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Mathematical problems in image processing. Partial differential equations and the calculus of variations. Foreword by Olivier Faugeras. (English) Zbl 1109.35002
Applied Mathematical Sciences 147. New York, NY: Springer (ISBN 0-387-95326-4/hbk). xxv, 286 p. (2002).
Publisher’s description: 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.

MSC:
35-02 Research exposition (monographs, survey articles) pertaining to partial differential equations
49-02 Research exposition (monographs, survey articles) pertaining to calculus of variations and optimal control
68U05 Computer graphics; computational geometry (digital and algorithmic aspects)
94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
35J20 Variational methods for second-order elliptic equations
49J45 Methods involving semicontinuity and convergence; relaxation
49N99 Miscellaneous topics in calculus of variations and optimal control
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