A Well-Posedness Framework for Inpainting Based on Coherence Transport

Thomas März

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


Image inpainting is the process of touching up damaged or unwanted portions of a picture and is an important task in image processing. For this purpose Bornemann and März (J Math Imaging Vision, 28:259–278, 2007) introduced a very efficient method, called image inpainting based on coherence transport, that fills the missing region by advecting the image information along integral curves of a coherence vector field from the boundary toward the interior of the hole. The mathematical model behind this method is a first-order functional advection partial differential equation posed on a compact domain with all inflow boundaries. We show that this problem is well posed under certain conditions.
Original languageEnglish (US)
Pages (from-to)973-1033
Number of pages61
JournalFoundations of Computational Mathematics
Issue number4
StatePublished - Apr 23 2014
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2022-06-07
Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: The author would like to thank Folkmar Bornemann and Colin Macdonald for their advice and the inspiring discussions. This work was supported in part by the Graduiertenkolleg Angewandte Algorithmische Mathematik (GKAAM) funded by the Deutsche Forschungsgemeinschaft (DFG) at the Technische Universität München (TUM), and by Award KUK-C1-013-04 granted by King Abdullah University of Science and Technology (KAUST).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Computational Mathematics
  • Theoretical Computer Science
  • Applied Mathematics
  • General Mathematics


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