Geometric Partial Differential Equations and Image Analysis

Guillermo Sapiro

doi:10.1017/CBO9780511626319

This book provides an introduction to the use of geometric partial differential equations in image processing and computer vision. This research area brings a number of new concepts into the field, providing a very fundamental and formal approach to image processing. State-of-the-art practical results in a large number of real problems are achieved with the techniques described in this book. Applications covered include image segmentation, shape analysis, image enhancement, and tracking. This book will be a useful resource for researchers and practitioners. It is intended to provide information for people investigating new solutions to image processing problems as well as for people searching for existent advanced solutions.

‘ … enjoyable to read … an excellent introduction for someone interested in pursuing research in this area, with ample references to current work sprinkled throughout.’

Source: SIAM Review

‘ … every person interested in image analysis by partial differential equations or related fields, such as differential geometry and curve evolution, should read this book.’

Source: Mathematics of Computation

‘… this book will certainly be accepted as a standard text … A student who had worked through everything here would be very well equipped to develop powerful image processing software.’

Alex M. Andrew Source: Robotica

‘… a useful introduction to the subject.’

John Urbas Source: Zentralblatt für Mathematik

‘For those who are prepared to also take the mathematics, a marvellous world will open. This is applied mathematics at its best. Recommended for researchers and practitioners.‘

Source: Bulletin of the Belgian Mathematical Society

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Geometric Partial Differential Equations and Image Analysis

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Contents

Frontmatter
pp i-vi

Contents
pp vii-x

List of figures
pp xi-xiv

Preface
pp xv-xvi

Acknowledgments
pp xvii-xx

Introduction
pp xxi-xxvi

1 - Basic Mathematical Background
pp 1-70

2 - Geometric Curve and Surface Evolution
pp 71-142

3 - Geodesic Curves and Minimal Surfaces
pp 143-220

4 - Geometric Diffusion of Scalar Images
pp 221-266

5 - Geometric Diffusion of Vector-Valued Images
pp 267-283

6 - Diffusion on Nonflat Manifolds
pp 284-306

7 - Contrast Enhancement
pp 307-337

8 - Additional Theories and Applications
pp 338-358

Bibliography
pp 359-380

Index
pp 381-385

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Geometric Partial Differential Equations and Image Analysis

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