Many problems regarding color opponency are still unsolved. In this study the system of the uniform color scales of the Optical Society of America (OSA-UCS) is analyzed with the aim of obtaining answers to very general questions on color opponency. The perceptual color opponencies in the OSA-UCS system, represented by its coordinates appear to work in a mutually interacting way. On the hypothesis that such an interaction is due to a linear mixing of a pair of independent opponent mechanisms with scales satisfying a proper Weber fraction, three chromatic opponency functions are derived, whose sum is equal to zero. These functions are the logarithms of the ratios of two tristimulus values in a proper reference frame (called the “main reference frame”) and therefore are antisymmetric and zero-degree homogeneous functions of these tristimulus values. Any pair of these three functions is a set of two independent functions. A new formula for color opponency in the OSA-UCS system is derived in which the perceptual color opponencies are written as products of the lightness by a proper linear mixing of any pair of the three chromatic opponency functions. All this is possible because the lattice of the OSA-UCS system is composed of geodesic lines.
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Eriko Miyahara, Vivianne C. Smith, and Joel Pokorny
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