Partial Differential Equation Methods for Image Inpainting

Carola-Bibiane Schönlieb is a Lecturer in Applied and Computational Analysis and Head of the Cambridge Image Analysis group at the Department of Applied Mathematics and Theoretical Physics (DAMTP), University of Cambridge.

• 1. Introduction; 2. Overview of mathematical inpainting methods; 3. The principle of good continuation; 4. Second-order diffusion equations for inpainting; 5. Higher-order PDE inpainting; 6. Transport inpainting; 7. The Mumford–Shah image for inpainting; 8. Inpainting mechanisms of transport and diffusion; 9. Applications.

'Since the late 1990s, there has been a substantial amount of academic works on the application of partial differential equations (PDEs) to the restoration of missing parts in images, which is usually referred to as the 'inpainting problem'. This book provides a very comprehensive, clear, and well-written account of the use of PDEs for inpainting, and this is no minor feat, given the sizeable literature on the subject and the mathematical complexity of many of the techniques described.' Marcelo Bertalmío, Universitat Pompeu Fabra