Ricci curvature and flow for image denoising and super-resolution

Abstract

A discrete version of the Ricci flow, applicable to images, is introduced and applied in image denoising and in single-image-based enhancement and super-resolution. This flow is unique among the geometric flows that have been applied in image processing, in that it is the only flow wherein the metric of an image evolves rather than the image itself as is the case in other geometric flows applicable in image processing. The flow is based on the combinatorial Ricci curvature defined by Forman, that was previously introduced by the authors in the context of image processing. It is shown that the Ricci flow preserves image structure much better than the Beltrami flow and other state-of-the-art image enhancement schemes. Implementation of the Ricci flow is applicable also to general surfaces such as required in computer graphics and other applications.