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Nevin Manimala Statistics

The non-Riemannian nature of perceptual color space

Proc Natl Acad Sci U S A. 2022 May 3;119(18):e2119753119. doi: 10.1073/pnas.2119753119. Epub 2022 Apr 29.

ABSTRACT

SignificanceFor over 100 y, the scientific community has adhered to a paradigm, introduced by Riemann and furthered by Helmholtz and Schrodinger, where perceptual color space is a three-dimensional Riemannian space. This implies that the distance between two colors is the length of the shortest path that connects them. We show that a Riemannian metric overestimates the perception of large color differences because large color differences are perceived as less than the sum of small differences. This effect, called diminishing returns, cannot exist in a Riemannian geometry. Consequently, we need to adapt how we model color differences, as the current standard, [Formula: see text], recognized by the International Commission for Weights and Measures, does not account for diminishing returns in color difference perception.

PMID:35486695 | DOI:10.1073/pnas.2119753119

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