First Order Quasi-Linear Pdes with Bv Boundary Data and Applications to Image Inpainting

By Thomas Marz

This book investigates the well-posedness of the mathematical model behind the method "Image Inpainting Based on Coherence Transport". Image inpainting methods serve the purpose of touching up damaged or unwanted elements of a digital picture. The model behind the mentioned method is a Dirichlet problem for a first order quasi-linear hyperbolic functional partial differential equation where all points of the boundary are inflow points. The main concern of this thesis is to proof the existence and the uniqueness of a solution to such kind of problems as well as the solutions's continuous dependence on the data. The general theory finally is used to obtain the well-posedness of the inpainting model.

• Format: Paperback
• Language: English
• ISBN: 3832526390
• ISBN13: 9783832526399
• Release Date: December 2010
• Publisher: Logos Verlag Berlin
• Length: 187 Pages