Generalized Ricci curvature based sampling and reconstruction of images

Abstract

We introduce a novel method of image sampling based on viewing grayscale images as manifolds with density, and sampling them according to the generalized Ricci curvature introduced by Bakry, Emery and Ledoux. A variation of this approach, due to Morgan and his students is also considered. This new paradigm generalizes ideas and results that are by now common in Imaging and Graphics. We apply the new algorithm to natural and range images, as well as cartoons and show that the proposed method produces results similar to those obtained by employing more standard approaches. Furthermore, we show that our approach extends naturally to other types of images, in particular to MRI and CT, where its potential applications are maximal, as well as to meshes.