Cortical-inspired image reconstruction via sub-Riemannian geometry and hypoelliptic diffusion
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 t...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
EDP Sciences
2018-01-01
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| Series: | ESAIM: Proceedings and Surveys |
| Online Access: | https://doi.org/10.1051/proc/201864037 |
| _version_ | 1797971206709706752 |
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| author | Boscain Ugo Chertovskih Roman Gauthier Jean-Paul Prandi Dario Remizov Alexey |
| author_facet | Boscain Ugo Chertovskih Roman Gauthier Jean-Paul Prandi Dario Remizov Alexey |
| author_sort | Boscain Ugo |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-11T03:28:58Z |
| format | Article |
| id | doaj.art-599ee54b20a94ba698993fd055789ec9 |
| institution | Directory Open Access Journal |
| issn | 2267-3059 |
| language | English |
| last_indexed | 2024-04-11T03:28:58Z |
| publishDate | 2018-01-01 |
| publisher | EDP Sciences |
| record_format | Article |
| series | ESAIM: Proceedings and Surveys |
| spelling | doaj.art-599ee54b20a94ba698993fd055789ec92023-01-02T06:44:38ZengEDP SciencesESAIM: Proceedings and Surveys2267-30592018-01-0164375310.1051/proc/201864037proc186403Cortical-inspired image reconstruction via sub-Riemannian geometry and hypoelliptic diffusionBoscain UgoChertovskih RomanGauthier Jean-PaulPrandi DarioRemizov AlexeyIn 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.https://doi.org/10.1051/proc/201864037 |
| spellingShingle | Boscain Ugo Chertovskih Roman Gauthier Jean-Paul Prandi Dario Remizov Alexey Cortical-inspired image reconstruction via sub-Riemannian geometry and hypoelliptic diffusion ESAIM: Proceedings and Surveys |
| title | Cortical-inspired image reconstruction via sub-Riemannian geometry and hypoelliptic diffusion |
| title_full | Cortical-inspired image reconstruction via sub-Riemannian geometry and hypoelliptic diffusion |
| title_fullStr | Cortical-inspired image reconstruction via sub-Riemannian geometry and hypoelliptic diffusion |
| title_full_unstemmed | Cortical-inspired image reconstruction via sub-Riemannian geometry and hypoelliptic diffusion |
| title_short | Cortical-inspired image reconstruction via sub-Riemannian geometry and hypoelliptic diffusion |
| title_sort | cortical inspired image reconstruction via sub riemannian geometry and hypoelliptic diffusion |
| url | https://doi.org/10.1051/proc/201864037 |
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