图像处理与分析:变分,PDE,小波及随机方法(影印版)(精装)(国外数学名著系列)(Image processing and analysis variational,pde,wavelet and stochastic methods)
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品牌: 陈繁昌
基本信息·出版社：科学出版社
·页码：400 页
·出版日期：2009年
·ISBN：7030234855/9787030234858
·条形码：9787030234858
·包装版本：1版
·装帧：精装
·开本：16
·正文语种：英语
·丛书名：国外数学名著系列
·外文书名：Image processing and analysis variational,pde,wavelet and stochastic methods
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内容简介《图像处理与分析:变分,PDE,小波及随机方法》(影印版)(精装)：Image Processing and Analysis: Variational, PDE, Wavelet, andStochastic Methods is systematic and well organized, The authorsfirst investigate the geometric, functional, and atomic structures ofimages and then rigorously develop and analyze several imageprocessors. The book is comprehensive and integrative, covering thefour most powerful classes of mathematical tools in contemporaryimage analysis and processing while exploring their intrinsicconnections and integration. The material is balanced in theory andcomputation, following a solid theoretical analysis of model buildingand performance with computational implementation and numericalexamples.
This book is written for graduate students and researchers inapplied mathematics, computer science, electrical engineering, andother disciplines who are interested in problems in imaging andcomputer vision. It can be used as a reference by scientists withspecific tasks in image processing, as well as by researchers with ageneral interest in finding out about the latest advances.
目录
List of Figures
Preface
1 Introduction
1.1 Dawning of the Era of Imaging Sciences
1.1.1 Image Acquisition
1.1.2 Image Processing
1.1.3 Image Interpretation and Visual Intelligence
1.2 Image Processing by Examples
1.2.1 Image Contrast Enhancement
1.2.2 Image Denoisirg
1.2.3 Image Deblurring
1.2.4 Image Inpainting
1.2.5 Image Segmentation
1.3 An Overview of Methodologies in Image Processing
1.3.1 Morphological Approach
1.3.2 Fourier and Spectral Analysis
1.3.3 Wavelet and Space-Scale Analysis
1.3.4 Stochastic Modeling
1.3.5 Variaticnal Methods
1.3.6 Partial Differential Equations （PDEs）
1.3.7 Different Approaches Are Intrinsically Interconnected
1.4 Organization of the Book
1.5 How to Read the Bcok
2 Some Modern Image Analysis Tools
2.1 Geometry of Curves and Surfaces
2.1.I Geometry of Curves
2.1.2 Geometry of Surfaces in Three Dimensions
2.1.3 Hausdorff Measures and Dimensions
2.2 Functions with Bounded Variations
2.2.1 Total Variatien as a Radon Measure
2.2.2 Basic Properties of BV Functions
2.2.3 The Co-Area Formula
2.3 Elements of Thermodynamics and Statistical Mechanics
2.3.1 Essentials of Thermodynamics
2.3.2 Entropy and Potentials
2.3.3 Statistical Mechanics of Ensembles
2.4 Bayesian Statistical Inference
2.4.1 Image Processing or Visual Perception as Inference
2.4.2 Bayesian Inference： Bias Due to Prior Knowledge
2.4.3 Bayesian Method in Image Processing
2.5 Linear and Nonlinear Filtering and Diffusion
2.5.1 Point Spreading and Markov Transition
2.5.2 Linear Filtering and Diffusion
2.5.3 Nonlinear Filtering and Diffusion
2.6 Wavelets and Multiresolution Analysis
2.6.1 Quest for New Image Analysis Tools
2.6.2 Early Edge Theory and Marr’s Wavelets
2.6.3 Windowed Frequency Analysis and Gabor Wavelets
2.6.4 Frequency-Window Coupling： Malvar-Wilson Wavelets
2.6.5 The Framework of Multiresolution Analysis （MRA）
2.6.6 Fast Image Analysis and Synthesis via Filter Banks
3 Image Modeling and Representation
3.1 Modeling and Representation： What, Why, and How
3.2 Deterministic Image Models
3.2.1 Images as Distributions （Generalized Functions）
3.2.2 Lp Images
3.2.3 Sobolev Images Hn（Ω）
3.2.4 BV Images
3.3 Wavelets and Multiscale Representation
3.3.1 Construction of 2-D Wavelets
3.3.2 Wavelet Responses to Typical Image Features
3.3.3 Besov Images and Sparse Wavelet Representation
3.4 Lattice and Random Field Representation
3.4.1 Natural Images of Mother Nature
3.4.2 Images as Ensembles and Distributions
3.4.3 Images as Gibbs’ Ensembles
3.4.4 Images as Markov Random Fields
3.4.5 Visual Filters and Filter Banks
3.4.6 Entropy-Based Learning of Image Patterns
3.5 Level-Set Representation
3.5.1 Classical Level Sets
3.5.2 Cumulative Level Sets
3.5.3 Level-Set Synthesis
3.5.4 An Example： Level Sets of Piecewise Constant Images
3.5.5 High Order Regularity of Level Sets
3.5.6 Statistics of Level Sets of Natural Images
3.6 The Mumford-Shah Free Boundary Image Model
3.6.1 Piecewise Constant 1-D Images: Analysis and Synthesis
3.6.2 Piecewise Smooth 1-D Images: First Order Representation
3.6.3 Piecewise Smooth I-D Images: Poisson Representation
3.6.4 Piecewise Smooth 2-D Images
3.6.5 The Mumford-Shah Model
3.6.6 The Role of Special B V Images
4 Image Denoising
4. 1 Noise: Origins. Physics. and Models
4.l. 1 Origins and Physics of Noise
4.1.2 A Brief Overview of 1-D Stochastic Signals
4.1.3 Stochastic Models of Noises
4.1.4 Analog White Noises as Random Generalized Functions
4.1.5 Random Signals from Stochastic Differential Equations
4.l.6 2-D Stochastic Spatial Signals: Random Fields
4.2 Linear Denoising: Lowpass Filtering
4.2.1 Signal vs. Noise
4.2.2 Denoising via Linear Filters and Diffusion
4.3 Data-Driven Optimal Filtering: Wiener Filters
4.4 Wavelet Shrinkage Denoising
4.4.1 Shrinkage: Quasi-statistical Estimation of Singletons
4.4.2 Shrinkage: Variational Estimation of Singletons
4.4.3 Denoising via Shrinking Noisy Wavelet Components
4.4.4 Variational Denoising of Noisy Besov Images
4.5 Variational Denoising Based on BV Image Model
4.5.1 TV. Robust Statistics. and Median
4.5.2 The Role of TV and BV Image Model
4.5.3 Biased Iterated Median Filtering
4.5.4 Rudin. Osher. and Fatemi's TV Denoising Model
4.5.5 Computational Approaches to TV Denoising
4.5.6 Duality for the TV Denoising Model
4.5.7 Solution Structures of the TV Denoising Model
4.6 Denoising via Nonlinear Diffusion and Scale-Space Theory
4.6.1 Perona and Malik's Nonlinear Diffusion Model
4.6.2 Axiomatic Scale-Space Theory
4.7 Denoising Salt-and-Pepper Noise
4.8 Multichannel TV Denoising
4.8.1 Variational TV Denoising of Multichannel Images
4.8.2 Three Versions of TV[u]
5 Image Deblurring
5.1 Blur: Physical Origins and Mathematical Models
5.1.1 Physical Origins
5.1.2 Mathematical Models of Blurs
5.1.3 Linear vs. Nonlinear Blurs
5.2 Ill-posedness and Regularization
5.3 Deblurring with Wiener Filters
5.3.1 Intuition on Filter-Based Deblurring
5.3.2 Wiener Filtering
5.4 Deblurring of BV Images with Known PSF
5.4.1 The Variational Model
5.4.2 Existence and Uniqueness
5.4.3 Computation
5.5 Variational Blind Deblurring with Unknown PSF
5.5.1 Parametric Blind Deblurring
5.5.2 Parametric-Field-Based Blind Deblurring
5.5.3 Nonparametric Blind Deblurring
6 Image Inpainting
6.1 A Brief Review on Classical Interpolation Schemes
6.1.1 Polynomial Interpolation
6.1.2 Trigonometric Polynomial Interpolation
6.1.3 Spline Interpolation
6.1.4 Shannon's Sampling Theorem
6.1.5 Radial Basis Functions and Thin-Plate Splines
6.2 Challenges and Guidelines for 2-D Image Inpainting
6.2.1 Main Challenges for Image Inpainting
6.2.2 General Guidelines for Image Inpainting
6.3 Inpainting of Sobolev Images: Green's Formulae
6.4 Geometric Modeling of Curves and Images
6.4.1 Geometric Curve Models
6.4.2 2-. 3-Point Accumulative Energies. Length. and Curvature.
6.4.3 Image Models via Functionalizing Curve Models
6.4.4 Image Models with Embedded Edge Models
6.5 Inpainting BV Images (via the TV Radon Measure)
6.5.1 Formulation of the TV Inpainting Model
6.5.2 Justification of TV Inpainting by Visual Perception
6.5.3 Computation of TV lnpainting
6.5.4 Digital Zooming Based on TV Inpainting
6.5.5 Edge-Based Image Coding via Inpainting
6.5.6 More Examples and Applications of TV Inpainting
6.6 Error Analysis for Image Inpainting
6.7 Inpainting Piecewise Smooth Images via Mumford and Shah
6.8 Image Inpainting via Euler's Elasticas and Curvatures
6.8.1 Inpainting Based on the Elastica Image Model
6.8.2 Inpainting via Mumford-Shah-Euler Image Model
6.9 Inpainting of Meyer's Texture
6.10 Image Inpainting with Missing Wavelet Coefficients
6.11 PDE Inpainting: Transport. Diffusion. and Navier-Stokes
6.11.1 Second Order Interpolation Models
6.11.2 A Third Order PDE Inpainting Model and Navier-Stokes
……
7 Image Segmentation
Bibliography
Index
……[看更多目录]
序言要使我国的数学事业更好地发展起来，需要数学家淡泊名利并付出更艰苦地努力。另一方面，我们也要从客观上为数学家创造更有利的发展数学事业的外部环境，这主要是加强对数学事业的支持与投资力度，使数学家有较好的工作与生活条件，其中也包括改善与加强数学的出版工作。
从出版方面来讲，除了较好较快地出版我们自己的成果外，引进国外的先进出版物无疑也是十分重要与必不可少的。从数学来说，施普林格（springer）出版社至今仍然是世界上最具权威的出版社。科学出版社影印一批他们出版的好的新书，使我国广大数学家能以较低的价格购买，特别是在边远地区工作的数学家能普遍见到这些书，无疑是对推动我国数学的科研与教学十分有益的事。
这次科学出版社购买了版权，一次影印了23本施普林格出版社出版的数学书，就是一件好事，也是值得继续做下去的事情。大体上分一下，这23本书中，包括基础数学书5本，应用数学书6本与计算数学书12本，其中有些书也具有交叉性质。这些书都是很新的，2000年以后出版的占绝大部分，共计16本，其余的也是1990年以后出版的。这些书可以使读者较快地了解数学某方面的前沿，例如基础数学中的数论、代数与拓扑三本，都是由该领域大数学家编著的“数学百科全书”的分册。对从事这方面研究的数学家了解该领域的前沿与全貌很有帮助。按照学科的特点，基础数学类的书以“经典”为主，应用和计算数学类的书以“前沿”为主。这些书的作者多数是国际知名的大数学家，例如《拓扑学》一书的作者诺维科夫是俄罗斯科学院的院士，曾获“菲尔兹奖”和“沃尔夫数学奖”。这些大数学家的著作无疑将会对我国的科研人员起到非常好的指导作用。
当然，23本书只能涵盖数学的一部分，所以，这项工作还应该继续做下去。更进一步，有些读者面较广的好书还应该翻译成中文出版，使之有更大的读者群。
总之，我对科学出版社影印施普林格出版社的部分数学著作这一举措表示热烈的支持，并盼望这一工作取得更大的成绩。
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