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A Cortical-Inspired Sub-Riemannian Model for Poggendorff-Type Visual Illusions
Emre Baspinar1, Luca Calatroni2, Valentina Franceschi3
1INRIA Sophia Antipolis Méditerranée, MathNeuro, 06902 Sophia Antipolis, France.
Journal of Imaging
|August 30, 2021
Summary
This study enhances computational models of visual perception, using a novel sub-Riemannian kernel to better explain orientation-dependent illusions like the Poggendorff effect in the brain
Area of Science:
- Computational neuroscience
- Mathematical modeling of visual illusions
Background:
- The Poggendorff illusion demonstrates orientation-dependent visual misperceptions.
- Existing models struggle to fully capture the complex neural processing in the visual cortex (V1).
Purpose of the Study:
- To develop an improved Wilson-Cowan model for describing orientation-dependent Poggendorff-like illusions.
- To incorporate the anisotropic functional architecture of V1 into a computational model.
Main Methods:
- Embedding a sub-Riemannian heat kernel into the neuronal interaction term of Wilson-Cowan models.
- Utilizing gradient descent and Fourier-based methods for numerical computation of sub-Laplacian evolution.
- Comparing the new model with previously proposed cortical-inspired approaches.
Main Results:
- The sub-Riemannian kernel approach provides a stronger numerical reproduction of visual misperceptions.
- The model successfully captures inpainting-type biases observed in visual processing.
- The enhanced model aligns better with the anisotropic nature of V1 connections.
Conclusions:
- The sub-Riemannian heat kernel offers a more effective mathematical tool for modeling visual illusions.
- This approach improves our understanding of neural mechanisms underlying visual perception and V1 function.
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