Premium
A generalization of Cahn‐Hilliard inpainting for grayvalue images
Author(s) -
Burger Martin,
He Lin,
Markowich Peter,
Schönlieb CarolaBibiane
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700377
Subject(s) - inpainting , generalization , binary number , cahn–hilliard equation , convergence (economics) , curvature , mathematics , flow (mathematics) , phase (matter) , class (philosophy) , image (mathematics) , mathematical analysis , computer science , artificial intelligence , geometry , arithmetic , partial differential equation , physics , quantum mechanics , economics , economic growth
The Cahn‐Hilliard equation has its origin in material sciences and serves as a model for phase separation and phase coarsening in binary alloys. A new approach in the class of fourth order inpainting algorithms is inpainting of binary images using the Cahn‐Hilliard equation. We will present a generalization of this fourth order approach for grayvalue images. 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. We will present some numerical examples for this approach and analytic results concerning existence and convergence of solutions. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)