In a previous report, the perceptual similarity or difference in 9 colors which vary in value and chroma, but constant in hue (5R), was analyzes by the method of multi-dimensional scaling. The configurations of the colors obtained from the experiment, if mapped in two-dimensional Euclidean space, were in good agreement with those defined in Munsell system. These results were also reported by Torgerson who developed this scaling method and applied it to the same problem.In this experiment, the variation in hue was introduced in addition to that employed in the previous experiment and 13 colored papers were used as stimuli Table 1). The degree of perceptual difference in these colors were converted into the spatial distances by the ratio method as follows : As the standard, colors k and i were presented in a certain distance and the difference perceived between these colors were defined to be represented by this distance. The subject was asked to express the perceived difference between colors k and j (j ≠ i) by displacing color j in such a way that the ratio of the distance k and j to that of k and i corresponds to the ratio of the perceptual difference k and j to that of k and i (Fig. 2). As the stimulus i was varied on four ways, 4 different standards k and i were employed with respect to a certain pair k and j, and, as a matter of course, the size of the unit for the differences between k and j and that of the unit for those between l and j was in general not the same. Hence, a kind of transformation [Equations (2)-(10)] was carried out in order to convert all distances into the distances based upon a single common unit and the distance matrix D was obtained. The laborious computational process of estimating the additonal constant could be got rid of this way.The data for two subjects were separately analyzed by the multi-dimensional analysis. The following results were obtained for each observer. The configurations of colors were found to lie in the three-dimensional Euclidean space in which the distance between any two colors represented the perceptual difference between them. In this psychological color space, the three attributes of color were identified as the cylindrical co-ordinate axes, i. e., the vertical axis represented the value (Fig. 4), and the radius vector orthogonal to the value axis represented the chroma (Fig. 3) and the argument represented the hue (Fig. 5). It should be noted that this co-oedinate system was empirically derived from the data themselves, not enforced from the definition of the Munsell system. The configurations of the colors agreed fairly well with the positions of these in the Munsell system as shown in Figs. 6 and 7, if the latter was superimposed upon the psychological color space in an appropriate way. The value was discovered to cotribute more to the impression of difference between colors than the chroma. These findings which were confirmed in both of the two observers of this experiment are in harmony with the results of the previous investigation which dealt with the two-dimensional color space.
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Jan 1, 1960
Wang Chih-Chiang 
Open Access
