On the Utility of Mathematical Spaces for Representing Color Stimuli and Color Perceptions

Fairchild has argued that color spaces are of questionable utility for understanding perception. Here, we go through various concepts of mathematical spaces, ranging from abstract topological spaces to Euclidean ones, and discuss how color stimuli, color matches, and color perceptions can be adequately represented by means of some of these spaces. In particular, we argue that the set of color perceptions can be represented as a metric space that is homeomorphic to a neither open nor closed convex cone in an n ‐dimensional Banach space of equivalence classes of “generalized metamers.” Finally, for higher color metrics, we sketch how Riemannian geometry can be used to create a unified representation of color stimuli and color perceptions.