- 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
  - 出版社：世界图书出版公司
  - ISBN：9787510005381
  - 出版日期：2009/10/01
  - 页数：377
- 售价：35.6

内容大纲
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，从而更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。
作者介绍
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

  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
      Regularization 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 of Characteristics
      Comments on the Shock-Filter Equation
    3.3.4  Neighborhood 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 al.Approach
      The Chan and Shen Curvature-Driven Difusion 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 Contribution
      The Aujol et al.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 Variational 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 Extended Notion of Gradient
    5.5.3  The Energy Method
    5.5.4  PDE-Based Methods
A  Introduction to Finite Difference Methods
  How to Read This Chapter
  A.1  Definitions and Theoretical Considerations Illustrated by the 1-D Parabolic Heat Equation
    A.1.1  Getting Started
    A.1.2  Convergence
    A.1.3  The Lax Theorem
    A.1.4  Consistency
    A.1.5  Stability
  A.2  Hyperbolic Equations
  A.3  Diference Schemes in Image Analysis
    A.3.1  Getting Started

    A.3.2  Image Restoration by Energy Minimization
    A.3.3  Image Enhancement by the Osher and Rudin Shock Filters
    A.3.4  Curve Evolution with the Level-Set Method
      Mean Curvature Motion
      Constant Speed Evolution
      The Pure Advection Equation
      Image Segmentation by the Geodesic Active Contour Model
B  Experiment Yourself
  How to Read This Chapter
  B.1  The CImg Library
  B.2  What Is Available Online
References
Index

内容大纲

作者介绍

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