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Robert Ennis, Qasim Zaidi; The geometry of color similarities. Journal of Vision 2014;14(15):18. doi: https://doi.org/10.1167/14.15.18.
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© ARVO (1962-2015); The Authors (2016-present)
Color spaces are invaluable for specifying colors. However, color-matching spaces only predict which spectral distributions will match, while most perceptual color spaces describe the discrimination of small color differences. Yet, color perception involves more than matching and discrimination. For example, similarities between colors (Zaidi & Bostic, 2008) and between color changes (Zaidi, 1998) guide material identification across illuminants. Unfortunately, uniform color spaces based on multi-dimensional scaling of similarity ratings rely on untenable Euclidean assumptions (Wuerger, et al, 1995). We investigated the geometrical structure underlying relative similarity judgments. In a metric space, distance would represent similarity magnitude, but even in a weaker Affine space, ratios of distances along a line would provide measures of relative similarity; parallelism would define similarity between color changes. We tested whether Affine geometry holds for a mid-point setting task. We chose quadrilaterals in the MacLeod-Boynton (1979) equiluminant color plane. Observers viewed three colored patches. Two test patches were vertices of one color quadrilateral edge. Observers were instructed to consider the color change between the test patches in terms of “reddish-greenish“ and “bluish-yellowish” components and adjusted the hue and saturation of the third patch to the combined midpoint on these two dimensions. After finding the four edge midpoints, observers set the midpoints between the two pairs of opposing mid-points. The two final mid-points for each quadrilateral coincided, satisfying Varignon's Theorem (an Affine test). These settings also held for different adaptation conditions. A perceptual color space based on relative similarities across large color differences might have Affine structure.
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