Geometry of the visual cortex with applications to image inpainting and enhancement
Equipping the rototranslation group SE(2) with a sub-Riemannian structure inspired by the visual cortex V1, we propose algorithms for image inpainting and enhancement based on hypoelliptic diffusion. We innovate on previous implementations of the methods by Citti, Sarti, and Boscain et al., by propo...
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| Format: | Article |
| Language: | English |
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Elsevier
2025-02-01
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| Series: | Graphical Models |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S1524070324000274 |
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| _version_ | 1846139899433975808 |
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| author | Francesco Ballerin Erlend Grong |
| author_facet | Francesco Ballerin Erlend Grong |
| author_sort | Francesco Ballerin |
| collection | DOAJ |
| description | Equipping the rototranslation group SE(2) with a sub-Riemannian structure inspired by the visual cortex V1, we propose algorithms for image inpainting and enhancement based on hypoelliptic diffusion. We innovate on previous implementations of the methods by Citti, Sarti, and Boscain et al., by proposing an alternative that prevents fading and is capable of producing sharper results in a procedure that we call WaxOn-WaxOff. We also exploit the sub-Riemannian structure to define a completely new unsharp filter using SE(2), analogous to the classical unsharp filter for 2D image processing. We demonstrate our method on blood vessels enhancement in retinal scans. |
| format | Article |
| id | doaj-art-8524e166278747d8ab9b76a3a73554a2 |
| institution | Kabale University |
| issn | 1524-0703 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Graphical Models |
| spelling | doaj-art-8524e166278747d8ab9b76a3a73554a22024-12-06T05:13:06ZengElsevierGraphical Models1524-07032025-02-01137101239Geometry of the visual cortex with applications to image inpainting and enhancementFrancesco Ballerin0Erlend Grong1Corresponding author.; Department of Mathematics, University of Bergen, NorwayDepartment of Mathematics, University of Bergen, NorwayEquipping the rototranslation group SE(2) with a sub-Riemannian structure inspired by the visual cortex V1, we propose algorithms for image inpainting and enhancement based on hypoelliptic diffusion. We innovate on previous implementations of the methods by Citti, Sarti, and Boscain et al., by proposing an alternative that prevents fading and is capable of producing sharper results in a procedure that we call WaxOn-WaxOff. We also exploit the sub-Riemannian structure to define a completely new unsharp filter using SE(2), analogous to the classical unsharp filter for 2D image processing. We demonstrate our method on blood vessels enhancement in retinal scans.http://www.sciencedirect.com/science/article/pii/S1524070324000274Image inpaintingImage enhancementNeurogeometrySub-Riemannian diffusionRototranslation groupUnsharp filter |
| spellingShingle | Francesco Ballerin Erlend Grong Geometry of the visual cortex with applications to image inpainting and enhancement Graphical Models Image inpainting Image enhancement Neurogeometry Sub-Riemannian diffusion Rototranslation group Unsharp filter |
| title | Geometry of the visual cortex with applications to image inpainting and enhancement |
| title_full | Geometry of the visual cortex with applications to image inpainting and enhancement |
| title_fullStr | Geometry of the visual cortex with applications to image inpainting and enhancement |
| title_full_unstemmed | Geometry of the visual cortex with applications to image inpainting and enhancement |
| title_short | Geometry of the visual cortex with applications to image inpainting and enhancement |
| title_sort | geometry of the visual cortex with applications to image inpainting and enhancement |
| topic | Image inpainting Image enhancement Neurogeometry Sub-Riemannian diffusion Rototranslation group Unsharp filter |
| url | http://www.sciencedirect.com/science/article/pii/S1524070324000274 |
| work_keys_str_mv | AT francescoballerin geometryofthevisualcortexwithapplicationstoimageinpaintingandenhancement AT erlendgrong geometryofthevisualcortexwithapplicationstoimageinpaintingandenhancement |