When dealing with manifold-valued data one faces the same challenging processing tasks as, e.g., in classical imaging. In this talk we consider image inpainting for manifold-valued data in which missing information have to be filled in suitably. We present a generalization of the graph infinity-Laplacian to manifold-valued data based on the min-max characterization of the local discrete Lipschitz constant. We derive a numerical scheme to solve the obtained manifold-valued infinity-Laplace equation and inpaint missing data.

This presentation is part of Minisymposium “MS31 - Variational Approaches for Regularizing Nonlinear Geometric Data (3 parts)”
organized by: Martin Storath (Universität Heidelberg) , Martin Holler (École Polytechnique, Université Paris Saclay) , Andreas Weinmann (Hochschule Darmstadt) .

Authors:

Ronny Bergmann (Technische Universität Chemnitz)

Daniel Tenbrinck (University of Münster)

Keywords:

image reconstruction, inverse problems, manifold-valued data, nonlinear optimization, optimization on manifolds