Nonlocal Inpainting of Manifold-Valued Data on Finite Weighted Graphs

  • Ronny BergmannEmail author
  • Daniel Tenbrinck
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10589)


Recently, there has been a strong ambition to translate models and algorithms from traditional image processing to non-Euclidean domains, e.g., to manifold-valued data. While the task of denoising has been extensively studied in the last years, there was rarely an attempt to perform image inpainting on manifold-valued data. In this paper we present a nonlocal inpainting method for manifold-valued data given on a finite weighted graph. We introduce a new graph infinity-Laplace operator based on the idea of discrete minimizing Lipschitz extensions, which we use to formulate the inpainting problem as PDE on the graph. Furthermore, we derive an explicit numerical solving scheme, which we evaluate on two classes of synthetic manifold-valued images.


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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Fachbereich MathematikTechnische Universität KaiserslauternKaiserslauternGermany
  2. 2.Institute for Computational and Applied MathematicsWestfälische Wilhelms-Universität MünsterMünsterGermany

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