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 proposing an alternative that prevents fading and 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 using $SE(2)$, analogous of the classical unsharp filter for 2D image processing, with applications to image enhancement. We demonstrate our method on blood vessels enhancement in retinal scans.