Geometric models for color perception




Yilmaz, Resnikoff, Jordan Algebras, relativity, quantum mechanics, mathematical models for color perception


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. 


Berthier, M. (2020). Geometry of color perception. Part 2: perceived colors from real quantum states and Hering's rebit. The Journal of Mathematical Neuroscience, 10, 14.

Berthier M., Provenzi E. (2019). When geometry meets psycho-physics and quantum mechanics: Modern perspectives on the space of perceived colors. International Conference on Geometric Science of Information. Springer, pp. 621-630.

Prencipe, N., Garcin, V., Provenzi, E. (2020). Origins of hyperbolicity in color perception. Journal of Imaging, MDPI, 6 (42), pp.1-19.

Provenzi, E. (2020). Geometry of color perception. Part 1: Structures and metrics of a homogeneous color space. The Journal of Mathematical Neuroscience, 10 (7), pp.1-19.

Resnikoff, H.L. (1974). Differential geometry and color perception. Journal of Mathematical Biology, 1, 97-131.

Schrödinger E. (1920). Grundlinien einer theorie der farbenmetrik im tagessehen (Outline of a theory of colour measurement for daylight vision). Available in English in Sources of Colour Science, Ed. David L. Macadam, The MIT Press (1970), 134-82. Annalen der Physik, 63(4):397–456; 481–520.

Yilmaz, H. (1962). On color perception. The Bulletin of Mathematical Biophysics; 24, 5-29.

Yilmaz, H. (1962). Color vision and a new approach to general perception, Biological Prototypes and Synthetic Systems. Springer: Boston, MA, USA; pp. 126-141.

Wyszecki, G., & Stiles, W. S. (1982).?Color science?(Vol. 8). New York: Wiley.




How to Cite

Prencipe, N. and Provenzi, E. (2021) “Geometric models for color perception ”, Cultura e Scienza del Colore - Color Culture and Science, 13(02), pp. 50–56. doi: 10.23738/CCSJ.130206b.