The Location of Optimal Object Colors with More Than Two Transitions (Preprint)

TL;DR

This paper investigates the shape of optimal object colors on the color solid, revealing non-convexities and higher transition counts, and introduces a linear programming method to locate these colors.

Contribution

It develops a linear programming approach to identify higher-transition optimal colors on the color solid, expanding understanding beyond traditional two-transition models.

Findings

Optimal colors can have more than two transitions.

Non-convexity affects the shape of optimal color distributions.

Higher transition regions exhibit point-symmetric structures.

Abstract

The chromaticity diagram associated with the CIE 1931 color matching functions is shown to be slightly non-convex. While having no impact on practical colorimetric computations, the non-convexity does have a significant impact on the shape of some optimal object color reflectance distributions associated with the outer surface of the object color solid. Instead of the usual two-transition Schrodinger form, many optimal colors exhibit higher transition counts. A linear programming formulation is developed and is used to locate where these higher-transition optimal object colors reside on the object color solid surface. The regions of higher transition count appear to have a point-symmetric complementary structure. The final peer-reviewed version (to appear) contains additional material concerning convexification of the color-matching functions and and additional analysis of modern "physiologically-relevant" CMFs transformed from cone fundamentals.