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.

基于受视觉皮层 V1 启发并赋予 rototranslation 群 SE (2) 一个次黎曼结构，我们提出了一种基于次椭球扩散的图像修复和增强算法。通过我们称之为 WaxOn-WaxOff 的过程，我们创新性地改进了 Citti、Sarti 和 Boscain 等人之前的方法的实现，以防止消失并能够产生更清晰的结果。我们还利用次黎曼结构为 SE (2) 定义了一个全新的类似于经典二维图像处理中的 unsharp 滤波器的 unsharp filter，并应用于图像增强。我们在视网膜扫描中的血管增强上演示了我们的方法。