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Stochastic geometry for image analysis /

"This book develops the stochastic geometry framework for image analysis purpose. Two main frameworks are described: marked point process and random closed sets models. We derive the main issues for defining an appropriate model. The algorithms for sampling and optimizing the models as well as...

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Detalles Bibliográficos
Clasificación:	Libro Electrónico
Otros Autores:	Descombes, Xavier
Formato:	Electrónico eBook
Idioma:	Inglés
Publicado:	London : Hoboken, NJ : ISTE ; Wiley, 2012.
Colección:	Digital signal and image processing series.
Temas:	Image processing > Statistical methods. Stochastic geometry. Traitement d'images > Méthodes statistiques. Géométrie stochastique. TECHNOLOGY & ENGINEERING > Imaging Systems. Image processing > Statistical methods Stochastic geometry
Acceso en línea:	Texto completo (Requiere registro previo con correo institucional)

Tabla de Contenidos:

Chapter 1. Introduction / X. Descombes
Chapter 2. Marked Point Processes for Object Detection / X. Descombes
2.1. Principal definitions
2.2. Density of a point process
2.3. Marked point processes
2.4. Point processes and image analysis
2.4.1. Bayesian versus non-Bayesian
2.4.2. A priori versus reference measure
Chapter 3. Random Sets for Texture Analysis / C. Lantǔjoul, M. Schmitt
3.1. Introduction
3.2. Random sets
3.2.1. Insufficiency of the spatial law
3.2.2. Introduction of a topological context
3.2.3. The theory of random closed sets (RACS)
3.2.4. Some examples
3.2.5. Stationarity and isotropy
3.3. Some geostatistical aspects
3.3.1. The ergodicity assumption
3.3.2. Inference of the DF of a stationary ergodic RACS
3.3.2.1. Construction of the estimator
3.3.2.2. On sampling
3.3.3. Individual analysis of objects
3.4. Some morphological aspects
3.4.1. Geometric interpretation
3.4.1.1. Point
3.4.1.2. Pair of points
3.4.1.3. Segment
3.4.1.4. Ball
3.4.2. Filtering
3.4.2.1. Opening and closing
3.4.2.2. Sequential alternate filtering
3.5. Appendix: demonstration of Miles' formulae for the Boolean model
Chapter 4. Simulation and Optimization / F. Lafarge, X. Descombes, E. Zhizhina, R. Minlos
4.1. Discrete simulations: Markov chain Monte Carlo algorithms
4.1.1. Irreducibility, recurrence, and ergodicity
4.1.1.1. Definitions
4.1.1.2. Stationarity
4.1.1.3. Convergence
4.1.1.4. Irreducibility
4.1.1.5. Aperiodicity
4.1.1.6. Harris recurrence
4.1.1.7. Ergodicity
4.1.1.8. Geometric ergodicity
4.1.1.9. Central limit theorem
4.1.2. Metropolis-Hastings algorithm
4.1.3. Dimensional jumps
4.1.3.1. Mixture of kernels
4.1.3.2. & pi;-reversibility
4.1.4. Standard proposition kernels
4.1.4.1. Simple perturbations
4.1.4.2. Model switch
4.1.4.3. Birth and death
4.1.5. Specific proposition kernels
4.1.5.1. Creating complex transitions from standard transitions
4.1.5.2. Data-driven perturbations
4.1.5.3. Perturbations directed by the current state
4.1.5.4. Composition of kernels
4.2. Continuous simulations
4.2.1. Diffusion algorithm
4.2.2. Birth and death algorithm
4.2.3. Muliple births and deaths algorithm
4.2.3.1. Convergence of the distributions
4.2.3.2. Birth and death process
4.2.4. Discrete approximation
4.2.4.1. Acceleration of the multiple births and deaths algorithm
4.3. Mixed simulations
4.3.1. Jump process
4.3.2. Diffusion process
4.3.3. Coordination of jumps and diffusions
4.4. Simulated annealing
4.4.1. Cooling schedule
4.4.2. Initial temperature T₀
4.4.3. Logarithmic decrease
4.4.4. Geometric decrease
4.4.5. Adaptive reduction
4.4.6. Stopping criterion/final temperature
Chapter 5. Parametric Inference for Marked Point Processes in Image Analysis / R. Stoica, F. Chatelain, M. Sigelle
5.1. Introduction
5.2. First question: what and where are the objects in the image?
5.3. Second question: what are the parameters of the point process that models the objects observed in the image?
5.3.1. Complete data
5.3.1.1. Maximum likelihood
5.3.1.2. Maximum pseudolikelihood
5.3.2. Incomplete data: EM algorithm
5.4. Conclusion and perspectives
5.5. Acknowledgments
Chapter 6. How to Set Up a Point Process? / X. Descombes
6.1. From disks to polygons, via a discussion of segments
6.2. From no overlap to alignment
6.3. From the likelihood to a hypothesis test
6.4. From Metropolis-Hastings to multiple births and deaths
Chapter 7. Population Counting / X. Descombes
7.1. Detection of Virchow-Robin spaces
7.1.1. Data modeling
7.1.2. Marked point process
7.1.3. Reversible jump MCMC algorithm
7.1.4. Results
7.2. Evaluation of forestry resources
7.2.1. 2D model
7.2.1.1. Prior
7.2.1.2. Data term
7.2.1.3. Optimization
7.2.1.4. Results
7.2.2. 3D model
7.2.2.1. Results
7.3. Counting a population of flamingos
7.3.1. Estimation of the flamingo color
7.3.2. Simulation and optimization by multiple births and deaths
7.3.3. Results
7.4. Counting the boats at a port
7.4.1. Initialization of the optimization algorithm
7.4.1.1. Parameter & gamma;<sub>d</sub>
7.4.1.2. Calibration of the do parameter
7.4.2. Initial results
7.4.3. Modification of the data energy
7.4.3.1. First modification of the prior energy
7.4.3.2. Second modification of the prior energy
Chapter 8. Structure Extraction / F. Lafarge, X. Descombes
8.1. Detection of the road network
8.2. Extraction of building footprints
8.3. Representation of natural textures
8.3.1. Simple model
8.3.1.1. Data term
8.3.1.2. Sampling by jump diffusion
8.3.1.3. Results
8.3.2. Models with complex interactions
Chapter 9. Shape Recognition / F. Lafarge, C. Mallet
9.1. Modeling of a LIDAR signal
9.1.1. Motivation
9.1.2. Model library
9.1.2.1. Energy formulation
9.1.3. Sampling
9.1.4. Results
9.1.4.1. Simulated data
9.1.4.2. Satellite data: large footprint waveforms
9.1.4.3. Airborne data: small footprint waveforms
9.1.4.4. Application to the classification of 3D point clouds
9.2. 3D reconstruction of buildings
9.2.1. Library of 3D models
9.2.2. Bayesian formulation
9.2.2.1. Likelihood
9.2.2.2. A priori
9.2.3. Optimization
9.2.4. Results and discussion
Bibliography
List of Authors
Index.

Stochastic geometry for image analysis /

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