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E-grāmata: Partial Differential Equation Methods for Image Inpainting

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(University of Cambridge)
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Partial Differential Equation Methods for Image InpaintingPalielināt
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This book introduces the mathematical concept of partial differential equations (PDE) for virtual image restoration. It provides insight in mathematical modelling, partial differential equations, functional analysis, variational calculus, optimisation and numerical analysis. It is addressed towards generally informed mathematicians and graduate students in mathematics with an interest in image processing and mathematical analysis.

This book is concerned with digital image processing techniques that use partial differential equations (PDE) 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 PDE to automate this task. This book introduces the mathematical concept of PDE 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.

Recenzijas

'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 Bertalmķo, 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 Supérieure de Cachan

Papildus informācija

This book introduces the mathematical concept of partial differential equations (PDEs) for virtual image restoration.
Preface ix
1 Introduction
1(7)
1.1 Digital Image Restoration in Modern Society
1(2)
1.2 What is a Digital Image?
3(2)
1.3 Image Inpainting
5(3)
2 Overview of Mathematical Inpainting Methods
8(18)
2.1 Variational and PDE Methods
10(11)
2.2 Structure Versus Texture Inpainting
21(3)
2.3 Inpainting of Colour Images
24(1)
2.4 Video Inpainting
25(1)
3 The Principle of Good Continuation
26(6)
3.1 Gestalt Theory
27(2)
3.2 Kanizsa's Amodal Completion
29(3)
4 Second-Order Diffusion Equations for Inpainting
32(31)
4.1 An Axiomatic Approach to Image Inpainting
32(9)
4.2 Harmonic Image Inpainting
41(4)
4.3 Total Variation Inpainting
45(10)
4.4 Absolutely Minimising Lipschitz Extensions
55(4)
4.5 Further Reading and Some Extensions
59(4)
5 Higher-Order PDE Inpainting
63(74)
5.1 Second- Versus Higher-Order Approaches
63(3)
5.2 Curvature-Based Inpainting
66(19)
5.3 Cahn-Hilliard and TV-H--1 Inpainting
85(34)
5.4 Low Curvature Image Simplifiers
119(2)
5.5 Second-Order Total Variation Inpainting
121(12)
5.6 Further Reading and Some Extensions
133(4)
6 Transport Inpainting
137(24)
6.1 Inpainting by Transport Along Level Lines
137(7)
6.2 Inpainting with Coherence Transport
144(6)
6.3 GuideFill: Fast Artist-Guided Transport Inpainting
150(11)
7 The Mumford-Shah Image Model for Inpainting
161(13)
7.1 Inpainting with Mumford-Shah
161(9)
7.2 Mumford-Shah-Euler Inpainting
170(4)
8 Inpainting Mechanisms of Transport and Diffusion
174(6)
9 Applications
180(31)
9.1 Restoration of Medieval Frescoes
180(9)
9.2 Road Reconstruction
189(2)
9.3 Sinogram Inpainting for Limited Angle Tomography
191(13)
9.4 Inpainting for 3D Conversion
204(7)
Appendix A Exercises 211(6)
Appendix B Mathematical Preliminaries 217(12)
Appendix C MATLAB Implementation 229(2)
Appendix D Image Credits 231(2)
Glossaries 233(4)
References 237(16)
Index 253
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.
Biežāk uzdotie jautājumi par e-grāmatām Biežāk uzdotie jautājumi par e-grāmatām
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