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Abstract
Categorical color constancy in normal trichromats has been found to be very robust in real scenes. In this study, we investigated categorical color constancy in red-green dichromats and anomalous trichromats. Eight dichromats (two protanopes and six deuteranopes), eight anomalous trichromats (four protanomalous and four deuteranomalous trichromats), and eight normal trichromats sorted 208 Munsell matte surfaces into Berlin and Kay’s basic color categories under D65 illuminant, F illuminant with correlated color temperature 4200 K, and TL84 illuminant with correlated color temperature 2700 K. Color constancy was quantified by a color constancy index. The results showed that the constancy index of dichromats (0.79) was considerable and significantly lower than that of normal trichromats (0.87) while that of anomalous trichromats (0.84) was not. The impairment of color constancy performance in dichromats was expected to be caused by their large intra-subject variabilities in color naming. The results indicate robust categorical color constancy along daylight locus in red-green dichromats and anomalous trichromats, which might be contributed by cone adaptation mechanism and be independent of color discrimination mechanism. It suggests that the color categorization by color vision deficient subjects can be reasonable without any assistants of artificial equipment in daily life under sunlight and common illuminations.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Most of people have normal trichromatic color vision system in which color information is encoded by initial three kinds of photoreceptors, that is, L-, M-, and S-cones, and subsequent red-green and blue-yellow chromatic opponent channels and luminance channel. However, due to the variation of genes, some people are congenitally color-deficient. As the most common type of color deficiency, red-green color deficiency can be divided into two main types: dichromats and anomalous trichromats. In the dichromatic color vision system, only two kinds of cones are functioning: L- and S-cones functioning and M-cone lost in deuteranopia, and M- and S-cones functioning and L-cone lost in protanopia. In the anomalous trichromatic system, three kinds of cones are functioning but with spectral sensitivity change of M-cone, namely deuteranomaly, or L-cone, namely protanomaly. Deuteranomaly may occur when one array has a parental L gene as the first gene, a hybrid as the second gene, and a parental M gene as the third gene; protanomaly may occur when one array has multiple M class genes with different spectral sensitivities [1]. Anomalous trichromats show large individual variation in color discrimination; their color discrimination can be close to that of normal trichromats or dichromats [2]. Normal trichromats need a mixture of three colored lights to match any test color. Dichromats can match a test color with only two colored lights. Anomalous trichromats need a mixture of three colored lights as normal trichromats, but in the different proportions: deuteranomalous trichromats need more green light, and protanomalous trichromats need more red light in the matching. According to a previous study [3], in European Caucasians, the prevalence of inherited red-green color deficiency is about 8% in men and about 0.4% in women; in Chinese, the prevalence is between 4% and 6.5% in men and 0.4% and 1.7% in women.
Normal trichromatic color vision has the ability to keep constant color perception of objects under different lighting conditions (see Foster [4] for a review). Color constancy of normal trichromats has been mainly investigated by four kinds of experimental methods: asymmetric color matching, achromatic setting, color naming, and the discrimination of illuminant changes from surface-reflectance changes [4]. The mechanisms mediating color constancy can be roughly divided into chromatic adaptation mechanism [5] that occurs at photoreceptoral or postreceptoral stages [6,7] and illuminant estimation mechanism in which the illuminant is estimated with the aid of various cues in the viewing environment and then discounted by the visual system [8,9].
Several studies investigated color constancy of red-green color-deficient subjects with stimuli simulated on the monitor. In Rüttiger et al.’s study [10], an achromatic setting method was used and red-green color-deficient subjects showed color constancy similar to that of normal trichromats. Baraas et al. [11] asked color-deficient subjects to discriminate illuminant changes from surface-reflectance changes, and found that with stimuli simulated with Munsell spectral reflectances dichromats performed more poorly than normal trichromats, and anomalous trichromats performed as well as normal trichromats. Ma et al. [12] used an asymmetric color matching method and found that the adaptation degree of S-cone and blue-yellow opponent channel of color-deficient subjects was similar to that of normal trichromats. In Álvaro et al.’s study [13], color constancy of red-green dichromats was investigated by asking subjects to discriminate a correlated color temperature change and an intensity change of illuminants from natural scenes simulated on a CRT monitor, and showed no significant differences from that of normal trichromats.
As one of main methods to investigate color constancy, color naming method can help to collect data in real scenes easily. It was found that the categorical color constancy performance of normal trichromats was robust and better than color constancy performance obtained by an asymmetric color matching method [14]. The color naming accuracy of color-deficient subjects was influenced by their reduction or loss of red-green color discrimination ability. A previous study [15] showed that only 37% of color-deficient subjects were able to name colors without any errors; anomalous trichromats made fewer errors than deuteranopes and protanopes. However, color-deficient subjects can name surfaces with color terms that normal trichromats use [16–19]. This means that color-deficient subjects, in particular dichromats, can classify surfaces into several color categories like normal trichromats, although their classification results may be different from those of normal trichromats [20]. It was suggested that a third cone pigment [16], lightness of surfaces [18], or learning factors [19] may contribute to the color categorization of dichromats in the three dimensions.
How constant the categorical color perception of dichromats and anomalous trichromats will be across illumination changes is less clear. The previous study [18] investigated categorical color perception of deuteranopes and protanopes under various illuminant conditions, but focused on the analysis of trichromatic-like color naming of dichromats. In that study, the centroid distribution of color categories for one protanope and two deuteranopes was almost invariant across different illuminants, indicating good color constancy. The first purpose of the present study was to quantify the degree of categorical color constancy of red-green dichromats and anomalous trichromats.
Although color-deficient subjects can use color terms correctly, their lower red-green color discrimination ability may influence the accuracy of categorization, which may in turn affect categorical color constancy. Baraas et al. [11] found that the degree of color constancy in anomalous trichromats could not be predicted by Rayleigh anomaloscope matches. The second purpose of the present study was to examine whether the degree of categorical color constancy of red-green color-deficient subjects was related with their intra-subject variability in color naming and color discrimination ability indicated by total error scores in Farnsworth-Munsell 100-Hue test, respectively.
2. Methods
2.1 Apparatus
The experiment was performed in a color assessment cabinet (Shenzhen Qiantongcai Color Management Co., Ltd) located in a dark room (Fig. 1(a)). The color assessment cabinet has a height of 625 mm, width of 710 mm, and depth of 540 mm. All lamps used to produce illuminants were located in the ceiling of the viewing cabinet. The subject viewed surfaces at a distance of 40 cm and an angle of approximately 45°. The ground of the viewing cabinet was gray with a spectral reflectance of about 25%, roughly corresponding to the gray of Munsell surface N5.5/. In this condition, almost all surfaces had a lower luminance than the gray background.
Fig. 1. (a) The photograph of the experimental setup with stimuli and subject; (b) Munsell surface collection used in the experiment from the perspective of normal trichromats; (c) Simulation of deuteranopic perspective; (d) Simulation of protanopic perspective.
2.2 Stimuli
Two hundred and seven chromatic and 1 achromatic (N5/) Munsell surfaces were used as stimuli. The chromatic Munsell surfaces were selected from the plane with Value 5/ in the Munsell Book of Color Matte Finish Collection, and included 40 hues with all Chroma levels available for each Hue. The size of each surface was about 2 cm × 3.4 cm (2.8 deg × 4.8 deg). The photograph of the surface collection under a room illumination is shown in Fig. 1(b). Figure 1(c) and 1(d) show the surface collection that is expected to be perceived by deuteranopes and protanopes and simulated based on the previous studies [21,22]. In the experiment, all 208 surfaces were laid out on the ground of the viewing cabinet in a random arrangement (cf. Figure 1(a)).
The experiment was conducted under D65 illuminant, F illuminant, and TL84 illuminant. D65 illuminant was produced by two Philips MASTER TL-D 90 Graphica 36 W 965 fluorescent lamps, F illuminant by two 40W tungsten lamps, and TL84 illuminant by two Philips TLD 18W/840 fluorescent lamps. The spectral power distributions of three illuminants were measured by a spectroradiometer (PR-655, Photo Research Inc.) from the Munsell matte white surface and were shown in Fig. 2. Table 1 shows the corresponding correlated color temperature, CIE1976 u′v′ chromaticity coordinates, and luminance values measured from the white surface.
Table 1. Correlated color temperature and CIE1976 u´v´ chromaticity coordinates of all illuminants
We measured the reflectance spectra of all 208 Munsell surfaces by the spectroradiometer PR-655 and compared the CIE1976 u′v′ chromaticity coordinates and CIELAB coordinates of all surfaces under three illuminants with those calculated with reflectance spectra provided by the University of Eastern Finland (https://www.uef.fi/spectral/spectral-database). The ΔEuv in the CIE1976 u′v′ chromaticity diagram between the chromaticity points of 208 surfaces calculated by two sets of reflectance spectra ranged between 0.0001 and 0.0226 with an average of 0.0044 and a standard deviation of 0.0032 for D65 illuminant (ΔE*ab values calculated in CIELAB color space are 0.057, 8.535, 1.866, and 1.432, respectively), between 0.0002 and 0.0253 with an average of 0.0043 and a SD of 0.0041 for F illuminant (ΔE*ab values are 0.064, 7.735, 2.042, and 1.467), and between 0.0001 and 0.0232 with an average of 0.0049 and a SD of 0.0035 for TL84 illuminant (ΔE*ab values are 0.187, 10.174, 2.522, and 1.825). There was a small difference between chromaticity coordinates calculated by two sets of reflectance spectra. Considering surrounding environment light may affect the measurement accuracy of PR-655 in our laboratory, we used reflectance spectra provided by the University of Eastern Finland in the calculation. Figure 3 shows CIE1976 u′v′ chromaticity coordinates of all surfaces with reflectance spectra measured by our lab under D65, F illuminant, and TL84 illuminant. In the calculation, CIE1931 standard color matching functions were used; spectra were sampled at an interval of 4 nm and integrated over 380-780 nm.
Fig. 3. CIE1976 u′v′ chromaticity coordinates of all surfaces under D65, F illuminant, and TL84 illuminant.
2.3 Subjects
Totally, 24 subjects, aged 18 to 24 years, participated in the experiments. All of them are students of Taiyuan University of Technology. There were 2 protanopes (all male), 6 deuteranopes (all male), 4 protanomalous (all male) and 4 deuteranomalous (3 female, 1 male) trichromats, and 8 normal trichromats (4 female, 4 male) who act as controls. All subjects had normal or corrected-to-normal acuity. All subjects performed three color-vision tests: pseudoisochromatic plates (YU Ziping version, China), the Farnsworth D-15 test, and the Farnsworth-Munsell 100-Hue test under a room illumination with correlated color temperature 6100 K. The FM100-Hue test was also performed under D65 illuminant in the color assessment cabinet, which was used for data analysis in Results part. All color-deficient subjects additionally performed Rayleigh match in a Neitz anomaloscope (OT-II, Neitz co. Ltd.), and their color vision was classified by it. The experiments were performed in accordance with the Declaration of Helsinki. All subjects were naïve to the purpose of experiments and asked to write informed consent prior to the experiments.
2.4 Procedure
Several studies [16–19,23] have shown that dichromats can use the basic color terms to categorize colors like normal trichromats, which might be due to the effect of a social environment and a normative language system [19,23], although they confuse red-green colors. As is the previous study [18], we used the Berlin and Kay’s eleven basic color terms [24] in the classification for both normal and color-deficient subjects. Before the experiment, each subject was shown the eleven basic color terms (red, orange, yellow, green, brown, blue, purple, gray, white, and black) in English and Chinese, and was told that his or her task was to classify the surfaces into eleven categories. Each color-deficient subject was also asked to choose the best example for each category. It was found that their responses were basically consistent with those of normal trichromats. Subjects were not given any additional instructions on the accomplishment of the classification task. In the classification under each illuminant, the subject first adapted to illuminant for 3 min, and then classified surfaces wearing white gloves. White and black terms were actually not used in the experiment by any subject as the luminance of the surfaces was not extremely higher or lower than that of the gray background.
Each subject completed one session of classification corresponding to one illuminant condition a day. The completion sequence of illuminants was D65, F illuminant, TL84 illuminant, and D65. The classification results under two sessions of D65 illuminant conditions were used to analyze intra-subject ΔE*ab (cf. Fig. 6) and color naming consistency (cf. Figure 7). The first session of D65 illuminant was used as a training session and the second session as a standard illuminant condition from which the color constancy performance was evaluated under F and TL84 illuminants. Each session took about 20-40 min, depending on individual subjects.
2.5 Data analysis
We used a color constancy index that was proposed by Arend et al. [25] to evaluate color constancy degree in asymmetric color matching to measure the degree of categorical color constancy for all color vision types of subjects. Arend et al.’s constancy index was defined as
where b denotes the ΔEuv in the CIE1976 u′v′ chromaticity diagram between the matched point and the theoretical point (the chromaticity coordinates of the color patch under test illumination) of one color patch; a denotes the ΔEuv between the standard point (the chromaticity coordinates of the color patch under standard illumination, e.g. D65 illuminant) and the theoretical point. When the matched point overlapped with the theoretical point, there would be perfect color constancy, corresponding to an index of 1. When the matched point coincided with the standard point, there would be no color constancy, corresponding to an index of 0.The calculation of constancy index in this study was exactly the same as that of Arend et al. except that the chromaticity coordinates of the standard point, theoretical point, and matched point were the averages of u′v′ chromaticity coordinates of all surfaces in a certain color category. That is, the centroid of a given color category was used in the calculation, instead of chromaticity point of one color patch. The standard centroid of one color category (corresponding to standard point in Arend et al.’s constancy index) was calculated by averaging the u′v′ chromaticity coordinates under D65 illuminant of all surfaces that were classified into this category under D65 illuminant condition. The observed centroid (matched point) was calculated by averaging the u′v′ chromaticity coordinates under F or TL84 illuminant of all surfaces that were classified into this category under F or TL84 illuminant condition. The theoretical centroid (theoretical point) was the average of u′v′ chromaticity coordinates under F or TL84 illuminant of all surfaces that were classified into this color category under D65 illuminant condition. If perfect color constancy was achieved, all surfaces classified into a color category under D65 illuminant would continue to be classified into this category under F or TL84 illuminant. In this case, the observed centroid would overlap with the theoretical centroid, corresponding to an index of 1. If there was no color constancy, subjects would name surfaces according to their reflected spectra under F or TL84 illuminant. In this case, the observed centroid would overlap with the standard centroid, corresponding to an index of 0. The constancy index calculated with centroids of color categories was also used in our previous study [26] to evaluate categorical color constancy of normal trichromats under RGB-LED light sources.
3. Results
3.1 Inter- and intra-subject variability in color classification
This section compared the classification results under D65 illuminant across different subjects or different sessions in CIELAB color space. Figure 4 shows the classification data for two normal trichromats (a and b), one protanomalous (c) and one deuteranomalous (d) subjects, two protanopes (e and f), and two deuteranopes (g and h) under the second session of D65 illuminant in CIELAB color space. The distribution of color categories for one protanomalous (c) and one deuteranomalous (d) subject is basically similar with that of normal trichromats. The other anomalous subjects showed similar classification results and their data were not presented here.
Fig. 4. Classification results under the second session of D65 illuminant of two normal trichromats (a and b), one protanomalous (c) and one deuteranomalous (d) subjects, two protanopes (e and f), and two deuteranopes (g and h) represented in CIELAB color space.
Compared to the classification result of one normal trichromat (#N1), in the classification result of one protanope (#P1) in Fig. 4(e), the area of gray category was between green and blue categories; the area of brown category was larger. By calculation, 17% and 25% of green surfaces for the normal trichromat (#N1) were respectively named as brown and gray by this protanope; 21% and 27% of blue surfaces were named as purple and gray; 41% of purple surfaces were named as pink. For the other protanope (#P2) in Fig. 4(f), the relative location of color categories was roughly similar with normal trichromats; 21%, 15%, and 15% of green surfaces for the normal trichromat (#N1) were respectively classified as brown, yellow, and gray by this protanope. For one deuteranope (#D1) in Fig. 4(g), 33% and 27% of green surfaces for the normal trichromat (#N1) were named as brown and gray; 55% of blue surfaces were named as purple. The distribution of color categories for the other deuteranope (#D2) in Fig. 4(h) was similar with normal trichromats to some extent, except for almost nonexistence of yellow category; most of yellow surfaces for the normal trichromat (#N1) were classified into brown category by this deuteranope. Generally, by inspection of classification data of all subjects, dichromats used almost all color names that normal trichromats used to name surfaces, but showed large individual variations in color classification.
Figure 5(a) shows the centroids of nine color categories averaged over 8 normal trichromats (denoted by triangles), 8 dichromats (circles), and 8 anomalous trichromats (squares), respectively. The centroid of each color category was calculated by averaging the CIELAB coordinates of all surfaces classified into this category under the second session of D65 illuminant. The centroids of all color categories for dichromats were basically close to those for anomalous and normal trichromats. This result indicates dichromats can perform categorical color naming as like normal trichromats although they cannot perceive red and green colors.
Fig. 5. (a) The centroids of nine color categories under the second session of D65 illuminant averaged over three types of subjects; (b) and (c) Standard deviations of the centroids along a* and b* axes. Labels on abscissa axis in panels (b) and (c) correspond to red (R), green (G), blue (B), yellow (Y), orange (O), purple (P), brown (Br), pink (Pk), and gray (Gr) categories from left to right.
The standard deviations of the centroids along a* axis were shown in Fig. 5(b) and those along b* axis shown in Fig. 5(c). The standard deviations for all color categories along both a* and b* axes were close between anomalous trichromats and normal trichromats, while those of dichromats were substantially larger than them. A two-way ANOVA analysis with the factors color vision type (dichromat, anomalous trichromat, and normal trichromat) and axis (a* and b* axes) was performed on standard deviation. The result revealed that both color vision type and axis had significant main effects (F(2, 48) = 26.098, p < 0.001; F(1, 48) = 6.656, p = 0.013), while there was no significant interaction effect between them (F(2, 48) = 0.531, p = 0.591). By multiple comparisons using Bonferroni correction, standard deviations were significantly higher for dichromats than for anomalous (p < 0.001) and normal trichromats (p < 0.001) who had no significant difference between each other (p = 1.000). This result indicates that the inter-subject variability of dichromats in the location of the centroids of color categories was larger than that of anomalous and normal trichromats, although they used all color terms that normal trichromats used to classify. That the standard deviations along a* axis were significantly higher than those along b* axis indicates that subjects have larger inter-subject variability in the location of the category centroid along red-green direction than along blue-yellow direction.
We also examined the intra-subject variability of dichromats, anomalous trichromats, and normal trichromats by comparing the classification results of the same subject between two sessions of D65 illuminant. Figure 6 shows the color differences ΔE*ab in CIELAB color space between the centroids of color categories under two sessions of D65 illuminant (intra-subject ΔE*ab) averaged over subjects of each color vision group. Ideally, the color difference between the centroids of two sessions for one color category should be equal to 0. That is, the smaller the ΔE*ab is, the more stable the color naming of this category is. As presented in the figure, ΔE*ab of intra-subject was higher for dichromats than for anomalous trichromats and normal trichromats. A two-way ANOVA analysis performed for ΔE*ab of intra-subject showed that both color vision type and color category had significant main effects (F(2, 183) = 36.355, p < 0.001; F(8, 183) = 5.817, p < 0.001), and there was no significant interaction effect between them (F(16, 183) = 1.143, p = 0.319). Multiple comparisons using Bonferroni correction showed that intra-subject ΔE*ab of dichromats was significantly higher than that of anomalous (p < 0.001) and normal trichromats (p < 0.001). The result indicates that the intra-subject variability of dichromats in color classification is large, while that of anomalous trichromats is low and comparable to that of normal trichromats. For comparison, inter-subject ΔE*ab under the second session of D65 illuminant was also shown in the figure. A one-way ANOVA analysis indicated that ΔE*ab of intra-subject was significantly lower than that of inter-subject (F(1, 932) = 38.789, p < 0.001).
Fig. 6. Color differences ΔE*ab between the centroids of color categories under two sessions of D65 illuminant, that is, ΔE*ab of intra-subject, compared to ΔE*ab of inter-subject. Error bars denote standard errors of the means across subjects of each color vision group.
The naming consistency [14] that was defined as the proportion of surfaces named consistently across two illuminant conditions in the whole surface collection were also used to evaluate the intra-subject variability. Ideally, the naming consistency across two sessions of D65 illuminant for one subject should be 1 (100%). In Fig. 7, the color naming consistency of anomalous trichromats across two sessions of D65 illuminant was slightly lower than that of normal trichromats, while that of dichromats was much lower than that of anomalous and normal trichromats. Initially, it is expected that the naming consistency between D65 illuminant and F (or TL84) illuminant should be lower than that between two sessions of D65 illuminant. However, Fig. 7 shows that they were almost the same with the latter for all three types of subjects.
Fig. 7. Color naming consistency between the second session of D65 illuminant and a given other illuminant condition. D65(1) denotes the first session of D65 illuminant and D65(2) the second session of D65 illuminant. Error bars denote standard errors of the means across subjects.
By a two-way ANOVA analysis, we found a significant main effect of color vision type (F(2, 63) = 27.047, p < 0.001), but no main effect of illuminant (F(2, 63) = 1.115, p = 0.334). No interaction effect was found between two factors (F(4, 63) = 0.905, p = 0.467). Multiple comparisons using Bonferroni correction showed that the color naming consistency of dichromats was significantly lower than that of anomalous trichromats (p < 0.001) and normal trichromats (p < 0.001) that were not significantly different from each other (p = 0.354).
Figure 8 shows total error scores in FM100-Hue test under D65 illuminant in individual dichromats, anomalous trichromats, and normal trichromats plotted against the ΔE*ab of the centroids between two sessions of D65 illuminant averaged over all color categories (a) and color naming consistency averaged over illuminants (b). Regression lines have been added for all subjects. The coefficient of determination R2 for the regression line in panel (a) is 0.349 (F(1, 22) = 13.326, p = 0.001) and R2 in panel (b) is 0.525 (F(1, 22) = 26.460, p < 0.001). This indicates that color discrimination ability of subjects can predict their intra-subject variability in color naming to some extent. In addition, it can be noted that total error score 100 cannot be used as the cutoff point between normal and color-deficient subjects. Actually it has been reported [27] that about 50% of color-deficient subjects obtained total error scores less than 100, suggesting that FM100-Hue test is not accurate for color vision screening.
Fig. 8. (a) The comparison between total error scores in FM100-Hue test and the ΔE*ab of the centroids between two sessions of D65 illuminant. (b) The comparison between total error scores and naming consistency.
3.2 Color constancy index
Figure 7 showed no significant difference of color naming consistency between D65 and two chromatic illuminants, meaning that color naming consistency cannot reflect color constancy degree. We used constancy index involving the shift of centroids of color categories in CIE1976 u′v′ chromaticity diagram across illuminant changes to measure the degree of color constancy. The reason for this choice of chromaticity diagram, instead of CIELAB color space, was as follows. Color constancy refers to a phenomenon where we have the ability to remain constancy of color perception although the reflected spectrum of one surface changes with change of the spectral radiance of illuminant. The investigation on color constancy is to measure to what extent we can remain constant color perception of the surface when its XYZ tristimulus values change with illuminant change. CIELAB color space has involved in the adaptation to illumination. It cannot be used to calculate constancy index to evaluate color constancy performance.
Figure 9 shows the location in CIE1976 u′v′ chromaticity diagram of standard centroids, theoretical centroids, and observed centroids of nine color categories averaged over 8 normal trichromats (a and b), 8 anomalous trichromats (c and d), and 8 dichromats (e and f) for illumination changes from D65 to F illuminant (left) and TL84 illuminant (right). The circles denote the centroids of color categories classified by subjects under the second session of D65 illuminant, open triangles the theoretical centroids, and solid triangles the observed centroids. If perfect color constancy was achieved, the observed centroids (solid triangles) would overlap with the theoretical centroids (open triangles). In the case of no color constancy, the observed centroids would overlap with the standard centroids (open circles), meaning subjects performed categorical color naming according to the chromaticity coordinates of surfaces under F or TL84 illuminant. From Fig. 9, for dichromats, anomalous trichromats, and normal trichromats under both F and TL84 illuminants, the observed centroids of nine color categories were quite close to the theoretical centroids, indicating good color constancy.
Fig. 9. The standard centroids, theoretical centroids, and observed centroids of all color categories under F (left) and TL84 (right) illuminants shown in CIE1976 u′v′ chromaticity diagram for normal trichromats (a and b), anomalous trichromats (c and d), and dichromats (e and f). Colors of symbols correspond to color categories. Open circles denote standard centroids, open triangles theoretical centroids, and solid triangles observed centroids. For one group of centroids, open triangles overlap with solid triangles where it is invisible.
Figure 10 shows constancy indices of nine color categories under F (panel a) and TL84 (panel b) illuminants averaged over dichromats, anomalous trichromats, and normal trichromats. Under F illuminant, constancy indices of dichromats were slightly lower than those of anomalous trichromats and normal trichromats. Under TL84 illuminant, the constancy indices among three types of color vision were close to each other.
Fig. 10. Color constancy indices of all color categories under F (a) and TL84 (b) illuminants for dichromats, anomalous trichromats, and normal trichromats. Data were averaged over subjects. Error bars represent SEM.
We conducted three-way ANOVA analysis with illuminant (F and TL84 illuminants), color vision type (dichromat, anomalous trichromat, and normal trichromat), and color category as factors. The result showed that the effect of color vision type was significant (F(2, 364) = 7.362, p = 0.001); there was a significant interaction effect between illuminant and color category (F(8, 364) = 2.458, p = 0.013). No other significant interaction effects were found. Multiple comparisons using Bonferroni correction showed that the constancy index (0.79) of dichromats was significantly lower than that (0.87) of normal trichromats (p = 0.003), while there were no significantly differences between dichromats and anomalous trichromats (p = 0.104), and anomalous trichromats and normal trichromats (p = 0.626).
Constancy indices were calculated based on the classification results of each subject under D65 and a chromatic illuminant, that is, the constancy index might be affected by intra-subject variability. The poor color constancy performance reflected from constancy indices might be due to the intrinsic high intra-subject variability of color naming on these categories that was initially caused by bad color discrimination ability. To test it, in Fig. 11, constancy indices from individual subjects were compared with color naming consistency averaged over the three types of illuminant change (a) and the ΔE*ab of the centroids between two sessions of D65 illuminant averaged over all color categories (b). Indices have been averaged over nine color categories and the two types of illuminant change. The coefficient of determination R2 for the regression line in panel (a) is 0.629 (F(1, 22) = 40.033, p < 0.001) and R2 in panel (b) is 0.473 (F(1, 22) = 21.626, p < 0.001). This result indicates that the intra-subject variability of dichromats indeed affected their constancy index. It can be seen from the slopes of regression lines that this effect on constancy index is somehow small.
Fig. 11. Constancy indices for individual subjects as a function of naming consistency (a) and the ΔE*ab of the centroids between two sessions of D65 illuminant (b).
Figure 12(a) shows constancy indices from all subjects plotted against total error scores in FM100-Hue test. Indices have been averaged over nine color categories and the two types of illuminant change. The coefficient of determination R2 for the regression line is 0.088 (F(1, 22) = 3.211, p = 0.087). Although constancy index was found to be affected by intra-subject variability that in turn correlated with total error scores, it had no direct correlation with total error score in FM100-Hue test. The total error scores spread in a relatively large range, while color constancy index clustered in a small range from 0.7 to 0.9. This indicates although subjects had various degrees of color discrimination, they all showed relatively good color constancy.
Fig. 12. (a) Constancy indices for all subjects as a function of total error scores in FM100-Hue test; (b) Constancy indices for all anomalous trichromats as a function of Rayleigh anomaloscope matching range. The straight lines are linear regressions.
Figure 12(b) shows constancy indices for all anomalous trichromats plotted against matching ranges in Rayleigh anomaloscopy matches. The coefficient of determination R2 for the regression line is 0.053 (F(1, 6) = 0.338, p = 0.582). No correlation was indicated. This is consistent with what Baraas et al. [11] reported: no correlations between matching ranges in Rayleigh anomaloscopy matches and color constancy indices were found for protanomalous trichromats and deuteranomalous trichromats.
4. Discussion
4.1 Comparison with previous studies
Several previous studies used different methods to investigate color constancy of red-green color-deficient subjects across illuminant changes along daylight locus. Rüttiger et al. [10] used an achromatic matching method with stimuli simulated on the monitor and showed color constancy of red-green color-deficient subjects as good as normal trichromats. The present results are basically consistent with theirs except that color constancy of dichromats was slightly weakened due to high intra-subject variability of dichromats in color naming. Baraas et al. [11] investigated color constancy performance of dichromats and anomalous trichromats with Munsell and natural surfaces simulated on the monitor by using the method of discriminating illuminant changes from reflectance changes. They found dichromats performed more poorly than normal trichromats with Munsell surfaces; anomalous trichromats performed as well as normal trichromats; mean color constancy indices for dichromats, anomalous trichromats, and normal trichromats were respectively 0.40, 0.71, and 0.78. Color constancy indices in our study showed similar tendency: the index of dichromats (0.79) was lower than those of anomalous (0.84) trichromats and normal trichromats (0.87) which were close to each other. However, it should be noted that there are two differences between our and their results: color constancy indices in our study were higher than theirs for all types of subjects; the difference of index between dichromats and the other two types of subjects was much larger in their study than in our study. These two differences might be due to the use of real scenes and categorical color naming method in our study. Uchikawa [18] used categorical color naming method with real OSA color chips and illuminants produced by a LC projector to investigate categorical color perception of dichromats across different illuminants. By observing the centroid distributions of one protanope and two deuteranopes across different illuminants in their study, good color constancy was indicated for three dichromats, which is in accordance with the present result. Álvaro et al. [13] investigated color constancy of red-green dichromats by examining thresholds of subjects detecting changes in the color or the intensity of illuminants on complex images of natural scenes. They found that color constancy of dichromats was robust and comparable to that of normal trichromats. Although the present study and Álvaro et al.’s study adopted quite different experimental methods, both of them showed robust color constancy of dichromats.
4.2 Color constancy and color discrimination
In this study, we also explored the relationship between color constancy indices and total error scores in FM100-Hue test for all subjects, and color constancy indices and Rayleigh anomaloscope matching range for anomalous trichromats. Both of them showed no correlation between two factors. These results indicate color constancy performance of color-deficient subjects cannot be predicted from their color discrimination ability. The color discrimination ability of dichromats and anomalous trichromats was bad, but their color constancy can be almost as good as normal trichromats. The weakened color discrimination ability of dichromats contributed to large individual differences in color naming, but each subject showed basically very constant color classification on almost all color categories across illumination changes. The only effect of bad color discrimination on color constancy performance was from large intra-subject variability that it leads to, which in turn slightly impaired categorical color constancy performance. Rüttiger et al. [10] also examined the relationship between color constancy performance and color detection threshold that reflected color discrimination ability; no correlation was found. Baraas et al. [11] plotted color constancy indices of anomalous trichromats against their Rayleigh anomaloscope matching ranges and found no correlation between them.
In the present study, Munsell surfaces were presented in a uniform background, and no familiar objects were present in the viewing background. This experimental setting excluded the possible effect of object identity on color constancy. The present results support the proposal of previous studies [10–11,13,28] that chromatic discrimination and color constancy are two independent mechanisms.
It may be argued that only two protanopes participated in the present experiment, which may influence the experimental results. Both protanopes and deuteranopes perceive only two opponent colors, blue and yellow, but reddish colors appear darker to protanopes than to deuteranopes. That means protanopes can use lightness cues more effectively to recognize red-green colors. If more protanopes would attend the experiment, it is expected that the categorical color constancy performance of dichromats should be similar to or even better than the present results.
4.3 von Kries model prediction
We used von Kries model to analyze classification data in terms of L-, M-, and S-cone responses. LMS cone responses were calculated from XYZ tristimulus values by using the transformation matrix of Smith-Pokorny’s cone fundamentals [29]. First, we calculated LMS cone responses of each surface under D65 illuminant by transformation from XYZ values, and then calculated von Kries model predicted LMS cone responses of that surface under F or TL84 illuminant. In the calculation of von Kries model predicted values, the constants were defined as the inverse of the L-, M-, and S-cone responses for a perfect white surface under the D65 illumination and test illumination (F or TL84 illuminant). According to the von Kries model, after adaptation to illuminants, subjects should have the exactly same classification performance between D65 illuminant and F (or TL84 illuminant) conditions. Thus, LMS cone responses predicted by the von Kries model of the centroid of each color category under F or TL84 illuminant were defined as the averages of von Kries model predicted values of surfaces that were classified into that color category under D65 illuminant.
Figure 13 shows the comparison between the observed LMS cone responses and von Kries model predicted ones under F illuminant (open squares) and TL84 illuminant (solid triangles). As shown in the figure, under both F and TL84 illuminants, the L-cone responses of deuteranomalous trichromats and deuteranopes are similar with those of normal trichromats; the M-cone responses of protanomalous trichromats and protanopes are also similar with those of normal trichromats; the observed S-cone responses of all color-deficient subjects are similar with those of normal trichromats. Under F illuminant, the observed L-cone responses deviated systematically from the von Kries model prediction, which is consistent with the result under red illumination in our previous study [12]; the observed M-cone responses clustered; S-cone responses fall on the diagonal line. Under TL84 illuminant, the observed L-, M-, and S-cone responses all fall on the diagonal line, following the von Kries model. Our previous study [12] has explored in detail the prediction of von Kries model at receptoral and postreceptoral stages for color constancy of red-green color-deficient subjects. Generally, these results suggest that the categorical color constancy by red-green color-deficient subjects is similar to color vision normal subjects in daily life under sunlight and common illuminations.
Fig. 13. The comparison between the observed and predicted L-cone responses on nine categories for normal trichromats (a), deuteranomalous trichromats (b), and deuteranopes (c); that between the observed and predicted M-cone responses for normal trichromats (d), protanomalous trichromats (e), and protanopes (f); that between the observed and predicted S-cone responses for normal trichromats (g), deuteranomalous trichromats (h), deuteranopes (i), protanomalous trichromats (j), and protanopes (k). Open squares denote data under F illuminant, and solid triangles under TL84 illuminant. Error bars represent SEM.
Funding
National Natural Science Foundation of China (61705011); Japan Society for the Promotion of Science (18H03323); Natural Science Foundation for Young Scientists of Shanxi Province (201901D211068); Kochi University of Technology (Focused Research Laboratory Support Grant).
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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