Spectral Matching Functions and Ellipse Mappings in Search for More Uniform Chromaticity and Color Spaces

Abstract

In this study, modifying the CIE xyz color matching functions was considered to achieve a more uniform chromaticity space. New color matching functions resulting both from the non-negative tensor factorization and from the optimization were combined with two ellipse mapping approaches. In both approaches the original MacAdam ellipses were mapped to the new space. The first mapping approach depended on the dominant wavelengths and the second one on the spectral information for the five points on the locus of each ellipse. Equal semiaxis lengths (a constant radius) and equal areas for the mapped MacAdam ellipses were the characteristics for the uniformity of the new chromaticity space. The new color matching functions were modelled with the non-uniform rational B-splines and the optimization modified the independent parameters, namely the control points, for NURBS. The cost function was based on the size and shape of the mapped MacAdam ellipses. NURBS were also utilized as a smoothing operator when the color matching functions were directly output from the optimization task. The results indicate that modified color matching functions yield in more uniform chromaticity space. There still remains uncertainty about the ellipse mapping approaches and formulation on the cost function in the optimization tasks.