UNCONDITIONALLY STABLE SCHEMES FOR HIGHER ORDER INPAINTING

Carola-Bibiane Schoenlieb; Andrea Bertozzi

doi:10.4310/cms.2011.v9.n2.a4

UNCONDITIONALLY STABLE SCHEMES FOR HIGHER ORDER INPAINTING

Carola-Bibiane Schoenlieb, Andrea Bertozzi

Research output: Contribution to journal › Article › peer-review

100 Scopus citations

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 language	English (US)
Pages (from-to)	413-457
Number of pages	45
Journal	COMMUNICATIONS IN MATHEMATICAL SCIENCES
Volume	9
Issue number	2
DOIs	https://doi.org/10.4310/cms.2011.v9.n2.a4
State	Published - 2011
Externally published	Yes

Bibliographical note

KAUST Repository Item: Exported on 2021-09-16
Acknowledgements: King Abdullah University of Science and Technology (KAUST).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

ASJC Scopus subject areas

Applied Mathematics
General Mathematics

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10.4310/cms.2011.v9.n2.a4

Cite this

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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). {\textcopyright} 2011 International Press.",

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UNCONDITIONALLY STABLE SCHEMES FOR HIGHER ORDER INPAINTING

Abstract

Bibliographical note

ASJC Scopus subject areas

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