Spherical Model of Color and Brightness Discrimination

Abstract

The most important problem confronting color science is the construction of a uniform color space, i.e.. a geometrical model of color discrimination in which Euclidean distances between the points representing colors are proportional to perceived color differences. The traditional approach to the construction of a metric color space is based on the integration of just-noticeable color differences (Wyszecki <& Stiles, 1982). Experimental data show, however, that the integral of Justnoticeable differences between colors does not coincide with direct estimations of the subjective differences between the colors (Judd, 1967;Izmailov, 1980). We suggest another way to construct a uniform color space, namely, to analyze large color differences by multidimensional scaling. This paper reports three groups of experimental data of the measurement of large color differences. Based on these data, we suggest a new color space model taking into account nontraditional relations between threshold and suprathreshold differences. The first group of data includes the results of research on color discrimination for a set of equibright monochromatic lights. The second group includes data on the discrimination of achromatic light stimuli resulting from different relations between test and background luminances. The third group consists of results of color-naming classification of lights varying in chromaticity and brightness. Chromatic differences between spectral stimuli of equal brightness, varying in hue and saturation, and differences in brightness between achromatic lights varying in luminance were analyzed separately. The results are compared with a general color space of colors of different hue. saturation, and brightness. The color spaces were constructed by the same multidimensional scaling technique. An important advantage of multidimensional scaling is that it offers the possibility of finding the dimensionality of a color space directly from experimental data, as we demonstrate for the analysis of color discrimination data for equibright stimuli.

Research note: A multidimensional scaling comparison of color metrics for response times and rated dissimilarities

“…This achromatic axis provides only a small reduction in stress, and accounts for only a small proportion of the model's variance accounted for: .13, as opposed to .49 and .32 for the first two dimensions. However, it fits the spherical model of color perception (Izmailov & Sokolov, 1991). A suspicion lingers that this curvature is an artifact of scaling a planar structure in three dimensions, in the same way that items with an underlying one-dimensional structure often arrange themselves in a parabola-the horseshoe artifact-when two dimensions are available.…”

The Semantic Component of the Evoked Potential of Differentiation

“…Saturation of the spectral colors of blue-green, yellow and orange are half that of blue, green, and red and this corresponds to our data on the categorical and quantitative characteristics of the space of artificial color names (Izmailov & Sokolov, 1992). It should be noted that the geometric structure of color names, based on the amplitude of EPD, as well as on semantic assessments of differences does not exactly reproduce the quantitative structure of the color space based on data from measurements of differences among colored light stimuli using psychophysical methods (Izmailov & Sokolov, 1991;Shepard & Carroll, 1966). However, it is in good accord with the geometric structure of the space of color differentiation based on the amplitudes of early components of EPD (N87 and N87-P120), obtained in response to abrupt substitution of light stimuli of different spectral components and intensities Paulus, et al, 1984;Riggs et al, 1969).…”

“…Under these conditions, the points representing the stimuli in Euclidean space always form a strictly circular trajectory (in the form of a circle or its parts), leading to this type of space being called a spherical model of differences between stimuli (Fomin, Sokolov, & Vaitkyavichus, 1979;Izmailov, 1980;Sokolov & Izmailov, 2006). Unlike Shepard, who explains this circularity with reference to the need to coordinate the structure of subjective experience with the physical structure of the environment (Shepard, 1987(Shepard, , 2001, we hypothesize that this circularity follows from the structure of the two-channel neuronal net that generates sensory representations of stimuli in the visual system (Izmailov, Sokolov, & Chernorizov, 1989;Izmailov & Chernorizov, 2005;Izmailov & Sokolov, 1991). Thus, we may add to the traditional formal criteria, a substantive criterion for the correct solution: circularity in the structure of the differentiation data.…”

The representation of colors in spherical space

“…In 2001, on the basis of the experimental results reported by Izmailov and Sokolov, 5 the physicist Y.P. Leonov defined the spherical color space in Riemannian geometry.…”

“…Sokolov at Moscow State University demonstrated that perceived colors could be represented on a surface in 4D space. 5 The form of the surface was found to be relatively simple, a sphere in 4D space. This model made it possible to define precisely the linear element of the Riemannian space.…”