A Well-Posedness Framework for Inpainting Based on Coherence Transport

作者：Maerz Thomas

来源：Foundations of Computational Mathematics, 2015, 15(4): 973-1033.

DOI：10.1007/s10208-014-9199-7

• Functional PDEs
• Method of characteristics
• Lyapunov functions
• Functions of bounded variation
• Fixed-point theory
• Image inpainting

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 Marz (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.

• 出版日期2015-8