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...
| Otros Autores: | |
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| Formato: | Libro electrónico |
| Idioma: | Inglés |
| Publicado: |
London : Hoboken, N.J. :
ISTE ; Wiley
c2012.
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| Edición: | 1st edition |
| Colección: | ISTE
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| Materias: | |
| Ver en Biblioteca Universitat Ramon Llull: | https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009628497606719 |
Tabla de Contenidos:
- Cover; Title Page; Copyright Page; Table of Contents; Chapter 1.Introduction; Chapter 2.Marked Point Processes for Object Detection; 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; 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 isotropy3.3. 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
- 4.1. Discrete simulations: Markov chain Monte Carlo algorithms4.1.1. 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.π-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 kernels4.1.5.1. Creating complex transitions fromstandard transitions; 4.1.5.2. Data-driven perturbations; 4.1.5.3. Perturbations directed by thecurrent 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 birthsand deaths algorithm; 4.3. Mixed simulations; 4.3.1. Jump process; 4.3.2. Diffusion process
- 4.3.3. Coordination of jumps and diffusions4.4. 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; 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
