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...

Full description

Saved in:
Bibliographic Details
Main Authors: Francesco Ballerin, Erlend Grong
Format: Article
Language:English
Published: Elsevier 2025-02-01
Series:Graphical Models
Subjects:
Online Access:http://www.sciencedirect.com/science/article/pii/S1524070324000274
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1846139899433975808
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