Geodesic
Cortical-inspired image reconstruction via sub-Riemannian geometry and hypoelliptic diffusion
Ugo Boscain1, 2 ; Roman Chertovskih3, 4 ; Jean-Paul Gauthier5 ; Dario Prandi6 ; Alexey Remizov7
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 Cet article a éte moissonné depuis la source EDP Sciences

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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

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 
@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},
     year = {2018},
     volume = {64},
     doi = {10.1051/proc/201864037},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201864037/}
}
TY  - JOUR
AU  - Ugo Boscain
AU  - Roman Chertovskih
AU  - Jean-Paul Gauthier
AU  - Dario Prandi
AU  - Alexey Remizov
TI  - Cortical-inspired image reconstruction via sub-Riemannian geometry and hypoelliptic diffusion
JO  - ESAIM. Proceedings
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DO  - 10.1051/proc/201864037
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%0 Journal Article
%A Ugo Boscain
%A Roman Chertovskih
%A Jean-Paul Gauthier
%A Dario Prandi
%A Alexey Remizov
%T Cortical-inspired image reconstruction via sub-Riemannian geometry and hypoelliptic diffusion
%J ESAIM. Proceedings
%D 2018
%P 37-53
%V 64
%U http://geodesic.mathdoc.fr/articles/10.1051/proc/201864037/
%R 10.1051/proc/201864037
%G en
%F EP_2018_64_a3
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

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