Mathematical Problems in Image Processing

1. Front Matter

   Pages i-xii

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2. Introduction

   Pages 1-21

3. Guide to main mathematical concepts and their application

   Pages 23-24

4. Notations and symbols

   Pages 25-29

5. Mathematical preliminaries

   Pages 31-65

6. Image Restoration

   Pages 67-135

7. The Segmentation Problem

   Pages 137-187

8. Other Challenging Applications

   Pages 189-236

9. Back Matter

   Pages 237-294

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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.

• 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

From the reviews:

MATHEMATICAL REVIEWS

"The authors have substantially contributed to many aspects of the subject…The level of the book is advanced, and the exposition very clear, developed in depth, and to some extent self-contained. The proofs of the main theorems are usually given in detail; when necessary there is also a precise reference to the ample literature on the specific topic. This book will certainly interest both mathematicians (some interesting, still open theoretical questions there are highlighted) and researchers in computer vision…The books substantial and up-to-date body for reference is a detailed guide to the literature on the many aspects of image processing."

 

G. Aubert and P. Kornprobst

Mathematical Problems in Image Processing

Partial Differential Equations and the Calculus of Variations

"This book is devoted to a detailed presentation of several aspects of mathematical problems in image processing . . . The authors have substantially contributed to many aspects of their subject . . . The level of the book is advanced, and the to some extent self-contained . . . This book will certainly interest both mathematicians (some interesting, still open theoretical questions here are highlighted) and researchers in computer vision."—MATHEMATICAL REVIEWS

• Laboratoire J.-A. Dieudonnie, University of Nice-Sophia Antipolis U.M.R. no. 6621 du C.N.R.S., Nice Cedex 02, France

  Gilles Aubert

• INRIA, Sophia Antipolis, France

  Pierre Kornprobst

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