Combinatorial Ricci Curvature and Laplacians for Image Processing

A new Combinatorial Ricci curvature and Laplacian operators for grayscale images are introduced and tested on 2D synthetic, natural and medical images. The effectiveness of the notions introduced herein, as compared with more classical methods, is shown by a variety of experimental results. Analogue formulae for voxels are also obtained. This novel approach is based upon more general concepts developed by R. Forman. Further applications, in particular a fitting Ricci flow, are discussed.