A Metric for Three-Dimensional Color Discrimination Derived from V1 Population Fisher Information

Abstract: We derive a Riemannian metric on three-dimensional color space from the Fisher information of neural population codes in the visual pathway. Photoreceptor adaptation, retinal opponent channels, and cortical population encoding each map onto a geometric construction, producing a metric tensor whose components correspond to measurable neural quantities. The resulting 17-parameter model is fitted jointly to four independent threshold datasets: MacAdam's (1942) chromaticity ellipses, the Koenderink et al. (2026) three-dimensional ellipsoids, Wright's (1941) wavelength discrimination function, and the Huang et al. (2012) threshold color difference ellipses, covering 96 independently measured discrimination conditions across varied chromaticities and luminances. The joint fit achieves STRESS of 23.9 on MacAdam, 20.8 on Koenderink et al., 30.1 on Wright, and 30.8 on Huang et al.