Calculus of Variations and Geometric Measure Theory

E. Baspinar - L. Calatroni - V. Franceschi - D. Prandi

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

created by franceschi on 04 Jan 2021
modified on 18 Mar 2021


Published Paper

Inserted: 4 jan 2021
Last Updated: 18 mar 2021

Journal: Journal of Imaging
Year: 2020

ArXiv: 2012.14184 PDF


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 realisation 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.