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

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

doi:10.1051/proc/201864037

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

Ugo Boscain ^1,² ; Roman Chertovskih ^3,⁴ ; Jean-Paul Gauthier ⁵ ; Dario Prandi ⁶ ; Alexey Remizov ⁷

¹ CNRS, LJLL, Université Pierre et Marie Curie, Paris, France
² Équipe INRIA Paris CAGE
³ SYSTEC, FEUP, University of Porto, Portugal
⁴ Samara University, Russia
⁵ LSIS, Université de Toulon, France
⁶ CRNS, L2S, CentraleSupélec, Gif-sur-Yvette, France
⁷ CMAP, École Polytechnique, Palaiseau, France

ESAIM. Proceedings, Tome 64 (2018), pp. 37-53.

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Résumé

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.

DOI : 10.1051/proc/201864037

Affiliations des auteurs :

Ugo Boscain ^{1, 2} ; Roman Chertovskih ^{3, 4} ; Jean-Paul Gauthier ⁵ ; Dario Prandi ⁶ ; Alexey Remizov ⁷

@article{EP_2018_64_a3,
     author = {Ugo Boscain and Roman Chertovskih and Jean-Paul Gauthier and Dario Prandi and Alexey Remizov},
     title = {Cortical-inspired image reconstruction via {sub-Riemannian} geometry and hypoelliptic diffusion},
     journal = {ESAIM. Proceedings},
     pages = {37--53},
     publisher = {mathdoc},
     volume = {64},
     year = {2018},
     doi = {10.1051/proc/201864037},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201864037/}
}

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Ugo Boscain; Roman Chertovskih; Jean-Paul Gauthier; Dario Prandi; Alexey Remizov. Cortical-inspired image reconstruction via sub-Riemannian geometry and hypoelliptic diffusion. ESAIM. Proceedings, Tome 64 (2018), pp. 37-53. doi : 10.1051/proc/201864037. http://geodesic.mathdoc.fr/articles/10.1051/proc/201864037/

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