Contrast invariant inpainting with a 3rd order, optimal PDE

PDE-based image inpainting has become a very active area of research after the pioneering works of Masnou and Morel (1998), Bertalmio et al. (2000) and Ballester et al. (2001). In this paper we take a different approach, inspired by the excellent work of Caselles et al. (1998). We view the inpainting problem as a particular case of image interpolation in which we intend to propagate level lines. Expressing this in terms of local neighborhoods and using a Taylor expansion we derive a third order PDE that performs inpainting. This PDE is optimal in the sense that it is the most accurate third order PDE which can ensure continuation of level lines. It is also contrast invariant. This is a novel PDE, which both in its accuracy and contrast invariance outperforms the approaches cited above.