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Volume: 5 | Article ID: art00062
On Curvature of Color Spaces and its Implications
  DOI :  10.2352/CGIV.2010.5.1.art00062  Published OnlineJanuary 2010

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 well-known 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 multipatch Riemann coordinates for spaces with the positive curvature.

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Toko Kohei, Jinhui Chao, Reiner Lenz, "On Curvature of Color Spaces and its Implicationsin Proc. IS&T CGIV 2010/MCS'10 5th European Conf. on Colour in Graphics, Imaging, and Vision 12th Int'l Symp. on Multispectral Colour Science,  2010,  pp 393 - 398,

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