Partial Differential Equation Methods for Image Inpainting

Carola-Bibiane Schönlieb (University of Cambridge)

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English

Cambridge University Press
26 October 2015

Differential calculus & equations; Integral calculus & equations; Mathematical modelling; Computer science; Image processing

Series: Cambridge Monographs on Applied and Computational Mathematics

This book is concerned with digital image processing techniques that use partial differential equations (PDEs) for the task of image 'inpainting', an artistic term for virtual image restoration or interpolation, whereby missing or occluded parts in images are completed based on information provided by intact parts. Computer graphic designers, artists and photographers have long used manual inpainting to restore damaged paintings or manipulate photographs. Today, mathematicians apply powerful methods based on PDEs to automate this task. This book introduces the mathematical concept of PDEs for virtual image restoration. It gives the full picture, from the first modelling steps originating in Gestalt theory and arts restoration to the analysis of resulting PDE models, numerical realisation and real-world application. This broad approach also gives insight into functional analysis, variational calculus, optimisation and numerical analysis and will appeal to researchers and graduate students in mathematics with an interest in image processing and mathematical analysis.

By: Carola-Bibiane Schönlieb (University of Cambridge)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Volume: 29
Dimensions: Height: 236mm, Width: 159mm, Spine: 16mm
Weight: 560g
ISBN: 9781107001008
ISBN 10: 1107001005
Series: Cambridge Monographs on Applied and Computational Mathematics
Pages: 250
Publication Date: 26 October 2015
Audience: Professional and scholarly , Professional and scholarly , Undergraduate , Undergraduate
Format: Hardback
Publisher's Status: Active

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.

Reviews for Partial Differential Equation Methods for Image Inpainting

'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 Bertalmio, Universitat Pompeu Fabra 'Image inpainting is a new mathematical and technological problem with manifold applications in science and entertainment. In the past twenty years, it has challenged mathematicians and computer scientists alike. They have deployed a treasure of imagination and mathematical skills to solve it. Incorporating striking experiments, reproducible algorithms, and a simple and complete mathematical account, this book is a must-read on the subject.' Jean-Michel Morel, CMLA, Ecole Normale Superieure de Cachan 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 Bertalmio, Universitat Pompeu Fabra Image inpainting is a new mathematical and technological problem with manifold applications in science and entertainment. In the past twenty years, it has challenged mathematicians and computer scientists alike. They have deployed a treasure of imagination and mathematical skills to solve it. Incorporating striking experiments, reproducible algorithms, and a simple and complete mathematical account, this book is a must-read on the subject. Jean-Michel Morel, CMLA, Ecole Normale Superieure de Cachan