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# Mathematical Problems in Image Processing

## Partial Differential Equations and the Calculus of Variations

• Gilles Aubert
• Pierre Kornprobst
Book

Part of the Applied Mathematical Sciences book series (AMS, volume 147)

## Table of contents

1. Front Matter
Pages i-xii
2. Pages 1-21
3. Pages 25-29
4. Pages 31-65
5. Pages 67-135
6. Pages 137-187
7. Pages 189-236
8. Back Matter
Pages 237-294

## About this book

### Introduction

Partial differential equations and variational methods were introduced into image processing about 15 years ago, and intensive research has been carried out since then. The main goal of this work is to present the variety of image analysis applications and the precise mathematics involved. It is intended for two audiences. The first is the mathematical community, to show the contribution of mathematics to this domain and to highlight some unresolved theoretical questions. The second is the computer vision community, to present a clear, self-contained, and global overview of the mathematics involved in image processing problems.
The book is divided into five main parts. Chapter 1 is a detailed overview. Chapter 2 describes and illustrates most of the mathematical notions found throughout the work. Chapters 3 and 4 examine how PDEs and variational methods can be successfully applied in image restoration and segmentation processes. Chapter 5, which is more applied, describes some challenging computer vision problems, such as sequence analysis or classification. This book will be useful to researchers and graduate students in mathematics and computer vision.

### Keywords

Calculus of Variations Mathematica PDE PDEs in image processing Partial Differential Equations computer computer vision differential equation image analysis image processing image restoration mathematics partial differential equation variational methods in image processing

#### Authors and affiliations

• Gilles Aubert
• 1
• Pierre Kornprobst
• 2
1. 1.Laboratoire J.-A. DieudonnieUniversity of Nice-Sophia Antipolis U.M.R. no. 6621 du C.N.R.S.Nice Cedex 02France
2. 2.INRIASophia AntipolisFrance

### Bibliographic information

• DOI https://doi.org/10.1007/b97428
• Copyright Information Springer-Verlag New York, LLC 2002
• Publisher Name Springer, New York, NY
• eBook Packages
• Print ISBN 978-0-387-95326-7
• Online ISBN 978-0-387-21766-6
• Series Print ISSN 0066-5452
• Buy this book on publisher's site
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