An empirical three-dimensional metric field for color space

Abstract

A complete empirical characterization of color discrimination in three dimensions has long remained out of reach. Classical studies, beginning with MacAdam's ellipses, provided local measurements in restricted chromatic planes, but a spatially dense and internally consistent mapping of discrimination structure across full color space has not yet been achieved. Here, we present such a systematic three-dimensional measurement of color discrimination in the standardized sRGB stimulus space. Eight observers measured discrimination regions at 35 reference colors distributed on a body-centered cubic lattice within the RGB cube. At each location, color differences were probed along seven orientations, yielding 14 directional extents. These measurements defined centrally symmetric convex regions that were fitted with minimum-volume ellipsoids, providing a compact description of local discrimination structure. Ellipsoids were represented as symmetric positive-definite matrices and analyzed using a Frobenius geometry, enabling normalization across observers and smooth interpolation to arbitrary locations. The resulting metric field is spatially smooth, highly structured, and remarkably consistent across observers up to an individual global scale factor. Grain size increases along the achromatic axis and exhibits systematic chromatic asymmetries. Comparison with CIEDE2000 reveals substantial agreement in overall scale variation but systematic differences in local anisotropy. Because the metric field is defined geometrically, it can be transformed into linear RGB or any other color representation through the corresponding coordinate transformations. Together, these data provide a coherent three-dimensional empirical mapping of color discrimination across a large ecologically relevant volume of color space and establish an empirical framework for perceptual color metrics.