图书信息

作者简介

内容简介

目录

图书信息

出版社: 世界图书出版公司; 第2版 (2009年10月1日)

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

平装: 377页

正文语种: 英语

开本: 24

ISBN: 7510005388, 9787510005381

条形码: 9787510005381

尺寸: 22 x 15 x 1.8 cm

重量: 558 g

作者简介

作者：(法国)奥伯特(Gjlles Aubert) (法国)Pierre Kornprobst

内容简介

《图像处理中的数学问题(第2版)(英文版)》内容简介：Introduction、The Image Society、What Is a Digital Image、About Partial Differential Equations（PDEs）、Detailed Plan、Mathematical Preliminaries、How to Read This Chapter、The Direct Method in the Calculus of Vgriations、Topologies on Banach Spaces、Convexity and Lower Semicontinuity、Rclaxation、Aboutr-Convergence、The Space of Functions of Bounded Variation、Basic Definitions on Measures、Definition ofBV（Ω）、Properties ofBV（Ω）、Convex Functions of Measures、Viscosity Solutions in PDEs等等。

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 Image7

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 Vgriations

2.1.1 Topologies on Banach Spaces

2.1.2 Convexity and Lower Semicontinuity

2.1.3 Rclaxat.ion

2.1.4 About r-Convergence

2.2 The Space of Functions of Bounded Variation

2.2.1 Basic Definitions on Measures

2.2.2 Definition ofBV（Ω）

2.2.3 Properties ofBV（Ω）

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 0ther 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了heorem

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

3.2.6 Some Remarks on the Nonconvex CaSe

3.3 PDE-BaSed Methods

3.3.1 Smoothing PDEs

The Heat Equation

Nonlinear DiRusion

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

Regutarization of the Perona and Malik Model：Catte et aL

3.3.3 Enhancing PDEs

The Osher and Rudin Shock Filters

A Case Study：Construction of a Solution by the Method ofCharacteristics

Comments on the Shock-Filter Equation

3.3.4 NeighborbOOd Filters，Nonlocal Means Algorithm，and PDEs

Neighborhood Filters

How to Suppress the Staircase Effect？

Nonlocal Means Filter（NL-Means）

4 The Segmentation Problem

How to Read This Chapter

4.1 Definition and Objectives

4.2 The Mumford and Shah Functional

4.2.1 A Minimization Problem

4.2.2 The Mathematical Framework for the Existence of a Solution

4.2.3 Regularity of the Edge Set

4.2.4 Approximations of the Mumford and Shah Functional

4.2.5 Experimental Results

4.3 Geodesic Active Contours and the Level.Set Method

4.3.1 The Kass-Witkin-Terzopoulos model

4.3.2 The Geodesic Active Contours Model

4.3.3 The Level-Set Method

4.3.4 The Reinitialization Equation

CharaCterization of the Distance Function

Existence and Uniqueness

4.3.5 Experimental Results

4.3.6 About Some Recent Advances

Global Stopping Criterion

Toward More General Shape Representation

5 Other Challenging AppliCations

How to Read This Chapter

5.1 Reinventing Some Image Parts by Inpainting

5.1.1 IntroduCtion

5.1.2 Variational Models

The Masnou and Morel Approach

The Ballester et al.Approach

The Chan and Shen Total Variation Minimization

Approach

5.1.3 PDE-Based Approaches

The Bertalmio et a1.Approach

The Chan and Shen Curvature-Driven Diffusion Approach

5.1.4 Discussion

5.2 Decomposing an Image into Geometry and Texture

5.2.1 Introduction

5.2.2 A Space for Modeling Oscillating Patterns

5.2.3 Meyer’S Model.

5.2.4 An Algorithm to Solve Meyer’S Model

Prior Numerical C：ontribution

The Aujol et a1.Approach

Study of the Asymptotic Case

Back to Meyer's Model

5.2.5 Experimental Results

Denoising Capabilities

Dealing With Texture

5.2.6 About Some Recent Advances

5.3 Sequence Analysis

5.3.1 Introduction

5.3.2 The Optical Flow：An Apparent Motion

The Optical Flow Constraint（OFC）

Solving the Aperture Problem

Overview of a Discontinuity.Preserving

Variational Approach

Alternatives to the OFC

5.3.3 Sequence Segmentation

Introduction

A Vriational Formulation

Mathematical Study of the Time-Sampled Energy

Experiments

5.3.4 Sequence Restoration

Principles of Video Inpainting

Total Variation（tV）Minimization Approach

Motion Compensated（MC）Inpainting

5.4 Image Classification

5.4.1 Introduction

5.4.2 A Level-Set Approach for Image Classification

5.4.3 A Variational Model for Image Classification and Restoration

5.5 Vector-Valued Images

5.5.1 Introduction

5.5.2 An FXtended Nbtion of Grudieut

A Introduction to Finite Digerence Methods

B Experiment Yourself！

References

Index