In this talk, we present a framework for processing discrete manifold-valued data, for which the underlying (sampling) topology is modeled by a graph. We introduce the notion of a manifold-valued derivative on a graph and based on this exemplarily deduce a family of manifold-valued graph p-Laplace operators. We discuss a simple numerical scheme to compute a solution to corresponding parabolic PDEs and apply this algorithm to different manifold-valued data in denoising and inpainting applications.

This presentation is part of Minisymposium “MS4 - Graph Techniques for Image Processing (2 parts)”
organized by: Yifei Lou (University of Texas at Dallas) , Jing Qin (Montana State University) .

Authors:

Daniel Tenbrinck (University of Münster)

Ronny Bergmann (Technische Universität Chemnitz)

Keywords:

graph methods, image reconstruction, inpainting, inverse problems, manifold-valued data, partial differential equation models