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On Curvature of Color Spaces and Its Implications

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Title On Curvature of Color Spaces and Its Implications
Title of Series The 5th European Conference on Colour in Graphics, Imaging, and Vision and the 12th International Symposium on Multispectral Colour Science (CGIV 2010/MCS'10)
Part Number 23
Number of Parts 43
Author Kohei, Toko
Chao, Jinhui
Lenz, Reiner
License CC Attribution - NoDerivatives 2.0 UK: England & Wales:
You are free to use, copy, distribute and transmit the work or content in unchanged form for any legal purpose as long as the work is attributed to the author in the manner specified by the author or licensor.
DOI 10.5446/18270
Publisher River Valley TV
Release Date 2011
Language English
Production Place Joensuu, Finland

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Subject Area Computer Science
Abstract In this paper we discuss the role of curvature in the context of color spaces. Curvature is a differential geometric property of color spaces that has attracted less attention than other properties like the metric or geodesics. In this paper we argue that the curvature of a color space is important since curvature properties are essential in the construction of color coordinate systems. Only color spaces with negative or zero curvature everywhere allow the construction of Munsell-like coordinates with geodesics, shortest paths between two colors, that never intersect. In differential geometry such coordinate systems are known as Riemann coordinates and they are generalizations of the wellknown polar coordinates. We investigate the properties of two measurement sets of just-noticeable-difference (jnd) ellipses and color coordinate systems constructed from them. We illustrate the role of curvature by investigating Riemann normal coordinates in CIELUV and CIELAB spaces. An algorithsm is also shown to build multi-patch Riemann coordinates for spaces with the positive curvature.
Keywords The 5th European Conference on Colour in Graphics, Imaging
Vision and the 12th International Symposium on Multispectral Colour Science
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