Mathematical Problems in Image Processing

The 2nd edition presents image analysis applications, outlines their precise mathematics and shows how to discretize them. It reviews progress in image processing applications covered by the PDE framework, and updates the existing material. Also provides programming tools for creating simulations.

In its updated 2nd edition, this book presents a variety of image analysis applications, reviews their precise mathematics and shows how to discretize them. The book is intended for two audiences. First, the mathematical community, showing the contribution of mathematics to this domain, and highlighting some unsolved theoretical questions. The second is the computer vision community, presenting a clear, self-contained and global overview of the mathematics involved in image procesing problems. This work will serve as a source of reference and inspiration for researchers in Applied Mathematics and Computer Vision, as well as being a basis for advanced courses within these fields. The second edition offers a coherent review of progress in the range of image processing applications covered by the PDE framework, and updates the existing material. In addition, the book provides readers with the programming tools to create simulations of their own with minimal effort.

The two most important problems in image analysis, namely image restoration and segmentation, are treated in details and allow to present most of the mathematical concepts useful in this field Not only presents theoretical concepts but also provides numerical algorithms and main ideas to discretize PDE-based approaches C++ image library and source codes of some classical approaches are available

Contenu
Foreword.- 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!- References.- Index.