Ricci flow for image processing

摘要

A new discrete model of the Ricci flow for images is presented, using a purely combinatorial method for calculating the Ricci curvature, based on R. Forman's work on generalized Laplacians for cell complexes. We describe the discrete Ricci curvature operator, and the implementation of the Ricci flow, and then proceed to show the results of applying the flow to both synthetic and real images. Finally, we implement the discrete Ricci flow in some applications of image processing and vision, such as high dynamic range (HDR) imaging, forward-and-backward (FAB) Ricci flow, and change detection in aerial images.