A Well-Posedness Framework for Inpainting Based on Coherence Transport

Image inpainting is the process of touching up damaged or unwanted portions of a picture and is an important task in image processing. For this purpose Bornemann and März (J Math Imaging Vision, 28:259–278, 2007 ) introduced a very efficient method, called image inpainting based on coherence transport , that fills the missing region by advecting the image information along integral curves of a coherence vector field from the boundary toward the interior of the hole. The mathematical model behind this method is a first-order functional advection partial differential equation posed on a compact domain with all inflow boundaries. We show that this problem is well posed under certain conditions.