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Robert Ennis, Qasim Zaidi; Geometrical structure of perceptual color space is affine. Journal of Vision 2013;13(9):295. doi: https://doi.org/10.1167/13.9.295.
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© ARVO (1962-2015); The Authors (2016-present)
Color spaces (e.g., CIE, Macleod-Boynton, and CIELUV) are invaluable for specifying colors. However, CIE and M-B space only predict which spectral distributions will match, while CIELUV deals with the discrimination of small color differences. There is much more to color perception than matching and discrimination. For example, similarities between colors (Zaidi & Bostic, 2008) and between color changes (Zaidi, 1998) can be used to identify materials across illuminants. Uniform color spaces based on multi-dimensional scaling of similarity ratings do exist, but these rely on Euclidean assumptions shown to be untenable (Wuerger, et al, 1995). We investigated the geometrical structure underlying relative similarity judgments. In a metric space, the distance between chromaticities would represent their magnitude of similarity, but even in a weaker affine space, ratios of distances between colors on a line would provide measures of relative similarity, and parallelism would define similarity between color changes. We tested whether affine geometry holds for a mid-point setting task. We chose two large quadrilaterals in the M-B equiluminant color plane. On each trial, observers viewed three colored patches, two of which were the endpoint colors forming one side of the quadrilateral. Observers were instructed to consider the color change between the test patches in terms of "reddish-greenish" and "bluish-yellowish" components and to set the color of the middle patch, by adjusting its hue and saturation, to the combined midpoint of the change on the two dimensions. After finding the mid-point for the four sides, observers set the midpoints between the two pairs of facing mid-points. For four observers, the two final mid-points for each quadrilateral coincided, thus satisfying Varignon’s Theorem and passing the affine test. A perceptual color space based on relative similarities across large color differences thus has an affine structure.
Meeting abstract presented at VSS 2013
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