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

TL;DR

This paper introduces a cortical-inspired Wilson-Cowan-type model that incorporates orientation-dependent information to better simulate contrast perception phenomena, including illusions and visual biases, in the primary visual cortex.

Contribution

It extends existing models by explicitly encoding local orientation information, enabling the simulation of complex visual perception phenomena and long-range cortical connectivity.

Findings

Successfully reproduces orientation-dependent illusions like grating induction

Identifies threshold parameters distinguishing perception from inpainting

Demonstrates the model's ability to simulate long-range V1 connectivity

Abstract

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 the 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 thus defined in the space of positions and orientation and it is capable to describe assimilation and contrast visual bias at the same time. We report several numerical tests showing the ability of the model to reproduce, 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 and describing long-range connectivity between different hypercolumns in V1.