图像处理中的数学问题 pdf下载

基本信息

• 商品名称：图像处理中的数学问题(第2版)(英文版)
• 作者：(法)奥伯特|责编:刘慧//高蓉
• 定价：89
• 出版社：世界图书出版公司
• ISBN号：9787510005381

其他参考信息（以实物为准）

• 出版时间：2009-10-01
• 印刷时间：2020-06-01
• 版次：1
• 印次：2
• 开本：24开
• 包装：平装
• 页数：377
• 字数：330千字

内容提要

本书向读者介绍了图像 应用及相关的数学知识，主 要面向两类读者，一类是数 学专业人士，从中他们可以 了解数学对于图像处理领域 的贡献，从而 致力于研究 一些尚未解决的问题；另一 类是计算机视觉领域人士， 从中可以学到与图像处理有 关数学理论。
    

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 T-Convergence
2.2 The Space of Functions of Bounded Variation
2.2.1 Basic Definitions on Measures
2.2.2 Definition of BV (Ω)
2.2.3 Properties of BV (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 Diferential 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 λ
3.2.6 Some Remarks on the Nonconvex Case