From Riemannian trichromacy to quantum color opponency via hyperbolicity

Michel Berthier (1) , Edoardo Provenzi (2)

1 MIA - Mathématiques, Image et Applications - EA 3165
2 IMB - Institut de Mathématiques de Bordeaux

We propose a mathematical description of human color perception that relies on a hyper-bolic structure of the space P of perceived colors. We show that hyperbolicity allows us to reconcile both trichromaticity, from a Riemannian point of view, and color opponency, from a quantum viewpoint. In particular, we will underline how the opponent behavior can be represented by a rebit, a real analog of a qubit, whose state space is endowed with the Hilbert metric.

Domaines: Géométrie différentielle [math.DG]; Traitement du signal et de l'image [eess.SP]; Physique Quantique [quant-ph]

Michel Berthier, Edoardo Provenzi. From Riemannian trichromacy to quantum color opponency via hyperbolicity. 2020. ⟨hal-02479897⟩