Unconditionally Stable Schemes for Higher Order Inpainting

Abstract. Inpainting methods with third and fourth order equations have certain advantages in comparison with equations of second order such as the smooth interpolation of image information even over large distances. Because of this such methods became very popular in the last couple of years. Solving higher order equations numerically can be a computational demanding task though. Discretizing a fourth order evolution equation with a brute force method may restrict the time steps to a size up to order ∆x where ∆x denotes the step size of the spatial grid. In this work we will present a more educated way of discretization, namely efficient semi-implicit schemes that are guaranteed to be unconditionally stable. We will explain the main idea of these schemes and present applications in image processing for inpainting with the Cahn-Hilliard equation, TV-H inpainting, and inpainting with LCIS (low curvature image simplifiers).