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Image inpainting is a special image restoration problem for which image prior models play a crucial role. Euler's elastica was first introduced to computer vision by Mumford Algebraic Geometry and its Applications, Springer-Verlag. New York, 1994, pp. 491-506 as a curve prior model. By functionalizing the elastica energy, Masnou and Morel Proceedings of the 5th IEEE International Conference Image Processing, 3 (1998), pp. 259-263 proposed an elastica-based variational inpainting model. The current paper is intended to contribute to the development of its mathematical foundation and the study of its properties and connections to the earlier works of Bertalmio, Sapiro, Caselles, and Ballester SIGGRAPH 2000, ACM Press, New York, 2000 and Chan and Shen J. Visual Comm. Image Rep., 12 (2001), pp. 436-449. A computational scheme based on numerical PDEs is presented, which allows the automatic handling of topologically complex inpainting domains.
Shen et al. (Wed,) studied this question.