Cortical-inspired image reconstruction via sub-Riemannian geometry and hypoelliptic diffusion

Ugo Boscain; Roman Chertovskih; Jean-Paul Gauthier; Dario Prandi; Alexey Remizov

Cortical-inspired image reconstruction via sub-Riemannian geometry and hypoelliptic diffusion

Ugo Boscain ^{1, 2} Roman Chertovskih ³ Jean-Paul Gauthier ⁴ Dario Prandi ^{5, 1} Alexey Remizov ⁶

1 CNRS - Centre National de la Recherche Scientifique

2 LJLL - Laboratoire Jacques-Louis Lions

3 IEPT - Institute of Earthquake Prediction Theory and Mathematical Geophysics

4 LSIS - Laboratoire des Sciences de l'Information et des Systèmes

5 L2S - Laboratoire des signaux et systèmes

6 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

Abstract : In this paper we review several algorithms for image inpainting based on the hypoelliptic diffusion naturally associated with a mathematical model of the primary visual cortex. In particular, we present one algorithm that does not exploit the information of where the image is corrupted, and others that do it. While the first algorithm is able to reconstruct only images that our visual system is still capable of recognize, we show that those of the second type completely transcend such limitation providing reconstructions at the state-of-the-art in image inpainting. This can be interpreted as a validation of the fact that our visual cortex actually encodes the first type of algorithm.

Document type :

Conference papers

Domain :

Mathematics [math] / Optimization and Control [math.OC]

Computer Science [cs] / Numerical Analysis [cs.NA]

Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-01721718
Contributor : Dario Prandi <>
Submitted on : Friday, March 2, 2018 - 2:26:05 PM
Last modification on : Tuesday, April 2, 2019 - 2:03:29 AM

Cortical-inspired image reconstruction via sub-Riemannian geometry and hypoelliptic diffusion

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Cortical-inspired image reconstruction via sub-Riemannian geometry and hypoelliptic diffusion

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