Geometry of the Visual Cortex with Applications to Image Inpainting and Enhancement

TL;DR

This paper introduces a novel sub-Riemannian geometric framework on the rototranslation group for image processing, improving inpainting and enhancement techniques by preventing fading and producing sharper results, with applications to retinal blood vessel enhancement.

Contribution

It proposes an alternative hypoelliptic diffusion method called WaxOn-WaxOff that enhances image inpainting and sharpening, and introduces a new unsharp filter based on the $SE(2)$ structure.

Findings

Enhanced retinal blood vessel images using the proposed method.

Prevention of fading in inpainting results.

Sharper image reconstructions compared to previous methods.

Abstract

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.