图像分析中的模型和逆问题

Foreword by Henri MaitreAcknowledgmentsList of FiguresNotation and Symbols1  Introduction1.1   About Modeling1.1.1  Bayesian Approach1.1.2  Inverse Problem1.1.3  Energy-Based Formulation1.1.4  Models1.2   Structure of the BookSpline Models2  Nonparametrie Spline Models2.1   Definition2.2   Optimization2.2.1  Bending Spline2.2.2  Spline Under Tension2.2.3  Robustness2.3   Bayesian Interpretation2.4   Choice of Regularization Parameter2.5   Approximation Using a Surface2.5.1  L-Spline Surface2.5.2  Quadratic Energy2.5.3  Finite Element Optimization3  Parametric Spline Models3.1   Representation on a Basis of B-Splines3.1.1  Approximation Spline3.1.2  Construction of B-Splines3.2   Extensions3.2.1  Multidimensional Case3.2.2  Heteroscedasticity3.3   High-Dimensional Splines3.3.1  Revealing Directions3.3.2  Projection Pursuit Regression4  Auto-Associative Models4.1   Analysis of Multidimensional Data4.1.1  A Classical Approach4.1.2  Toward an Alternative Approach4.2   Auto-Associative Composite Models4.2.1  Model and Algorithm4.2.2  Properties4.3   Projection Pursuit and Spline Smoothing4.3.1  Projection Index4.3.2  Spline Smoothing4.4   IllustrationⅡ  Markov Models5  Fundamental Aspects5.1   Definitions5.1.1  Finite Markov Fields5.1.2  Gibbs Fields5.2   Markov-Gibbs Equivalence5.3   Examples5.3.1  Bending Energy5.3.2  Bernoulli Energy5.3.3  Gaussian Energy5.4   Consistency Problem6  Bayesian Estimation6.1   Principle6.2   Cost Functions6.2.1  Cost b-hnction Examples6.2.2  Calculation Problems7  Simulation and Optimization7.1   Simulation7.1.1  Homogeneous Markov Chain7.1.2  Metropolis Dynamic7.1.3  Simulated Gibbs Distribution7.2   Stochastic Optimization7.3   Probabilistic Aspects7.4   Deterministic Optimization7.4.1  ICM Algorithm7.4.2  Relaxation Algorithms8  Parameter Estimation8.1   Complete Data8.1.1  Maximum Likelihood8.1.2  Maximum Pseudolikelihood8.1.3  Logistic Estimation8.2   Incomplete Data8.2.1  Maximum Likelihood8.2.2  Gibbsian EM Algorithm8.2.3  Bayesian CalibrationⅢ  Modeling in Action9  Model-Building9.1   Multiple Spline Approximation9.1.1  Choice of Data and Image Characteristics9.1.2  Definition of the Hidden Field9.1.3  Building an Energy9.2   Markov Modeling Methodology9.2.1  Details for Implementation10 Degradation in Imaging10.1  Denoising10.1.1 Models with Explicit Discontinuities10.1.2 Models with Implicit Discontinuities10.2  Deblurring10.2.1 A Particularly Ill-Posed Problem10.2.2 Model with Implicit Discontinuities10.3  Scatter10.3.1 Direct Problem10.3.2 Inverse Problem10.4  Sensitivity Functions and Image Fusion10.4.1 A Restoration Problem10.4.2 Transfer Function Estimation10.4.3 Estimation of Stained Transfer Function11 Detection of Filamentary Entities11.1  Valley Detection Principle11.1.1 Definitions11.1.2 Bayes-Markov Formulation11.2  Building the Prior Energy11.2.1 Detection Term11.2.2 Regularization Term11.3  Optimization11.4  Extension to the Case of an Image Pair12 Reconstruction and Projections12.1  Projection Model12.1.1 Transmission Tomography12.1.2 Emission Tomography12.2  Regularized Reconstruction12.2.1 Regularization with Explicit Discontinuities12.2.2 Three-Dimensional Reconstruction12.3  Reconstruction with a Single View12.3.1 Generalized Cylinder12.3.2 Training the Deformations12.3.3 Reconstruction in the Presence of Occlusion13 Matching13.1  Template and Hidden Outline13.1.1 Rigid Transformations13.1.2 Spline Model of a Template13.2  Elastic Deformations13.2.1 Continuous Random Fields13.2.2 Probabilistie AspectsReferencesAuthor IndexSubject Index