Mathematical Problems in Image Processing

Partial differential equations and the calculus of variations

Gilles Aubert, Pierre Kornprobst - Collection Applied Mathematical Sciences

416 pages, parution le 02/10/2006 (2^eme édition)

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Résumé

Partial differential equations (PDEs) and variational methods were introduced into image processing about fifteen years ago. Since then, intensive research has been carried out. The goals of this book are to present a variety of image analysis applications, the precise mathematics involved and how to discretize them.

Thus, this book is intended for two audiences. The first is the mathematical community by showing the contribution of mathematics to this domain. It is also the occasion to highlight some unsolved theoretical questions. The second is the computer vision community by presenting a clear, self-contained and global overview of the mathematics involved in image processing problems. This work will serve as a useful source of reference and inspiration for fellow researchers in Applied Mathematics and Computer Vision, as well as being a basis for advanced courses within these fields.

During the four years since the publication of the first edition, there has been substantial progress in the range of image processing applications covered by the PDE framework. The main goals of the second edition are to update the first edition by giving a coherent account of some of the recent challenging applications, and to update the existing material. In addition, this book provides the reader with the opportunity to make his own simulations with a minimal effort. To this end, programming tools are made available, which will allow the reader to implement and test easily some classical approaches.

Written for: Researchers and graduate students

Sommaire

Preface to the Second Edition
Preface
Guide to the Main Mathematical Concepts and their Application
Notation and Symbols
Introduction
Mathematical Preliminaries
Image Restoration
The Segmentation Problem
Other Challenging Applications
A. Introduction to Finite Difference Methods
B. Experiment Yourself

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Gilles Aubert, Pierre Kornprobst
Collection	Applied Mathematical Sciences
Parution	02/10/2006
Édition	2^eme édition
Nb. de pages	416
Format	16 x 24
Couverture	Relié
Poids	700g
Intérieur	Noir et Blanc
EAN13	9780387322001
ISBN13	978-0-387-32200-1