The Location of Optimal Object Colors with More Than Two Transitions (Preprint)
This work provides insights into color theory for researchers in color science and imaging, though it appears incremental as it builds on existing models of optimal colors.
The study addressed the non-convexity in the CIE 1931 chromaticity diagram, revealing that it causes optimal object colors to have more than two transitions in reflectance distributions, contrary to the typical two-transition form, and used linear programming to locate these regions on the object color solid surface.
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.