Hypoelliptic diffusion and human vision: a semi-discrete new twist on the Petitot theory
Abstract
This paper is devoted to present an algorithm implementing the theory of neurogeometry of vision, described by Jean Petitot in his book. We propose a new ingredient, namely working on the group of translations and discrete rotations SE(2,N). We focus on the theoretical and numerical aspects of integration of an hypoelliptic diffusion equation on this group. Our main tool is the generalized Fourier transform. We provide a complete numerical algorithm, fully parallellizable. The main objective is the validation of the neurobiological model.