}^2}$.
Fig. 2. CIE 1931 $xy$ chromaticity coordinates of center colors. Blue and yellow symbols denote center colors used in the first three sessions and used in the second three sessions for Obs#1 and Obs#2, respectively. Symbols surrounded by large red circles denote the colors used to test Obs#3–Obs#5 in Exp. 1. Symbols surrounded by large black diamonds denote the colors used in Exp. 2. Cross denotes D65. Four control colors were shown by names attached. Blue dashed lines denote the constant ${S}$-cone lines and tritan line. Black triangle denotes monitor gamut. Log ${S}$-cone stimulation values were indicated in the panel. Black circles on the spectrum locus denote reference points for the dominant wavelength calculation. See text for details.
C. Procedures
Trials began after 3 min of dark adaptation and 3 min of adaptation to a white screen (D65, ${20}\;{{\rm cd/m}^2}$). Two center-surround stimuli were shown side by side for 1 s. After the presentation, a checkerboard mask pattern consisting of white (${35}\;{{\rm cd/m}^2}$) and gray (${25}\;{{\rm cd/m}^2}$) squares of ${1.36}^\circ \;{\times }\;{1.36}^\circ$ was presented for 2.75 s after a 0.25 s interval. The checkerboard pattern reduced afterimages and adaptation to the annulus. After each 4.5 s presentation cycle or during the presentation of the checkerboard pattern, the observer was asked to press a left or right key button to indicate the center-surround stimulus that was a “better brown.” The time course of one trial is shown in Fig. 1. The stimuli were observed freely with the observer’s preferred eye while the other eye was covered with a patch. After the button press, the next trial started; the observer could take a break as desired.
In the paired-comparison method, the number of stimuli, ${n_s}\!$, is important since it determines the number of trials in all combinations, ${n_t}({n_t} = {_{\textit{ns}}}{C_2})$. In Exp. 1, the first two observers (Obs#1 and Obs#2) were tested in three sessions for each stimulus set in which 18 colors were measured in 306 trials in one session with left and right positions counterbalanced. For three subsequent observers (Obs#3–Obs#5), one session had 420 trials with 21 colors and they performed five sessions; all trials in one session were presented in pseudo-random order. In Exp. 2, comparisons were made between two center stimuli with varying surround luminance, and the number of trials was 306 in one session in pseudo-random order. The observers performed six sessions. Most observers participated in one session per day and some observers finished two sessions in a day.
D. Data Analysis
The results of the paired-comparison method were first described in terms of the win–loss (chosen–not-chosen) scores for each combination of the colors of the center field and/or the luminance of the annulus. Because the number of trials was different between observers and experiments, we used the win–loss ratio in which the number of wins was divided by the number of trials in one combination (i.e., six, 10, or 12 trials). Using the averaged win–loss ratio of one condition with all other conditions, and the standard deviation of the ratios of all conditions with all combinations for each observer, the win–loss ratios in each experimental condition for each observer were transformed to ${Z}$-scores. The results of the win–loss ratio have a high compatibility to the ${Z}$-score since they are distributed symmetrically with a mean of 0.5. To avoid extreme values in the ${Z}$-score calculation which could be too dominant in the average calculation, all wins (six, 10, or 12 wins) and no wins were reduced by 0.15 wins or increased by 0.15, respectively. This modification of win–loss ratio defines theoretical upper or lower limits of the ${Z}$-score which depend on the number of trials per combination.
3. RESULTS
A. Influence of Dominant Wavelength and ${S}$-Cone Stimulation on Brown Perception (Exp. 1)
1. Z-Score of Brown Selection as a Function of Dominant Wavelength for Different S-Cone Stimulation Levels
Figure 3 shows ${Z}$-scores of the better brown selection in all observers in Exp. 1. On average the best brown perception was obtained at dominant wavelengths around 585–595 nm in lower ${S}$-cone stimulation.
Fig. 3. ${Z}$-score of the better brown selection plotted as a function of dominant wavelength in ${S}$-cone stimulation. Panels (a), (b), and (c) show log ${S} = - {1.83}$, ${-}{1.41}$, and ${-}{1.20}$, respectively. Different symbols denote ${Z}$-scores of different observers as shown in figure keys. Red crosses denote the simple average of all observers. Blue, green, and red center colors were plotted at the points of 545, 550, and 645 nm, respectively. Error bars denote $\pm {2.78}$ S.E.M. (95% confidence interval). Black horizontal lines denote the upper limit, average, and lower limit of ${Z}$-scores. On average, the dominant wavelengths of the best brown perception were around 585–595 nm at lower ${S}$-cone stimulation.
An analysis of variance (ANOVA) was performed in MATLAB (ver. 2022b) using the ${Z}$-score data of each center field condition in Exp. 1, with observers, dominant wavelength, and ${S}$-cone stimulation being the within subjects factors. For this analysis, the number of dominant wavelengths was reduced in order not to have the dominant wavelength which had the data only in one ${S}$-cone stimulation condition and the number of dominant wavelength data was balanced to four in each ${S}$-cone stimulation condition. The control stimuli of red, green, yellow, and blue were not included since the purpose of the analysis was to find the factor influencing “brown” perception.
The results of the three-way ANOVA revealed that the dominant wavelength and S-cone stimulation had significant main effects [$F({5},\;{48}) = {23.07}$, $p \lt {0.0001}$; $F({2},\;{48}) = {9.68}$, $p = {0.0003} \lt {0.001}$], while the main effect of observer was not significant. In a two-way ANOVA using dominant wavelength and ${S}$-cone stimulation there was a significant interaction [$F({4},{48}) = {8.03}$, $p = {0.000049} \lt {0.0001}$] (since the dominant wavelengths were not common in all three $S$-cone conditions, the degrees of freedom were adjusted accordingly). Further analyses using a new factor ($a^*$) reveal the significant interaction between the observer factor and $a^*$ (see Section 3.A.3).
2. Z-Scores of Brown Selection Plotted in xy Chromaticity Coordinates (Exp. 1)
The interaction between the dominant wavelength and ${S}$-cone stimulation was statistically significant in the ANOVA. The relation between the chromaticity coordinates of the center colors and ${Z}$-scores of brown comparison was not clear in Fig. 3, thus the ${Z}$-score data were replotted in CIE 1931 $xy$ color space using the contour line expression. Figure 4 shows the ${Z}$-score data of the better brown selection plotted in $x,y$ chromaticity coordinates for the average of all observers. In Fig. 4 data coordinates circled by triangles and squares denote low and high ${Z}$-score groups, respectively, defined by the result of multiple comparison in the ANOVA and 95% confidence interval; the differences of the ${Z}$-score between the data coordinates in the low ${Z}$-score group and those in the high ${Z}$-score group were statistically significant ($p \lt {0.05}$) for all combinations. Note that only the data coordinates in the dominant wavelength of 580 nm in the ${-}1.41$ and ${-}{1.20}$ log ${S}$-cone condition were included.
Fig. 4. ${Z}$-scores of the better brown selection for the average of all observers in Exp. 1 plotted in CIE 1931 $x,y$ chromaticity coordinates using the contour line expression with ${Z}$-score color scale. Stimulus conditions of dominant wavelength and ${S}$-cone stimulation (21 conditions) were indicated in the text near by the coordinates of each stimulus (red and blue conditions were not shown due to limited space). Green point denotes D65 for reference (no ${Z}$-score data). Data points circled by triangles and squares denote low and high ${Z}$-score groups, respectively (see text for details). On average for all observers, peak conditions in the better brown selection were widely spread in the chromaticity coordinates.
3. Z-Scores of Brown Selection Plotted in L* a* b* Chromaticity Coordinates (Exp. 1)
Five observers is a small number to test for a main effect, but for interactions with other factors, the number of the data were not too few in terms of the power (0.80 by 35 pairs based on [20]) and effective size (0.491 in Exp. 1). Thus, we asked: are the stimulus conditions of the center field color for the better or best brown perception defined by the dominant wavelength or by the strength of red–green and yellow–blue chromatic opponent responses? The averaged data of all observers in the CIE 1931 $xy$ color space (Fig. 4) suggest that the better brown is mainly determined by the area in the color space rather than the dominant wavelength defined from D65 to the spectrum locus. We replotted the averaged data in 1976 L* a* b* color space, as shown in Fig. 5. The ${Z}$-scores higher than the 0.45 contour line distribute in the area of $a^*$ (red/green) from 5 to 28 and $b^*$ (yellow/blue) over 6. The vertical edge of the area in the whitish (lower $a^*$) side can be described by the dominant wavelength of 580 nm; however, in the reddish (higher $a^*$) side it is difficult to describe the edge by a single dominant wavelength. The dominant wavelengths of the edge were about 595 nm in saturated colors but about 620 nm in desaturated colors. This suggests that the amount of redness ($a^*$) is the main factor for the stimulus conditions even though observers perceived little redness in a center field.
Fig. 5. Z-score of the better brown for the average of all observers in Exp. 1 plotted in CIE 1976 $L^*\, a^*\,b^*$ chromaticity space. The chromaticity (D65) and luminance (${60}\;{{\rm cd/m}^2}$) of the surround field were set as the standard illumination ($L^* = {100}$). In the average of all observers, peak conditions in the better brown selection were widely spread in the area of $a^*$ (red/green) from 5 to 28 and $b^*$ (yellow/blue) over 6.
For this analysis we redefined three factors: (1) Observer: [Obs#1, Obs#2, Obs#3, Obs#4, Obs#5]; (2) $a^*$: [a1, a2, a3, a4, a5]; and (3) $b^*$: [39.0 (corresponding to log ${S} = - {1.83}$), 20.6 (log ${S} = - {1.41}$), 8.94 (log ${S} = - {1.20}$)]. In the $a^*$ factor, the elements of a1, a2, a3, a4, and a5 sets were [570 nm in log ${S} =\def\LDeqbreak{} - {1.83}$, 570 nm in log ${S} = - {1.41}$, 560 nm in log ${S} = - {1.20}$] ($a^*\;{\rm mean} = - {8.10}$), [580 nm, 580 nm, 580 nm]($a^*\;{\rm mean} = {4.33}$), [585 nm, 585 nm, 595 nm] ($a^*\;{\rm mean} = {12.1}$), [590 nm, 595 nm, 610 nm] ($a^*\;{\rm mean} = {21.8}$), and [600 nm, 605 nm, 640 nm] ($a^*\;{\rm mean} = {34.0}$), respectively. The total number of data points were 75, calculated by multiplying the number of the observers ($= {5}$), the $a^*\;(={5})$, and the $b^*\;(= {3})$. The results of the two-way ANOVA between the observer and $a^*$ factors revealed that the $a^*$ factor had significant main effects [$F({4},{50}) = {60.8},p \lt {0.0001}$], while the observer factor was not significant. The interaction between them was also statistically significant [$F({16},{50})= {4.24}, p \lt {0.0001}$]. In contrast, the results of the two-way ANOVA between the observer and $b^*$ factors indicated that both factors were not significant as main effects; the interaction between them was not significant either. The results of the two-way ANOVA between the $a^*$ and $b^*$ factors indicated that the $a^*$ factor was significant [$F({4},{60}) = {34.01}, p \lt {0.0001}$] but not the $b^*$ factor as main effects; the interaction between them was not statistically significant.
In the results of the ANOVA, the $a^*$ was a significant influence on perception of brown. In addition, the brown perception can be different between observers in terms of the $a^*$ value, suggesting significant observer variation in the relation between the $a^*$ value and brown perception. Figure 6 shows the ${Z}$-score averaged in all $b^*$ conditions (since the difference of $b^*$ was not significant). The ${Z}$-score values for Obs#1 were higher in [a1] and [a2], and lower in [a4] and [a5]. Those of Obs#2 were lower in [a3], and for Obs#5 were higher in [a3]. Individual Z-score distributions in $a^*\,b^*$ coordinates are presented in Appendix A.
Fig. 6. ${Z}$-score averaged for all $b^*$ conditions ($b^* = {39.0}$, 20.6, and 8.9) as a function of $a^*$ (a1–a5) for five observers. Different symbols denote ${Z}$-scores of different observers as shown in the figure key. Red crosses denote the mean of all observers. Vertical error bars denote $\pm{2.78}$ S.E.M. (95% confidence interval). Horizontal error bars denote $\pm{\rm SD}$ of the $a^*$. Asterisks denote data points higher or lower than the confidence interval at each $a^*$ value. Mean values of a1 and a5 are significantly lower than the means in a3 and a4 (for a1, also a2). Four ${Z}$-score values for Obs#1, and those of Obs#2 and Obs#5 in a3 are out of the confidence interval (statistically significant).
B. Influence of Surround Field Luminance on Brown Perception (Exp. 2)
1. Z-Score of Brown Selection as a Function of Surround Field Luminance for Different S-Cone Stimulation Level (Exp. 2)
It is known that the amount of blackness induced in a center field increases monotonically with the luminance of a surround field [3–5]. Because the perception of brown in the center field requires a certain amount of induced blackness, brown perception must be influenced by the surround luminance. Thus, we measured the stimulus condition for better brown when the surround luminance was changed. Figure 7 shows the ${Z}$-score of the selection rate in the comparison of brown perception plotted as a function of log surround luminance. From the results of Exp. 1, we selected two center field colors: the dominant wavelengths were 590 nm for log ${S} = - {1.83}$ (a), and 595 nm for log ${S} = - {1.20}$ (b).
Fig. 7. ${Z}$-score of the selection rate in the comparison of brown perception plotted as a function of log surround luminance (Exp. 2) in center fields of (a) 590 nm and log ${S} = - {1.83}$, and (b) 595 nm and log ${S} = - {1.20}$. Different symbols denote the ${Z}$-scores of each observer; red crosses denote the mean of all observers. Error bars denote $\pm 2.78$ S.E.M. (95% confidence interval). Asterisks denote data points higher or lower than the 95% confidence interval at each log surround luminance in both log ${S} = - {1.83}$ and ${-}{1.20}$ conditions and asterisks with parenthesis [“($^*$)” in (a) and “[$^*$]” in (b)] denote those higher or lower than the confidence intervals of log ${S} = - {1.83}$ or ${-}{1.20}$ conditions, respectively. See text for details.
We also performed an ANOVA on the ${Z}$-score data obtained from the selection rates of each surround luminance in the paired comparisons (Exp. 2). Because we used two conditions of the center field (590 nm for log ${S} = - {1.83}$, and 595 nm for log ${S} = - {1.20}$), we considered three factors: (1) observer, (2) surround luminance (the surround luminance was treated not as numeric values but as codes), and (3) center field color. The total number of the data points was 90 calculated by multiplying the number of the observers ($= {5}$), the surround luminance ($= \;{9}$ each), and center field color ($= {2}$). The result of a three-way ANOVA revealed that the surround luminance was a significant main effect [$F({7},{10}) = {68.72}$, $p \lt {0.0001}$], while the center field color and observer factor were not the significant main effects. The interaction between the observer factor and the surround luminance (or the center color) were statistically significant [$F({28},{10}) = {3.41}$, $p = {0.023} \lt {0.05};\def\LDeqbreak{}F({4},{10}) = {29.1}$, $p \lt {0.0001}$]; the interactions between the surround luminance and center field color were statistically significant [$F({7},{10}) = {6.03}$, $p = {0.0059} \lt {0.01}$], and the interaction between all three factors was significant [$F({28},{10}) = {3.05}$, $p = {0.0337} \lt {0.05}$]. This is consistent with the conclusion that the surround luminance and center field color significantly influence the perception of brown; this suggests that the brown perception can be changed by the contrast between the center and surround luminance and the color of the center as expected. In addition, brown perception can be different between observers, suggesting the observer variation in the brown perception in the relations with the luminance contrast and the center color. Thus, the results in Exp. 2 show that the luminance of the surround for the best brown perception was different between observers. In Fig. 7, error bars denote 95% confidence interval, and the differences outside the interval are statistically significant. Overall, the observer variation in ${Z}$-scores is larger in Exp. 2 than Exp. 1.
2. Z-Scores of Brown Selection Plotted in Luminance and S-Cone Stimulation Space (Exp. 2)
From the results shown in Fig. 7 it was difficult to compare the ${Z}$-scores between different center colors. Since we calculated ${S}$-cone stimulation in cone luminance unit (${\rm cd}/{{\rm m}^2}$), luminance can be expressed as the summation of ${L}$- and ${M}$-cone stimulations. Thus, the ${Z}$-score data were replotted in luminance (${L}$- and ${M}$-cone stimulation) and ${S}$-cone stimulation space in the contour line expression, similar to Section 3.A.2. Figure 8 shows ${Z}$-scores of the better brown selection plotted in log surround luminance (${L}$- and ${M}$-cone stimulation) and log ${S}$-cone stimulation space for the average of all observers. In Fig. 8, the difference of log ${S}$-cone stimulation was treated in 20% in the space. The differences of the ${Z}$-score between the data points in the low ${Z}$-score group (denoted by cyan triangles) and that in the middle and high ${Z}$- score groups (squares) were statistically significant at the 5% level in any combinations. The differences between the upper-low ${Z}$-score group (red triangles) and the high ${Z}$-score groups (cyan squares) were significant. In the center color of 590 nm and log ${S} = - {1.83}$, the average data showed the highest ${Z}$-score at the maximum surround luminance (${99.6}\;{{\rm cd/m}^2}$, ${2.00}\;{\log}\;{{\rm cd/m}^2}$). This means that brown perception could be stronger if higher surround luminance would be used. In the center color of 595 nm and log ${S} = - {1.20}$, the highest ${Z}$-score was obtained in the luminance range from 36.2 to ${77.3}\;{{\rm cd/m}^2}$ (from 1.56 to 1.89 log ${\rm cd}/{{\rm m}^2}$). Thus, the ${Z}$-score area higher than 0.45 contour lines exists only in the lower ${S}$-cone stimulation condition (log ${S} = - {1.83}$). Individual ${Z}$-score distributions in luminance and ${S}$-cone stimulation space are presented in Appendix B.
Fig. 8. ${Z}$-scores of the better brown selection plotted in log surround luminance (${L}$- and ${M}$-cone stimulation) and log ${S}$-cone stimulation space using the contour line expression with ${Z}$-score color scale for average of all observers. ${S}$-cone stimulation was set to ordinate and numeric values are indicated by the text in panels. Data points circled by cyan and red triangles denote low and upper-low ${Z}$-score groups, respectively. Data points circled by cyan and red squares denote middle and high ${Z}$-score groups, respectively (see text for details).
4. DISCUSSION
This research and others revealed that there can be relatively large observer variation in brown perception. This research also shows the statistically significant observer variation as the interaction with the $a^*$ value (the amount of redness) in Exp. 1 and the interactions with the surround luminance and ${S}$-cone stimulation (saturation) in Exp. 2.
In terms of the observer variation, the balance of the strength between yellowness and blackness can be different between observers since the amount of blackness in the best brown can be different. In addition, the amount of induced blackness by the luminance contrast between the center and surround fields can be different between observers [4]. Our previous work on blackness perception [5] indicates that the amount of blackness induced in a center field depends on the contrast of the brightness of the center and the luminance of the surround; the blackness in the center field will be induced more in desaturated colors of the center which have less brightness at the same luminance. This suggests that Obs#1 preferred to have more blackness in the center field for the better brown. In contrast, other observers (the average of all observers) preferred stronger redness ($a^*$).
Observer variation of brown perception is relatively large compared to other basic colors such as yellow [21]. It may suggest that brown perception is not so strongly normalized by the natural environment. It may be different with red–green and blue–yellow opponent responses which are strongly normalized to zero by the white daylight (D65) even in old observers [22]. However, we emphasize that observer variation in brown perception includes both the variation of the induced blackness and stimulus conditions. In terms of the center field condition, the dominant wavelength is longer than the wavelength of unique yellow and tritan yellow passing through D65; the wavelength of a monochromatic light of unique yellow was surveyed from 574 to 580 nm [23] and the results in this study showed that the dominant wavelength for the better brown selection was longer (from 585 to 590 nm). The distribution of the high ${Z}$-score in CIE 1976 $L^*\,a^*\,b^*$ color space [Fig. 5] also supports this. However, we emphasize that the redness perceived in no or low luminance contrast by the surround field would not be perceived in high luminance contrast [13]. Although the better brown was selected in this study, this shift toward the more red (higher $a^*$) direction could be caused by the surround field and the redness could be little in the color appearance of the center. This is supported by the result that ${Z}$-scores in the ${S}$-cone silent red condition were much lower than those in the main conditions, as shown in Fig. 3; strong red that could be perceived was not for the better brown. The appearance of brown can also be measured through the impression of a center field color [24,25] and it will help to figure out the mechanisms of brown.
Our averaged results correspond qualitatively to the results of Bartleson’s study [6] in which the brown strength was measured for a single observer by magnitude estimation and the peak brown strength was obtained between ${Y}$ and $\textit{YR}$ but closer to $\textit{YR}$ in Munsell hue; about the chroma, the evaluated brown strength showed the peak at most saturated colors in chroma /7 between chroma /3, /5, and /7 conditions in value 3/. In color chips in value 5/, the chroma /6 showed the peak in chroma /2, /4, /6, /8, and /12 conditions of hue $\textit{YR}$. It can be expected that the Munsell colors in value /5 reduced the luminance contrast and the observer required more induced blackness using desaturated colors.
5. CONCLUSION
We investigated the relations between brown perception and stimulus conditions. In Exp. 1, a chromatic center was changed in a fixed luminance (${5}\;{{\rm cd/m}^2}$) in terms of dominant wavelength and saturation defined by log ${S}$-cone stimulation in a fixed surround luminance (${60}\;{{\rm cd/m}^2}$). In Exp. 2, the influence of the surround luminance (from 13.1 to ${99.6}\;{{\rm cd/m}^2}$) was measured in two center field colors. We employed a paired-comparison method in which the observer selected one of two center-surround stimulus sets presented for 1 s on a monitor under a criterion of better brown. The results of the paired comparisons were expressed as win–loss ratios in each combination of stimulus conditions and converted to ${Z}$-scores.
The ANOVA for the ${Z}$-score data in Exp. 1 did not reveal a significant main effect of the observer factor or its interactions with the dominant wavelength or the ${S}$-cone stimulation but revealed its significant interaction with $a^*$ (red/green). The averaged data plotted in 1976 $L^*\,a^*\,b^*$ color space indicate that the high ${Z}$-score values were widely distributed in the area of $a^*$ from 5 to 28 and $b^*$ over 6 instead of showing a single peak condition. The ANOVA in Exp. 2 showed that the observer factor was not a significant main effect but the interactions with the surround luminance or the center field color were statistically significant. In the results of Exp. 2, the average showed the highest surround luminance with saturated center was the best brown; however, Obs#1 significantly preferred the desaturated center while Obs#8 preferred significantly lower surround luminance for the better brown.
Fig. 9. $Z$-score as in Fig. 5 except for Obs#1 (a), Obs#2 (b), and Obs#5 (c). The $a^*b^*$ coordinates of elements in the sets of a1–a5 circled by cyan squares (in the case of higher) and red squares (lower) denote the average of ${Z}$-score in terms of $b^*$ were out of the 95% confidence interval (see text for details).
APPENDIX A: INDIVIDUAL ${Z}$-SCORE DATA PLOTTED IN $L^*\,A^*\,B^*$ CHROMATICITY COORDINATES (EXP. 1)
Figure 9 shows the ${Z}$-score data for observers (Obs#1, Obs#2, and Obs#5) showing the statistically significant differences (as shown in Fig. 6 confirmed by the ANOVA) with the averaged ${Z}$-score data (Fig. 5). In Fig. 9(a), the high ${Z}$-score area was shifted horizontally to lower $a^*$ direction in Obs#1 compared to the average shown in Fig. 5. This could be explained that Obs#1 preferred the desaturated colors to obtain more induced blackness in the center field since the high ${Z}$-score area of Obs#1 distributed even in a greenish region (${a}^* \lt {0}$). The statistical differences among Obs#2 and Obs#5 were caused by the differences of the high ${Z}$-score areas at low $b^*$ value (log ${S}\;{\rm cone} = - {1.20}$). Figure 10 shows the individual distribution for observers (Obs#3 and Obs#4) not showing a statistical difference.
APPENDIX B: $Z$-SCORES OF BROWN SELECTION PLOTTED IN LUMINANCE AND S-CONE STIMULATION SPACE (EXP. 2)
Figure 11 shows ${Z}$-scores of the better brown selection plotted in log surround luminance (${L}$- and ${M}$-cone stimulation) and log ${S}$-cone stimulation space for Obs#1 and Obs#8 showing the statistically significant differences (as shown in Fig. 7) with the averaged ${Z}$-score data (Fig. 8). In Obs#1 ${Z}$-scores were significantly lower in the log ${S} = - {1.83}$ condition but higher at ${1.45}\;{\log}\;{{\rm cd/m}^2}\;({28.1}\;{{\rm cd/m}^2})$ and ${1.56}\;{\log}\;{{\rm cd/m}^2}\def\LDeqbreak{}({36.2}\;{{\rm cd/m}^2})$ in the log ${S} = - {1.20}$ condition; the significant difference between the center colors and the highest ${Z}$-score at the maximum surround luminance in the log ${S} = - {1.20}$ condition suggest that this observer preferred to have more blackness in the center field for the better brown perception. Obs#8 had the best brown at significantly lower surround luminance [${1.56}\;{\log}\;{{\rm cd/m}^2}\;({36.2}\;{{\rm cd/m}^2})$ in the log ${S} = - {1.83}$ condition and ${1.34}\;{\log}\;{{\rm cd/m}^2}$ (${21.8}\;{{\rm cd/m}^2}$) in the log ${S} = - {1.20}$ condition]; it can be expected that a small amount of induced blackness was preferred by this observer. Figure 12 shows the individual distribution for other observers.
Fig. 11. ${Z}$-scores as in Fig. 8 except for Obs#1 (a) and Obs#8 (b). Data points circled by cyan triangles and squares denote higher or lower than the 95% confidence interval at each log surround luminance in both log ${S} = - {1.83}$ and ${-}{1.20}$ conditions, respectively, and data points circled by red triangles and squares denote higher or lower than the confidence intervals in the same log ${S}$ condition (${-}{1.83}$ or ${-}{1.20}$).
Fig. 12. ${Z}$-scores as in Fig. 8 except for Obs#4 (a), Obs#6 (b), and Obs#7 (c). There is no statistical difference between these observers.
Funding
National Eye Institute (EY 024239); Japan Society for the Promotion of Science (18H03323, 20K07947); Kochi University of Technology (Focused Research Laboratory Support Grant).
Acknowledgment
We acknowledge Ms. Susan Garcia and Mr. Brennan Marsh Armstrong for help in experiments, and Drs. Paul R. Martin, Steven L. Buck, Galina V. Paramei, and Tanner DeLawyer for valuable comments at the ICVS 2022 conference. The anonymous reviewers and the editor are acknowledged for their thoughtful comments.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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