Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations

Gilles Aubert, Pierre Kornprobst (auth.)0387953264, 9780387953267, 9780387217666

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. This book will be useful to researchers and graduate students in mathematics and computer vision.

---

Table of contents :
Front Matter….Pages i-xii
Introduction….Pages 1-21
Guide to main mathematical concepts and their application….Pages 23-24
Notations and symbols….Pages 25-29
Mathematical preliminaries….Pages 31-65
Image Restoration….Pages 67-135
The Segmentation Problem….Pages 137-187
Other Challenging Applications….Pages 189-236
Back Matter….Pages 237-294