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Lindsey N Hutchinson, Angela M Brown, Delwin T Lindsey; What is halfway between a starfish and a locomotive? Studies of the intrinsic geometric structure of Hering color-opponency.. Journal of Vision 2019;19(10):251. doi: https://doi.org/10.1167/19.10.251.
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© ARVO (1962-2015); The Authors (2016-present)
Color scientists have long tried to use geometry to represent human color perception. While color space is not generally Euclidean, Ennis&Zaidi, 2013 (“E&Z”) suggested that perceptual color space may be affine under a Hering color-opponent mental representation (“HCOR”). Consider the following construction: First, bisect the four edges of any quadrilateral within a vector space. Then, bisect the opposite-edge bisection intervals. By Varignon’s theorem (“VT”), if the space is at least affine, these bisection midpoints (BSMs) will coincide (Todd, 2001). Twelve subjects viewed equiluminant colors pairwise, and adjusted a third color in hue and saturation to bisect the perceived interval between each pair, following the VT paradigm. Like E&Z, we found that uninstructed BSMs were far from coincident, but subjects did better for small quadrilaterals than for large quadrilaterals (LQ). However, unlike E&Z, we found little effect of HCOR instructions. To further test HCOR, we manipulated the choice of LQ colors. We chose one LQ enclosing white (as in E&Z) and two LQs shifted in redness/greenness. We predicted that if subjects were truly bisecting colors in a metrical HCOR space, the chosen BSMs should move with the LQ colors. Four subjects received extensive practice and a tutorial on the geometric representation of colors in Hering color-opponent space. Subjects’ BSMs were more nearly coincident than before instruction, but there was no shift in red/green locations of the BSMs across LQs (ChiSq=2.92,p=0.232). This suggests that E&Z’s LQ centered on white was a special case for which categorical and metrical judgments happen to give the same result. Our subjects did not judge colors in a metrical, color-opponent space, but rather sought colors that were categorically distinct from the endpoints. Halfway between two categorically different items (like red and green, or a starfish and a locomotive) is not defined within any continuous, affine space.
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