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

arXiv: https://arxiv.org/abs/2103.06997 · HTML: https://mlsanity.com/paper/2103.06997/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 34 references that are in the map.
- First posted on arXiv 11 Mar 2021.

## Builds on (most cited first, 2 of 2)

- [Spherical sampling methods for the calculation of metamer mismatch volumes](https://mlsanity.com/paper/1901.08419/) (2019)
- [Chromatic Adaptation Transform by Spectral Reconstruction (Preprint)](https://mlsanity.com/paper/1902.10160/) (2019)

## Abstract (arXiv)

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.