Partial Differential Equation Methods for Image Inpainting

Inbunden, Engelska, 2015

Del 29 i serien Cambridge Monographs on Applied and Computational Mathematics

1 309 kr

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Beskrivning

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.

Produktinformation

Utgivningsdatum:2015-10-26
Mått:159 x 236 x 16 mm
Vikt:560 g
Format:Inbunden
Språk:Engelska
Serie:Cambridge Monographs on Applied and Computational Mathematics
Antal sidor:266
Förlag:Cambridge University Press
ISBN:9781107001008

Utforska kategorier

Fotoredigering och bildredigering inom Data och IT

Mer om författaren

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.

Recensioner i media

'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

Innehållsförteckning

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.