Calculus of Variations and Geometric Measure Theory

M. Bertalmío - L. Calatroni - V. Franceschi - B. Franceschiello - D. Prandi

Cortical-inspired Wilson-Cowan-type equations for orientation-dependent contrast perception modelling

created by franceschi on 04 Mar 2020
modified on 15 May 2020


Published Paper

Inserted: 4 mar 2020
Last Updated: 15 may 2020

Journal: JMIV
Year: 2020

ArXiv: 1910.06808 PDF


We consider the evolution model proposed in 9, 6 to describe illusory contrast perception phenomena induced by surrounding orientations. Firstly, we highlight its analogies and differences with widely used Wilson-Cowan equations 48, mainly in terms of efficient representation properties. Then, in order to explicitly encode local directional information, we exploit the model of the primary visual cortex V1 proposed in 20 and largely used over the last years for several image processing problems 24,38,28. The resulting model is capable to describe assimilation and contrast visual bias at the same time, the main novelty being its explicit dependence on local image orientation. We report several numerical tests showing the ability of the model to explain, in particular, orientation-dependent phenomena such as grating induction and a modified version of the Poggendorff illusion. For this latter example, we empirically show the existence of a set of threshold parameters differentiating from inpainting to perception-type reconstructions, describing long-range connectivity between different hypercolumns in the primary visual cortex.