Introduction

When a physical object is illuminated by some spectral power distribution (e.g. daylight or tungsten lamp), a modified spectral power distribution is emitted according to the reflectance properties of the object. This reflected stimulus enters the eye and is perceived as an “object color.” If we consider all possible object colors produced by a given illuminant, and map them into a three-dimensional color space (like sRGB or XYZ tristimulus values), they collectively form what is known as the object color solid. The object colors that map to the outer surface of the object color solid are known as “optimal colors.” They can be thought of as the most saturated object color for a given hue and lightness. A long-standing theoretical question is, “what is the nature of the object spectral reflectance distribution that is associated with an optimal object color?” This journal article investigates and answers that question.

Abstract

The chromaticity diagram associated with the 1931 2-degree CIE 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 located on the outer surface of the object color solid. Instead of the usual two-transition Schrödinger 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 high-transition behavior is shown to be largely absent in more modern color-matching functions, such as the recent “physiologically-relevant” color-matching functions transformed from cone fundamentals.

Link to PDF

The PDF of this journal article can be found here: The location of optimal object colors with more than two transitions, Burns 2021