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

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.

arXiv commentThis is the revised extended invited journal version of the SSVM 2019 conference proceeding arXiv:1812.07425

References in corpus (8)

• A constructive mean field analysis of multi population neural networks with random synaptic weights and stochastic inputs
• A Multi-Orientation Analysis Approach to Retinal Vessel Tracking
• Derivatives and Inverse of Cascaded Linear+Nonlinear Neural Models
• Geometrical Optical Illusion via Sub-Riemannian Geodesics in the Roto-Translation Group
• Numerical Approaches for Linear Left-invariant Diffusions on SE(2), their Comparison to Exact Solutions, and their Applications in Retinal Imaging
• Highly corrupted image inpainting through hypoelliptic diffusion
• A semidiscrete version of the Citti-Petitot-Sarti model as a plausible model for anthropomorphic image reconstruction and pattern recognition
• Fourier descriptors based on the structure of the human primary visual cortex with applications to object recognition

Cited by in corpus (3)

• A cortical-inspired sub-Riemannian model for Poggendorff-type visual illusions
• Reproducibility via neural fields of visual illusions induced by localized stimuli
• Multi-frequency image completion via a biologically-inspired sub-Riemannian model with frequency and phase