Riemannian Inhomogeneity and Anisotropy of Perceptual Color Space

The geometry of perceived color space is widely recognized as non-Euclidean, with the Riemannian framework commonly adopted for its analysis. However, existing evidence, such as the principle of diminishing returns, suggests that the color space may be globally non-Riemannian. In this work, we investigate the local inhomogeneities of the perceived color space under the Riemannian setting. Specifically, we evaluate the local agreement between the Riemannian model and the color-difference function. To achieve this, we perform numerical experiments to assess the accuracy of the parallelogram law, a necessary condition for the local validity of the metric tensor. Furthermore, we introduce several measures of local anisotropy to quantify directional variations in perceived color distances and compute these measures within the chromatic planes of the CIELAB color space. Our findings describe the spatial variation of Riemannian inhomogeneities and distance anisotropy, which can be used to construct adaptive spatial meshes and improve the accuracy of computations in color space. While our techniques are demonstrated on the CIELAB color model with the ΔE2000 metric, they are generalizable to the discretization of arbitrary non-Euclidean metric spaces.