UNCONDITIONALLY STABLE SCHEMES FOR HIGHER ORDER INPAINTING

Carola-Bibiane Schoenlieb, Andrea Bertozzi

Research output: Contribution to journalArticlepeer-review

77 Citations (SciVal)

Abstract

Higher order equations, when applied to image inpainting, have certain advantages over second order equations, such as continuation of both edge and intensity information over larger distances. Discretizing a fourth order evolution equation with a brute force method may restrict the time steps to a size up to order Δx4 where Δx denotes the step size of the spatial grid. In this work we present efficient semi-implicit schemes that are guaranteed to be unconditionally stable. We explain the main idea of these schemes and present applications in image processing for inpainting with the Cahn-Hilliard equation, TV-H-1 inpainting, and inpainting with LCIS (low curvature image simplifiers). © 2011 International Press.
Original languageEnglish (US)
Pages (from-to)413-457
Number of pages45
JournalCOMMUNICATIONS IN MATHEMATICAL SCIENCES
Volume9
Issue number2
DOIs
StatePublished - 2011
Externally publishedYes

ASJC Scopus subject areas

  • Applied Mathematics
  • Mathematics(all)

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