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Is Perceptual Color Space a Differentiable Manifold?

The third question that should be considered is, ``Is perceptual color space a differentiable manifold?'' I have found no reference to the differentiability of color space in the literature. For the perceptual color space to be differentiable, the total difference between two stimuli must always be able to be found by integrating just noticeable differences along the shortest continuous path between the two stimuli.

It is unclear whether the perceptual color space will be able to be represented as a differentiable manifold. The issue of differentiability has been largely ignored in that colorimetric researchers have worked primarily with just noticeable differences rather than attempting to see how the differences over a large scale compare with integrations across the assumed metric of just noticeable difference.

Ideally we would want to organize our representation of the photic environmental space and color perceptual space so that both spaces are metric and both are differentiable manifolds, and furthermore so that there exists a continuous function which maps one onto the other in a one--to--one fashion. Work which pertains to this problem has mostly taken two forms: that of psychophysical work on color ordering systems, which attempt to organize the perceptual color space into just noticeable differences; and that of neurophysiological work, which attempts to describe and model the mechanics of the mapping function by studying the nervous system. Another approach would be one which attempted to reorganize our concept of the photic environmental space in order to simplify the theoretical mapping function between stimuli and perceptual space.

Steven M. Boker
Sun Feb 12 19:24:36 EST 1995