List of Figures
Preface
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 1-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 BV Images
4 Image Denoising
5 Image Deblurring
6 Image Inpainting
7 Image Segmentation
Bibliography
Index
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