1. INTRODUCTION

We previously showed that impressions of nine semantic words expressing abstract meanings (like “tranquil”) can be expressed by hues [12 vivid colors in the Practical Color Co-ordinate System (PCCS)] using a paired comparison method (Experiment 1) on 10 color vision normal (CVN) observers [1]. Color impressions were also estimated by a set of 35 semantic words using a semantic differential (SD) method (Experiment 2) [1]. In the study, the data of Exp. 1 and Exp. 2 were analyzed by principal component analysis (PCA) [1]. A two-dimensional distribution of the first and second principal component (PC) loadings revealed how the set of hues was structured to express all word impressions; a 2D distribution of the first and second PC scores showed the structural relationship between words when the words were evaluated by hues. From the SD method data obtained in Exp. 2, a 2D word distribution of loadings and a 2D color distribution of scores were obtained. Since the relationship between words and colors were measured twice in reverse directions, differences between the two distributions of the words or colors indicate the stability and appropriateness of the word-color relationship [1].

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. As confirmed by the results of the SD method [2,3], regarding the case of expressing a simple meaning like “cold,” the relationship between the meaning expressed by a word and a color (which can be referred as color-word association) is relatively simple and tight; the impression of one color (i.e., dark blue) tends to be associated with a simple word meaning (i.e., cold) by daily experiences when the color is isolated from complex environments and situations that are commonly referred to as “context.” As we previously described [1], in the case of a simple semantic word like “cold,” it is easy to obtain a color having the same or a close meaning through the color-word association by retroactive reflection on the impression of the word “blue” or “bluish color.” Thus, it is expected that in many simple-meaning semantic words, the impression of a word can be obtained via the memorized color impression under the color-word association obtained by experiences [1]. We tested a possible expansion of this concept; we tried to answer “whether the impression of semantic words representing complex concepts (such as ‘tranquil’) can be expressed by selection of colors, since we usually do not have experiences connecting such words to colors” [1].

We have been interested in the possibility that the data set showing the relationship between semantic words and colors will be doubled; if the impressions of semantic words could be evaluated in terms of colors as being in the opposite direction of the usual evaluation tasks when the color impression is measured by the SD method. Total analysis of that data set could indicate a bidirectional relationship. If there is a bidirectional relationship between semantic words and hues, and if it is stable in the same observer group, the two distributions of the word impressions should be similar after linear expansion and rotation. If there is no bidirectional relationship to which the coordinates of words correspond, it would be too artificial to connect such semantic words to hues. Thus, we used the comparison of the coordinates of the words to show the appropriateness of connections between words and hues, as this comparison enables us to classify the association between the hue and the semantic element [1].

The reason to investigate the bidirectional relationships between words and colors concerns color design and color psychology. Designers of products have to select colors to make design objects most attractive and comfortable. One possible (and the simplest) method is to compare alternative colors for objects in environments where the objects will be used; however, this kind of comparison is not necessarily practical because of time limitations and the variation between users. One more sophisticated solution is to have universal color-impression maps measured by a SD method [2]. In the SD method, each color is evaluated in the context of many semantic word pairs of antonyms (positive and negative meaning words) with a set of grade points (e.g., $ - {3} \sim {0} \sim {3}$) [4,5]. All colors’ sets of the grade points are then subjected to factor analysis (FA) to find a few dominant factors that can explain the tendencies of the color impression. Previous studies suggested two main factors, “Heat (warm-cool)” and “Softness (soft-hard),” to explain a color distribution in a factor-axes space [2,3]. More recent studies suggest three main factors, “Activity (active-passive),” “Weight (heavy-light)” and “Heat” [6], and two additional factors, “Brightness” (Lightness) (light-dark) and “Softness” [7]. “Activity” was one of three core factors [Activity, Potency (superior-inferior or powerful-powerless), and Evaluation (beautiful-ugly or favorable-unfavorable)] in evaluation by the original SD method [4,5]. Thus, it is natural that “Activity” would be used in explanations of color distribution. On the contrary, “Potency” was expressed by “Weight” and “Heat.”

When we think about color psychology, first we have to understand how the set of colors is conceptually recognized and linked to semantics, although it is difficult to define and operationalize the concept of color and color recognition. In the process to approaching these concepts, we at least have to think about the methodology to measure and analyze the structure of color impression. As described above, the most common method to measure color impression is the SD method, and the data is regularly analyzed by FA; however, we used principal component analysis (PCA) to analyze the SD method data [8]. This can be considered as a special application of FA so as to constrain the axis directions to make the variance between items maximum in distribution. In most cases of FA, factors were obtained by a cluster of semantic words that have similar directions in their word distribution map; however, the purpose of this study was not to find new factor names but to investigate the structure of color and word distributions. Instead of the direct measurement of color impression, features of colors were used to find the conceptual structure of colors. For that purpose, multi-dimensional scaling (MDS) is a useful method to obtain the distribution of elements that depends on the defined “distance” between elements. Color distributions have been measured by distance using such categories as large chromatic difference [9], similarity [10], discriminative reaction time [11], and dissimilarity [12].

Our previous study indicated that the semantic words could be associated by hues; “for the word ‘Vigorous’ the most frequently selected color was yellow and the least selected was blue to purple; for ‘Tranquil’ the most selected was yellow to green and the least selected was red” [1]. PCA of the selection data indicated that “the cumulative contribution rate of the first two components was 94.6%, and in the 2D space of the components, all hues were distributed as hue-circle shape” [1]. In addition, comparison with additional data of color impressions measured by the SD method suggested that “most semantic word impressions can be stably expressed by hue, but the impression of some words, such as ‘Magnificent’ cannot” [1]. These results suggest that semantic word impression can be expressed reasonably well by color, and that hues are treated as impressions from the hue circle, not from color categories [1].

We expected that this approach would help to investigate the unsolved question of how a color vision deficient (CVD) observer treats the relationship between their color appearance and associated meanings of colors. For example, in Red-Green color-deficient observers such as protanopes and deuteranopes, it is expected that reddish colors do not have strong colorfulness [13]. Even if so, will the Red-Green color deficients treat vivid (bright and saturated) Red as a “vigorous” color? Previous studies using the MDS investigated the difference of the color distribution between CVN and CVD observers [9–12]; however, because they used the “distance” of color properties, their results cannot answer this question about the word-color relationship directly. In this study, one hypothesis could exist if one condition would be satisfied; the condition was that the color distribution of PCA score values from the SD method data (Exp. 2) in the CVDs and the color distribution of PCA loading values from the paired comparison data (Exp. 1) in the CVNs and CVDs would match to the original hue circle of vivid PCCS colors. Then, this first hypothesis could exist that the colors in the evaluation by semantic words in the SD method (Exp. 2) in the CVDs would either be treated in the same color structure as the one of the CVN observers, or the meanings of the semantic words in the SD method (Exp. 2) would have been well shifted by experiences in the CVD observers to make the color distribution match, even though the color appearance would be different between the CVD and CVN observers. In the same way, the second hypothesis could exist under the second condition in which the word distribution of score values obtained by the paired comparison of colors (Exp. 1) in the CVDs would match the word distribution of loading values obtained by the SD method (Exp. 2) in the CVNs and CVDs. The second hypothesis could be either that the words evaluated by hue in the paired comparison (Exp. 1) in CVDs would be treated in the same word structure in the CVNs, orthat the colors in the paired comparison method (Exp. 1) in the CVDs would have been well shifted accidentally to make the word distribution match the CVNs’ distribution. The results of the present study indicated that the first condition was satisfied and the second condition was not; it might suggest that the first hypothesis would be true and the second hypothesis would not. The potential explanation should be one of the following two. The first possible explanation is that the color structures in the SD method were the same between the CVN and CVD observers; however, in the paired comparison, the color structures were not the same or the color structure of the CVD observers was not well shifted. The second explanation is that the meanings of the semantic words in the SD method were well shifted between observers; however, the word structure was not the same in the paired comparison. Both of the explanations are difficult to accept because of the asymmetrical results between two experiments, and this issue will be elaborated on in the Discussion section.

In this study, White, Gray, and Black were added to the 12 hues in the paired comparison method (Exp. 1) because these neutral colors had already been used in the SD method (Exp. 2) since the previous study [1]. Ten CVN and 10 CVD observers participated, and the data of nine CVN and seven CVD observers (one protanope and six deuteranopes) were analyzed by the PCA separately. Since Kendall’s coefficient of concordance is relatively high, we also applied the PCA to one set of data of five CVN and five deuteranopes together; this procedure made common sets of loading values, and thus the score values of the CVNs and deuteranopes can be compared directly without expansion and/or rotation.

2. METHODS

A. Observers

Nine CVN observers (6 female and 3 male) of age 20 to 24 (mean: 22.3) and 10 CVD observers (one protanope, six deuteranopes, one protanomalous observer, and two deuteranomalous observers; all male) of age 19 to 22 years old (mean: 21.2) participated in the experiments involving evaluation of word impression by hue (Exp. 1) and evaluation of color impression via the SD method (Exp. 2). All CVN observers and one CVD observer were Japanese students of the Kochi University of Technology (KUT), and the seven CVD observers were Japanese students of the Kanazawa Institute of Technology (KIT); two CVD observers were Japanese students at a technical college. All KIT student observers were tested at the KIT campus. Six CVN observers had participated in our previous study [1] and were naïve regarding colorimetry and the purpose of each experiment; three CVN observers (1 male and 2 female) and all CVD observers newly participated in the experiments and were naïve regarding colorimetry, color psychology, and the purpose of each experiment; the authors did not serve as observers. One other new CVN male observer participated in the experiments; however, he could not complete all sessions because of difficulty with the tasks in Exp. 1.

All observers had normal or corrected-to-normal acuity with best-corrected visual acuity (BCVA) better than 0.6 (1.67 min. of visual angle). The color vision of 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). We did not use the Farnsworth–Munsell 100 hue test and the Cambridge Color Test (CCT) for the color vision test because the influence of the aging effect can be ignored in the ages of the observers [14]. We used the Neitz OT II anomaloscope (LED lamp model, Neitz co. Ltd.) to classify color-deficient observers. One protanope and six deuteranopes could make anomaloscope matches over the full range of R/G setting (0–75), indicating that they were dichromats [15]. Two anomalous observers were classified as severe deuteranopes by other tests; however, they showed relatively small R/G setting range in the anomaloscope test. Thus, although all anomalous observers completed all color vision tests and experiments, we did not include these anomalous observers’ 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 [14–16].

The procedures and experiments described in this study conform to the principles expressed in the Declaration of Helsinki and were approved by the Kochi University of Technology Research Ethics Committee (the receipt number: 7-C11). Written informed consent was obtained from each observer prior to testing. Under the approval of the research ethics committee, brief explanations about color vision testing was performed by the authors after all color vision tests for each observer; after all experiments, details of color vision deficiency were explained to the CVD observers upon request.

B. Apparatus and Calibration

Color stimuli were presented on a 19-inch (48.3 cm) CRT monitor (CPD-G220, Sony Corporation) placed at KUT and on a 27-inch (68.6 cm) LCD monitor (ColorEdge CS2730, EIZO Corporation) placed at KIT; the monitors were placed in dark rooms with no illumination. The distance between the monitor screen and subject eyes was 55.0 cm at KUT and 73.0 cm at KIT. In one trial of this study, all color stimuli were fixed in luminance and chromaticity coordinates, and we set RGB values of all color stimuli before the session. The accuracy of color stimuli was determined by calibration of each color stimulus, and the gamma functions of the monitors were not used to determine the RGB values of these stimuli. We asked the observer to respond using a left-or-right judgement in a paired comparison (Exp. 1) through a ten-key board that had only the 4, 6, and enter keys. All other responses were handwritten by the observer and the experimenter.

Chromaticity coordinates and luminance of all colors in the stimuli were measured by colorimeter (CS-200, Konica-Minolta, Inc.) and spectral radiometer (CS-1000, Konica-Minolta, Inc.) at KUT. The monitor used at KIT was calibrated again after shipping by a colorimeter (CS-150, Konica-Minolta, Inc.) at KIT. Other details are the same as our previous study [1].

C. Color Stimulus

Twelve stimulus colors were selected from vivid tone (24 color chips) in the PCCS by Japan (Nihon) Color Research Institute: v2(R) [=Red], v4(rO) [=reddish-Orange], v6(yO) [=yellowish-Orange], v8(Y) [=Yellow], v10(YG) [=Yellow-Green], v12(G) [=Green], v14(BG) [=Blue-Green], v16(gB) [=greenish-Blue], v18(B) [=Blue], v20(V) [=Violet], v22(P) [=Purple], and v24(RP) [=Red-Purple]. The tone is a core concept of the PCCS that combines both lightness and saturation; in one tone, lightness and saturation are simultaneously and systematically changed in different hues to make one impression. All tones are called by the impression of the tone: “Pale,” “Light-grayish,” “Grayish,” and “Dark-grayish” in most desaturated colors; “Light,” “Soft,” “Dull,” and “Dark” in moderately saturated colors; “Bright,” “Strong,” and “Deep” in saturated colors; and “Vivid” in mostly saturated colors. In the vivid tone, the lightness of the chips was systematically changed from /10 to /14 in Munsell Value to create the most-saturated colors in different hues, instead of keeping equal lightness or luminance; the yellow chip has the highest lightness, and the blue, purple, and violet chips have the lowest lightness. Three neutral colors were added to 12 hues: White, Gray and Black, which were the same as D65 on the white standard plate, background gray, and the black of the border line, respectively. The luminance and chromaticity coordinates of stimuli for the monitor presentation were calculated from spectral reflectance of chips and D65-illumination simulation; the luminance of D65 on the monitor was set to ${77}.{4}\;{{\rm cd}/{\rm m}^2}$ using the spectral reflectance of a standard white plate. Luminance of the gray background was ${12}.{7}\;{{\rm cd}/{\rm m}^2}$, which is equivalent to N4.7 in the Munsell system. Thus, there was no blackness induction on the colors of the rectangles [17,18].

 

Fig. 1. Twelve stimulus colors and neutral colors [White (D65), Gray (N4.7), and Black]. (Top panel) Diamonds, squares, and crosses denote lightness ${\rm L}^*$ of protanope, deuteranope, and color vision normal, respectively (see text for details). (Bottom panel) Color chip number and PCCS names are presented near each point. The circle and cross denote chromaticity coordinates of Gray (N4.7) and White (D65), respectively. Red thin-dotted curves and green thin-solid curves are protan and deutan confusion lines for each stimulus color, respectively. Red thick-dotted curves and green thick-solid curves are protan and deutan confusion lines of White in ${77}.{4}\;{{\rm cd}/{\rm m}^2}$. The outer gray curve denotes the gamut of the monitor. Black ellipse and black solid lines denote the best ellipse fits to 12 hues and short and long axes, respectively. The distribution of 12 stimulus colors consisted of a hue circle in color appearance space with smooth lightness change.

Download Full Size | PDF

In the calculations for test stimulus and data analysis of this study, we assumed that the deuteranopes had L and S cones, which are the same in spectral sensitivity as those of color normal observers, and that the protanope had M and S cones. Luminous efficiency functions for the protanope and deuteranope were assumed to be the same as the sensitivities of the M cone and L cone, respectively. We used Smith–Pokorny’s cone fundamentals [19] and CIE 1931 color matching function [20] with the cone matrix by Kaiser and Boynton [21].

Figure 1 shows ${\rm L}^*$ (top panel), and ${{\rm a}^*}$ and ${{\rm b}^*}$ (bottom panel) of stimulus colors in CIE 1976 (${\rm L}^*, {\rm a}^*, {\rm b}^*$) Color Space defined by the International Commission on Illumination (CIE). The protan and deutan lightness ${\rm L}^*$ were calculated using the protan and deutan luminous efficiency functions, respectively. The protan and deutan confusion lines (curves) defined by CIE 1931 $xy$ chromaticity coordinates and luminance of each stimulus color are also presented; the co-punctual points of the protan and deutan were (${\rm x}, {\rm y}) = ({0.7465}, {0.2523}$) and (1.4, $ - {0}.{4}$) in CIE1931xy, respectively. Since ${{\rm a}^*}$ and ${{\rm b}^*}$ depend on luminance, the confusion curves for Gray (N4.57) and White (D65) are different. The gamut of the monitor was calculated using the luminance of three stimulus colors that were closest to the gamut curve at the top, left-bottom, and right sides. In the theoretical deuteranope, the chromatic appearances (${{\rm a}^*}$ and ${{\rm b}^*}$) of v2 (Red) and v12 (Green) are almost identical. However, the color-naming study [22] demonstrated that protanopes and deuteranopes can identify Red and Green to monochromatic lights in a color-naming task when colors were presented for a 2 s duration (although the 95% confidence levels increase compared to color normal observers). As stated in that study [22], even when the luminance was equated by the CIE $V(\lambda )$ function, protanopes and deuteranopes could still identify Red and Green because of the differences of luminous efficiency functions in color deficients and the Abney effect, which influenced the brightness of stimulus colors. In this study, the lightness contrasts of these two colors were 1.64, 1.07, and 1.21 in the protanope, deuteranope, and CVN, respectively, and thus we expect that all observers could identify Red and Green to the colors in longer duration time in this study (as shown in the Procedure section). The distribution of 12 hues was approximated by the best-fitting ellipse obtained by the least-squares error method; since the function of the least-squares error changed monotonically when the initial values of parameters were reasonably close to the best values, the approximation was performed by an Excel solver (Excel for Mac ver. 15, Microsoft). Although there are some slight discrepancies at v10 (Yellow-Green), v12 (Green) and v16 (greenish-Blue), the distribution of the stimulus colors consisted of a hue circle in the chromatic appearance space. The center of the ellipse is at (${\rm x}, {\rm y}, {\rm L}) = ({0}.{360}, {0}.{358}, {77}.{40}$), and the correlated color temperature is 4507 K.

In the evaluation of word impressions by hues, it is important to confirm independence between colors and between evaluative words; if they were not independent, the evaluation results would usually be arbitrary since one color and one word could be easily replaced by another color and another word. In the control experiment [1], the 12 stimulus colors were separated into seven categories by a categorical color-naming method: Red (v2), Orange (v4 and v6), Yellow (v8), Green (v12), Blue (v14, v16, and v18), Purple (v22), and Pink (v24). v10 (Yellow and Green) and v20 (Blue and Purple) were at the borders of these categories. We would like to mention that if the distribution of hues would be expressed by color categories in the evaluation of semantic words, these two colors (v4 and v6) and three colors (v14, v16, and v18) would be treated as almost the same color in the distribution.

One color rectangle was ${7.0}\;{\rm deg}\;({\rm width}) \times {6.4}\;{\rm deg}$ (height) in visual angle, edged with black lines of 10 min in width. In the paired comparison experiment, two rectangles were presented side by side with 2 deg gap; otherwise only one chromatic rectangle was presented in the center of the screen. In all presentations, the chromatic rectangle was shifted 1.86 deg below vertical center for subject comfort during continuous viewing.

D. Semantic Words for Evaluation

Nine semantic words used for evaluation by hues in this study were the same with words selected in our previous study [1], in which the additional analysis on the data of a semantic differential method in a previous study [23] was performed. We found that the 25 semantic words [23] were separated into seven categories based on the distribution of the first and second PC loading values of the PCA and one additional category based on the third PC loading value [1]. We set eight new semantic words corresponding to these eight categories, giving consideration to the semantic words in each category [1]. We used Japanese semantic words because all subjects in the study were typical Japanese university students who were not bilingual in Japanese and English, suggesting that the similarity in recognition of word meanings between observers is relatively high [24]. The eight semantic words were GENKI-NA (Vigorous), NODOKA-NA (Tranquil), JYUUKOU-NA (Massive), KAGEKI-NA (Extreme), SEIREN-NA (Clean), SABIRETA (Deserted), SENSAI-NA (Fine), and SOUREI-NA (Magnificent). In Japanese, the meaning of SEIREN-NA is somewhat vague but closer to “Clean-fingered” rather than to “Clear”; the meaning of SENSAI-NA includes the meanings of “Delicate” and “Exquisite” but it is different from “Great” or “Good.” The other word was MEDATSU (Visible), because visibility of color is one of the important topics in color research for applications [1]. In this study, we mostly refer to these words by their English translations.

The independence of nine semantic words was also tested in the control experiment of our previous study [1]. The impressions of the words were evaluated by the traditional SD method using three core scales [Activity (active-inactive), Potency (superior-inferior), and Evaluation (beautiful-ugly)] [4,5], although we used Japanese words [SUGURETA—OTTOTA (excellent-poor)] in the Potency evaluation. “Deserted” was in the other quadrant to the other eight words in the axes of Potency and Evaluation; nine evaluative words were separated conceptually into five categories by the distance in the word space of Activity and Evaluation axes: [Vigorous, Visible, Extreme], [Massive], [Magnificent, Clean], [Fine, Tranquil], and [Deserted].

In the experiment by the SD method, we added 26 semantic word pairs to these nine words. Twenty-five words were from the previous study [23], and 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, and Light. We added one word, KIHAKUNA (Thin), as an antonym to KOI (Thick) to fill an empty space in the word distribution [1]. We mention that the words of Soft and Warm are expected to be the strongest and orthogonal in the word distribution of the SD method [2,3]. We would like to note some of the original Japanese words corresponding to these English words to avoid possible confusion: HAGESHII (Hard), IKIIKISHITA (Vivid), JYUUJITSUSHITA (Full), and HAKKIRISHITA (Clear).

Additionally, we would like to mention two ways to make a pair of semantic words; one way is to use an antonym for paired words having extreme and opposite meanings (for example, active-passive, superior-inferior, and beautiful-ugly); the other way is to use a word of negative expression of the original word (for example, active-inactive, powerful-powerless, and favorable-unfavorable) [4,5]. Since 25 semantic words from the previous study [23] were paired with extreme words, we tried to set all nine of the new words to be paired with extreme words. In three pairs (clean–corrupt, vigorous–infirmity, and visible–concealed), however, negative-extreme words were not commonly used as the antonyms to the positive words in the meanings first considered in Japanese, although positive-extreme words were suitably selected [1]. Thus, to avoid a possible influence from these antonyms in which the meanings of the positive words would be distorted unexpectedly, we used a negative expression of the words: [SEIREN-NA–SEIREN-DENAI (clean–not clean)], [GENNKI-NA–GENKI-DENAI (vigorous–not vigorous)], and [MEDATSU–MEDATANAI (visible–invisible)]. These three negative-expressions of the words were not used in the paired comparison method and were only three pairs in the set of 35 paired words in the SD method; therefore, the influence of the different method to make paired words is likely to be small.

E. Procedure

In Experiment 1 involving the evaluation of word impression by hue, a gray background [Gray (N4.7)] was first presented to each subject for 5 min. After the background adaptation period, one semantic word for evaluation was presented until the subject agreed to start the trials. After that, two color rectangles were presented simultaneously side by side in pseudo-random order for all 210 permutations successively; since 12 vivid colors and three neutral colors were used, and a position of one color at left or right was considered, one set of trials consisted of ${210}\;( = {_{15}{{\rm P}_2}})$. The observer was asked to select the one color of each pair of colors that was closer to the word impression by pressing one button (4 for left selection and 6 for right selection). A set of 210 trials took about 13 to 16 min (from 3.7 to 4.6 s per trial), and all nine words were measured in random order in one session. During any one session and between sessions, the observer could take a rest freely but was asked to watch the screen of the gray background. Three sessions were conducted for each word for each observer, that one color combination under one word was tested in six trials (each color placed 3 times on the right and 3 times on the left); each color in a pair with the other color would show from zero to six wins as the result of the comparison.

In the Experiment 2, involving the evaluation of color impression via the SD method, after the 5 min background adaptation period, one color rectangle was presented, and the subject evaluated the color by writing a “$\sqrt {\!} $” mark on a line scale having seven crosses (denoting $ - {3},{ - 2},{ - 1},{0},{1},{2},{3}$, although the numbers were not shown) for each paired semantic word. It also took 6 to 9 min to assess all 35 word pairs for one color. Each color was presented until the subject completed the evaluation. All 12 colors and three additional colors (White, Black, and Gray) were evaluated in one session in pseudo-random order, and three sessions were performed in different days for one observer. Again, the observer could take a rest freely.

3. RESULTS

A. Principal Component Analysis to Modified Selection Rate of Hue for Semantic Word (Exp. 1)

The data of Exp. 1 for any one word are initially shown as the number of wins in the paired comparison for each hue. The number of wins was modified before calculating the selection rate: 6 wins (all wins) was modified to 5.5 wins and 0 wins (no wins) was modified to 0.5 wins. Then the number was divided by 6 to get a win ratio. We set the (modified) selection rate by subtracting 0.5, which is the guaranteed average of all selection rates, from the 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 Z-score under the assumption of normal distribution in which the standard deviation equals 1. We thought that to use this modified selection rate would be safer than using the true Z-score, which requires an assumption in the treatment of standard deviations between the CVN and CVD observers. This modification to the ratio also helped to avoid unexpected distortions in calculated PCA results and model curves fitted to the modified selection rate data suitably.

1. Color Distribution Expressed by the First and Second Principal Component Loadings

We used PCA, in which the number of PCs (dimensions) reaches minimum and 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 [1]. The PCA was performed by the software “R” [25], and the components were verified by the software “HAD” [26]. In this study, the PCA was applied to the data of individual selection rates of stimulus colors for the nine evaluative words because we would like to analyze the observer variation; in the analysis of this section, the CVN data of nine CVN observers and the CVD data of one protanope and six deuteranopes were analyzed separately. In this study, no axis rotation was used in the PCA.

Figure 2 shows the proportions of variance from first to eighth PCs in the paired comparison data (Exp. 1) and in the SD method data (Exp. 2). In all experiments, the proportions of variance are similar between observer groups. To determine the number of components in the PCA, we performed a Scree test and parallel analysis [27] by HAD, and the results are presented in Table 1. The Scree test is regularly used to determine the number of factors in the FA, and it tends to show higher numbers in order not to miss a possible factor in the FA [26]. The parallel analysis determines the number of components in which the eigenvalues generated from the data matrix are larger than the eigenvalues generated from a Monte Carlo simulated matrix created from random data of the same size, and it tends to show the minimum number of the components [26,27]. As described in the Introduction section, our purpose of the PCA is to investigate the structure of color and word distributions, and thus we chose the number of components determined by parallel analysis.

 

Fig. 2. Proportion of variance from the first to eighth PCs in paired comparison data (denoted by circles) and in semantic differential method data (denoted by triangles). Filled and open symbols denote CVN data and CVD data, respectively. First PCs are more dominant in paired comparison data, and proportions of variance are similar between observer groups.

Download Full Size | PDF

Loading values for the first and second PCs for each stimulus colors show the contribution of colors to the evaluation of all words through the PCs. Figure 3 shows the loading values of the first and second PCs for each stimulus color in the CVN and CVD data sets. The black ellipse is the best fit to all data points: the lengths of the shorter and longer axes are 0.338 and 0.401, respectively, and the axis ratio is 0.843 in the CVN data; in the CVD data, the lengths of the shorter and longer axes are 0.314 and 0.479, respectively, and the axis ratio is 0.657. The black ellipses are not so different from dotted ellipses, which are the best fit under the limitations of no central point shift and no rotation of ellipse axes. The contribution of hues to the selection rates of semantic words is described by the hue circles (ellipses) maintaining antagonistic coordinates of colors placed at the opposite positions in the original PCCS hue circle (e.g., v2 versus v14, v8 versus v20). However, we would like to mention the difference of the color distribution from the distribution in the previous study [1]: the loading value points of v14 (Blue-Green), v16 (greenish-Blue), and v18 (Blue) are converged in both observer groups’ data. Considering the fact that six of nine CVN observers participated in both our previous study [1] and this study, this difference cannot be caused by the difference of observers between studies. But it could be caused by the difference of the color stimulus set; the presence of new stimulus colors, white, gray, and black, influenced the result of the loading values. One possible explanation is that these neutral colors expanded the range of lightness scaling in the appearance of all colors; this phenomenon caused compression of relatively small differences in lightness appearance between these three bluish colors and made the difference of their color appearance much smaller. Then these bluish colors were treated almost equally, especially because the differences of the chromatic appearance between the colors expressed by ${\rm a}^*$ and ${\rm b}^*$ are relatively small, and they were categorized in the same color name: blue [1]. The color distribution is similar between observer groups, although there are some small differences. However, as shown in Section 3.A.2, the word distributions defined by the first and second PC score values are largely different.

Table 1. Determined Number of Components in PCA by Scree Test and Parallel Analysis

View Table

 

Fig. 3. Distribution of stimulus colors as defined by the first and second PC loading values in CVN data (top panel) and in CVD data (bottom panel). Color chip number and names in PCCS are presented near each point. Black ellipses denote the best fit to all data points. Dotted ellipses denote the best fit under the limitations of no central point shift and no rotation of ellipse axes. The color distribution is similar between observer groups, and neutral colors (White, Gray, and Black) can also be fitted by the ellipses.

Download Full Size | PDF

 

Fig. 4. Modified selection rate as a function of stimulus color for CVN observers (denoted by color chip number and neutral color names) for nine semantic words. Error bars denote ${ \pm }\;{2.26}$ S.E.M. as a 95% confidence interval. Blue curves are fits by the first and second PCs with no offset. The order of the stimulus color was obtained from Fig. 3. Modified section rates change smoothly, and model fits can predict the data reasonably well, except for the three neutral colors (White, Gray, and Black).

Download Full Size | PDF

The other interesting result in the distribution of stimulus colors as loadings are the positions of the white, gray, and black stimuli. These neutral colors can also be fitted by an ellipse. It may suggest that these neutral colors may be treated as colors in a “special” hue circle. In the experiment using the SD method in our previous study [1], we have already included these neutral colors; that result and the results of this study presented in a later section indicate that these neutral colors are not placed on the ellipse for fits, and it suggests that these neutral colors are not used as colors in a hue circle.

These differences in the distribution of stimulus colors as loadings between this study and our previous study [1] were caused by using neutral colors in the paired comparison, and it may suggest that a process of the word evaluation by colors was changed with these neutral colors. To test this possibility, the modified selection rates of stimulus colors for each semantic word were fitted by the first and second PCs with no offset; gradual change of the rate as a function of the stimulus color and smooth function shape of the model fits would indicate that the stimulus colors are treated separately in the word evaluation process, but not in categories; good fits to neutral colors would suggest that these neutral colors are also involved to the special hue circle. Different tendencies of the gradual change in the selection rate from v2 to v24 indicate the rough categorization of evaluated words. Figures 4 and 5 show the selection rate data as a function of stimulus color for all semantic words for CVN and CVD observers, respectively. The order of the stimulus color in the abscissa was obtained from the distribution of stimulus colors in Fig. 3 in the counterclockwise direction from v2. The order of the panels (from left top to right bottom) is the order of the activity points (descending order) of the control experiment to evaluate semantic words in the SD method in our previous study [1]. Error bars denote ${ \pm }{2.26}$ standard error of the mean (S.E.M.) and ${\pm }{2.37}$ S.E.M. for CVN and CVD observers, respectively, which show a 95% confidence interval. The blue curves are model fits using first and second PCs with no offset. The selection rates of each word changed gradually in continuous hue for all semantic words; this indicates that assignment of hue to semantic words does not depend on the individual impression of a single hue or a few hues but rather on the set of neighboring hues in the hue circle.

 

Fig. 5. Modified selection rate as in Fig. 4, but for CVD observers, and error bars denote ${\pm }\;{2}.{37}$ S.E.M.

Download Full Size | PDF

The differences of the selection rates in data points of three bluish colors (v14, v16, and v18) indicate that these colors are treated separately, although in some words, the model fits show the same value for these colors; it suggests that the convergence of these colors is just the result of the PCA calculation, and it is not reflecting that these colors are treated as one color category. On the other hand, in the case of these neutral colors, the data points of the selection rates are far from the model fits; the model prediction tends to fail for the three neutral colors at the 95% significance level; the rates of the model prediction failure (per word and per color) for the three neutral colors are 0.67 and 0.44 for CVN and CVD observers, respectively; the rates for the other 12 colors are 0.25 and 0.19; and the failure rates are 2.7 and 2.4 times higher for CVN and CVD observers, respectively. Thus, these neutral colors are not treated in the same hue circle, although these neutral colors can be fitted by the same ellipse in the distribution of the stimulus colors. The good fit by the ellipse reflects that the rate data of the three neutral colors were smoothly involved as the part of the first and second PCs as a function of stimulus color; it can be caused by the paired comparison method in which the selection rates of the win-lose results are automatically balanced in all pairs with other colors.

The difference between observer groups are clearer in the selection rate data and specified to certain semantic words. When the most selected color for CVN observers was Yellow (v8) or close to Yellow (e.g., v2 and White), the tendency of the gradual change in the selection rate from v2 to v24 are similar between CVN and CVD observers; those are the cases of the first three words (panels) in Figs. 4 and 5. Opposite cases happen when the most selected colors were dark colors (Gray, v22, Black, and v24); the tendency in the selection rate are also similar between observer groups, and those are cases of Massive and Deserted (fourth and fifth panels). On the other hand, when the most selected colors were Green to Blue (v12, v14, and v18) for CVN observers, the tendency changes for CVD observers; in the cases of Magnificent, Clean, and Tranquil, a peak shift to Yellow and White occurs, although this shift is not clear in Tranquil. In the case of Fine, the selection rate is almost the same between colors in CVD observers, suggesting that CVD observers could not select the color for the word Fine.

 

Fig. 6. Point distribution of semantic words obtained by the first and second PC score values in CVN data (top panel) and in CVD data (bottom panel). Different symbols and colors denote all observers’ score-value points for semantic words of Extreme (gray triangles), Vigorous (blue squares), Visible (open diamonds), Magnificent (red circles), Clean (black triangles), Tranquil (green squares), Fine (yellow diamonds), Deserted (pink asterisks), and Massive (purple circles). Crosses and ellipses in the same colors denote the centroids (means) and areas of point distributions of each word, respectively. In CVN data, the ellipse of Vigorous is the same as the ellipse of Visible. In CVD data, the ellipse of Deserted is the same as the ellipse of Massive. Symbol labels of the observer number and word denote outliers from the area ellipses, and in the CVD data, the orange ellipse denotes the point-distribution area of observer #4, except Clean and Fine. In CVD data, area ellipses were distributed on the first axis, and the influence of the second PC value is much smaller.

Download Full Size | PDF

2. Word Distribution Expressed by the First and Second Principal Component Scores

Score sets of the PCA were calculated as the weight parameters of each PC’s contribution to a semantic word. The scores of the first and second PCs for each word indicate how the word is expressed by sets of hues and show the distributions of all words in two-dimensional space. Since we applied the PCA to individual selection rates, the score values of all observers were obtained separately; under the limitation of using the common loading values in the PCA, the distribution of score values for individual observers would be presented. Since a color deficiency can be treated as an individual difference between observers in color vision, we expected that the score-value points may show the tendency of color deficiency as being similar to a confusion line in the chromaticity diagram. In this subsection, we separately performed the PCA to CVN and CVD observers; thus, the limitation by the loading values was separated between observer group as shown in Fig. 3. In the later subsection, the PCA for both observer groups (five CVN observers and five deuteranopes) would be performed. Figure 6 shows the point distribution of semantic words obtained by the first and second PC score values in the CVN and CVD data. All observers’ score value points of all words were plotted, and the centroids of all observers for each word were denoted by crosses. The areas of the point distribution for each word were presented by handwritten ellipses; the common area ellipses were used for Vigorous and Visible in the CVN observer group (denoted by black-dotted ellipses) and for Deserted and Massive in the CVD observer group (denoted by purple ellipses) since the ellipses were almost identical. In some words, one observer’s score value point was far from all others’ points; we treated such the one point as an outlier and excluded from the area ellipse, although we included the outlier in the average calculation. In the figure panels, outliers were labeled by the observer number and the word. We found only four outliers in the CVN data; however, we found many outliers in the CVD data caused by the deuteranopic observer #4. The score values of this observer tended to be small, except Tranquil and Deserted. Although the score-value points of Clean and Fine were inside of the area ellipses, we indicated an area ellipse of observer #4 in the CVD data panel (denoted by an orange ellipse); smaller score values reflect the fact that the modified selection rates are close to 0, and this observer did not select stimulus colors consistently. In the PCA for the set of the CVN and deuteranopic observer data used in a later section, this observer #4 will be excluded from the deutan group.

The point distribution of score values was largely different between observer groups, although the distribution of loading values (shown in Fig. 3) was similar. It suggests that in the CVD observers, although the stimulus colors are treated in the hue-circle structure, the impressions and meanings of colors are different from these in the CVN observers. In the CVD data, the area ellipses were distributed on the first axis, and the influence of the second PC value is much smaller. It means that the semantic words were evaluated almost in one-dimensional scaling. The shape and size of area ellipses of the point distribution for words were not significantly different between observer groups; however, the area ellipse of Tranquil in the CVDs spread widely in antagonistic quadrants (second and fourth quadrants). Thus, Tranquil can be expressed by antagonistic sets of colors, Red-Orange and Blue-Violet, which depends on the observer in the CVDs. Further comparison of the score values between observer groups is difficult and less accurate because the loading values between observer groups were different; thus, in the later section we would use the sets of the data including both the CVN and CVD observers.

B. Evaluation of Color Impression by Means of the SD Method (Exp. 2)

1. Word Distribution Expressed by the First and Second Principal Component Loadings

We also conducted an experiment involving the evaluation of color impression by means of the SD method using 35 semantic words. The PCA was applied to the sets of individual grading points for each semantic word to the 15 colors (12 hues, white, gray, and black) separately in nine CVN and seven CVD observers. The proportions of variance from first to eighth PCs were shown in Fig. 2. The cumulative contribution rates in the CVN and CVD data were 0.514 and 0.513 until the second PC, and 0.701 and 0.704 until the fourth PC, respectively. The number of components determined by parallel analysis is 4 as shown in Table 1. This means that it is appropriate to use four PCs to express the results of the PCA. However, the distributions of stimulus colors in score values and their difference between observer groups looked so complex, and we could not analyze them well; in the third and fourth PCs, the comparison between observer groups was not realized since factors of these PCs could not be understood. The other critical point was that in this analysis, the loading values were different between observer groups; thus, precise comparison was less meaningful, since small differences could be changed if the loading values would be changed. In other words, arguments about small differences of score values between observer groups would be worth pursuing only if the common loading values were used; otherwise, the differences between observer groups can exist both in loading values and score values, and these differences of score values cannot be evaluated by using different loading values. Thus, the word distribution in loading values and the color distribution of score values defined by the third and fourth PCs are not shown in this section. These distributions would be presented in the PCA to the data set of the CVN and CVD observers.

In the results of the evaluation of color impression by semantic words, the loading values of the first and second PCs for each semantic word show a 2D contribution of word to the evaluation of all colors through the PCs. Figure 7 shows the distribution of semantic words defined by the first and second PCs loading values. In Fig. 7, the ordinate was flipped to match the direction of the axis to the score-value data in Fig. 6. The word distributions of loadings are basically similar between the CVN and CVD observers when the word spaces of the CVN data and the CVD data are rotated to plumb their directions of Soft. However, in the nine core semantic words, the distances of points between observer groups are large in Massive, Deserted, and Tranquil although the distances of Fine, Vigorous, and Extreme are small; the distances of Visible, Magnificent, and Deserted are medium. It is difficult to estimate the similarity between observer group in all data sets quantitatively because no reasonable criterion of the distance limit for the reasonable or acceptable similarity is provided. Thus, we used two approaches about the similarity; as described in the previous paragraph, the first approach was that by combining the data sets of the CVN and CVD observers for the simultaneous PCAs in which the loading values would be shared between observer groups, the distances between score-value points in the paired comparison and loading value points in the SD method would be calculated, and we would estimate what words would be similar and what other words would not be between observer groups by using these distances. The second approach was indirect assessment to the concordance of the data of the words and stimulus colors; we introduced the Kendall’s coefficient of concordance to the original data. It is the indirect approach to think about the similarity of loading values in the SD method, since the concordance of one word is the comparison of the color responses between observers obtained in the paired comparison. Thus, in this approach about the word distribution, the data of Exp. 1 would be used but not the data of Exp. 2. For these reasons, the details and the results of these approaches are shown in the Discussion section; the quantitative comparison between the word distribution results for scores in Exp. 1 and loadings in Exp. 2 would also be performed by PCA to the data set of the CVN and CVD observers and is described in the Discussion section.

 

Fig. 7. Distribution of nine core semantic words (denoted by sky-blue font), two important words (Warm and Soft, denoted by red squares and larger size lack font), and 24 semantic words (denoted by smaller size black font) defined by the first and second PC loading values in CVN data (top panel) and in CVD data (bottom panel). Semantic words are shown near their symbols. The symbol colors for nine core semantic words were the most selected color in the mean of all observers. The dotted lines denote the orthogonal corner obtained by Warm and Soft (see the text for details). The ordinate was flipped to match the direction of the axis to the score-value data in Fig. 6.

Download Full Size | PDF

2. Color Distribution Expressed by the First and Second Principal Component Scores

The scores of the first and second PCs for 12 colors give an indication of how color is expressed by sets of semantic words. Figure 8 shows the distribution of all colors obtained from the first and second principal component score values. In this data, unlike in Fig. 6, individual data were not shown because of overlapping distributions. Instead, we showed a confidence interval of 95% denoted by error bars. In this result, the black and blue ellipses, showing the best fits to 12 hue points (white, gray, and black were excluded) in the data of the CVNs and CVDs, are slanted $ - {15.91}\;{\rm deg}$ and $ - {7.76}\;{\rm deg}$ from the vertical line, and their center are shifted to (0.246, $ - {0.141}$) and ($ - {0}.{421}, { - 0.379}$), respectively; the lengths of the shorter and longer axes are 1.450 and 3.492, and 0.931 and 3.950, respectively.

 

Fig. 8. Distribution of 12 hues, White, Gray, and Black obtained from the first and second principal component score values in CVN data (top panel) and in CVD data (bottom panel). Error bars denote the confidence interval of 95%. Color chip number and names in PCCS are presented near each point. Black and blue ellipses denote the best fit to all hue points (White, Gray, and Black excluded) in CVN and CVD observers, respectively. Dotted ellipses denote the best fits under the limitations of no central point shift and no rotation of ellipse axes. Small black circles and broken lines denote the directions of Soft and Warm in Fig. 7 defined by the orthogonal corner. The ordinate is flipped to correspond to the loading value data in Fig. 7. Twelve hues are still contained in a hue circle and not compressed to one-dimensional scaling from Blue to Yellow.

Download Full Size | PDF

As shown in Fig. 8, the distribution of hues basically maintains the structure of the hue circle, but some points are strongly distorted, especially those for Red (v2), Yellow-Green (v10), Green (v12), Blue-Green (v14), and Red-Purple (v24). Details of this point and the comparison with the result of loading value data in the paired comparison will be discussed in the Discussion section using the PCA to the data sets of the CVN and CVD observers. One interesting result is that axes’ directions of the fit ellipses are almost the same as the direction of Warm and Soft defined by the loading values. It supports that in the distribution of colors obtained by the SD method, “Heat (warm)” and “Softness” are two dominant axes as described in the previous study [2,3]; it may be caused by the relationship between “Heat,” “Softness,” and the semantic words used in this study and Osgood’s core concepts in the SD method (Activity, Potency, and Evaluation). The axis ratios of the ellipses in the CVN and CVD data are 0.415 and 0.236, respectively; the length of the shorter axis is only 56.8% in the CVD data. Color deficiency may reduce the strength of the color distribution in the second dimension, although the correspondence of chromatic-opponent relationship between Red (v2) and Green (v12) to the short axes is not clear in both observer groups. However, at least in the results of the SD method, the hues are still treated in the hue circle and not compressed to one-dimensional scaling from Blue to Yellow, which is theoretically expected in protanopes and deuteranopes. One criticism exists in that this is not exactly like the paired comparison method. In the SD method, we used 35 semantic words including some simple words like Warm-Cold (“Heat”) and Bright-Dark; these words may influence the results strongly and construct a common-type (stereotype) hue circle. However, as can be seen in the distribution of the words in Fig. 7, not only these “easy” words but also from three to six core semantic words used in this study also showed similar positions in the word distribution between observer groups. It suggests that the unexpected effects of using some “easy” words are not so dominant; rather the structure of the word distribution is empirically obtained in CVD observers. Further investigation is required for this point with a limited number of semantic words.

C. Principal Component Analysis to the Combined Set of Selected CVN and CVD Observers

1. PCA to Modified Selection Rate of Hue for Semantic Word (Exp. 1)

We thought the assumption that the similarities between the CVN and CVD data in both experiments shown in Figs. 3 and 7 were reasonably high; this assumption will be checked by the comparison of concordance between inter- and intra-variation of observer groups in the Discussion section. If the data of the CVN and CVD observers are combined, common loading values are obtained, and the score values of the CVN and CVD observers can be compared directly using the common loading values. This procedure helps in quantitative comparison between observer groups. In the CVD observers, one protanope was excluded from the data set because of the small observer number in this color-deficiency type. In addition, the deuteranopic observer #4 was excluded who made small score values, reflecting too small differences in the color selection. We used the data of five deuteranopes in the CVD observer group. The number of the CVN observers was set to five to keep the balance of influence by different observer groups. We excluded four CVN observers by the number of outliers in the score-value data in Exp. 1 and Exp. 2 (the data are not shown individually). This data set of five CVN observers and five deuteranopes was used for the PCA.

The proportions of variance from the first to third PCs were 0.523, 0.221, and 0.090, respectively; the proportions are about the average between observer groups shown in Fig. 2. As can be seen in Table 1, the determined number of components was 2 according to parallel analysis. Figure 9 shows the loading values of first and second PCs for stimulus colors. In the best fit ellipse, the lengths of the shorter and longer axes are 0.339 and 0.401, respectively, and the axis ratio is 0.846. The color distribution is about the middle of the two distributions of the CVNs and CVDs shown in Fig. 3. Figure 10 shows the distribution of averaged score value points for semantic words obtained by the first and second PC score values in the CVN and deutan observers. The word distribution was largely different between observer groups. The word distribution of the CVNs can be fitted by an ellipse; however, the word distribution of the deuteranopes can be separated to two categories by the first PC score value: Extreme, Vigorous, Visible, and Magnificent are in the first category, and the other five words are in the second category. The points of the second category can be fitted by one line with a high coefficient of determination (${{ R}^2} = {0}.{9856}$); the slope is 0.737. These five semantic words were evaluated in one-dimensional scaling. The direction of the linear fit line for five words is shown in the color distribution in Fig. 9; the line is almost going through white to gray and black. We tested the relationship between this direction and lightness. Figure 11 shows the correlation of weighted summation of the first and second PC loading values in the ratio of 0.737 to luminance, L- and M-cone stimulations. L- and M-cone stimulation values were calculated from cone sensitivities, and their sum equals luminance. The coefficients of determination are high, and the correlations are significant. The one-dimensional scaling for these five words is supposed to consist of the lightness factor.

 

Fig. 9. Distribution of hues as defined by the first and second PC loading values in CVN and deutan observers. Other details are the same as Fig. 3 except the green line denotes the linear fit in Fig. 10 (see the text for details). The color distribution is approximately in the middle of the two distributions of the CVNs and CVDs shown in Fig. 3.

Download Full Size | PDF

 

Fig. 10. Distribution of semantic words obtained by the first and second PC score values in CVN and deutan observers. Circles and diamonds denote average of score-value points for one semantic word in CVN and deutan observers, respectively. Different colors denote semantic words of Extreme (Gray), Vigorous (Blue), Visible (White), Magnificent (Red), Clean (Black), Tranquil (Green), Fine (Yellow), Deserted (Pink), and Massive (Purple). Error bars denote the confidence interval of 95%. The gray ellipse denotes the best fit to all word points of CVN data. Green line denotes linear fit to five word points of deutan data, and the parameters of the fit are shown at left bottom. Red and blue ellipses denote categories defined by absolute values greater than 70% of the maximum absolute values. The word distribution was largely different between observer groups, and five words of the deutan observers can be fitted by one line.

Download Full Size | PDF

 

Fig. 11. Correlation of weighted summation of the first and second PC loading values in ratio of 0.737 to luminance, L- and M-cone stimulations. Circles, squares and diamonds denote the point of luminance, L-cone stimulation, and M-cone stimulation, respectively. Coefficients of determination are presented near each correlation line.

Download Full Size | PDF

In the first category, the first PC score values are very close. In Fig. 10, the points that have absolute values greater than 70% of the maximum absolute values of score values are indicated by red ellipses for the first PC values and blue ellipses for the second PC values. All four words are included in the category of high and positive score values. Vigorous, Visible, and Magnificent have small and similar second PC score values, and only Extreme can be separated significantly from Visible by the second PC score value. Thus, except Extreme, the word distribution can be predicted only by the first PC score value. As described previously, in the deuteranopes, although the stimulus colors are treated in the hue-circle structure as shown in Fig. 9, the impressions and meanings of colors are different from those in the CVN observers. If the difference of the word distribution between observers could be explained only by the difference of the color appearance, we would like to point out that in the words of the first category, as shown in Fig. 5, the most selected color in the CVD observers was Yellow (v8), which is the strongest color in deuteranopes; this might be the reason that the nine semantic words were separated into two categories.

2. Evaluation of Color Impression by Means of the SD Method (Exp. 2)

The evaluation data of color impression by means of the SD method was also analyzed in five CVN observers and five deuteranopes. The PCA was applied to the sets of individual grading points separately for each semantic word for the 15 colors. The proportions of variance from the first to fifth PCs were 0.326, 0.193, 0.137, 0.056, and 0.038, respectively; again, the proportions are about the average between observer groups shown in Fig. 2. The cumulative contribution rates were 0.519 until the second PC and 0.712 until the fourth PC; it is appropriate to use four PCs to express the results of the PCA. This was confirmed by the parallel analysis as shown in Table 1. Figure 12 shows the distribution of semantic words defined by the loading values of the first and second PCs and the third and fourth PCs. The word distribution of the first and second loadings is about the average of the CVN and CVD data shown in Fig. 7. The word distribution in the third and fourth PCs is difficult to be understood; the points of Extreme and Vigorous are opposite in the fourth PC value, and Visible and Deserted are almost at the same position.

 

Fig. 12. Distribution of nine core semantic words, two important words, and 24 semantic words defined by the first and second PC loading values (top panel) and by the third and fourth PC loading values (bottom panel) in CVN and deutan observers. The dotted lines denote the orthogonal corner obtained by Warm and Soft (top panel only). Other details are the same as Fig. 7, except no axis was flipped.

Download Full Size | PDF

Figure 13 shows the distribution of 12 hues, white, gray, and black obtained from the first and second PC score values (top panel) and from the third and fourth PC score values (bottom panel) in the CVN and deutan observers. In this result, the gray and blue ellipses, showing the best fits to the averaged 12 hue points (white, gray, and black were excluded) of the CVN and deutan observers, are slanted $ - {12.67}\;{\rm deg}$ and $ - {27.33}\;{\rm deg}$ from the vertical line, and their centers are shifted to (0.294, 0.031) and (0.891, 0.677), respectively; the lengths of the shorter and longer axes are 1.976 and 3.883, and 1.496, and 4.046, respectively. The difference of the angle is 14.66 deg, larger than the difference of 8.15 deg in Fig. 8 because there is no difference in the direction of Soft and Warm in the loading value space between observer groups in this analysis. Again, the distribution of hues basically maintains the structure of the hue circle, although some points are not on the ellipse: Blue-Green (v14), Purple (v22), and Red-Purple (v24). The axes directions of the fit ellipse to the CVN data are almost the same as the directions of Warm and Soft defined by the loading values. The results of the SD method using one set of loading values confirmed that the hues are still treated in the hue circle and not compressed to one-dimensional scaling. It is not surprising that the distance between white and black is longer in the deutans because they need more steps in lightness (brightness) to compensate for the loss of Red-Green chromatic change in appearance [28,29].

 

Fig. 13. Distribution of 12 hues, White, Gray, and Black obtained from the first and second PC score values (top panel) and from the third and fourth PC score values (bottom panel) in CVN and deutan observers. Circles and diamonds denote average of score-value points for one color in CVN and deutan observers, respectively. Color chip number and names in PCCS are presented near each point. (Top panel) Error bars denote the confidence interval of 95%. Gray and blue ellipses denote the best fit to all hue points (White, Gray, and Black excluded) in CVN and deutan observers, respectively. Small black circles and broken lines denote the directions of Soft and Warm in the top panel of Fig. 12 defined by the orthogonal corner. (Bottom panel) Black-dotted, red-solid, and blue-thick lines denote connections of score-value points between CVN and deutan data categorized to the first, second, and third categories, respectively. The distribution of hues basically maintains the structure of hue circle in the first and second PC score values, and the third and fourth PCs may have a role in explaining the difference between observer groups.

Download Full Size | PDF

Although it is still difficult to understand the color distribution obtained from the third and fourth PCs, connections of score-value points between the CVN and deutan data can help to categorize the colors; the first category includes yellowish colors of reddish-Orange (v4), yellowish-Orange (v6), Yellow (v8), and Yellow-Green (v10), in which the connections from points of the CVN observers to these of deuteranopes are from the left-top to the right-bottom direction (denoted by black-dotted lines in Fig. 13); the second category includes bluish colors of Blue-Green (v14), greenish-Blue (v16), Blue (v18), and Violet (v20), in which the connections are in the opposite directions from right-bottom to left-top (denoted by red solid lines); the third category includes reddish colors of Red (v2), Violet (v20), and Red-Purple (v24), in which the connections are in the orthogonal directions from left-bottom to right-top or opposite (denoted by blue thick lines). The roles of the third and fourth PCs is not clear; these systematic differences in the directions of the connections suggest that the third and fourth PCs have a role to explain the difference in grade rating of the words between observer groups.

4. DISCUSSION

A. Comparison of Data from Two Experiments

We performed two different experiments in this study: word impression evaluation by colors and color impression evaluation by words. The observer task should be processed by several different neural systems, not only by the visual information processing system but also by verbal communication and language processing systems in combination with a decision-making system (at a minimum) [1]. This complex structure of processing should cause the performance in the two experiments to differ. Nevertheless, the data from these two experiments are mathematically symmetric in terms of the PCA. In traditional studies [6–8], since only experimentation using the SD method was performed, it would be of little use to try the other PCA in the other direction of analysis using a transposed matrix of the data [1]. The reason is simply that these two sets of results obtained by the one SD experiment are mathematically equivalent. However, in the previous study as well as in this study, we performed two experiments on the same observers and obtained two sets of data independently. The direction from input to output in the PCA will mathematically affect the distribution since the variance of the target variable (score) will be maximized. However, we carefully selected one variable, colors from the PCCS hue circle, and determined the other variable, words, after the comprehensive analysis in our previous study [1] to make these variables distributions as symmetric as possible within each distribution; these all-directional distributions of dependent variables (for loadings) help to avoid unexpected distortions in the distribution of target variables (for scores). Thus, we can compare the distribution of hues (colors) and the distribution of semantic words in the two results of experiments in which the data structure of colors is the same and the data structure of the words is perfectly overlapping.

 

Fig. 14. Comparison between color distribution defined by loading values of color selection in the pair comparison method (denoted by squares; labeled by color chip number and name in PCCS) and color distributions obtained by score values of word grade rating in SD method in five CVN observers (circles; “SD,” number and name) and five deuteranopes (diamonds; “SD-CVD,” number and name) for the first and second PCs. Two color distributions of score values (by the SD method) were separately expanded, rotated, and shifted using the best fit ellipses (shown in Fig. 13) for the best fit to the distribution of the loading values. In the point labeled as “SD-CVD-black” (the lowest point in the space), the value of the second PC axis was halved for presentation. Gray, black, and blue ellipses denote the best fit ellipses to all hue points (White, Gray, and Black excluded) after displacement of points for fit, to points in CVN observers, and to points in deuteranopes, respectively. Some colors were stable in the structure comparison defined by the distances, but others were not.

Download Full Size | PDF

The time course of the stimulus observation was not accurately controlled in the procedure of both experiments. In the color paired comparison method, the subject looked at colors only briefly because the task was a much simpler one, responding left or right and then determining numerical grades for 35 semantic words for one color. The influence of short duration on the color distribution using MDS has been reported [11]; however, it was observed in comparisons with duration times of about 1.4 s and less. In terms of chromatic flash processes, 1 s is sufficient time compared to the chromatic impulse response [30–32]. It was also reported that 5 s duration does not strongly influence color constancy [33]. In this study, the observer who completed one session in the shortest time took about 3.7 s as the average for one trial of the paired comparison; thus, the influence of the observation-time difference is expected to be little, although it could occur that in some trials the judgement was completed in a very short time, and in some other trials it took a much longer time.

The results of evaluations of word impression by colors with those of evaluations of color impression by words were compared in the first and second PCs. The PCs were optimized to explain each result, and the PCs of different PCAs are not corresponding to each other; thus, for a meaningful comparison, color distributions of score values by the SD method had to be adjusted. We used the structure of the best-fit ellipse for the best fit for loading values; the color space for each color distribution data set was expanded in the direction of short and long axes from the center of the ellipse independently. The entire color space was rotated at the center of the ellipse; the center of the ellipse was shifted for the best fit in the method of least squares for the errors (distances) of each color. As they were for the original best-fit ellipses, Black, Gray, and White were excluded in the calculation of errors in the fits. Figure 14 shows the comparison between color distribution defined by the loading values of color selection in the pair comparison method and color distributions obtained by the score values of word grade rating in the SD method in five CVN observers (denoted by circles) and five deuteranopes (diamonds) after the displacement of points for fit. After the best fits using the ellipses, the color distributions of the paired comparison and SD methods are reasonably close, except for Red-Purple (v24), Black, Gray, and White. The amount of distance (error) for each color between loading value points and score-value points in five CVN observers and five deuteranopes after the displacement of points for fits was calculated as shown in Fig. 15. We used a ${ \pm }\;{0.5}\;{\rm SD}$ range from the mean obtained from the CVN observer data for quantitative analysis to the distances. Since the distances were calculated after adjustment of the ellipse axes and ellipse rotation for the score data by the SD method, the distance of colors in Fig. 15 shows the discrepancy from the ellipse-shape distribution, which suggests an irregularity in some colors from the possible hue circle.

 

Fig. 15. Distance between loading value points in the pair comparison method and score-value points in the SD method in five CVN observers (denoted by circles) and five deuteranopes (diamonds) after displacement of points for fits as shown in Fig. 14. Dotted lines denote [mean ${ \pm }\;{0.5}$ SD] calculated from CVN observer data. All data points and horizontal lines of Black, Gray, and White were halved for presentation.

Download Full Size | PDF

Some colors were stable in the structure comparison defined by the distances, but others were not; antagonistic relationships in the hue circle were basically kept in reddish-Orange (v4) to Blue-Green (v14) and in yellowish-Orange (v6) and Violet (v20). However, the antagonistic relationship commonly seen was not as stable in Red (v2) and Yellow-Green (v10) $\sim{\rm Green}$ (v12) for the deuteranopes. The other antagonistic relationship of Yellow (v8) and Blue (v18) was more stable in both observer groups. These correspond to the theory of Red-Green color deficiency [13]. The reason for the long distance in Purple (v24) is not clear. The three new colors (Black, Gray, and White) indicated very long distances compared to these of the other hues; the distance is also much longer in the deuteranopes than in the CVN observers. The simple explanation is that Black, Gray, and White were initially not on the best-fit ellipses to the color distributions of score values because these neutral colors are treated differently in the evaluation of color impression by words. Since CVD observers depend more on luminance difference for color recognition [15,34], the color recognition may further differ from the CVN observers. Further investigation is required to test the influence of neutral colors by using more neutral colors with different lightnesses.

 

Fig. 16. Comparison between semantic-word distribution defined by loading values of word grade rating in the SD method (denoted by squares; labeled by word) and word distributions obtained by score values of color selection in pair comparison method in five CVN observers (circles; “Pa” and word) and five deuteranopes (diamonds; “Pa-CVD” and word) for the first and second PCs. Two word distributions of score values (by paired comparison method) were separately expanded, rotated, and shifted using the best fit ellipses (shown in Fig. 10 for CVN data) for the best fit to the distribution of the loading values (see text for details). Black and gray ellipses denote the best fit to all word points of the word distribution of loadings and scores in CVN observers after displacement of points for fit, respectively. The green line denotes the best fit to score points of Deserted, Massive, Fine, Tranquil, and Clean in deuteranopes after displacement of points for fit. Red dotted lines denote the connection for each semantic word between loading points (square) and score points in CVN observers (circles).

Download Full Size | PDF

 

Fig. 17. Distance between loading value points in the SD method and score-value points in the paired comparison method in five CVN observers (denoted by circles) and five deuteranopes (diamonds) after displacement of points for fits as shown in Fig. 16. Dotted lines denote [mean ${ \pm }\;{0}.{5}$ SD] calculated from CVN observer data. Order of semantic word is ascending order of the mean of the two data.

Download Full Size | PDF

 

Fig. 18. Kendall’s coefficient of concordance $W$ applied to hue selection data from the paired comparison in order of the words in Fig. 10 going counterclockwise from “Extreme” (top panel) and grade-rating data from the SD method in order of color chip number (bottom panel). Symbols denote the data set of all observers (${\rm N} = {16}$) (denoted by squares), CVN observers (${\rm N} = {9}$) (circles), CVD observers (${\rm N} = {7}$) (diamonds), and five CVNs and five deutans (${\rm N} = {10}$) (triangles). Black, gray, green, and blue horizontal lines denote the limit of ${W}$ for 95% statistical significance for the data sets of ${\rm N} = {16}$, ${\rm N} = {9}$, ${\rm N} = {7}$, and ${\rm N} = {10}$, respectively.

Download Full Size | PDF

The word distribution was also compared by a procedure that is equivalent to that of the color distribution. Figure 16 shows comparison between semantic-word distribution defined by loading values of word grade rating in the SD method (denoted by squares) and word distributions obtained by the score values of color selection in the pair comparison method in five CVN observers (circles) and five deuteranopes (diamonds) after the displacement of points for fit. After the best fits using the ellipses, word distributions of the SD and paired comparison methods are not similar. Figure 17 shows the amount of distance (error) between corresponding points or the two sets of results for each word. As shown in Fig. 17, some words are robust for different methods of measurement; the distances for “Vigorous,” “Deserted,” and “Extreme” were small, suggesting that these semantic words can easily be described by hues. Conversely, the distances for “Massive” and “Fine” were large, suggesting that it is not so suitable to describe semantic words by hues; we can imagine that it was rather difficult for the subjects to select hues for these words, or alternatively, it may be difficult to use words for hues in most of the observers. In our previous study [1], “Massive” had a small distance, but it had the largest distance in this study. The possible explanation is that the lesser similarity of the word distributions may cause changes of words for “anchors” in the fits, especially because the data for the deuteranopes were included. It is interesting that the short distance for “Visible” in the CVN observers became much longer in the deuteranopes, suggesting that it is not so easy to find a “Visible” color for the deuteranopes. To find a “Fine” color is also more difficult for them. For the word “Magnificent,” the distance is much less for them that for the CVN observers. The most selected colors for “Magnificent” in the paired comparison were Blue (v18) and Yellow (v8) for the CVN observers and the CVD observers, respectively (in the separated PCA), and it became White in the combined data set. It suggests that the different color appearance for the deuteranopes causes changes in the evaluation of word impression by colors. This point is further discussed in the last section.

Interestingly, the comparison between the results of evaluation of word impression by hue and evaluation of color impression by the SD method reveals which colors (hues) are suitable for expressing word impressions and which words are suitable for expressing color impressions; thus, colors and words can be classified using this methodology in terms of color-concept association [1]. In the previous study [1], we expected that the relationship between colors and words may reveal a mechanism of evaluation processes in the human brain, consisting of the visual information processing system and verbal communication/language processing systems in combination with a decision-making system. However, the distance data about the word distribution is reinforced by the concordance data shown Section 4.B.

B. Calculation of Concordance for Observer Variation and for Difference between Words and Colors in Evaluation by Colors and Semantic Words

We calculated concordance of observer variation for two reasons. The first reason is to estimate observer variations within and between observer groups, especially for the validity of combining the data of the CVN observers and the deuteranopes for one PCA. As shown in Figs. 6 and 8, observer variations within groups are relatively large. If the concordance of the combined data set is as high as the data sets of each observer group, the observer variation would be reasonably small for the PCA. The other reason is that the concordance can show the observer variation for each word in the paired comparison and for each color in the SD method because the concordance is calculated for one unit of the data set. If the concordance is high, most of the observers have the same tendency for that word or color; thus, it can be expected that the word or color is also stable in a bidirectional relationship, although the concordance test itself is not bidirectional. We used Kendall’s coefficient of concordance for this purpose.

Figure 18 shows Kendall’s coefficient of concordance $W$ applied to hue selection data in paired comparison (in the order of words in Fig. 10 from Extreme going counterclockwise) and grade-rating data using the SD method (in the order of color chip number). The limits of $W$ for 95% statistical significance are determined by observer number $N$ and number of objects $O$; $O$ is 15 of the stimulus colors in the paired comparison and 35 of the semantic words in the SD method. In both experiments, $W$ dramatically changed between words and stimulus colors, but the difference between data sets of observers for one word and one color was relatively small. In the paired comparison data, the $W$s of the CVN observer data set were the highest except for “Magnificent,” but in the SD method the $W$s of the CVD observer data set were the highest except for v2(R), v6(yO), v22(P), v24(RP), and Gray. In the paired comparison, the impression of words between the CVN and CVD observers can be small, but the smaller difference of color appearance between stimulus colors in the CVD observer may cause higher inconsistency of hue selection compared to that of the CVN observers. In the combined data sets of all observers the $W$s were reduced, but not strongly. Surprisingly, the $W$s in the combined data set of five CVNs and five deutans were in the range between the $W$s of the CVN data set and that of the CVD data set except “Visible,” “Tranquil,” “Clean,” and v24 (RP). This indicates that the data set of five CVN observers and five deuteranopes is acceptable in terms of sharing one set of loading values between observer groups.

In the paired comparison data, “Magnificent” and “Fine” were the worst two words in $W$ because of the large discrepancy of $W$ between the CVN and CVD observer data sets as presented in Figs. 4 and 5. “Vigorous” and “Visible” were the highest two words in $W$; “Extreme,” “Massive,” and “Deserted” were reasonably high. However, the distance data in Fig. 17 show that the distances were short in “Vigorous,” “Deserted,” and “Magnificent,” and longest in “Massive” and “Fine.” The discrepancy of the results between the concordance and the distance in “Magnificent” and “Massive” can be explained by the difference of the distance. The difference of the distance of “Magnificent” between the CVNs and the deutans was the largest and that of “Massive” was small; the concordance $W$ reflects the difference between observers. Thus, the concordance is very low in “Magnificent” and reasonably high in “Massive.” This suggests that the similarity of the data in different observer groups can be considered in two aspects.

In the SD method data, the distance data in Fig. 15 show that v8 (Y), v16 (gB), v22 (P), and v24 (RP) had longer distances in the CVN observers and v2 (R), v10 (YG), v12 (G), v18 (B), and v24 (RP) had longer distances in the deuteranopes. The concordance data show that v10 (YG), v22 (P), and v24 (RP) had lower $W$ in the CVNs and v2 (R), v10 (YG), v22 (P), and v24 (RP) had lower value in the deutans. The discrepancy between the distance and concordance data exists at v8, v12, v16, and v18 where the distances were longer but the coefficient of concordance were reasonably high. Regardless of this discrepancy in the color data, the distance data obtained by the PCA from the SD method can reasonably predict the concordance data obtained from the data set of the SD method.

C. Bidirectional Relationships between Semantic Words and Hues

We found the large observer variation within the observer group as shown in Figs. 6 and 8, and the differences of the bidirectional relationship between the protanope and deuteranopes were small. These suggest that a large protan and deutan observer set is required to separate the specific difference between them; thus, in this study we focused on the difference between the CVN observers and the deuteranopes. Since a gender effect in the judgement of similarity on the appearance of colors has been reported [35], the difference of the word distribution between the CVNs and the deuteranopes might be influenced by the gender of the observers; however, this difference should be included in the color vision type because protanopic and deuteranopic vision appear mostly in males since it is caused by a congenital difference in the X chromosome.

1. Semantic Word Impression Evaluated by Hues and Neutral Colors

The compressed differences between bluish colors (v14, v16, and v18) as shown in Fig. 3 might be considered as evidence to support that the stimulus colors used in the evaluation were treated under the color categories. However, we have to consider the fact that the evaluation was performed by the paired comparison method; the selection rates as a function of color chip number depend on the selection results of such bluish colors to other colors. When stimulus colors were similar and the selection results of other colors would be the same, these bluish colors would have the same selection rate; this causes the same loading values in the PCA for the paired comparison data.

The contribution of hues to the modified selection rates of semantic words is described by the hue circle, maintaining antagonistic coordinates of colors placed at the opposite positions in the original PCCS hue circle on the ellipse. It is natural because colors can be described in three-dimensional scaling, including lightness as an intensity axis. It may happen that complex impressions of semantic words have a relationship with color impressions through less complex words like “Soft” and “Warm.” For example, “Tranquil” is treated as “Soft” and somewhat like “Cool,” which is the opposite word of “Warm.” “Soft” is associated with Green, and cool is associated with darker colors rather than brighter colors. Thus, Green (v12), not Yellow-Green (v10), was most selected for “Tranquil.”

As presented in Figs. 4 and 5, the color selection results for semantic words were reproducible using two variables in the CVN and CVD observers. Thus, there was the possibility that the semantic words could also be evaluated using two-dimensional variables [1]. That possibility may mean a simple transformation of information. Using a three-dimensional color set to evaluate semantic words, with variations of hue, saturation, and lightness was suggested [1]. Although we could not change saturation and lightness of hue colors by a practical limitation of a number of stimulus combinations in the paired comparison, neutral colors Black, Gray and White were added. These neutral colors influenced the color distribution of loading score values and, as described above, these could be fitted by an ellipse just as the other hues could. In the paired comparison experiment, a perfect “winner” or “loser” of a color for all of words in the selection has zero (no) contribution to PCs; it causes the color to be at the origin point in the color distribution of loading values. The fact that the points of the loading score values of colors can be fitted by an ellipse means that all hues, including neutral colors, contribute to the first and second PCs, and all stimulus colors are used in two-dimensional color distribution. The cumulative proportion of the CVN observers in Exp. 1 until the second PC is 78.2%, less than the proportion of 94.6% in our previous study [1].

We checked the one-dimensional distributions of stimulus colors defined by the loading values of the third PC, the fourth PC, or both the third and fourth PCs in the CVN observers and confirmed that white-gray-black lines, which can express the lightness scale, do not appear in these loadings. As shown in Figs. 9 and 11, the lightness scaling appears in the color distribution by the first and second PCs in both the CVN observers and deuteranopes; when the variation of the third dimension, lightness, is included, stimulus-color distribution is still in two dimensions. The distribution of hues defined by loadings is still similar to the one without the neutral colors. These indicate that the two-dimensional color distribution is not directly reflecting two of three dimensions in the structure of color appearance [36]. The first and second loading values are just reflecting the key factors for the evaluation of words, and thus it is not surprising that the color distribution of loadings in the CVD observers was similar to the one in the CVN observers; even if the color appearance is different between observer groups, the key factor can be still similar. As shown in the word distribution obtained by score values, however, the assignment of colors to the words is different in the paired comparison experiment.

2. Bidirectional Relationship in CVN Observers and Deuteranopes

Regarding the color distribution, it is interesting that for the CVD observers it is reasonable that the distance is longer and the concordance is low at the reddish and greenish colors caused by Red-Green color deficiency. However, these colors tend to have longer distance and lower concordance for the CVN observers. In the distance data, it may be caused by the combined data set in the PCA; however, the concordance of the CVN observers still shows this tendency. This point should be investigated further in the future.

We would like to raise one interesting question: the results of evaluations of word impression by colors in the paired comparison indicated the large difference in the word distribution as shown in Figs. 6, 10, and 16 between the CVN observers and the deuteranopes. The results of evaluations of color impression by words in the SD method, however, indicated relatively small differences in the color distribution as shown in Figs. 8, 13, and 14. The difference of 2D color distribution between the CVN and CVD observers has already been tested by the rank order method, in which an observer was asked to order cards (“names only,” “colors only,” and “names+colors”) depending on the similarity between the two colors [10]. The result showed that the CVN observers represented both colors-only and names-only cards in Newton’s color circle shape in which Red-Green and Yellow-Blue color opponents are almost antagonistic in the circle. Deuteranopes and protanopes did not represent colors-only cards in the circle; instead they represented one curve in which Red-Green difference was compressed. However, these CVD observers could represent names-only and names+colors cards in the Newton’s color circle shape. A recent study using magnitude estimation to the dissimilarities between a pair of colors showed that in dichromats colors were separated into about four categories (white, black, dark colors, and warm colors) but not on one curve in a 2D color distribution by a non-metric MDS [12]. In that study [12], the color distribution of the CVD observers is in the hue circle in which Red-Green and Yellow-Blue color opponents are not rightly antagonistic; that hue circle can be similar to the one in this study, although the effect of the neutral color for making the lightness axis in that 2D space may distort the simple chromatic-opponency shape of the hue circle in the 2D space. It has been reported that the boundaries of color categories cannot be explained simply by Red-Green and Yellow-Blue color opponencies in the analyzed data from color-naming and hue-scaling patterns [37]. When the color distribution was obtained by reaction time as the index of color discrimination in judgement of the same color or different [9], the color distribution of the CVNs is in the hue circle in which Red-Green and Yellow-Blue color opponents are not rightly antagonistic, although there is some distortion around bluish colors because of the processing speed of colors mediated through S cones is slower than through L and M cones [11,30,32,38].

These data suggest that the CVD observers can understand the hue-circle concept in color names (words), but it is not corresponding to the color appearance of the CVD observers. The relationships between colors and semantic words are different between the two directions: word impression evaluated by colors and color impression evaluated by words. This asymmetry in the bidirectional relationship helps the CVD observes to keep their performance through color [10,12,15], although the limited number of colors and color names could help to create the conceptual hue circle in the CVD observers. The usage of the limited color set in which color names and meanings have already been known by users through instruction can practically happen in the design of interface and data presentation [39]. Thus, our results indicate that the color distribution in the relationships between semantic words and color impression is mainly reflecting the hue circle, and we can again describe that “semantic word impression can be expressed reasonably well by color,” and that “hues are treated as impressions from the hue circle, not from color categories” as in our previous study [1]. In the hue circle obtained in this study, some colors were converged as observed in the results in Fig. 14. Such distortion of the color distribution was also found in the one obtained by MDS of large chromatic differences [9]. We used only 12 hues to express all hue, and thus the chromatic differences were relatively large, so these results correspond to each other.

Overall, in our experiment when the direction of the relationship between semantic words and color impressions is from colors to words, the relationship in the CVDs is similar to that of the CVNs because in the SD method (Exp. 2) the color sample can be recognized by color names in this experimental condition. However, when the direction of the relationship is from words to colors, the relationship is distorted in the CVDs because in the paired comparison method the selection of colors in the pair simply depends on their color appearance. The CVDs tend not to select a variety of colors to express semantic meanings. The number of perceived hues may not be sufficient to express abstract meanings for the CVDs; lightness and saturation may also have more important roles in the semantic expression than it does in the CVNs.

5. CONCLUSION

We performed two different experiments in this study: word impression evaluation by colors and color impression evaluation by words. In the experiments of the paired comparison, the selection rates of hues for evaluation of semantic words changed gradually under continuous hue. This supports that assignment of hue to semantic words is not the simple assignment of a color name obtained from color categories [40–43]. The word impression was expressed by a set of hues in the order of the hue circle. The color selection results for semantic words were reproducible using two variables in the CVN and CVD observers; the colors used in this study were in the same hue circle, with the same tone (impression of both saturation and lightness), and thus all differences among these colors can be expressed by two-dimensional variables (two PCs).

However, for the deuteranopes who have much less or no detection of Red-Green opponent colors, the selection of hues for the evaluation of semantic words becomes different from those of the CVN observers; the results indicated that except words showing higher score values in the first PC (Extreme, Vigorous, Visible, and Magnificent), semantic words in this study were evaluated in one-dimensional scaling, which has high correlation to lightness (or brightness).

When Black, Gray, and White are added to the hues, these neutral colors expand the perceptual range, especially in lightness, and the differences of bluish colors were compressed; the selection rates will be the same between colors with small chromatic difference, and these colors will show the same loading values.

The distance data of semantic word distribution and the concordance data of hue selections in the paired comparison suggest the presence of four series of words: the first is the highly stable word group including Vigorous and Deserted; the second is the moderately stable word group including Extreme, Visible, and Tranquil; the third is the constantly unstable group including Fine. The last is the word group in which stability changes by the criteria including Magnificent, Massive, and Clean. As described in the previous sections, this categorization must depend on the suitability of words for evaluation with hues in the CVN and CVD observers; the difference of the concordance between observer groups caused by the reduced color differences in stimulus colors in the deuteranopes strongly affect the grouping of the words, especially in the fourth group.

The score results for the SD method indicate that Black, Gray, and White do not exist on the ellipses reflecting the hue circle. We have already explained this phenomenon in the previous study [1]; because the points are plotted in the coordinates of the PCs, neutral colors are not placed at the center of the ellipses like a color system. The placement of Black, Gray, and White outside of the ellipse is an intuitively reasonable result, since these neutral colors have special lightness, which can be much higher than, much lower than, or exactly the same as the background, and some effect of lightness difference caused a stronger impression than colors in the hue circle.

The results of this study suggest that the CVD observers can understand the hue circle concept in color names but it is not corresponding to the color appearance of the CVD observers. In the SD method (Exp. 2), the color sample can be recognized by color names in this experimental condition; however, in the paired comparison method (Exp. 1), the selection of colors in the pair simply depends on their color appearance. This bidirectional relationship helps the CVD observes to keep their performance similar to that of CVN observers when the limited number of colors and color names help to create the conceptual hue circle, although the CVD observers tend not to select a variety of colors to express semantic meanings. Our results indicate that semantic word impression can be expressed reasonably well by color and that hues are treated as impressions from the hue circle, not from color categories in both CVN and CVD observers.