Introduction |
Bayesian Image Analysis: Introduction / Part I: |
The Bayesian Paradigm / 1: |
Warming up for Absolute Beginners / 1.1: |
linages and Observations / 1.2: |
Prior and Posterior Distributions / 1.3: |
Bayes Estimators / 1.4: |
Cleaning Dirty Pictures / 2: |
Boundaries and Their Information Content / 2.1: |
Towards Piccewiso Smoothing / 2.2: |
Filters, Smoothers, and Bayes Estimators / 2.3: |
Boundary Extraction / 2.4: |
Dependence on Hyperparameters / 2.5: |
Finite Random Fields / 3: |
Markov Random Fields / 3.1: |
Gibbs Fields and Potentials / 3.2: |
Potentials Continued / 3.3: |
The Gibbs Sampler and Simulated Annealing / Part II: |
Markov Chains: Limit Theorems / 4: |
Preliminaries / 4.1: |
The Contraction Coefficient / 4.2: |
Homogeneous Markov Chains / 4.3: |
Exact Sampling / 4.4: |
Inhomogeneous Markov Chains / 4.5: |
A Law of Large Numbers for Inhomogeneous Chains / 4.6: |
A Counterexample for the Law of Large Numbers / 4.7: |
Gibbsian Sampling and Annealing / 5: |
Sampling / 5.1: |
Simulated Annealing / 5.2: |
Discussion / 5.3: |
Cooling Schedules / 6: |
The ICM Algorithm / 6.1: |
Exact MAP Estimation Versus Fast Cooling / 6.2: |
Finite Time Annealing / 6.3: |
Variations of the Gibbs Sampler / Part III: |
Gibbsian Sampling and Annealing Revisited / 7: |
A General Gibbs Sampler / 7.1: |
Sampling and Annealing Under Constraints / 7.2: |
Partially Parallel Algorithms / 8: |
Synchronous Updating on Independent Sets / 8.1: |
The Swendson-Wang Algorithm / 8.2: |
Synchronous Algorithms / 9: |
Invariant Distributions and Convergence / 9.1: |
Support of the Limit Distribution / 9.2: |
Synchronous Algorithms and Reversibility / 9.3: |
Metropolis Algorithms and Spectral Methods / Part IV: |
Metropolis Algorithms / 10: |
Metropolis Sampling and Annealing / 10.1: |
Convergence Theorems / 10.2: |
Best Constants / 10.3: |
About Visiting Schemes / 10.4: |
Generalizations and Modifications / 10.5: |
The Metropolis Algorithm in Combinatorial Optimization / 10.6: |
The Spectral Gap and Convergence of Markov Chains / 11: |
Eigenvalues of Markov Kernels / 11.1: |
Geometric Convergence Rates / 11.2: |
Eigenvalues, Sampling, Variance Reduction / 12: |
Samplers and Their Eigenvalues / 12.1: |
Variance Reduction / 12.2: |
Importance Sampling / 12.3: |
Continuous Time Processes / 13: |
Discrete State Space / 13.1: |
Continuous State Space / 13.2: |
Texture Analysis / Part V: |
Partitioning / 14: |
How to Tell Textures Apart / 14.1: |
Bayesian Texture Segmentation / 14.2: |
Segmentation by a Boundary Model / 14.3: |
Julesz's Conjecture and Two Point Processes / 14.4: |
Random Fields and Texture Models / 15: |
Neighbourhood Relations / 15.1: |
Random Field Texture Models / 15.2: |
Texture Synthesis / 15.3: |
Bayesian Texture Classification / 16: |
Contextual Classification / 16.1: |
Marginal Posterior Modes Methods / 16.2: |
Parameter Estimation / Part VI: |
Maximum Likelihood Estimation / 17: |
The Likelihood Function / 17.1: |
Objective Functions / 17.2: |
Consistency of Spatial ML Estimators / 18: |
Observation Windows and Specifications / 18.1: |
Pseudolikelihood Methods / 18.2: |
Large Deviations and Full Maximum Likelihood / 18.3: |
Partially Observed Data / 18.4: |
Computation of Pull ML Estimators / 19: |
A Naive Algorithm / 19.1: |
Stochastic Optimization for the Full Likelihood / 19.2: |
Main Results / 19.3: |
Error Decomposition / 19.4: |
Supplement / 19.5: |
A Glance at Neural Networks / 20: |
Boltzmann Machines / 20.1: |
A Learning Rule / 20.2: |
Three Applications / 21: |
Motion Analysis / 21.1: |
Tomographic Image Reconstruction / 21.2: |
Biological Shape / 21.3: |
Appendix / Part VIII: |
Simulation of Random Variables / A: |
Pseudorandom Numbers / A.1: |
Discrete Random Variables / A.2: |
Special Distributions / A.3: |
Analytical Tools / B: |
Concave Functions / B.1: |
Convergence of Descent Algorithms / B.2: |
A Discrete Gronwall Lemma / B.3: |
A Gradient System / B.4: |
Physical Imaging Systems / C: |
The Software Package AntsInFields / D: |
References |
Symbols |
Index |
Introduction |
Bayesian Image Analysis: Introduction / Part I: |
The Bayesian Paradigm / 1: |