Image analysis, random fields and Markov chain Monte Carlo methods: a mathematical introduction
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2006
|
| Edition: | 2. ed., 3. print. |
| Series: | Stochastic modelling and applied probability; 27
27 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Frühere Aufl. erschienen als Bd. 27 in: Applications of mathematics |
| Physical Description: | XVI, 387 S. graph. Darst. CD-ROM (12 cm) |
| ISBN: | 9783540442134 |
Staff View
MARC
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| 100 | 1 | |a Winkler, Gerhard |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Image analysis, random fields and Markov chain Monte Carlo methods |b a mathematical introduction |c Gerhard Winkler |
| 250 | |a 2. ed., 3. print. | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2006 | |
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| 490 | 1 | |a Stochastic modelling and applied probability; 27 | |
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Record in the Search Index
| _version_ | 1804137332846100480 |
|---|---|
| adam_text | Contents
Introduction
,
Part
I. Bayesian Image Analysis: Introduction
1.
The Bayesian Paradigm
................................... 9
1.1
Warming up for Absolute Beginners
...................... 10
1.2
Images and Observations
................................ 14
1.3
Prior and Posterior Distributions
......................... 20
1.4
Bayes
Estimators
....................................... 24
2.
Cleaning Dirty Pictures
.................................. 29
2.1
Boundaries and their Information Content
................. 30
2.2
Towards Piecewise Smoothing
............................ 31
2.3
Filters, Smoothers, and
Bayes
Estimators
.................. 41
2.4
Boundary Extraction
................................... 48
2.5
Dependence on Hyperparameters
......................... 50
3.
Finite Random Fields
..................................... 55
3.1
Markov Random Fields
................................. 55
3.2
Gibbs Fields and Potentials
.............................. 60
3.3
Potentials Continued
.................................... 66
Part II. The Gibbs Sampler and Simulated Annealing
4.
Markov Chains: Limit Theorems
.......................... 75
4.1
Preliminaries
........................................... 75
4.2
The Contraction Coefficient
.............................. 81
4.3
Homogeneous Markov Chains
............................ 84
4.4
Exact Sampling
........................................ 92
4.5
Inhomogeneous Markov Chains
...........................102
4.6
A Law of Large Numbers for Inhomogeneous Chains
........106
4.7
A Counterexample for the Law of Large Numbers
..........110
5.
Gibbsian
Sampling and Annealing
........................ 113
5.1
Sampling
.............................................. 113
5.2
Simulated Annealing
.................................... 120
5.3
Discussion
............................................. 125
6.
Cooling Schedules
........................................129
6.1
The ICM Algorithm
....................................129
6.2
Exact MAP Estimation Versus Fast Cooling
...............131
6.3
Finite Time Annealing
..................................139
Part III. Variations of the Gibbs Sampler
7.
Gibbsian Sampling and Annealing Revisited
..............143
7.1
A General Gibbs Sampler
...............................143
7.2
Sampling and Annealing under Constraints
................147
8.
Partially Parallel Algorithms
.............................153
8.1
Synchronous Updating on Independent Sets
................154
8.2
The Swendson-Wang Algorithm
..........................156
9.
Synchronous Algorithms
..................................159
9.1
Invariant Distributions and Convergence
..................159
9.2
Support of the Limit Distribution
........................163
9.3
Synchronous Algorithms and Reversibility
.................168
Part IV. Metropolis Algorithms and Spectral Methods
10.
Metropolis Algorithms
....................................179
10.1
Metropolis Sampling and Annealing
......................179
10.2
Convergence Theorems
..................................180
10.3
Best Constants
.........................................185
10.4
About Visiting Schemes
.................................187
10.5
Generalizations and Modifications
........................191
10.6
The Metropolis Algorithm in Combinatorial Optimization
. . . 193
11.
The Spectral Gap and Convergence of Markov Chains
.... 197
11.1
Eigenvalues of Markov Kernels
...........................197
11.2
Geometric Convergence Rates
............................201
12.
Eigenvalues, Sampling, Variance Reduction
...............203
12.1
Samplers and their Eigenvalues
...........................203
12.2
Variance Reduction
.....................................204
12.3
Importance Sampling
...................................206
13.
Continuous Time Processes
...............................209
13.1
Discrete State Space
....................................210
13.2
Continuous State Space
.................................211
Part V. Texture Analysis
14.
Partitioning
..............................................217
14.1
How to Tell Textures Apart
..............................217
14.2
Bayesian Texture Segmentation
..........................221
14.3
Segmentation by a Boundary Model
......................223
14.4
Julesz s Conjecture and Two Point Processes
...............225
15.
Random Fields and Texture Models
......................231
15.1
Neighbourhood Relations
................................233
15.2
Random Field Texture Models
...........................235
15.3
Texture Synthesis
......................................240
16.
Bayesian Texture Classification
...........................243
16.1
Contextual Classification
................................244
16.2
Marginal Posterior Modes Methods
.......................246
Part VI. Parameter Estimation
17.
Maximum Likelihood Estimation
.........................251
17.1
The Likelihood Function
................................252
17.2
Objective Functions
....................................257
18.
Consistency of Spatial ML Estimators
....................263
18.1
Observation Windows and Specifications
..................263
18.2
Pseudolikelihood Methods
...............................268
18.3
Large Deviations and Full Maximum Likelihood
............277
18.4
Partially Observed Data
.................................279
19.
Computation of Full ML Estimators
......................281
19.1
A Naive Algorithm
.....................................281
19.2
Stochastic Optimization for the Full Likelihood
.............285
19.3
Main Results
..........................................286
19.4
Error Decomposition
....................................291
19.5
L2-Estimates
..........................................295
Part
VII.
Supplement
20.
A Glance at Neural Networks
............................301
20.1
Boltzmann Machines
....................................302
20.2
A Learning Rule
.......................................306
21.
Three Applications
.......................................313
21.1
Motion Analysis
........................................313
21.2 Tomographie
Image Reconstruction
.......................317
21.3
Biological Shape
........................................321
Part
VIII.
Appendix
A. Simulation of Random Variables
..........................327
A.I Pseudorandom Numbers
.................................327
A.
2
Discrete Random Variables
..............................331
A.3 Special Distributions
....................................334
B. Analytical Tools
..........................................343
B.I Concave Functions
......................................343
B.2 Convergence of Descent Algorithms
.......................346
B.3 A Discrete Gronwall Lemma
.............................347
B.4 A Gradient System
.....................................347
C. Physical Imaging Systems
................................351
D. The Software Package AntsInFields
.......................355
References
....................................................357
Symbols
......................................................379
Index
.................. .......................................381
|
| adam_txt |
Contents
Introduction
,
Part
I. Bayesian Image Analysis: Introduction
1.
The Bayesian Paradigm
. 9
1.1
Warming up for Absolute Beginners
. 10
1.2
Images and Observations
. 14
1.3
Prior and Posterior Distributions
. 20
1.4
Bayes
Estimators
. 24
2.
Cleaning Dirty Pictures
. 29
2.1
Boundaries and their Information Content
. 30
2.2
Towards Piecewise Smoothing
. 31
2.3
Filters, Smoothers, and
Bayes
Estimators
. 41
2.4
Boundary Extraction
. 48
2.5
Dependence on Hyperparameters
. 50
3.
Finite Random Fields
. 55
3.1
Markov Random Fields
. 55
3.2
Gibbs Fields and Potentials
. 60
3.3
Potentials Continued
. 66
Part II. The Gibbs Sampler and Simulated Annealing
4.
Markov Chains: Limit Theorems
. 75
4.1
Preliminaries
. 75
4.2
The Contraction Coefficient
. 81
4.3
Homogeneous Markov Chains
. 84
4.4
Exact Sampling
. 92
4.5
Inhomogeneous Markov Chains
.102
4.6
A Law of Large Numbers for Inhomogeneous Chains
.106
4.7
A Counterexample for the Law of Large Numbers
.110
5.
Gibbsian
Sampling and Annealing
. 113
5.1
Sampling
. 113
5.2
Simulated Annealing
. 120
5.3
Discussion
. 125
6.
Cooling Schedules
.129
6.1
The ICM Algorithm
.129
6.2
Exact MAP Estimation Versus Fast Cooling
.131
6.3
Finite Time Annealing
.139
Part III. Variations of the Gibbs Sampler
7.
Gibbsian Sampling and Annealing Revisited
.143
7.1
A General Gibbs Sampler
.143
7.2
Sampling and Annealing under Constraints
.147
8.
Partially Parallel Algorithms
.153
8.1
Synchronous Updating on Independent Sets
.154
8.2
The Swendson-Wang Algorithm
.156
9.
Synchronous Algorithms
.159
9.1
Invariant Distributions and Convergence
.159
9.2
Support of the Limit Distribution
.163
9.3
Synchronous Algorithms and Reversibility
.168
Part IV. Metropolis Algorithms and Spectral Methods
10.
Metropolis Algorithms
.179
10.1
Metropolis Sampling and Annealing
.179
10.2
Convergence Theorems
.180
10.3
Best Constants
.185
10.4
About Visiting Schemes
.187
10.5
Generalizations and Modifications
.191
10.6
The Metropolis Algorithm in Combinatorial Optimization
. . . 193
11.
The Spectral Gap and Convergence of Markov Chains
. 197
11.1
Eigenvalues of Markov Kernels
.197
11.2
Geometric Convergence Rates
.201
12.
Eigenvalues, Sampling, Variance Reduction
.203
12.1
Samplers and their Eigenvalues
.203
12.2
Variance Reduction
.204
12.3
Importance Sampling
.206
13.
Continuous Time Processes
.209
13.1
Discrete State Space
.210
13.2
Continuous State Space
.211
Part V. Texture Analysis
14.
Partitioning
.217
14.1
How to Tell Textures Apart
.217
14.2
Bayesian Texture Segmentation
.221
14.3
Segmentation by a Boundary Model
.223
14.4
Julesz's Conjecture and Two Point Processes
.225
15.
Random Fields and Texture Models
.231
15.1
Neighbourhood Relations
.233
15.2
Random Field Texture Models
.235
15.3
Texture Synthesis
.240
16.
Bayesian Texture Classification
.243
16.1
Contextual Classification
.244
16.2
Marginal Posterior Modes Methods
.246
Part VI. Parameter Estimation
17.
Maximum Likelihood Estimation
.251
17.1
The Likelihood Function
.252
17.2
Objective Functions
.257
18.
Consistency of Spatial ML Estimators
.263
18.1
Observation Windows and Specifications
.263
18.2
Pseudolikelihood Methods
.268
18.3
Large Deviations and Full Maximum Likelihood
.277
18.4
Partially Observed Data
.279
19.
Computation of Full ML Estimators
.281
19.1
A Naive Algorithm
.281
19.2
Stochastic Optimization for the Full Likelihood
.285
19.3
Main Results
.286
19.4
Error Decomposition
.291
19.5
L2-Estimates
.295
Part
VII.
Supplement
20.
A Glance at Neural Networks
.301
20.1
Boltzmann Machines
.302
20.2
A Learning Rule
.306
21.
Three Applications
.313
21.1
Motion Analysis
.313
21.2 Tomographie
Image Reconstruction
.317
21.3
Biological Shape
.321
Part
VIII.
Appendix
A. Simulation of Random Variables
.327
A.I Pseudorandom Numbers
.327
A.
2
Discrete Random Variables
.331
A.3 Special Distributions
.334
B. Analytical Tools
.343
B.I Concave Functions
.343
B.2 Convergence of Descent Algorithms
.346
B.3 A Discrete Gronwall Lemma
.347
B.4 A Gradient System
.347
C. Physical Imaging Systems
.351
D. The Software Package AntsInFields
.355
References
.357
Symbols
.379
Index
.'.381 |
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| discipline | Informatik Mathematik Wirtschaftswissenschaften |
| discipline_str_mv | Informatik Mathematik Wirtschaftswissenschaften |
| edition | 2. ed., 3. print. |
| format | Book |
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| id | DE-604.BV023083854 |
| illustrated | Illustrated |
| index_date | 2024-07-02T19:38:22Z |
| indexdate | 2024-07-09T21:10:37Z |
| institution | BVB |
| isbn | 9783540442134 |
| language | English |
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| publishDate | 2006 |
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| series | Stochastic modelling and applied probability; 27 |
| series2 | Stochastic modelling and applied probability; 27 |
| spelling | Winkler, Gerhard Verfasser aut Image analysis, random fields and Markov chain Monte Carlo methods a mathematical introduction Gerhard Winkler 2. ed., 3. print. Berlin [u.a.] Springer 2006 XVI, 387 S. graph. Darst. CD-ROM (12 cm) txt rdacontent n rdamedia nc rdacarrier Stochastic modelling and applied probability; 27 Frühere Aufl. erschienen als Bd. 27 in: Applications of mathematics Imágenes, Tratamiento de las Markov, Procesos de Monte-Carlo, Método de Markov-Kette (DE-588)4037612-6 gnd rswk-swf Bildanalyse (DE-588)4145391-8 gnd rswk-swf Zufälliges Feld (DE-588)4191094-1 gnd rswk-swf Monte-Carlo-Simulation (DE-588)4240945-7 gnd rswk-swf Bildanalyse (DE-588)4145391-8 s Zufälliges Feld (DE-588)4191094-1 s Markov-Kette (DE-588)4037612-6 s Monte-Carlo-Simulation (DE-588)4240945-7 s DE-604 Stochastic modelling and applied probability; 27 27 (DE-604)BV019623501 27 Digitalisierung UB Augsburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016286827&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Winkler, Gerhard Image analysis, random fields and Markov chain Monte Carlo methods a mathematical introduction Stochastic modelling and applied probability; 27 Imágenes, Tratamiento de las Markov, Procesos de Monte-Carlo, Método de Markov-Kette (DE-588)4037612-6 gnd Bildanalyse (DE-588)4145391-8 gnd Zufälliges Feld (DE-588)4191094-1 gnd Monte-Carlo-Simulation (DE-588)4240945-7 gnd |
| subject_GND | (DE-588)4037612-6 (DE-588)4145391-8 (DE-588)4191094-1 (DE-588)4240945-7 |
| title | Image analysis, random fields and Markov chain Monte Carlo methods a mathematical introduction |
| title_auth | Image analysis, random fields and Markov chain Monte Carlo methods a mathematical introduction |
| title_exact_search | Image analysis, random fields and Markov chain Monte Carlo methods a mathematical introduction |
| title_exact_search_txtP | Image analysis, random fields and Markov chain Monte Carlo methods a mathematical introduction |
| title_full | Image analysis, random fields and Markov chain Monte Carlo methods a mathematical introduction Gerhard Winkler |
| title_fullStr | Image analysis, random fields and Markov chain Monte Carlo methods a mathematical introduction Gerhard Winkler |
| title_full_unstemmed | Image analysis, random fields and Markov chain Monte Carlo methods a mathematical introduction Gerhard Winkler |
| title_short | Image analysis, random fields and Markov chain Monte Carlo methods |
| title_sort | image analysis random fields and markov chain monte carlo methods a mathematical introduction |
| title_sub | a mathematical introduction |
| topic | Imágenes, Tratamiento de las Markov, Procesos de Monte-Carlo, Método de Markov-Kette (DE-588)4037612-6 gnd Bildanalyse (DE-588)4145391-8 gnd Zufälliges Feld (DE-588)4191094-1 gnd Monte-Carlo-Simulation (DE-588)4240945-7 gnd |
| topic_facet | Imágenes, Tratamiento de las Markov, Procesos de Monte-Carlo, Método de Markov-Kette Bildanalyse Zufälliges Feld Monte-Carlo-Simulation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016286827&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV019623501 |
| work_keys_str_mv | AT winklergerhard imageanalysisrandomfieldsandmarkovchainmontecarlomethodsamathematicalintroduction |