The Geometry of Color in the Light of a Non‐Riemannian Space

Abstract We formalize Schrödinger's definitions of hue, saturation, and lightness, building on the foundational idea from Helmholtz that these perceptual attributes can be derived solely from the perceptual metric. We identify three shortcomings in Schrödinger's approach and propose solutions to them. First, to encompass the Bezold‐Brücke effect, we replace the straight‐line definition of stimulus quality between a color and black with the geodesic path in perceptual color space. Second, to model diminishing returns in color perception, we employ a non‐Riemannian perceptual metric, which introduces a potential ambiguity in defining lightness, but our experiments show that this ambiguity is inconsequential. Third, we provide a geometric definition of the neutral axis as the closest color to black within each equal‐lightness surface—a definition feasible only in a non‐Riemannian framework. Collectively, our solutions provide the first comprehensive realization of Helmholtz's vision: formal geometric definitions of hue, saturation, and lightness derived entirely from the metric of perceptual similarity, without reliance on external constructs.