On the questionable use of CIEL* to infer geometric properties of achromatic perception.

In the paper "The non‐Riemannian nature of perceptual color space," the authors analyze the data of visual experiments conducted using triad of CIE L* achromatic stimuli. The statistical analysis of their results leads them to claim that the L* axis cannot be endowed with a Riemannian metric coherent with observers' responses. In this communication we provide a mathematical analysis which, in our opinion, refutes the main claim of the quoted paper. Furthermore, we raise questions on the soundness of using an achromatic perceptual coordinate to describe non‐chromatic perception. We inform about an alternative in which achromaticity emerges from the very act of observing colors (Provenzi E. SIAM J Imag Sci, 15(4):1944–1976, 2022; Berthier M, Provenzi E. Proc R Soc A, 478(2258):20210508, 2022). [ABSTRACT FROM AUTHOR]