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 .