Geometric models for color perception

Abstract

In 1962 and 1974, respectively H. Yilmaz and H.L. Resnikoff published two groundbreaking articles about color perception, which were ignored by the scientific community. Yilmaz showed the striking analogy between Lorentz transformations and the modification of color perception under illuminant changes. On the other hand, Resnikoff, using mathematical techniques coming from theoretical physics, studied the possible geometrical representations of a homogeneous space of perceived colors, i.e. a space in which all the elements have “the same importance”. Both works come up to the same conclusion: the structure of the space of perceived colors can be better characterized through hyperbolic geometry, while usual color spaces have a Euclidean structure. In this work, we show how a modern revision of these important articles allows us to highlight a correlation between the colorimetric attributes and some objects of special relativity theory and quantum mechanics, opening innovative perspectives in the theoretical comprehension of perceptual phenomena related to human chromatic vision. A remarkable result of this new formalism concerns the retinal chromatic encoding expressed by the sum of an achromatic signal and two opponent chromatic signals (typically called red-green and yellow-blue). This looks as an intrinsic description of a so-called “color state”, in contrast to what happens in natural image statistics, where such an encoding is not an intrinsic result of the theory, but it is obtained through a principal component analysis.