A cortical-inspired sub-Riemannian model for Poggendorff-type visual illusions

Abstract

We consider Wilson-Cowan-type models for the mathematical orientation-dependent description of Poggendorff-like illusions. Our modelling improves the cortical-inspired approaches used in [1,2] by encoding within the neuronal interaction term the sub-Riemannian heat kernel, in agreement with the intrinsically anisotropic functional architecture of V1 based both on local and lateral connections. For the numerical realization of both models, we consider standard gradient descent algorithms combined with Fourier-based approaches for the efficient computation of the sub-Laplacian evolution. Our numerical results show that the use of the sub-Riemannian kernel allows to reproduce numerically visual misperceptions and inpainting-type biases that standard approaches were not able to replicate [3].