Image inpainting is an image restoration problem, in which image models play a critical role, as demonstrated by Chan, Kang & Shen's  recent inpainting schemes based on the bounded variation and the elastica  image models. In this paper, we propose two novel inpainting models based on the Mumford–Shah image model , 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 .
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