1. INTRODUCTION

It is widely known that color has a psychological or emotional impact [1] that can be called color psychology. For example, red, orange, and yellow are called “warm colors,” and blue and violet are called “cold colors,” since the sensation of “warm” arises when people see warm colors. These color impressions are often applied in our lives. Colors expressing a “dangerous” image (e.g., red) are used for traffic signs, and colors expressing a “pretty” image are used for clothing. These are examples of direct color image usage, but color image usage is not necessarily restricted to direct usage. Recognition or memorization can be enhanced when the color of the target is matched to its image [2,3]. As we have stated [4], “Psychological effects of colors are not necessarily limited to the impression of colors and/or colored objects: colors are also expected to have a connection to word meanings.” For example, a simple meaning of “cold” can be associated easily with the color “dark blue.” This kind of color–word association is straightforward and has been obtained by daily experiences which have constructed and enhanced “context.” In our previous studies [5], we have expanded this concept to complex and abstract meanings, and we found that the impression of semantic words representing complex concepts (such as “tranquil”) can also be expressed by a selection of colors [5]. In addition, the concept of color psychology is not limited to vision. It affects other modalities like taste [6], odor [7], and sound [3].

Concerning the image of colors, we have to consider that there are people with congenital color vision deficiency (CVD) who have difficulties with distinguishing particular color combinations because one type of cone photopigment is not functioning, as in the case of dichromats, or the spectral sensitivity of one type of cone photopigment is too close to another type of cone photopigment, as in the case of anomalous trichromats [8–10]. In most of the cases, the color vision deficiency appears as red-green color blindness in dichromats and incomplete red-green color blindness in anomalous trichromats [10,11]. This means that people with color vision deficiency have little or no redness and greenness in their color appearance. Since responses of red-green and blue-yellow color opponent pathways determine hue and saturation in colors, colors detected by people with color vision deficiency differ greatly from those detected by people with normal color vision (CVN) [10]. In addition, the particular color combinations in which two colors are different only in the amount of redness or greenness cannot be distinguished [10,12].

Recently, it has become important to consider the convenience factor in the daily lives of people with color vision deficiency, and many products employ modified color coordination, which can be distinguished easily by individuals with CVD. This is called color universal design (CUD) [13], and CUD tends to focus on the distinguishability of colors. However, the psychological image and impact of the color should also be considered. There are many studies about the color discrimination and CVD observers (for example, previous literature about computer-based color vision tests [14–17]), but studies about the color psychology of people with color vision deficiencies are rare [4,18–21].

In our previous study [4], we investigated the bidirectional relationship between colors and semantic words in CVN and CVD (deutan) observers. The impressions of nine semantic words were measured using twelve hues and three neutral colors (white, gray, and black). Using a set of 35 paired words, color impressions were also estimated using the semantic differential (SD) method [22,23] (see Section 2.C for details about the SD method). Data from the word evaluation were analyzed using the principal component analysis (PCA) [24] (see Section 2.E for details about the PCA), and the results showed that although all hues used as loadings were distributed in a hue-circle shape for both observer groups, the coordinates of five words were approximately on one line, reflecting that the colors used in the paired comparison were treated as one-dimensional scaling in the CVD group. However, in the results of the SD method, the word distribution of loadings was similar between the CVN and CVD groups, and the color score distribution had a similar tendency of showing an ellipse-shaped hue circle. Thus, we considered that the CVD observers’ experience with the associated color names, rather than the color appearance of the stimuli, caused the impression of colors, but in assigning colors to the words, red and green were rarely selected for some of the semantic words like “Vigorous” because of their color appearance.

The results of our previous study [4] revealed that CVD observers can understand the impression of colors if the color names can be recognized, even if they cannot perceive redness and greenness. This finding has given rise to the next question: how can CVD (deuteranopic) observers recognize reddish and greenish colors and their color names in various colors? If saturated red or green will be presented, then it is expected that deuteranopes simply will recognize dark yellow (or brown) as an object color in color appearance, since the color can be estimated as red, green, or dark yellow (in color names by normal trichromats) according to the color appearance model of dichromats [25]. In such a case, the deuteranopes tend to use the strategy that if the color looks bright, then it would be most likely to be red, not green [26]. However, even if a presented color would be the simulated deutan color that was defined as the converted color (e.g., dark yellow) by the deuteranope’s color appearance model [25] from a normal color (e.g., red) defined by the color appearance of normal trichromats, what color will deuteranopes recognize as the presented color? Since the appearance of the simulated deutan color and the normal color would be almost identical in terms of color appearance of the deuteranopes, the deuteranopes would be able to treat the simulated deutan color as the normal color. In this case, the result of the color impression measured by the simulated deutan colors in the SD method would be the same as the one obtained by normal (original) colors. The PCA score values of both the normal and simulated deutan colors would be distributed in a two dimensional circle (hue circle). Contrarily, if the deuteranopes would be able to recognize the simulated deutan colors as reduced stimulus colors, which are not the same as normal colors in the color appearance of the normal trichromats, the result of the SD method would be different. The PCA score values of the simulated deutan colors would distribute one dimensionally in the space of the principal component axes, while the normal colors would distribute two dimensionally to the hue circle. On the other hand, the simulated deutan colors and the normal colors are completely different from each other in the CVN observers.

The purpose of this study is to investigate the difference between normal colors and simulated deutan colors in terms of the bidirectional relationships between semantic words and hues [4,5] in CVN and deutan observers. We investigated chromatic representation of semantic words by Thurstone’s paired comparison method in Experiment 1 (Exp.1) and semantic representation of colors by the SD method in Experiment 2 (Exp. 2). Because the simulated colors would be obtained by the color appearance model of protanopes or deuteranopes, we focused the experiments on deutan observers using the simulated deutan colors. We compared the results of the simulated deutan colors with those of the normal colors in CVN and deutan observers.

2. METHODS

A. Observers

Ten color vision normal (CVN) observers (nine male and one female) and seven color vision deficient (CVD) observers (four deuteranopes, one protanomalous, and two deuteranomalous observers, all male) ages 20 to 23 years old (Mean, 21.4), participated in all experiments involving the evaluation of word impressions by hue (Exp.1) and the evaluation of color impressions via the SD method (Exp.2). All CVN and five CVD observers were Japanese students at the Kanazawa Institute of Technology (KIT), and the two CVD observers were Japanese students at the Kochi University of Technology (KUT). All CVD observers had participated in our previous study [4]. The authors did not serve as observers. The purpose of the experiments was not informed to the observers. One other CVD male observer participated in the experiments. However, he could not complete all sessions.

All observers had normal or corrected-to-normal acuity better than 1.67 min. of visual angle. The color vision of the observers was tested by a series of color vision tests: Ishihara color test plates (International 38 plates edition), the Farnsworth D-15 test, and Standard Pseudo-Isochromatic Plates (SPP, Ichikawa version). We used the Neitz OT II anomaloscope (LED lamp model, Neitz Co. Ltd.) to classify the CVD observers. All four deuteranopes could make anomaloscope matches over the full range of the R/G setting (0–75). Although all the anomalous observers completed all the color vision tests and experiments, we did not include their data in the analysis because we were afraid of the small number of anomalous observers compared to the complex variation among individuals with anomalous color vision [17,27,28].

All procedures and experiments, including the color vision testing, conformed to the principles expressed in the Declaration of Helsinki and were approved by Kochi University of Technology Research Ethics Committee (receipt number 244). Written informed consent was obtained from each observer prior to testing.

B. Color Stimuli

The apparatus and calibration of this study is the same as our previous study [4]. Color stimuli were presented on a 27-inch LCD monitor (ColorEdge CS2730, EIZO Corporation) placed in a dark room at KIT and on a 17-inch CRT monitor (CPD-G220, Sony Corporation) placed in a dark room at KUT. We asked the observer to respond using a left-or-right judgement in a paired comparison (Exp.1) with a ten-key keyboard, and all other responses were handwritten by the observer and the experimenter. The viewing distance in the experiments was 73 cm at KIT and 53 cm at KUT.

We prepared two color stimulus sets, a normal color stimulus set, and a simulated deutan color stimulus set, as shown in Fig. 1. Both color stimulus sets consisted of twelve chromatic and three achromatic colors. Twelve chromatic colors in the normal color stimulus set were selected from the vivid tone of the PCCS (Practical Color Coordinate System) established by the Japan Color Research Institute. Their color codes in the PCCS were v2, v4, v6, v8, v10, v12, v14, v16, v18, v20, v22, and v24. The three achromatic colors were the white [denoted by (w) and set to be the standard white of the correlated color temperature 6,505 K (D65) in ${77.4}\;{\rm{cd/}}{{\rm{m}}^2}$], gray [(g), N4.7/ in ${12.7}\;{\rm{cd/}}{{\rm{m}}^2}$], and black [(b), the screen RGB was set to (0, 0, 0)].

 

Fig. 1. Color Stimuli used in the normal color stimulus condition (top row) and the simulated deutan color stimulus condition (bottom row). Neutral colors [white (denoted by w), gray (g), and black (b)] were the same between conditions. Color codes are from the PCCS. “D-” denotes the simulated deutan colors. D-v2 and D-v24 were renamed as D-Mv2 and D-Mv24. See text for details.

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The simulated deutan color stimuli were generated by converting colors in the normal color stimulus set to colors corresponding to their appearance by a standard deuteranope observer. The conversion was operated by the color universal assistant software UDing Simulator (Toyo Ink Co. Ltd.) [29] that simulates dichromats’ color vision (protanopes and deuteranopes) by using the concept of Brettel–Viénot–Mollon’s model [25] in order to prepare modifications of confusing color combinations [30]. The Brettel–Viénot–Mollon’s model [25] replaces each stimulus color by its projection onto a reduced stimulus surface defined for each type of color deficiency. In the CIE 1931 $xy$ color space, the reduced surface can be expressed by reduced stimulus lines. The chromaticity coordinates of a simulated color for the standard deuteranope is expressed by the intersection of a deuteranopic confusion line passing through the chromaticity coordinates of an original (normal) color from the deuteranopic co-punctual point [$(x,y) = ({1.000},{0.000})$] and one of the reduced stimulus lines. Brettel et al. [25] used the lines going through the chromaticity coordinates of a 475 nm monochromatic light on the spectral locus, a monitor white, and a 575 nm monochromatic light. Since we defined white by D65, the lines were arranged into two lines of 475 nm–D65 and D65–575 nm. In the conversion by the UDing Simulator, the reduced stimulus lines were 483 nm–D65 and D65–582 nm, as shown in Fig. 3.

Although the detailed algorithm of the UDing Simulator has not been disclosed, we expect there are two factors that account for the difference of the reduced stimulus lines. The first factor is that the UDing Simulator was an application meant mainly to be used to convert colors into surface colors painted by inks. This means that this software was intentionally adapted to a cyan–magenta–yellow–black (CMYK) color system in which the dominant wavelength of the yellow vertex in a common CMYK gamut is close to 578 nm and the wavelength of the cyan vertex is close to 483 nm. By selecting the line through 483 nm and D65 as the bluish part of a reduced stimulus line, the line through D65 and 582 nm would make almost a straight line from 483 nm to 582 nm. This modification enabled us to find more simulated protan and deutan colors in printing in terms of the CMYK gamut.

The other factor is that such a modification in the wavelengths of the reduced stimulus lines is reflecting the data of the unique blue and yellow wavelengths and an achromatic point (least amount of color) in a deuteranope. Rolf [31] surveyed the variation in the wavelength of unique yellow, and it tends to be longer than 575 nm. Schefrin and Werner [32] reported the wavelengths of unique blue and yellow (479.56 nm and 577.40 nm, respectively) in 20-year-olds by linear regression lines obtained from 50 observers. In terms of the achromatic point of deuteranopes, the wavelength is much longer. The mean wavelength of seven deuteranopes was 499.7 nm in the range from 495 to 505 nm [33]. Although we presented colors on the monitor, we used colors in the PCCS defined by a set of color chips similar to the Munsell color system. Thus, we used the reduced stimulus line of 483 nm–D65 and D65–582 nm in this study.

In the luminance calculation of the deutan color simulation, the luminous efficiency function for the deuteranope was assumed to be the same with the sensitivities of the L-cone, which is the same in spectral sensitivity as those of the color normal observers. Under this assumption, equal luminance in deutan simulation is equivalent to the equal L-cone stimulation. The transformation between the cone responses and the tristimulus values was performed using the Smith–Pokorny estimates of the cone photopigment spectral sensitivities [34] and the CIE 1931 color matching function [12] with the cone matrix by Kaiser and Boynton [35]. Since Brettel et al. [25] used the spectral cone contribution functions from Stockman et al. [36], the numeric values of the simulated luminance were slightly different. In the simulated deutan color stimulus set three achromatic colors were identical in the normal color stimulus set since the conversion does not change these neutral colors theoretically or practically. Simulated stimuli were also measured by spectrophotometers (CS-150 and CS-200, Konica-Minolta, Inc). In this study, the color codes of the simulated deutan color stimuli are defined as D-v2 to D-v24, which correspond to v2 to v24 in normal color stimuli, as shown in Fig. 1.

Figure 2 shows the $L^*$ (lightness) values of the color stimuli calculated by the standard method showing the lightness of a standard CVN observer and by the luminance adjustment in the deutan simulation. It was expected that the $L^*$ of the simulated color stimuli in the CVN observer (denoted by triangles) should match to the $L^*$ of the normal color stimuli in the (simulated) deutan observer (denoted by squares). However, in the conversion by the UDing simulator, $L^*$ was further controlled with chromaticity coordinates because its algorithm converts colors in the CIE1976 $u^*\;v^*$ color space [28] (see the paragraph after the next paragraph for details).

 

Fig. 2. Lightness ($L^*$) of the color stimuli calculated by the standard method (denoted by CVN in the figure caption) and by the deutan simulation (denoted by Deutan). Filled circles and triangles denote the $L^*$ of a standard CVN observer in normal color stimuli and simulated deutan color stimuli, respectively. Open squares and diamonds denote the $L^*$ of a standard deutan observer. The achromatic colors in the simulated deutan color stimuli were omitted since they were identical in both stimulus sets.

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Figure 3 shows the chromaticity coordinates of the normal color stimuli (denoted by squares) and simulated deutan stimuli (circles) in the CIE1976 $L^*a^*b^*$ color space. White (D65) is denoted by a cross, and black (b) is not plotted because its tristimulus values were not accurate due to a very low on-screen luminance. A dashed ellipse shows the best fit for the chromatic colors in the normal color stimulus set, and the dotted lines inside denote the major and minor axes of the ellipse. The deuteranopic color confusion loci with luminance adjustment in the deutan simulation are denoted by green curves. The gray curves indicate the gamut of the display calculated from luminance and chromaticity coordinates of RGB phosphors of the monitor at KIT. Red dotted, blue solid, and black solid curves denote the reduced stimulus lines of the Brettel–Viénot–Mollon’s model (475 nm–D65–575 nm), 477 nm–D65–576 nm (set to be closest to the ordinate), and 483 nm–D65–582 nm (expected to be used in the UDing Simulator), respectively.

 

Fig. 3. Chromaticity coordinates of the color stimuli in the CIE1976 $L^*a^*b^*$ color space. Squares denote color stimuli in the normal color stimulus set, and circles denote the simulated deutan color stimulus set. White (D65) is denoted by a cross, and black (b) is not plotted. The dashed ellipse shows the best fit for the chromatic colors in the normal color stimulus set, and the dotted lines inside denote its major and minor axes. The green curves show the simulated deuteranopic color confusion loci with luminance adjustment of the standard deuteranope. The gray curves indicate the gamut of the display. The red broken, blue solid, and black solid curves denote the reduced stimulus lines used in the deutan color simulation. The dotted and solid gray lines denote the directions of lightness ($L^*$) for the normal colors and the simulated deutan colors, respectively. See text for details.

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The chromaticity coordinates of most of the simulated deutan colors appear on or near the reduced stimulus lines (483 nm–D65–582 nm lines denoted by the black curve) and the deuteranopic color confusion loci (green curves). However, as shown in Fig. 2, there are some discrepancies in the simulated deutan color stimuli. The chromaticity coordinates of D-v8, D-v18, and D-v20 are not on the reduced stimulus lines probably because of the gamut limitation of the display. The chromaticity coordinates of D-v2 and D-v24 are on the 483 nm–D65–582 nm lines but not on the deuteranopic color confusion loci. The chromaticity coordinates of both D-v2 and D-v24 indicate that these colors have larger $L^*$ values than expected in the simulation. However, it is natural that the $L^*$ of these two simulated colors (and D-v4) were adjusted little (as shown in Fig. 2) because in the deutan simulation, the lightness (luminance) of such reddish colors are processed dominantly by the L-cone responses in a CVN observer, and the luminance adjustment in a deutan observer has little effect on lightness. Thus, we changed the color codes to D-Mv2 and D-Mv24 to indicate this discrepancy. D-v12 was the simulated deutan color stimulus of both v2 and v12, as shown in Fig. 3. Nevertheless, the higher lightness in D-Mv2 can be considered as the enhanced simulation reflecting the common behavior of deuteranopes. When a deuteranope recognizes dark yellow (or brown) in color appearance of an object, the deuteranope tends to use the strategy that if the color looks brighter, then it is most likely to be red, not green. Thus, D-Mv2 and D-v12 could be recognized stably as red and green, respectively, by deutan observers. While some discrepancies were involved, these simulated deutan color stimuli were on the reduced stimulus lines, indicating that the simulated colors can be treated as a set of colors in one chromatic dimension that is the expected property of dichromats’ color vision.

This simulated deutan color stimulus set and the normal color stimulus set would be theoretically identical in deutan observers. However, we did not perform the test to confirm this point because it is not critical for the experimental purpose that two stimulus sets would be perfectly identical in appearance as long as these two color stimulus sets would be recognized by deutan observers as sets of colors consisting of (different) hue circles. In addition, we thought it would be better not to arouse suspicion in the CVD observers regarding the difference between the two stimulus sets. A special test may cause the CVD observers to be much more careful about the stimulus colors since all the CVD observers in this study had already known about their color vision type and were familiar enough with the condition to feel that the appearance of color may be different for people with CVN . Although we did not perform a quantitative test, after the completion of all experimental sessions we obtained the insight of the deutan observers. They understood that some of colors were not the same with the first set of sessions (i.e., the normal color stimulus set), but they did not find that all the colors (except neutral colors) had been changed. In the Results section we show that the results of the paired comparison (Exp. 1) was not statistically different between the normal and simulated deutan stimulus color sets in the deutan observers.

Since we originally used a limited number of colors in the same PCCS tone in which the lightness ($L^*$) of colors are systematically different, as shown in Fig. 2, the lightness change is not necessarily independent of the red/green ($a^*$) and yellow/blue ($b^*$) chromatic changes. The dotted and solid gray lines in Fig. 3 denote the directions of lightness ($L^*$) for the normal colors and the simulated deutan colors, respectively. Each direction has the maximum correlation between the $L^*$ of the stimulus colors in ascending order in one stimulus color set and the $L^*$ in the order of the coordinates of colors projected on the line in that direction. The correlation coefficients ($r$) were 0.977 and 0.943, respectively. The lightness direction in normal colors was 104.4°. That is close to the $b^*$ (ordinate) axis. In contrast, the lightness direction in the simulated deutan colors was 147.7°, and that is different for both the $b^*$ and the $a^*$ (abscissa) axis. Thus, in the analyses of the color distributions in word expression (Exp. 1) and in the evaluation by words (Exp. 2), it was expected that in a normal color stimulus set, it would be difficult to select a more determinant factor between lightness ($L^*$) and yellow/blue ($b^*$). Contrarily, it would be theoretically possible to separate the contribution of lightness with red/green ($a^*$) and yellow/blue ($b^*$) in the simulated deutan color stimulus set.

In addition, we introduced saturation (chromaticness, $C^*$) in the CIE1976 $L^*a^*b^*$ color space defined in [Eq. (1)] and tried to use the amount of $C^*$ as a new factor,

In Exp. 1, the visual stimulus in one trial consisted of two color patches presented side-by-side with 2.0° separation. One color patch was a rectangle of 7.0° width by 6.4° height with black fringe of 10 min. width. The horizontal middle point of the two patches was on a horizontal center of the screen. The vertical center of the patches was 1.86° below the vertical center of the screen. The background was uniform gray, which was identical to the gray (N4.7) in the color stimulus sets. In Exp. 2, the visual stimulus in one trial consisted of one color patch, and the other conditions were the similar to the ones in Exp. 1 except that the horizontal center of the visual stimulus was defined at the horizontal center of the color patch.

The experimental data of the four deuteranopes using the normal color stimulus set in Exp. 1 and Exp. 2 has already been presented in our previous study [4]. In both experiments, these observers were newly tested for this study using the simulated deutan color stimulus set.

C. Semantic Words for Evaluation Tasks

In Exp. 1, we used a paired comparison method. The nine Japanese semantic words used for evaluation by hues in Exp. 1 were the same as the words selected in our previous studies [4,5]: GENKI-NA (Vigorous), NODOKA-NA (Tranquil), JYUUKOU-NA (Massive), KAGEKI-NA (Extreme), SEIREN-NA (Clean or “Clean-fingered”), SABIRETA (Deserted), SENSAI-NA (Fine or Delicate and Exquisite), SOUREI-NA (Magnificent), and MEDATSU (Visible). Independence of these words was also tested in the control experiment of our previous study [5] by using the traditional SD method and using three core scales [Activity (active-inactive), Potency (superior-inferior), and Evaluation (beautiful-ugly)] [22,23]. The nine evaluative words were conceptually separated into five categories by the distance in the space of the Activity and the Evaluation axes: [Vigorous, Visible, Extreme], [Massive], [Magnificent, Clean], [Fine, Tranquil] and [Deserted].

In Exp. 2, we used the SD method in which each color was evaluated in the context of many pairs of semantic words with a grade point (e.g., ${-}{{3}}$, ${-}{{2}}$, ${-}{{1}}$, 0, 1, 2, 3) set for each pair of semantic words [22,23]. For example, in the case that a pair of semantic words is “warm–cool” the impressions of perfect “warm” and perfect “cool” are graded by the maximum value (e.g., 3) and the minimum value (e.g., ${-}{{3}}$), respectively. The impression between these extremes is graded by a value between ${-}{{3}}$ and 3. In Exp. 2, we added twenty-six Japanese semantic word pairs to these nine words in order to avoid the possible case that only a few paired semantic words would dominantly determine the impression of colors. We also tried to avoid a possible empty space in the space of the first and second loading values (i.e., Fig. 9 in this study) where the coordinates of any positive words (i.e., the coordinates of the words in Fig. 9) and those of the corresponding negative words in the pairs of semantic words (not shown in Fig. 9 but the coordinates in origin symmetry to those of the corresponding positive words) would not exist. The positive items in the word pairs in English were Soft, Warm, Beautiful, Delicate, Deep, Fresh, Sweet, Strong, Bright, Grand, Full, Exciting, Hard, Smooth, Thick, Salty, Vivid, Erotic, Cloudy, Clear, Sharp, Permanent, Comfortable, Watery, Light [37], and Thin [5]. The words Soft and Warm are expected to be the strongest and orthogonal in the word distribution of the SD method [38,39], as shown in our previous studies [4,5].

D. Procedures

We investigated chromatic representation of semantic words by Thurstone’s paired comparison method in Exp. 1. At the beginning of a session, the gray background was presented to an observer for 5 min. After the background adaptation period, one Japanese semantic word for evaluation was presented until the subject agreed to start the trials. In a trial, the observer chose one color that was more appropriate for the impression of the semantic word in two presented colors by pressing one of two buttons. The two colors were pseudo-randomly selected from 15 colors in one color stimulus set used in that session: a normal color stimulus set in a normal color condition, or a simulated deutan color stimulus set in a simulated deutan color condition. For one semantic word, the observers performed the paired comparison for all 210 combinations of 15 colors, considering their left-or-right positions ($_{15}{{\rm{P}}_{2}} = {{15}} \times {{14}} = {{210}}$) successively. In each experimental session, the observer performed trials with all nine semantic words in series. The order of the words was also pseudo-randomized. The observer performed 1890 trials in one session. Each observer completed three sessions in one color condition. One color combination for one word in one color condition was tested in six trials (each color placed three times on the left and three times on the right). In the paired comparison, we counted as “one win” in the selected color and “one loss” in the not-selected color in one trial. Each color in a pair with the other color would show from zero to six wins as the result of the comparison. There was no time pressure in Exp. 1, and observers were allowed to take rests whenever they wanted. Most observers spent 30–50 min to complete one session, and many observers took only from 1.0 to 1.6 s. per trial, which was much faster than the times (from 3.7 to 4.6 s. per trial) in our previous study [4]. Most observers participated over two days, and some observers finished all the sessions in a day.

In Exp. 2, we investigated the semantic representation of colors by using the SD method. At the beginning of a session, an observer adapted to the gray background for 5 min. In a trial, the observer evaluated an impression of one presented color (from fifteen stimulus colors) on the screen in seven-level scaling (i.e., ${-}{{3}}$, ${-}{{2}}$, ${-}{{1}}$, 0, 1, 2, 3) using 35 paired semantic words and by using check marks (“$\sqrt {}$”) on each line scale in an evaluation sheet. In a session, the observer completed the evaluation on fifteen sheets, which corresponded to the fifteen colors in the normal color stimuli or simulated deutan color stimuli sequentially. The order of the words and colors were pseudo-randomized. The order of the words was constant for the colors in a session. Each observer completed three sessions in the normal color condition and three sessions in the simulated deutan color condition. There was no time pressure in Exp. 2 as was the case in Exp. 1. Most observers spent 50–60 min to complete one session of 15 sheets.

E. Data Analysis

Experiment 2 in this study was the evaluation of the item (color) impression by a pair of semantic words. Since this experiment used a common SD method, we first considered the data analysis in Exp. 2. In the traditional approach, all sets of the grade points for all paired semantic words were subjected to a factor analysis (FA) to find a few new factors for item scaling that have combined meaning of test semantic words (e.g., childish, accomplished, and so on) that can explain the tendency of the item impression (e.g., color impression) [40]. A principal component analysis (PCA) is also commonly used to analyze the data in which eigenvectors consisting of all factors (i.e., all pairs of the semantic words) with weight coefficients will be found one by one in order to have a larger summation of variances projected on that eigenvector in all items (e.g., all stimulus colors). Thus, in the FA, the distribution of items depends on the new factors and their directions in the coordinates. (In some cases, the vector directions of these new factors are not necessarily orthogonal.) In the PCA, the distribution of items simply depends on the summation of the items’ variances, and the PCA mathematically sets the sum of distances between items (in all combinations) at its maximum [24]. In the PCA of the data from the SD method, each semantic word has the optimized contribution values obtained by the best fit to the item (color) evaluation data in a linear combination of the principal components (PCs). The optimized contributions of the semantic words were expressed by the loading values in each PC, and the words were distributed in the space of the loading value axes of the PCs. Similar words would be distributed in closer positions.

In the data analysis in Exp. 2, one could expect the possible new factors to explain the distribution of colors as described in the Introduction section if we would use FA. However, it was expected that it would be too difficult to estimate those new factors in order to determine the distribution of semantic words if we would use FA in the data analysis in Exp. 1. Although a factor analysis provides more factors to explain an entire dataset, for the purpose of this study it was not necessary to analyze the data by as many factors, as in the studies of item semantics. Thus, we decided to use PCA in the data analysis in Exp. 1 and Exp. 2, in which the number of PCs (dimensions) reaches a minimum. The direction of the first PC maximizes the variance of the data to account for the data distribution. The second and subsequent PCs are determined in the same way under the constraint condition of orthogonality [24].

The data of each semantic word in Exp. 1 were initially a number of wins in the paired comparison for each color. The number of wins was modified in the cases of all wins or no win. Six wins and 0 wins were modified to 5.5 wins and 0.5 wins, respectively. The number was divided by 6 (number of trials) and subtracted by 0.5 (the total mean) to get a modified selection rate. Thus, the selection rate for all wins, 3 wins–3 losses, and the no wins data becomes 0.417, 0, and ${-}{0.417}$, respectively. This operation is equivalent to calculating the $Z$-score under the assumption of the normal distribution in which the standard deviation equals one, but we thought that to use this modified selection rate would be safer than to use the true $Z$-score, which requires the assumptions of a normal distribution and equality of the standard deviation between the CVN and the CVD observers. The modification of the ratio helped to avoid unexpected distortions in the calculated PCA results and the model curve fits to the selection rate data because all wins and no wins would be extreme results, but the number of comparisons was only six (trials) for each color in one semantic word per observer.

The PCA was performed by the software R (ver. 3.0.2) [41], and the components were verified by the software HAD (ver. 16.10) [42] and the software MATLAB (ver. 2021b). We used the [pca] command in MATLAB with the algorithm of the singular value decomposition (svd) of the data matrix $X$ (default), the “Centered” setting in which the [pca] centers $X$ by subtracting the column means before computing the singular value decomposition or the eigenvalue decomposition, and the “Variable Weight” setting in which the variable weights are the inverse of the sample variance (and the [pca] returns the PCs based on the correlation matrix with the “Centered” setting). The PC loading values were from the orthonormal coefficient matrix converted from the coefficient matrix by the [pca] command.

In the analysis in Exp.1, the PCA was applied to the individual modified selection rates of fifteen colors (twelve hues, white, gray, and black) for the nine words because we wanted to analyze the observer variation. In the analysis in Exp. 2, the PCA was applied to the sets of the individual grading points for each semantic word for the fifteen colors. In the first step of the analyses, the CVN data of ten CVN observers and the CVD data of four CVD (deutan) observers were analyzed separately. In the second step of the analyses, we used one set of the combined data in the selected four CVN and four CVD (deutan) observers to balance for the number of observers. As we described in Section 2.B, we compared the color distributions in the loading values (Exp. 1) and in the score values (Exp. 2) with the directions of lightness ($L^*$), red/green ($a^*$), and yellow/blue ($b^*$) to investigate possible factors that can influence the color distribution.

Table 1. Probabilities of the Main Effects and Interactions by ANOVA for All Data in Exp. 1^a

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3. RESULTS

A. Modified Selection Rates of Stimulus Colors for Semantic Words (Experiment 1)

1. Factors Affecting Modified Selection Rates

We performed an analysis of variance (ANOVA) using MATLAB (version 2021b) for the data of the modified selection rate in Experiment 1 (Exp. 1). We involved four factors. (1) The Observer’s color vision type, [CVN, Deutan]. (2) The stimulus set, [Normal color stimuli, Simulated deutan color stimuli]. (3) Nine evaluated semantic words: [Visible, Vigorous, ..., Tranquil]. (4) Fifteen stimulus colors: [v2, v4, …, v24, white, gray, black] (where each color stimulus set was separated by the second factor). The total number of the data was calculated by multiplying the number of the stimulus set(s) (=2 or 1), the number of the observers (=14, 10, or 4), the number of semantic words (=9), and the number of stimulus colors in one set (=15).

Table 1 shows the probability ($p$) obtained by the ANOVA. The second column shows the result of the analysis obtained by all data. If the probability would indicate not statistically significant in the case of $p \gt {0.05}$, then the main effects of the factors and interactions between factors did not statistically influence the selection of colors in the paired comparison in Exp. 1. The factors of the observer’s color vision type (denoted by Obs. CV type), stimulus set (St. set), and evaluated semantic words (Word) are statistically significant main effects, but the factor of the stimulus colors (Color) is not significant as a main effect. This means that when all the modified selection rate data for one stimulus color were considered that data was not statistically different from those of other stimulus colors. Nevertheless, an interaction between the observer color vision type and color is statistically significant; but an interaction between the stimulus set and color is not significant as expected from the main effect of [Color].

We were interested in the reason of the probability results of the ANOVA in Table 1. For example, the modified selection rates of each stimulus color in a CVN observer dataset seemed to be different between normal and simulated deutan color stimulus sets on the analysis in the next subsection, although this difference is not clear in a deutan observer dataset. For further analysis regarding the effect of the stimulus colors, we performed an ANOVA in the divided datasets. Table 2 shows the results of the ANOVA performed separately in a normal color stimulus set (the second column) and a simulated deutan color stimulus set (the third column), and Table 3 shows those in a CVN observers dataset (the second column) and a deutan observers dataset (the third column).

Table 2. Probabilities of the Main Effects and Interactions by ANOVA for Different Stimulus Sets in Exp. 1^a

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Table 3. Probabilities of the Main Effects and Interactions by ANOVA for Different Observer Color Vision Types in Exp. 1^a

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Three bold probabilities in the interaction [Obs. CV type * Color] in Table 2 show that in the normal color stimulus set, the CVN and deutan observers were not significantly different in the usage of colors but significantly different in the simulated deutan color stimulus set. This means that regardless of the expected difference in color appearance between observer groups, the color variation of the normal color stimuli were treated in similar ways. In contrast, the simulated deutan color stimuli were treated in significantly different ways, similar to the significance in the entire dataset, as shown in Table 1. This suggests that in the not significant results of this interaction in the normal color stimulus set did not strongly influence this interaction in all the datasets. In addition, three italic probabilities in the interaction [St. set * Color] in Table 3 show that in the CVN observers two sets of color stimuli were significantly different in terms of the usage of colors, but in the deutan observers were not significantly different and this caused this interaction to be not significant in all the dataset, as shown in Table 1. The results suggest that the CVN observers recognized that the two sets of color stimuli were completely different, but the deutan observers recognized the two sets as similar, or in an extreme case, as identical. Both results show that treatments of the color variation between the fifteen stimulus colors in Exp. 1 are not statistically different between the normal colors in the CVN observers and the normal and simulated deutan colors in the deutan observers. This suggests that the deutan observers treated the color variation of both stimulus sets similar to the normal color stimulus sets in the CVN observers.

An interaction [Word * Color] was not statistically significant in the entire dataset (denoted by the bold-underline in Table 1), but that was statistically significant in the simulated deutan color stimulus set (bold-underline in Table 2). Similarly, an interaction [Obs. CV type * Word * Color] was not statistically significant in the entire dataset (denoted by the italic-underline in Table 1), but that was statistically significant in both of the normal and simulated deutan color stimulus sets (italic-underline in Table 2). Possible explanations to the statistical significance in these two interactions are described in the next subsection.

2. Modified Selection Rate Fitted by Principal Components

PCA was performed separately for four datasets of the modified selection rate of each color for nine semantic words. The four datasets consisted of each dataset of the CVN and the deutan observers in normal color stimulus and simulated deutan color stimulus conditions in order to avoid dependency on assumptions of data equivalence. Figure 4 shows scree plots with parallel analysis in all number of factors (15 in colors and 35 in semantic words), although in the data of Exp.1 [Figs. 4(a) and 4(b)] the cumulative contribution rates reached to 100% at the 14th factor. In the normal color stimulus condition of the CVN observers, the proportion of variance from the first to the third principal components (PCs) were 47.0%, 32.0%, and 6.1%, and the cumulative contribution rates of the second PC was 79.0% (corresponding to open circles in Fig. 4(a), although the ordinate of the figure is the eigenvalues of the components). In the simulated deutan color stimulus condition, the proportions of variance were 43.2%, 36.4%, and 7.8%, and the cumulative contribution rates was 79.6% [triangles in Fig. 4(a)]. In the normal color stimulus condition of deutan observers, the proportions of variance were 58.0%, 15.1%, and 11.5%, and the cumulative contribution rates was 73.1% [open circles in Fig. 4(b)]. In the simulated deutan color stimulus condition, the proportions of variance were 52.9%, 21.6%, and 11.8%, and the cumulative contribution rates was 74.5% [triangles in Fig. 4(b)].

 

Fig. 4. Scree plots (data correlation matrix) and parallel analysis (random correlation matrix) of paired comparison data (Exp. 1) in (a) ten CVN observers, (b) four deutan observers, and (c) those of the SD method data (Exp. 2) in four CVN and four deutan observers.

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We performed a scree test and parallel analysis [40] using HAD [42] in order to determine the suitable number of components in the PCA, as presented in Table 4. As we stated in our previous study [4], the scree test tends to show higher numbers so as not to miss a possible factor in the factor analysis (FA) [42]. The parallel analysis tends to show the minimum number of the components [40,42]. Since our purpose for using PCA is to investigate the structure of color and word distributions, by using the results of parallel analysis we determined to use two components for the data of Exp. 1 (paired comparison) and three components for the data of Exp. 2 (the SD method). In the scree test results in Table 4, we also referred to the number of components by using parallel analysis based on the diagonal squared multiple correlation (SMC) [42].

Table 4. Determined Number of Components in the PCA by Scree Test and Parallel Analysis^a

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The loading values in the first and second PCs for each color stimulus show the contribution of colors to the evaluation of all words through the PCs. Figures 5(a) and 5(c) show the loading values of the first and second PCs for each stimulus set in ten CVN observers. We would like to point out that the positive direction of the first PC axis was reversed in both panels for better presentation since all PCs have arbitrariness in the positive/negative reversal. The ellipses are the best fits to all data points, and the dotted lines denote their major and minor axes. In the normal color stimulus condition, the radii of the minor and major axes are 0.346 and 0.386, respectively, and the axis ratio is 0.896. In the simulated deutan color stimulus condition, the radii of the minor and major axes are 0.334 and 0.404, respectively, and the axis ratio is 0.828. The similarity of the axis ratios suggests that the simulated deutan color stimuli as well as the normal color stimuli were used to evaluate these semantic words in the CVN observers.

 

Fig. 5. Distribution of the stimulus colors as defined by the first and second PC loading values in the normal color stimulus condition in (a) ten CVN observers and (b) four deutan observers. The simulated deutan stimulus condition in (c) ten CVN observers and (d) four deutan observers. Color chip number and names in the PCCS are presented near each point. Black ellipses denote the best fit to all data points, and dotted lines inside denote their major and minor axes. The blue solid and red and yellow broken lines denote directions of lightness ($L^*$), red/green ($a^*$), and yellow/green ($b^*$) at the highest correlation coefficients (values shown in panels) without neutral colors (white, gray, and black). In the normal color stimulus conditions, the colors on the ellipse are almost in the order of the code number reflecting a hue circle, and in the simulated deutan color stimulus condition, the colors distribute almost in the order of the $b^*$ values. The direction of lightness is almost identical to the second PC. In deutan observers, the direction of lightness is close to the first PC in both color stimulus conditions. See text for details.

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In the normal color stimulus condition the distribution of chromatic colors on the ellipse were almost in the order of their code number, reflecting the hue circle of the PCCS in both observer groups, as shown in Figs. 5(a) and 5(b) (except the order of v14 and v16 was reversed in the deutan observers). In addition, the stimulus color distribution maintains antagonistic coordinates of colors placed at the opposite positions in the original PCCS hue circle (e.g., v2 versus v14, and v8 versus v20) [4,5]. In contrast, in the simulated deutan color stimulus condition, colors distribute in the order of the $b^*$ values (see Fig. 3) in both observer groups, as shown in Figs. 5(c) and 5(d).

Thus, we investigated the possibility that in the simulated deutan color stimulus condition the two PC axes would not reflect red-green and blue-yellow color opponent responses but reflect blue-yellow color opponent response and lightness. We calculated the correlations of lightness ($L^*$), red/green ($a^*$), and yellow/blue ($b^*$) to the vector directions in the PC axes space. The blue solid, red dotted, and yellow dotted lines in Fig. 5 denote the directions of lightness, red/green and yellow/blue at the highest correlation coefficients. Neutral colors (white, gray, and black) were not included in the calculation of these coefficients since white and black have extreme values of the lightness.

In the normal color stimulus, condition of the CVN observers, the direction of $L^*$ and $b^*$ were around the middle of the two axes (34.4° and 24.4°, respectively, in the panel, and the correlation coefficients ($r$) are 0.905 and 0.954, respectively). However, considering the directions of $a^*$ (283.2° and $r = {0.945}$), it could be suggested that the CVN observers simply used the red-green ($a^*$) and yellow-blue ($b^*$) color opponent responses, although the $a^*$ and $b^*$ axes are not orthogonal. The contribution of yellow-blue ($b^*$) and lightness ($L^*$) cannot be separated clearly since these directions are close [Fig. 5(a)]. Those are initially close even in the orthogonal coordinates of $a^*$ and $b^*$ (Fig. 3), as stated in the Methods section.

In the simulated deutan color stimulus condition of the CVN observers [Fig. 5(c)], the directions of the lightness, red/green ($a^*$) and yellow/blue ($b^*$), were not largely separated. It can be expected that since the differences of the $a^*$ values in the normal color stimuli were compressed as a property of the simulated deutan color stimuli, then the value of $a^*$ was not used to determine the color distribution. However, it is difficult to understand that the directions of lightness ($L^*$) and yellow/blue ($b^*$) were close since these directions were different enough in the orthogonal coordinates of $a^*$ and $b^*$ (Fig. 3). This may suggest that one of the $L^*$ and the $b^*$ were not used to determine the color distribution similar to the $a^*$ factor. The difference of the color distributions of the loading values between color stimulus sets can be considered as statistically significant ($p \lt {0.0001}$) from the ANOVA, as shown in Table 1. We further discuss the dominant factor(s) to determine the distribution of colors in the Discussion section.

Figures 5(b) and 5(d) show the loading values of the first and second PCs for each stimulus set in four deutan observers. The positive direction of the first PC axis was reversed in Fig. 5(b) but not in Fig. 5(d). In both color stimulus conditions, the distributions of the chromatic colors on the best fit ellipses were basically in the same order as in the CVN observers [Figs. 5(a) and 5(c)], except that the order of v14 and v16 was reversed and D-v12 was not on the ellipse. This result in the normal colors stimulus condition follows the one in our previous study [4]. The radii of the minor and major axes in the best fit ellipse in the normal color stimulus condition are 0.299 and 0.521, respectively, and the axis ratio is 0.575. In the simulated deutan color stimulus condition the radii of the minor and major axes are 0.322 and 0.498, respectively, and the axis ratio is 0.646. The axis ratios are similar between stimulus sets, but in the deutan observers, the major axes, which are close to the second PC axes, are much longer than those in the CVN observers. Except for that point, the color distributions are similar between observer groups in the normal color stimulus condition as expected from the ANOVA ($p = {0.2287}$), although the lightness directions are different. The lightness direction of the deutan observers is 9.82° in the panel and $r$ is 0.926. This may suggest that the deutan observers used lightness as the most important information, but the direction of yellow/blue ($b^*$) is quite close (7.52°) to it, as shown in Fig. 3. Further details about these points are discussed in the Discussion (Section 4.A).

The color distributions between observer groups are different in the simulated deutan color stimulus condition ($p = {0.0244} \lt {0.05}$). The lightness direction is 14.5° in Fig. 5(d), and $r$ is 0.906. The deutan observers also used lightness as the most important information in this condition. As we will elaborate on in the Discussion section, $b^*$ could also contribute to the color distribution. In the deutan observers, the color distributions are considered to be similar between stimulus sets from the ANOVA ($p = {0.9634}$), although the color distributions look different.

The modified selection rates of the stimulus colors for each semantic word were fitted by the first and second PCs with no offset. Differences of the tendency in the gradual change of the selection rate from v2 to v24 or D-Mv2 to D-Mv24 would be able to categorize evaluated words. Figures 6 and 7 show the selection rate data of CVN (denoted by circles) and deutan observers (triangles) as a function of color stimulus for all semantic words in the normal color stimulus (Fig. 6) and the simulated deutan color stimulus (Fig. 7) conditions. The orders of the stimulus color in the abscissae were obtained from the distributions of colors in Figs. 5(a) and 5(b) in the counter-clockwise direction from v2 and clockwise from D-Mv2 in Figs. 5(c) and 5(d). The PCs smooth function is in the order of the color distributions, which could be different between the observer groups. Thus, we separated positions on the abscissae of v16, white and gray in the normal color stimulus condition (Fig. 6), and v12 in the simulated deutan color stimulus condition (Fig. 7). For example, the v16 of the CVN and the deutan observers are denoted by v16N and v16D, respectively. The model values used by PCs at the color stimuli only for the other observer group were the means of the values before and after those stimuli. The order of the panels for each word (from left top to right bottom) is the same as in our previous work [4], reflecting three categories of words ([Visible, Vigorous, Extreme], [Massive, Deserted], [Magnificent, Fine, Clean, Tranquil]). Error bars denote ${{\pm}}\;{2.26}$ S.E.M. (standard error of the mean) and ${{\pm}}\;{3.18}$ S.E.M. in CVN and deutan observers, respectively, which show a 95% confidence interval. The blue and green curves are model fits using the first and second PCs calculated in each separated dataset with no offset.

 

Fig. 6. Modified selection rate as a function of the stimulus color (denoted by the color code and the neutral color names) for the CVN (denoted by circles) and deutan (triangles) observers for nine semantic words in the normal color stimulus condition. The order of the stimulus color was obtained from Fig. 5. The positions on the abscissae of v16, white, and gray are different between the CVN (denoted by v16N, wN, and gN) and deutan (v16D, wD, and gD) observers. Error bars denote ${{\pm}}\;{2.26}$ SEM and ${{\pm}}\;{3.18}$ SEM in the CVN and deutan observers, respectively, as a 95% confidence interval. Blue and green curves are fitted by the first and second PCs with no off set for the CVN and deutan observers, respectively. Modified section rates change smoothly, and the model fits can predict the data reasonably well, except for the three neutral colors (white, gray, and black).

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Fig. 7. Modified selection rate as shown in Fig. 6, except that the simulated deutan color stimulus condition and the positions on the abscissa of Dv12 are different between the CVN (denoted by v12N) and deutan (v12D) observers.

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The selection rates of each word tended to change gradually in continuous color stimuli for all semantic words. This indicates that the assigning of colors to semantic words does not depend on the independent impression of a single or a few colors but rather on the set of neighboring colors in the hue circle or the systematic color changes in the simulated deutan color stimuli [4,5]. However, the model prediction tends to fail for the three neutral colors at the 95% significance level, as shown in our previous work [4]. In the normal color stimulus set (and in the simulated deutan color stimulus set), the rates of the model prediction failure (per word and per color) for the three neutral colors are 59.3% (51.9%) and 37.0% (33.3%) for the CVN and the deutan observers, respectively. The rates for the other twelve colors are 27.8% (15.7%) and 9.26% (9.26%), respectively. The failure rates are 2.1 (3.3) and 4.0 (3.6) times higher for the CVN and the deutan observers, respectively. Thus, these neutral colors may not be considered in the same hue circle, although these neutral colors can be fitted by the same ellipse in the distribution of the stimulus colors, except for black in the simulated deutan color stimuli for deutan observers.

In addition to the color distributions, the differences between observer groups are also indicated in the selection rate data and model fits. In both color stimulus conditions, the selection rates and model fits are similar in the first word category [Visible, Vigorous, Extreme], in which all observers tended to select yellow (v8) or close to yellow colors. In the second category [Massive, Deserted], in which dark colors (gray, v22, black, and v24) were more selected, the selection rates and model fits are also similar, although the data of [Massive] in the simulated deutan color stimulus condition look different. In the third category [Magnificent, Fine, Clean, Tranquil], in which CVN observes tended to select green to blue (v12, v14, and v18), the tendency of the selection rates are different between observer groups because deutan observers selected yellow and white more in the cases of [Magnificent, Clean, and Tranquil.] In the case of [Fine], the selection rate is almost the same between colors in deutan observers, suggesting that deutan observers could not select the color for the word [Fine] in the normal color stimulus condition. The deutan observers selected the dark blue (D-Mv24) in the simulated deutan color stimulus condition.

An interaction [Word * Color] was not statistically significant in the entire dataset, as shown in Table 1, but was statistically significant in the simulated deutan color stimulus set as shown in Table 2. In the normal color set, the colors at the peak of the modified selection rates were slightly different between words, but in the simulated deutan colors, the peak colors tended to be yellow (Dv8), white, or DMv24 (as shown in Fig. 7). Similarly, an interaction [Obs. CV type * Word * Color] was not statistically significant in the entire dataset but was statistically significant in both of the normal and simulated deutan color stimulus sets, as shown in Table 2. This suggests that each dataset had the same tendency in the modified selection rates with the same words, but the colors (e.g., the peak colors) are slightly different between the observer groups. This difference is represented in the difference in the order of colors, as shown in Fig. 5 and the order of colors in the abscissa in Figs. 6 and 7, although the smooth functions in Figs. 6 and 7 are similar between the normal and simulated deutan color stimulus sets in one observer group. (As shown in Table 3, the interaction [Word * Color] is not statistically significant in each observer group.)

The results of an ANOVA (not shown) indicate that in CVN observers, the modified selection rates of [Extreme, Massive, Deserted, Magnificent, Fine, and Clean] are statistically different between stimulus sets at the 5% significance level, except for the word [Clean], the differences can be observed in the difference of the colors at their peak. In deutan observers, the differences are significant in the rates of [Massive, Deserted and Clean]. Because of the larger error bars at the 95% confidence interval, the peak of the selection rates is not clear.

3. Word Distribution Expressed by Optimized Weight Coefficients of First and Second Principal Components of the Model (Exp. 1)

In the PCA, a set of scores was calculated for each evaluated word as a set of weight parameters of each PC’s contribution. A mapping of the scores of the first and second PCs for each word indicates how that word is expressed by sets of stimulus colors in comparison with the mapping of PC’s loading values (Fig. 5). The mapping of all words indicates a word distribution that reflects the meaning of the words defined (evaluated) by the stimulus colors. These scores, however, were the balanced values between all PCs and not optimized only for the first two PCs because the cumulative contribution rates of the second PC were not so high (from 73.1 to 79.6%). Thus, we thought that it would be more appropriate to use the optimized weight coefficients of the model for the first and second PCs, which were used in the fits shown in Figs. 6 and 7.

Figure 8 shows the distribution of semantic words obtained as the optimized weight coefficients for first and second PCs. The coordinates of the words were fitted by ellipses. The axes ratios were 0.559 and 0.222 in the normal color stimulus condition of the CVN and the deutan observers, and 0.496 and 0.279 in the simulated color stimulus condition of the CVN and the deutan observers, respectively. The highest axes ratio could be caused by the fact that the set of the normal color stimuli have wider variation of color appearance in the CVN observers. It could be followed that the axes ratio of the CVN observers was still higher in the simulated color stimulus condition than both of axes ratios in the deutan observers. There is a statistically significant difference in the word distribution evaluated by the normal color stimuli between observer groups ($p \lt {0.0001}$), although the color distribution of the loading values in the deutan observers was reasonably close to that in the CVN observers, as suggested by the figures [Figs. 5(a) and 5(b)] and the result of the ANOVA ($p = {0.2287}$). As shown in Fig. 8(b), the coordinates of seven words were almost on the lightness and yellow/blue lines, indicating that these words were evaluated differently only by the amount of the lightness or yellow/blue. Two words, [Extreme and Massive], were slightly shifted to the negative direction of the second PC. This follows the results of the previous study [4] and suggests that the appearance of the normal color stimuli are different between observer groups.

 

Fig. 8. Distribution of the semantic words obtained by optimized weight coefficients for the first and second PCs in the normal color stimulus condition of (a) CVN and (b) deutan observers and in the simulated color stimulus condition of (c) CVN and (d) deutan observers. Squares denote the coordinates of the semantic words shown near the symbol. The square colors denote the stimulus color of the maximum selection rate. The blue solid and red and yellow dotted lines denote the direction of lightness ($L^*$), red/green ($a^*$), and yellow/blue ($b^*$) from Fig. 5. Ellipses denote fits to all word coordinates.

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Fig. 9. Distribution of the nine core semantic words (denoted by sky-blue font), two important words (Warm and Soft, denoted by red squares and larger black font), and twenty-four semantic words (denoted by smaller black font) defined by the first and second PC loading values in (a) the CVN observers (${\rm{n}} = {{10}}$), (b) the deutan observers (${\rm{n}} = {{4}}$), and (c) the CVN and deutan observers (${\rm{n}} = {{8}}$). Semantic words are shown near their symbols. The symbol colors for the nine core semantic words were the most selected colors from Fig. 8(a), Fig. 8(b), and Fig. 8(a) for panels (a), (b), and (c), respectively. The dotted lines denote the orthogonal corner obtained by Warm and Soft (see the text for details). The abscissae and ordinate were flipped to match the directions of two important words, [Warm and Soft].

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Initially, we expected that the distribution of words evaluated by the simulated deutan color stimuli would be similar between observer groups since the color appearance of the stimuli should be very close. However, we found that the word distributions are significantly different in the ANOVA ($p = {0.0244}$). As shown in Fig. 5(c), the negative direction of the first PC in the CVN observers could be considered as the strength of color (saturation) or whiteness, but since the direction of saturation was 60.1° in the simulated deutan colors, it could be whiteness rather than saturation. The stimuli of the higher $b^*$ values correspond to the higher absolute first PC values in the negative. The coordinates of white is opposite to those of black. The angle of the major axis of the fitting ellipse in Fig. 8(c) to the lightness is 32.1° in the panel. The contribution of the first PC (61.4%) to the major axis is larger than the second PC (or lightness and yellow/blue, 38.6%). This suggests that the CVN observers tend to use chromatic (or whiteness) information of the stimulus colors in the word evaluation more than the intensity information (lightness). Contrarily, the deutan observer depends more on lightness and/or yellow/blue in the word evaluation. Although the word distributions of the deutan observers are statistically different between stimulus sets ($p = {0.0019}$), the color distribution of the loading values are not significantly different ($p = {0.9693}$) in the deutan observer, and lightness and yellow/blue are the key factors for the word evaluation. In the simulated deutan color stimulus, the deutan observers seem to use a little more chromatic (or whiteness) information since the contribution of lightness to the major axis of the ellipse is 70.0% in the simulated deutan color stimuli compared to the contribution in the normal color stimuli (98.5%). It is interesting that the directions of $a^*$ are largely different (123.9°) between the normal color and the simulated deutan color stimuli in the deutan observers, but the difference in the directions of the major axes is small (17.62°), suggesting that the influence of the $a^*$ difference should be less (see the Discussion section for details).

As in our previous work [4], the words can be separated into three categories of words from the word distributions ([Visible, Vigorous, Extreme], [Massive, Deserted], and [Magnificent, Fine, Clean, Tranquil]). The words in the last category are reasonably close to each other in Figs. 8(a) and 8(c), and on the lightness and yellow/blue lines [Fig. 8(b)], but they are distributed widely in Fig. 8(d).

Table 5. Probabilities of the Main Effects and Interactions by ANOVA in Exp, 2^a

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B. Evaluation of Color Impression by Means of the SD method (Experiment 2)

1. Factors Affecting Color Evaluation by Words in the SD Method

We conducted the other experiment involving the evaluation of color impression by means of the SD method using 35 paired semantic words. We also applied an ANOVA to the data of the color evaluation rating in Experiment 2 (Exp. 2). We involved four factors: the observer’s color vision type, the color stimulus set, fifteen stimulus colors, and thirty-five semantic words to evaluate the colors (SD words: [w1, w2, …, w35]). The total number of data was calculated in the same way in Exp. 1, except the number of semantic words was 35 in Exp. 2. Table 5 shows the probability, $p$, obtained by ANOVA. In the analysis for all the data (the second column), all four factors are statistically significant main effects. The probabilities in the interactions [Obs. CV type * SD word] and [St. set * SD word] show that the usage of the semantic words were not significantly different between the CVN and the deutan observers and between the normal color and the simulated deutan color stimulus sets. Thus, the PCA could be performed to one combined dataset. One set of the PC loading values could be shared in all conditions. Unlike the case in Exp. 1, the ANOVA results in Exp. 2 showed no change in statistical significance by using the divided datasets, in which the data were divided into CVN observer data and deutan observer data, and then divided into the normal color stimulus data and the simulated deutan color stimulus data (not shown in Table 5).

2. Word Distribution Expressed by Principal Component Loadings (Experiment 2)

The PCA was applied separately in ten CVN and four deutan observers to the sets of individual grading points for each semantic word to the fifteen colors (twelve hues, white, gray, and black). In this SD method, since only one color was presented in a trial of the grading task and the usage of semantic words should be the same between color stimuli in one observer group as supported by the ANOVA results in Table 5, we analyzed the data of the normal and simulated deutan color stimulus sets together. In the CVN observers the proportion of variance from the first to the fifth PCs were 35.9%, 21.4%, 11.1%, 3.8%, and 3.1%, respectively, and the cumulative contribution rates of the second PC was 57.2%. In the deutan observers, the proportions of variance were 33.1%, 20.6%, 11.4%, 8.1%, and 3.7%, respectively, and the cumulative contribution rate was 53.7%. The number of components determined by parallel analysis was four, as shown in Table 4 and Fig. 4(c). This means that it would be more appropriate to use four PCs to express the results of the PCA. However, as was the case in our previous study [4], the distributions of stimulus colors in the score values and the difference of them between observer groups looked too complex to be analyzed. The word distribution in the loading values and the color distribution of the score values defined by the third and fourth PCs are not shown in this study. In the results of the evaluation of the color impressions by semantic words, the loading values of the first and second PCs for each semantic word showed a 2D contribution of word to the evaluation of all colors through the first two PCs.

Figure 9 shows the distribution of semantic words defined by the first and second PCs loading values in the CVN (a) and the deutan (b) observers. In Fig. 9, the ordinate or the abscissae was flipped to match the direction of the axis to the score value data in Fig. 8. The word distributions of the loadings are basically similar between the CVN and CVD observers. As stated in the previous section, there was not a statistically significant difference in the word distribution between stimulus sets and observer groups. Thus, we analyzed one set of the data in four CVN and four deutan observers. The proportion of variance from the first to the fifth PCs were 33.5%, 21.5%, 11.2%, 5.4%, and 3.3%, respectively, and the cumulative contribution rates of the second PC was 55.1% in this combined dataset. The word distribution is shown in Fig. 9(c). The special meaning of two important words, [Warm and Soft], will be described in the Discussion section.

3. Color Distribution Expressed by Principal Component Scores (Experiment 2)

Figure 10 shows the distribution of twelve hues, white, gray, and black obtained from the first and second PC score values of the normal color stimuli in the CVN (a) and the deutan (b) observers and those of the simulated deutan color stimuli in the CVN (c) and the deutan (d) observers. The coordinates of the normal color stimuli were fitted by black and brown ellipses for the CVN and deutan observers’ data (white, gray, and black were excluded), respectively. The fitting ellipses for the data of the CVN and deutan observers are slanted ${-}{26.22}^\circ$ and $ {-} {0.64}^\circ$, and the axis ratios are 0.850 and 0.323, respectively. Since we used the common loading values in both observer groups, it was expected that the difference of the angle (25.6°) would reflect the difference of the dominant factor(s) to the color distribution. Thus, we calculated the correlation between the directions of lightness ($L^*$), red/green ($a^*$), and yellow/blue ($b^*$), and the coordinates of the score values for color stimuli without neutral colors (white, gray, and black). The directions of lightness (denoted by blue solid lines), $a^*$ (red dotted lines), and $b^*$ (yellow dotted lines) at the highest correlation coefficients are shown in Fig. 10. We would like to point out that these lines were not obtained from the loading values (as in Fig. 5) but from the final results (score values) of the color distribution. These correlations may reflect a pseudo-correlation.

 

Fig. 10. Distribution of twelve hues, white, gray and black obtained from the first and second PC score values in the normal color stimulus condition of (a) CVN and (b) deutan observers and in the simulated deutan color stimulus condition of (c) CVN and (b) deutan observers. Black-surrounded and brown-surrounded circles denote the means of the coordinates of the score values for each color of the normal color stimuli in the CVN and deutan observers, respectively. Blue-surrounded and orange-surrounded diamonds denote the means of the simulated color stimuli in the CVN and deutan observers, respectively. The color chip number and names in the PCCS are presented near each point. “CVN-” and “CVD-” denote the coordinates of the CVN and deutan observers, respectively. Black and brown ellipses denote the best fits to all the hue coordinates [neutral colors (white, gray, and black) excluded] in the CVN and deutan observers, respectively. Black and brown curves denote the best fits by cubic functions to color stimuli, except D-Mv2 and neutral colors in the CVN and deutan observers, respectively. The blue solid and red and yellow dotted lines denote directions of lightness ($L^*$), red/green ($a^*$), and yellow/blue ($b^*$) at the highest correlation coefficients (shown in panels) without neutral colors. The distribution of colors largely maintains the structure of hue circle in the first and second PC score values in the normal color stimulus condition, but the color distribution is on one curve in the simulated color stimulus condition in both the CVN and deutan observers.

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In the deutan observers the color distribution could be explained simply by the first and second PCs, which reflect the almost orthogonal response of the red-green ($a^*$) and the yellow-blue ($b^*$) color opponent responses. This result follows our previous findings that a deutan observer can treat colors (hues) in the structure of a hue circle without the perception of redness and greenness [4]. In contrast, in the CVN observers, the direction of lightness, $a^*$, and $b^*$ are not orthogonal. These points are similar to the structure of the color distributions in the loading values in Exp. 1 (Fig. 5). Further details about these points in the color distribution data of Exp. 1 are discussed in the Discussion (Section 4.A). Since the correlations may reflect the pseudo-correlation, as mentioned above, we did not use the data about these points from Exp. 2 in the discussion.

In addition, the direction of the major axis of the fitting ellipse does not match to the PC axes. On this point, this result does not match our previous study [4]. The distribution of normal colors largely maintains the structure of the hue circle, although some points are not on the ellipse, i.e., Yellow-Green (v10) and Violet (v20) in the CVN observers and Purple (v22) and Red-Purple (v24) in the deutan observers. The results of the SD method using one set of loading values confirmed that the hues are still treated as though they are in the hue circle and not compressed to one-dimensional scaling in the deutan observers. Further details of the dominant factors to determine the color distribution are provided in the Discussion section.

The color distribution of the simulated deutan color stimuli are completely different than that of the normal color stimuli. It was initially expected that the color distribution of the simulated deutan color stimuli would be fitted by one line. The color distribution in the score values in Exp. 2 could be fitted by the one curve that was obtained as the function of a cubic equation for the best fit to the coordinates of the color stimuli in the space. In the fits, neutral colors were initially excluded, and D-Mv2 was also excluded because the coordinates of D-Mv2 are far from the coordinates of the other colors. The order of the color stimuli on the curve reasonably corresponds to the order of the lightness and/or yellow/blue ($b^*$). These one curve fits suggest that the set of colors in the simulated deutan color stimuli could be recognized as the variation of colors in one dimensional and monotonic change, rather than the variations of colors on a hue circle.

4. DISCUSSION

A. Color Distributions in Experiment 1 and Experiment 2

The color distribution obtained in Experiment 1 (Exp. 1) was expressed as the loading values of the first and second PCs for each color of the normal color stimuli, which shows the contribution of colors in the evaluation of all words through the PCs. In the normal color stimulus condition the angles between red/green ($a^*$) and yellow/blue ($b^*$) are 101.2° in the CVN observers [Fig. 5(a)] and 92.2° in the deutan observers [Fig. 5(b)], and $a^*$ and $b^*$ are almost orthogonal. This indicates that in both observer groups the normal colors were treated similarly to the concept of red/green ($a^*$) and yellow/blue ($b^*$) in the CIE 1976 $L^*a^*b^*$ color space. Since the horizontal (the first PC) and vertical (the second PC) axes in the PCA loading coordinates reflect the directions to obtain the largest variance of items (colors) in order as explained in Section 2.E, the direction of the possible mechanism (i.e., $a^*$) depends on the color stimulus set. It is not contradictory that in the normal color stimulus condition the major and minor axes in the CVN observers did not match the horizontal axis and the vertical axes. Thus, it is quite natural that the color distribution in the CVN observers is similar to the hue circle of the PCCS color stimuli. As follows from our previous study [4], the color distribution of the normal colors in the deutan observers is also similar to the PCCS hue circle. Although the axis ratios of the color distribution ellipse is smaller than that in the CVN observers, the structure of the PCCS hue circle has been kept, wherein two colors placed at the antagonistic position in the hue circle have twelve differing numbers (ex. v4 and v16). In addition, these two color distributions are not statistically different.

Although these results follow the results in our previous study [4], it is still hard to understand that the color distributions in the normal color stimulus set between observer groups were similar because it was expected that the deutan observers do not have red-green chromatically opponent responses and do not use red/green ($a^*$) information in the treatment of colors. In the case of the deutan observers, we would like to mention that the contribution (the proportion of variance) of the first and second PCs are 58.0% and 15.1%, respectively, in the normal color stimulus condition, and 52.9% and 21.6% in the simulated deutan color stimulus condition, as shown in Section 3.A.2 and Fig. 4(b). The differences in the contribution between the first and the second PCs are much larger than those in the CVN observers (47.0% and 32.0% in the normal colors and 43.2% and 36.4% in the simulated deutan colors). This means that the color distributions in the deutan observers strongly depend on the first PC as compared to the first PC dependency in the CVN observer. Thus, this suggests that the deutan observers dominantly used yellow/blue ($b^*$) and/or lightness ($L^*$) in the treatment of colors in the paired comparison in Exp. 1. From this point of view, since in definition the second PC (vertical) axis is orthogonal to the first PC (horizontal) axis and the major axis of the fitting ellipse is orthogonal to the minor axis, it is not surprising that the direction of $a^*$ matches to the second axis and the major axis if the direction of $a^*$ is orthogonal to the direction of $b^*$ (and/or $L^*$). However, we regret to say that we cannot explain well why the correlation coefficient of $a^*$ ($r = {0.967}$) is as high as the correlation coefficient of $b^*\,(r = {0.926})$ and $L^*\;(r = {0.953})$. The correlation coefficient of $a^*$ should be quite low if the deutan observers failed to assess the strength of red/green in the normal colors. As we explained in the Method section (Section 2.B), we introduced saturation ($C^*$), but the direction of $C^*$ is -0.3° in the normal colors and ${-}{1.6}$ in the simulated deutan colors; the directions of $C^*$ are almost identical to those of $b^*$ and $L^*$. (Initially, the directions of $C^*$ are close to $b^*$ and $L^*$, respectively.)

Conversely, the color distributions in the simulated deutan color stimuli have statistically significant differences between observer groups in the ANOVA. But the order of the colors on the ellipses are similar. The difference could be caused by the 90° rotation in the color distribution. In the simulated deutan colors, the chromatic changes in a series of stimuli are monotonic from yellow to blue in the $b^*$ change and from light to dark in the lightness change. Nevertheless, the color distributions in both observer groups show the shape of the ellipses. These color distributions have one important feature compared to the color distributions in the normal color stimulus set, which is that there are widely open spaces in the distributions where the coordinates of white exist, as shown in Figs. 5(c) and 5(d). The gaps of the color distribution between D-v8 (Yellow) and D-v18 (Blue) are 73.7° (from 42.3° to ${-}{31.3}$°) in the CVN observers and 89.5° (from ${-}{6.9}^\circ$ to ${-}{96.4}^\circ$) in the deutan observers. This gap space corresponded to the blank of the color contribution which could be caused by the monotonic change of the colors. There is no color to evaluate words that correspond to this gap space except white. Thus, if there would be the coordinates of a word at this space, the impression of the word would be evaluated only by white or evaluated by D-v8 or D-v18 in a compromise. This may concern the fact that the directions of lightness ($L^*$), red/green ($a^*$), and yellow/blue ($b^*$) converge and are not orthogonal to each other in the color distribution of the simulated deutan colors in both observer groups, as shown in Figs. 5(c) and 5(d) [the direction of saturation ($C^*$) was also the same (not shown in Fig. 5)]. Rather, these directions are almost orthogonal to the direction from the origin to white.

This suggests that the circle shape of the color distribution is caused by the use of a selection rate and two-dimensional expression by two PCs. As shown in Figs. 6 and 7, the modified selection rates were fitted by the first and the second PCs optimized by the weight values. The optimized weight values of each PC can be positive or negative, but the minimum contribution of one PC is expressed by zero. The positive and negative peaks of the modified selection rates had to be fitted by two optimized weight values. As long as the absolute values of the positive and negative peaks are almost the same (because of the ratio of the win–loss results) and each PC function corresponds to a zero average in all color stimuli due to the paired comparison method, the distance from the origin to the coordinates of the colors in the two-dimensional space of the optimized weight values should be the same, or at least close to each other. Thus, the coordinates of color stimuli can be fitted by an ellipse. In other words, the ellipse shape of the loading values is not caused by the structure of the color stimuli (i.e., hue circle), as previously expected [5], but by the paired comparison method. Thus, it can be expected that if the color change is one directional and can be expressed by only one factor or by one combined factor [i.e., yellow/blue ($b^*$) and/or lightness ($L^*$) in this case], the color distribution can be explained by that factor determining the order of the stimulus colors and by the ellipse (circle) determining the circle shape of the stimulus colors in two-dimensional coordinates (i.e., the coordinates of the first and second PCs). Under this viewpoint, the second factor is not necessarily needed to explain the color distribution of the simulated deutan color stimulus condition.

The color distributions obtained by the SD method in Exp. 2 tend to reflect more of the structure of the original color stimuli, as expected from our previous studies [4,5]. In the normal color stimuli, the color distributions of both observer groups could be largely fitted by the ellipses, and the coordinates of the normal color stimuli were in order of the color code number corresponding to the gradual hue change. However, unlike the hue circle in the loading values, the structure of the antagonistic relations in the PCCS hue circle was not kept, as shown in Figs. 10(a) and 10(b). The reason for this is discussed in Section 4.C. The distribution of the simulated deutan color stimuli were on one curve instead of on an ellipse. Because we had no model to fit the coordinates of colors in this space, we simply fitted the coordinates of colors by cubic functions. The fitting curves are not simple horizontal lines, which are simply determined by the first PC, yellow/blue, or lightness in both observer groups, but a curve modulating to the vertical directions, as shown in Figs. 10(c) and 10(d). We suspect that it could be caused by the fact that the simulated deutan color stimuli were not perfectly aligned in one dimension in the CIE 1976 $L^*a^*b^*$ color space, Rather, stimuli were on the curve reflecting the reduced stimulus lines in the CIE 1931 color space, as shown in Fig. 3. If that would be the reason for the modulation in the space of the first and second PC score values, then the fitting lines in the fourth and second quadrants would be shifted to the positive and negative directions of $a^*$, respectively. The modulations in the fitting curves shown in Figs. 10(c) and 10(d) qualitatively satisfy this hypothesis. We discuss this issue further and the reason that the coordinates of D-Mv2 are not on the curve in Section 4.C.

Overall, the color distributions of the normal colors are reflecting the original hue circle of the PCCS both in Exp. 1 and Exp. 2. The color distributions of the simulated deutan colors are reflecting one dimensional change distorted by other factors: the ellipse shape caused by the (modified) selection rates in the paired comparison in Exp. 1 and possible red/green influence in Exp. 2. As we stated, it is still not clear how red/green information could influence the color distribution in the deutan observers.

B. Word Distributions in Experiment 1 and Experiment 2

The categories of semantic words in the word distributions from the results of experiments are shown in Table 6. The categories, including the words of “Vigorous,” “Tranquil,” “Clean,” “Deserted,” and “Extreme,” were painted in this word order by arbitrary colors for better presentation in Table 6. In our direct word evaluation using (only) three core scales [Activity (active-inactive), Potency (superior-inferior), and Evaluation (beautiful-ugly)] in the SD method [5], the nine semantic words were separated conceptually into five categories by the distance in the space of the Activity and the Evaluation axes: [Extreme, Visible, Vigorous], [Magnificent, Clean], [Tranquil, Fine], [Massive], and [Deserted] (the order was adjusted for better presentation in Table 6). In the evaluation of words using color stimuli (Exp. 1), the word distribution had three or four categories in the CVN observers: [Extreme, Visible, Vigorous], [Magnificent, Clean, Tranquil, Fine], and [Massive, Deserted] (or [Massive], [Deserted]). In the deutan observers the word distribution has five or four categories, as shown in Table 6.

Table 6. Categories of the Semantic Words in Word Distributions^a

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In the color evaluation of 35 words in the SD method (Exp. 2), the word structure of the first and second PC loading values shows six categories with different members in the combined CVN and deutan observers: [Visible, Vigorous, Magnificent], [Clean], [Tranquil], [Fine], [Extreme, Massive], and [Deserted]. In the results of Exp. 2 “Extreme” is not in the category of “Visible” and “Vigorous,” but it is in the category with “Massive.” Except for this case, the categories of words are relatively stable, and the change of members can be expressed by the changes of the category borders as shown in Table 6. This means that the meaning of the semantic words are influenced little by the color stimulus sets and observer’s color vision type as can be reasonably expected.

C. Dominant Factors and Mechanisms to Determine the Color and Word Evaluations

It was initially expected that the color distribution of the simulated deutan color stimuli were completely different with that of the normal color stimuli. Since the simulated deutan color stimuli were basically on the reduced stimulus lines of the deutan color appearance simulation, it was expected that the word distribution in the score values (the optimized weight values) in Exp. 1 and the color distribution in the score values in Exp. 2 would be close to a one-dimensional structure similar to the distribution on two lines, as shown in our previous study [4].

The word distributions of the deutan observers indicate more compressed structure in the direction of the minor axes of the fitting ellipses, as shown in Figs. 8(b) and 8(d). The coordinates of seven words are on or close to the line of lightness ($L^*$) or yellow/blue ($b^*$) in the normal color stimulus condition [Fig. 8(b)]. However, the word distributions still look like a hue- circle shape. It is difficult to find the dominant factors only from the word distribution if the direction of the lightness ($L^*$), the red/green ($a^*$), and the yellow/blue ($b^*$) are not orthogonal but close to each other (i.e., in the case of the simulated deutan color stimuli). The color distribution of the normal color stimuli in the deutan observers [Fig. 5(b)] suggests that the deutan observers could still recognize the large difference of red/green ($a^*$) using other factors, e.g., lightness ($L^*$) and yellow/blue ($b^*$). The color distributions in the score values in Exp. 2 suggest that in both observer groups lightness is one of the dominant factors, and red/green ($a^*$) or yellow/blue ($b^*$) could be the other factor. As stated in Section 4.A, the color distribution of the simulated deutan color stimuli in the CIE1976 $L^*a^*b^*$ color space suggests that the shift of the coordinates of the color stimuli could be caused by the effect of the difference in $a^*$. However, the direction of $a^*$ and $b^*$ are relatively close in both observer groups. Similarity of the color distribution between observer groups [Figs. 10(c) and 10(d)] suggests that yellow/blue ($b^*$) seems to be the other dominant factor because the variation of $b^*$ is much larger than the variation of $a^*$ in the simulated deutan color stimuli, and deutan observers could not detect the difference of red/green ($a^*$) well. Overall, we suggest that since the $a^*$ difference in the simulated deutan color stimuli was too small to be detected by the deutan observes, it would be expected that the modulation of the coordinates of the stimuli on the curve [Figs. 10(c) and 10(d)] reflects the effect of the yellow/blue ($b^*$) difference in the stimuli, which would be combined with the difference of lightness.

In the CVN observers’ data in Exp. 2 [Fig. 10(a)], the directions of red/green ($a^*$) and yellow/blue ($b^*$) are not orthogonal, and the direction of the major axis does not match to the direction of the PCs. This could be caused by the observation condition in the SD method. The observers looked at only one color at once in the SD method and they observed only fifteen colors in one session in about one hour. Unlike the observations of 3780 colors (two colors in 1890 trials) in the paired comparison method, the whole structure of a color stimulus set were not recognized strongly. If so, then the gradual change of redness or greenness, and yellowness or blueness in the series of color stimuli were not used in the color evaluation. Thus, the directions of $a^*$ and $b^*$ at the highest correlation coefficients do not reflect the dominant mechanism of the color distribution. Rather, the dominant color in the color appearance of the color stimulus could be important. As shown in Fig. 10(a), in the CVN observers, Red (v2) is on the first PC axis and has the largest value in the abscissa, and Green (v12) is close to the second PC axis and has the largest value in the ordinate. In the deutan observers [Fig. 10(b)] Yellow (v8) and White (white) are close to the first and second PC axes, respectively.

Concerning this hypothesis, we would like to discuss the reason why the neutral colors are not on the fitting ellipses or fitting curves. One possible reason is that in this PC score value space, the color distribution is determined by the hues reflecting the red-green and yellow-blue color opponent responses, and these neutral colors could not be positioned in the space well. This hypothesis qualitatively explains that the coordinates of the neutral colors are not aligned on the lightness and yellow/blue directions denoted by the blue and yellow dotted lines in Fig. 10. However, it does not seem that the neutral colors are randomly distributed. The coordinates of White and Black are moderately close to the positive and negative parts of the second PC axis, respectively. The color distributions in Exp. 2 suggest that a white-black connected line is not reflecting lightness or yellow/blue. Rather, white and black could be treated as if White and Black are one of the hues. The words “Clean” and “Massive” tended to be assigned by White and Black, respectively. In other words, the color distribution is not so strongly influenced by the lightness scale, but if the colors are white, black, or closer to these neutral colors, then the impression of these colors are expressed differently in the evaluation by words.

Recently, it is no longer considered that the color change between white, gray, and black is one of color opponencies, so called as the white-black color opponent channel [43]. Rather, the perception of blackness is caused by the center-surround relationship, which is not like regular hues [44,45]. But it influences the color appearance, especially the perception of brown [46], and could have an important role in color impression. This hypothesis would also be able to explain the reason why the coordinates of D-Mv2 are not on the fitting curve. As observed in Fig. 1, D-Mv2 looks darker than other non-neutral color stimuli. Thus, D-Mv2 was treated as the dark or blackish color, and the coordinates of D-Mv2 were shifted toward the negative direction of the second PC. Under this hypothesis we did not include D-Mv2 in the curve fit in the simulated deutan color stimuli.

The results of previous literature [38,39] about the color distribution measured by the SD method indicated that the directions of Warm and Soft in the loading value space are orthogonal and robust to the set of stimulus colors. The author, Kobayashi, proposed the color distribution “Image Scale” in which all colors are structured by three axes. The first axis is the Warm-Cool axis relating to hue, the second axis is the Soft-Hard axis relating to lightness, and the third axis is the Clear-Grayish axis relating to turbidity of color. The results of this study in Exp. 2 show some differences with Kobayashi’s studies [38,39]. In this study the direction of the Warm and Soft are orthogonal in the space of the loading values and close to the first and second PC axes, following his studies. However, the colors were not placed in a series of hues on the abscissa or in a series of lightness on the ordinate, as shown in Fig. 10. The reason of this differences is not clear yet, but it could also be explained by the influence of the number of color observations per session. In his studies, the color evaluation was performed only by three paired words, and the observer could look at many colors in a short time, suggesting that his observers could recognize the gradual change of hue, saturation, and lightness in color stimuli.

In the relation between color distributions and word distributions in the deutan observers, it must again be considered (as stated in the Introduction section) what color a deuteranope recognizes as the presented color. That is to say, if a presented color would be the simulated deutan color that was defined as the converted color (ex. dark yellow) by the deuteranope’s color appearance model from a normal color (ex. red) defined by the color appearance of normal trichromats. Regarding, the color distribution of the deutan observers, as stated in Section 4.A, the color distributions of the normal colors are reflecting the original hue circle of the PCCS both in Exp. 1 and Exp. 2. The color distributions of the simulated deutan colors are reflecting one- dimensional change distorted by other factors, the ellipse shape in Exp. 1 and possible red/green influence in Exp. 2. However, the white-black line can also contribute to the color and word distributions in the deutan observers. The distributions of White and Black in the color distributions in Exp. 2 (Fig. 10) are similar between observer groups, although the directions of the white-black line in the color distributions in Exp. 1 are similar only in the simulated deutan colors. In the word distribution, not only in the words “Clean” and “Massive” as with the CVN observers but also in all other words except “Extreme” (the words “Visible,” Vigorous,” “Deserted,” “Magnificent,” “Fine,” and “Tranquil”), White and Black tend to be assigned at the positive and/or negative peaks.

These results suggest that the deutan observers dominantly use yellow-blue color opponent responses ($b^*$) or that combined with lightness ($L^*$) in color and word evaluations and collaterally can use white-black responses in appearance (but not the lightness). Similarly, the CVN observers can use the white-black responses in the evaluation using the simulated deutan colors, but the relation between the white-black responses and the appearance of other stimulus colors is not clear since we used one (vivid) tone in the PCCS, which has little blackness in appearance. In addition, the deutan observers could recognize the difference between the normal color stimulus set and the simulated deutan color stimulus set not only in terms of the difference between these sets but also in terms of the structure of the stimulus colors in the color distributions, as shown in Figs. 5(b) and 5(d) in Exp. 1 and in Figs. 10(b) and 10(d) in Exp. 2. However, we cannot explain why the deutan observers could know the difference of the structure of stimulus colors since we still cannot explain well why the correlation coefficient of red/green ($a^*$) is as high as the correlation coefficient of yellow/blue ($b^*$) and lightness ($L^*$), as stated in Section 4.A.

5. CONCLUSION

The purpose of this study was to investigate the difference between the normal colors and the simulated deutan colors in CVN and deutan observers. We investigated chromatic representation of semantic words by Thurstone’s paired comparison method in Exp. 1 and semantic representation of colors by the SD method in Exp. 2. The data of ten CVN observers (nine male and one female) and four deuteranopes (all male) were analyzed. The normal color stimulus set consisted of twelve chromatic colors selected from the vivid tone of the Practical Color Coordinate System (PCCS) and three neutral colors (white, gray, and black). The simulated deutan color stimulus set was obtained by an algorithm using Brettel–Viénot–Mollon’s model with its projection onto a reduced stimulus surface defined for deuteranopes.

The modified selection rates for each semantic word and colors were obtained in Exp. 1. The ANOVA indicated that the CVN observers recognized the two sets of color stimuli were totally different, but the deutan observers recognized the two sets as similar. In the normal color stimulus condition the distribution of colors on the ellipse were in the order of their code number reflecting the hue circle of the PCCS. In the simulated deutan color stimuli, colors distributed in the order of yellow/blue ($b^*$) values. In the color distribution of the simulated color stimuli, there were widely open spaces in the distributions where only the coordinates of white existed, regardless of the observer groups. The comparison of the color distributions between the normal and simulated deutan color stimuli suggests that the circle shape of the color distribution is caused by the use of a selection rate and two-dimensional expression by two PCs and depends less on the color variation of the stimulus set. The modified selection rates could be fitted by the first and second PCs with no offset. We used the optimized weight coefficients of the model for the first and the second PCs to show the distribution of the semantic words. The coordinates of seven words were almost on the lightness line in the normal color stimulus condition of the deutan observers, indicating that these words were evaluated differently only by the amount of the lightness and/or yellow/blue ($b^*$) and suggesting that the appearance of the normal color stimuli is a one dimensional and monotonic series of colors in the deutan observers. We expected initially that the distribution of words evaluated by the simulated deutan color stimuli would be similar between observer groups since the color appearance of the stimuli should be very close. However, the coordinates of the words in the CVN observers distributed wider than those in the deutan observers. In the deutan observes the tendency of the word distribution was similar between stimulus sets. Nevertheless, the categories of words are relatively stable, and the change of members can be expressed by the changes of the category borders. This means that the meaning of the semantic words are influenced little by the color stimulus sets and observer’s color vision type, as was expected.

An ANOVA of the data of color evaluation by words in the SD method (Exp. 2) indicated that the word distribution as the loading values are not statistically different between stimulus sets and observer groups. Thus, the loading values were calculated from one set of data, including both stimulus sets and both observer groups. The color distributions of score values in the normal color stimuli were on the fitting ellipses, suggesting that the hues are still treated in the hue circle and not compressed to one-dimensional scaling in a deuteranope. The color distributions in the score values of the simulated deutan color stimuli were completely different from those of the normal color stimuli and could be fitted by cubic functions. The vertical modulation of the coordinates of the stimuli could reflect the effect of the yellow/blue ($b^*$) difference in the stimuli in combination with the difference of lightness.

In the color impression measured in Exp. 2, the color opponency, indicated by the directions of $a^*$ and $b^*$, may not reflect the dominant mechanism of the color distribution. Rather, the dominant color in the color appearance in each color stimulus could be important. In the CVN observers, Red (v2) was on the first PC axis and had the largest value in the abscissa, and Green (v12) was close to the second PC axis and had the largest value in the ordinate. In the deutan observers, Yellow (v8) and White (white) were close to the first and second PC axes, respectively. In both observer groups, the coordinates of White and Black were moderately close to the positive and negative parts of the second PC axis, respectively. The color distributions in Exp. 2 suggest that a white-black connected line is not reflecting the lightness. Rather, white and black could be treated as if White and Black are one of the hues. The words “Clean” and “Massive” in the CVN observers and all other words except “Extreme” in the deutan observers tended to be assigned to White and Black, respectively.

The color distribution is not so strongly influenced by the lightness scale, but if the colors are white, black, or closer to these neutral colors, then the impression of these colors are expressed differently in the evaluation by words. Overall, the results in this study suggest that the deutan observers dominantly use yellow-blue color opponent responses ($b^*$) or those combined with lightness ($L^*$) in color and word evaluations and can collaterally use white-black responses in appearance. The deutan observers could recognize the difference between the normal color stimulus set and the simulated deutan color stimulus set not only in terms of the difference in these sets but also in terms of the structure of the stimulus colors in the color distributions.