A Euclidean Metric in Trichromatic System : Trichromatic System in Computer Graphics (2)

Abstract

A Euclidean metric was applied to the trichromatic system to provide a common space for comparison and evaluation of various computer generated color solids. A well known application of this is the matrix R, an orthogonal projection matrix, projecting color stimulus vectors in the n-dimensional Euclidean vector space onto its three-dimensional subspace. This subspace is known as the 'fundamental metamer space'. Since the set of monochromatic stimuli of equal energy spectrum was assumed a priori to be an orthonormal basis, color solids in the subspace must have unusual achromatic axes oblique to planes of constant luminance. This paper firstly presents a parallel projector expressing an affine projection in the color stimulus space. Next, by introducing a Euclidean metric to the color stimulus space, representation of the parallel projector by orthogonal projection matrix was attempted. Since the space can be spanned by a number of orthonormal bases other than the monochromatic basis, the orthogonal matrix and the accompanying color space, other than matrix R and the fundamental metamer space respectively, can be obtained. Thus, an orthogonal projection matrix providing a vertical achromatic axis was achieved.