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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.
Esedoḡlu et al. (Thu,) studied this question.