Abstract

We consider Wilson-Cowan-type models for the mathematical description of orientation-dependent Poggendorff-like illusions. Our modelling improves two previously proposed cortical-inspired approaches, embedding the sub-Riemannian heat kernel into the neuronal interaction term, in agreement with the intrinsically anisotropic functional architecture of V1 based on both 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 us to reproduce numerically visual misperceptions and inpainting-type biases in a stronger way in comparison with the previous approaches.

Highlights

  • The question of how we perceive the world around us has been an intriguing topic since ancient times

  • A well-known and accepted theory of perception is that formulated within Gestalt psychology [1,2]

  • There have been many psychophysical studies which have attempted to provide quantitative parameters describing the tendencies of the mind in visual perception based on Gestalt psychology

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Summary

A Cortical-Inspired Sub-Riemannian Model for Poggendorff-Type Visual Illusions

Emre Baspinar 1,*,†, Luca Calatroni 2,†, Valentina Franceschi 3,† and Dario Prandi 4,†.

Introduction
The Functional Architecture of the Primary Visual Cortex
Main Contributions
Cortical-Inspired Modelling
Receptive Profiles
Horizontal Connectivity and Sub-Riemannian Diffusion
Reconstruction on the Retinal Plane
Describing Neuronal Activity via Wilson-Cowan-Type Models
A Sub-Riemannian Choice of the Interaction Kernel ωξ
Discrete Modelling and Numerical Realisation
Discrete Modelling and Lifting Procedure via Cake Wavelets
Sub-Riemannian Heat Diffusion
Discretisation via Gradient Descent
Pseudocode
Poggendorff Gratings
Dependence on Parameters
Poggendorff Illusion
Conclusions
Full Text
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