图像处理与分析 内容简介

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图像处理与分析 本书特色

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 therigorously develop and analyze several imageprocessors. The book is comprehensive and integrative， covering thefour most powerful classes of mathematical tools icontemporaryimage analysis and processing while exploring their intrinsicconnections and integration. The material is balanced itheory andcomputation， following a solid theoretical analysis of model buildingand performance with computational implementatioand numerical examples.
This book is writtefor graduate students and researchers inapplied mathematics， computer science， electrical engineering， andother disciplines who are interested iproblems iimaging andcomputer vision. It cabe used as a reference by scientists withspecific tasks iimage processing， as well as by researchers with ageneral interest ifinding out about the latest advances.

图像处理与分析 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 Interpretatioand 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 AOverview of Methodologies iImage 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 Organizatioof the Book
1．5 How to Read the Bcok
2 Some ModerImage Analysis Tools
2．1 Geometry of Curves and Surfaces
2．1．I Geometry of Curves
2．1．2 Geometry of Surfaces iThree Dimensions
2．1．3 Hausdorff Measures and Dimensions
2．2 Functions with Bounded Variations
2．2．1 Total Variatieas a RadoMeasure
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 BayesiaStatistical Inference
2．4．1 Image Processing or Visual Perceptioas Inference
2．4．2 BayesiaInference： Bias Due to Prior Knowledge
2．4．3 BayesiaMethod iImage 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 MultiresolutioAnalysis
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-WilsoWavelets
2．6．5 The Framework of MultiresolutioAnalysis （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 Constructioof 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 AExample： 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： PoissoRepresentation
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
4．1．6 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-DriveOptimal Filtering： Wiener Filters
4．4 Wavelet Shrinkage Denoising
4．4．1 Shrinkage： Quasi-statistical Estimatioof Singletons
4．4．2 Shrinkage： Variational Estimatioof Singletons
4．4．3 Denoising via Shrinking Noisy Wavelet Components
4．4．4 Variational Denoising of Noisy Besov Images
4．5 Variational Denoising Based oBV 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 MediaFiltering
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 SolutioStructures of the TV Denoising Model
4．6 Denoising via Nonlinear Diffusioand Scale-Space Theory
4．6．1 Perona and Malik's Nonlinear DiffusioModel
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
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 IntuitiooFilter-Based Deblurring
5．3．2 Wiener Filtering
5．4 Deblurring of BV Images with KnowPSF
5．4．1 The Variational Model
5．4．2 Existence and Uniqueness
5．4．3 Computation
5．5 Variational Blind Deblurring with UnknowPSF
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 oClassical InterpolatioSchemes
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 MaiChallenges 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 RadoMeasure)
6．5．1 Formulatioof the TV Inpainting Model
6．5．2 Justificatioof TV Inpainting by Visual Perception
6．5．3 Computatioof TV lnpainting
6．5．4 Digital Zooming Based oTV 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 othe 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 InterpolatioModels
6．11．2 A Third Order PDE Inpainting Model and Navier-Stokes
……
7 Image Segmentation
Bibliography
Index