A Well-Posedness Framework for Inpainting Based on Coherence Transport

Thomas März

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

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
Volume15
Issue number4
DOIs
StatePublished - Apr 23 2014
Externally publishedYes

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Computational Mathematics
  • Theoretical Computer Science
  • Applied Mathematics
  • Mathematics(all)

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