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Digital inpainting based on the Mumford–Shah–Euler image model

Published online by Cambridge University Press:  25 September 2002

SELIM ESEDOGLU  and
JIANHONG SHEN
SELIM ESEDOGLU
Affiliation:
Institute of Mathematics and its Applications (IMA), University of Minnesota, Minneapolis, MN 55455, USA; email: esedoglu@ima.umn.edu
JIANHONG SHEN
Affiliation:
School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA; email: jhshen@math.umn.edu
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Abstract

Image inpainting is an image restoration problem, in which image models play a critical role, as demonstrated by Chan, Kang & Shen's [12] recent inpainting schemes based on the bounded variation and the elastica [11] image models. In this paper, we propose two novel inpainting models based on the Mumford–Shah image model [41], and its high order correction – the Mumford–Shah–Euler image model. We also present their efficient numerical realization based on the Γ-convergence approximations of Ambrosio & Tortorelli [2, 3] and De Giorgi [21].

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 13 , Issue 4 , August 2002 , pp. 353 - 370
Copyright
2002 Cambridge University Press

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