Mathematical problems in image processing : partial differential equations and the calculus of variations - Aubert, Gilles; Kornprobst, Pierre (New York : Springer, 2002)
"Partial differential equations (PDEs) and variational methods were introduced into image processing about fifteen 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."--BOOK JACKET.
Guide to the Main Mathematical Concepts and Their Application -- 1. Introduction -- 2. Mathematical Preliminaries. 2.1. The Direct Method in the Calculus of Variations. 2.2. The Space of Functions of Bounded Variation. 2.3. Viscosity Solutions in PDEs. 2.4. Elements of Differential Geometry: Curvature. 2.5. Other Classical Results Used in This Book -- 3. Image Restoration. 3.1. Image Degradation. 3.2. The Energy Method. 3.3. PDE-Based Methods -- 4. The Segmentation Problem. 4.1. Definition and Objectives. 4.2. The Mumford and Shah Functional. 4.3. Geodesic Active Contours and the Level-Set Method -- 5. Other Challenging Applications. 5.1. Sequence Analysis. 5.2. Image Classification. A. Introduction to Finite Difference Methods.
Includes bibliographical references (p. [265]-281) and index.
Keywords: Image processing -- Mathematics