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.

翻译：受视觉皮层V1区启发的旋转平移群$SE(2)$上子黎曼结构，我们提出了基于亚椭圆扩散的图像修复与增强算法。针对Citti、Sarti及Boscain等人先前实现的方法，我们提出了一种可防止褪色现象并产生更清晰结果的替代方案，该流程称为WaxOn-WaxOff。同时利用子黎曼结构，我们定义了一种基于$SE(2)$的全新非锐化掩模——对应于经典二维图像非锐化滤波器的类似物——并将其应用于图像增强。我们以视网膜扫描图像中的血管增强为例展示了该方法的效果。