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

Abstract

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