Euler's elastica and curvature-based inpainting

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.