A Cortical-Inspired Sub-Riemannian Model for Poggendorff-Type Visual Illusions
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 i...
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doaj-e9a38d55fa5644de80becc7cd64864d12021-02-25T00:03:23ZengMDPI AGJournal of Imaging2313-433X2021-02-017414110.3390/jimaging7030041A Cortical-Inspired Sub-Riemannian Model for Poggendorff-Type Visual IllusionsEmre Baspinar0Luca Calatroni1Valentina Franceschi2Dario Prandi3INRIA Sophia Antipolis Méditerranée, MathNeuro, 06902 Sophia Antipolis, FranceCNRS, UCA, INRIA Sophia Antipolis Méditerranée, Morpheme, I3S, 06902 Sophia Antipolis, FranceDipartimento di Matematica Tullio Levi-Civita, Università di Padova, 35131 Padova, ItalyCNRS, CentraleSupélec, Laboratoire des Signaux et des Systèmes, Université Paris-Saclay, 91190 Gif-sur-Yvette, FranceWe 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.https://www.mdpi.com/2313-433X/7/3/41Wilson-Cowan modellingvisual illusionscortical-inspired imaginglocal histogram equalisationsub-Riemannian heat kernel |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Emre Baspinar Luca Calatroni Valentina Franceschi Dario Prandi |
spellingShingle |
Emre Baspinar Luca Calatroni Valentina Franceschi Dario Prandi A Cortical-Inspired Sub-Riemannian Model for Poggendorff-Type Visual Illusions Journal of Imaging Wilson-Cowan modelling visual illusions cortical-inspired imaging local histogram equalisation sub-Riemannian heat kernel |
author_facet |
Emre Baspinar Luca Calatroni Valentina Franceschi Dario Prandi |
author_sort |
Emre Baspinar |
title |
A Cortical-Inspired Sub-Riemannian Model for Poggendorff-Type Visual Illusions |
title_short |
A Cortical-Inspired Sub-Riemannian Model for Poggendorff-Type Visual Illusions |
title_full |
A Cortical-Inspired Sub-Riemannian Model for Poggendorff-Type Visual Illusions |
title_fullStr |
A Cortical-Inspired Sub-Riemannian Model for Poggendorff-Type Visual Illusions |
title_full_unstemmed |
A Cortical-Inspired Sub-Riemannian Model for Poggendorff-Type Visual Illusions |
title_sort |
cortical-inspired sub-riemannian model for poggendorff-type visual illusions |
publisher |
MDPI AG |
series |
Journal of Imaging |
issn |
2313-433X |
publishDate |
2021-02-01 |
description |
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. |
topic |
Wilson-Cowan modelling visual illusions cortical-inspired imaging local histogram equalisation sub-Riemannian heat kernel |
url |
https://www.mdpi.com/2313-433X/7/3/41 |
work_keys_str_mv |
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