Foreword by Henri Maitre
Acknowledgments
List of Figures
Notation and Symbols
1　Introduction
　1.1　 About Modeling
　　1.1.1　Bayesian Approach
　　1.1.2　Inverse Problem
　　1.1.3　Energy-Based Formulation
　　1.1.4　Models
　1.2　 Structure of the Book
　Spline Models
2　Nonparametrie Spline Models
　2.1　 Definition
　2.2　 Optimization
　　2.2.1　Bending Spline
　　2.2.2　Spline Under Tension
　　2.2.3　Robustness
　2.3　 Bayesian Interpretation
　2.4　 Choice of Regularization Parameter
　2.5　 Approximation Using a Surface
　　2.5.1　L-Spline Surface
　　2.5.2　Quadratic Energy
　　2.5.3　Finite Element Optimization
3　Parametric Spline Models
　3.1　 Representation on a Basis of B-Splines
　　3.1.1　Approximation Spline
　　3.1.2　Construction of B-Splines
　3.2　 Extensions
　　3.2.1　Multidimensional Case
　　3.2.2　Heteroscedasticity
　3.3　 High-Dimensional Splines
　　3.3.1　Revealing Directions
　　3.3.2　Projection Pursuit Regression
4　Auto-Associative Models
　4.1　 Analysis of Multidimensional Data
　　4.1.1　A Classical Approach
　　4.1.2　Toward an Alternative Approach
　4.2　 Auto-Associative Composite Models
　　4.2.1　Model and Algorithm
　　4.2.2　Properties
　4.3　 Projection Pursuit and Spline Smoothing
　　4.3.1　Projection Index
　　4.3.2　Spline Smoothing
　4.4　 Illustration
Ⅱ　Markov Models
5　Fundamental Aspects
　5.1　 Definitions
　　5.1.1　Finite Markov Fields
　　5.1.2　Gibbs Fields
　5.2　 Markov-Gibbs Equivalence
　5.3　 Examples
　　5.3.1　Bending Energy
　　5.3.2　Bernoulli Energy
　　5.3.3　Gaussian Energy
　5.4　 Consistency Problem
6　Bayesian Estimation
　6.1　 Principle
　6.2　 Cost Functions
　　6.2.1　Cost b-hnction Examples
　　6.2.2　Calculation Problems
7　Simulation and Optimization
　7.1　 Simulation
　　7.1.1　Homogeneous Markov Chain
　　7.1.2　Metropolis Dynamic
　　7.1.3　Simulated Gibbs Distribution
　7.2　 Stochastic Optimization
　7.3　 Probabilistic Aspects
　7.4　 Deterministic Optimization
　　7.4.1　ICM Algorithm
　　7.4.2　Relaxation Algorithms
8　Parameter Estimation
　8.1　 Complete Data
　　8.1.1　Maximum Likelihood
　　8.1.2　Maximum Pseudolikelihood
　　8.1.3　Logistic Estimation
　8.2　 Incomplete Data
　　8.2.1　Maximum Likelihood
　　8.2.2　Gibbsian EM Algorithm
　　8.2.3　Bayesian Calibration
　Ⅲ　Modeling in Action
9　Model-Building
　9.1　 Multiple Spline Approximation
　　9.1.1　Choice of Data and Image Characteristics
　　9.1.2　Definition of the Hidden Field
　　9.1.3　Building an Energy
　9.2　 Markov Modeling Methodology
　　9.2.1　Details for Implementation
10 Degradation in Imaging
　　10.1　Denoising
　　10.1.1 Models with Explicit Discontinuities
　　10.1.2 Models with Implicit Discontinuities
　　10.2　Deblurring
　　10.2.1 A Particularly Ill-Posed Problem
　　10.2.2 Model with Implicit Discontinuities
　　10.3　Scatter
　　10.3.1 Direct Problem
　　10.3.2 Inverse Problem
　10.4　Sensitivity Functions and Image Fusion
　　10.4.1 A Restoration Problem
　　10.4.2 Transfer Function Estimation
　　10.4.3 Estimation of Stained Transfer Function
11 Detection of Filamentary Entities
　11.1　Valley Detection Principle
　　11.1.1 Definitions
　　11.1.2 Bayes-Markov Formulation
　11.2　Building the Prior Energy
　　11.2.1 Detection Term
　　11.2.2 Regularization Term
　11.3　Optimization
　11.4　Extension to the Case of an Image Pair
12 Reconstruction and Projections
　12.1　Projection Model
　　12.1.1 Transmission Tomography
　　12.1.2 Emission Tomography
　12.2　Regularized Reconstruction
　　12.2.1 Regularization with Explicit Discontinuities
　 12.2.2 Three-Dimensional Reconstruction
　12.3　Reconstruction with a Single View
　　12.3.1 Generalized Cylinder
　　12.3.2 Training the Deformations
　　12.3.3 Reconstruction in the Presence of Occlusion
13 Matching
　13.1　Template and Hidden Outline
　　13.1.1 Rigid Transformations
　　13.1.2 Spline Model of a Template
　13.2　Elastic Deformations
　　13.2.1 Continuous Random Fields
　　13.2.2 Probabilistie Aspects
References
Author Index
Subject Index