【目录】: Foreword Preface to the Second Edition Preface to the First Edition Guide to the Main Mathematical Concepts and Their Application Notation and Symbols 1 Introduction 1.1 The Image Society 1.2 What Is a Digital Image? 1.3 About Partial Differential Equations (PDEs) 1.4 Detailed Plan 2 Mathematical Preliminaries How to Read This Chapter 2.1 The Direct Method in the Calculus of Variations... 2.1.1 Topologies on Banach Spaces 2.1.2 Convexity and Lower Semicontinuity . 2.1.3 Relaxation 2.1.4 About F-Convergence 2.2 The Space of Functions of Bounded Variation 2.2.1 Basic Definitions on Measures 2.2.2 Definition of BV(ft) 2.2.3 Properties of BV(f~) 2.2.4 Convex Functions of Measures 2.3 Viscosity Solutions in PDEs 2.3.1 About the Eikonal Equation 2.3.2 Definition of Viscosity Solutions 2.3.3 About the Existence 2.3.4 About the Uniqueness 2.4 Elements of Differential Geometry: Curvature 2.4.1 Parametrized Curves 2.4.2 Curves as Isolevel of a Function u 2.4.3 Images as Surfaces 2.5 Other Classical Results Used in This Book 2.5.1 Inequalities 2.5.2 Calculus Facts 2.5.3 About Convolution and Smoothing 2.5.4 Uniform Convergence 2.5.5 Dominated Convergence Theorem 2.5.6 Well-Posed Problems 3 Image Restoration How to Read This Chapter 3.1 Image Degradation 3.2 The Energy Method 3.2.1 An Inverse Problem 3.2.2 Regularization of the Problem 3.2.3 Existence and Uniqueness of a Solution for the Minimization Problem 3.2.4 Toward the Numerical Approximation The Projection Approach The Half-Quadratic Minimization Approach 3.2.5 Some Invariances and the Role of A 3.2.6 Some Remarks on the Nonconvex Case 3.3 PDE-Based Methods 3.3.1 Smoothing PDEs The Heat Equation Nonlinear Diffusion The Alvarez-Guichard-Lions-Morel Scale Space Theory Weickert's Approach Surface Based Approaches 3.3.2 Smoothing-Enhancing PDEs The Perona and Malik Model …… 4 The Segmentation Problem 5 Other Challenging Applications A Introduction to Finite Difference Methods B Experiment Yourself! References Index
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