Cahn–Hilliard Inpainting and a Generalization for Grayvalue Images

Martin Burger, Lin He, Carola-Bibiane Schönlieb

Research output: Contribution to journalArticlepeer-review

125 Scopus citations


The Cahn–Hilliard equation is a nonlinear fourth order diffusion equation originating in material science for modeling phase separation and phase coarsening in binary alloys. The inpainting of binary images using the Cahn–Hilliard equation is a new approach in image processing. In this paper we discuss the stationary state of the proposed model and introduce a generalization for grayvalue images of bounded variation. This is realized by using subgradients of the total variation functional within the flow, which leads to structure inpainting with smooth curvature of level sets.
Original languageEnglish (US)
Pages (from-to)1129-1167
Number of pages39
JournalSIAM Journal on Imaging Sciences
Issue number4
StatePublished - Jan 2009
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-I1-007-43
Acknowledgements: This work was partially supported by the WWTF (Wiener Wissenschafts-, Forschungs- und Technologiefonds) project CI06 003, by the FFG project Erarbeitung neuer Algorithmen zum Image Inpainting project 813610, and the Ph.D. program Wissenschaftskolleg taking place at the University of Vienna. Further, this publication is based on work supported by award KUK-I1-007-43, made by King Abdullah University of Science and Technology (KAUST).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.


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