Stochastic Geometry

Contributors, Preface, 1 Crash course in stochastic geometry, 1.1 Introduction, 1.2 Hitting probabilities and geometrical measures, 1.3 Linearity of expectation, 1.4 Integral geometry, 1.5 Independence, Poisson processes and Boolean models, 1.6 Incidence and vacancy, 1.7 Distances and waiting times, 1.8 Weighted distributions, 1.9 Conditioning and variational methods, 2 Sampling and censoring, 2.1 Spatial sampling bias, 2.2 Unbiased sampling rules, 2.3 Additive functionals, 2.4 Horvitz-Thompson estimators, 2.5 Sampling bias for point processes, 2.6 Censoring effects for point processes, 2.7 Line segment processes, 2.8 Censoring of random sets, 3 Likelihood inference for spatial point processes, 3.1 Introduction, 3.2 Families of unnormalized densities, 3.3 Examples of families of unnormalized densities, 3.4 Markov chain Monte Carlo, 3.5 Finite point processes, 3.6 Simulating finite point processes, 3.7 Stability conditions, 3.8 Markov Chain Convergence, 3.9 Two New Point Processes, 3.10 Monte Carlo Likelihood Inference, 3.11 Stochastic Approximation, 3.12 Reverse Logistic Regression, 3.13 Fitting the Saturation Model, 3.14 Hypothesis Tests, 3.15 Missing Data and Edge Effects, 3.16 Fitting the Triplets Process, 3.17 Comparing the Saturated and Triplets Models, 3.18 Conclusion, 4 Markov chain Monte Carlo and spatial point processes, 4.1 Introduction, 4.2 Setup, 4.3 Metropolis+/-Hastings algorithms for finite point processes, 4.4 Markovian models for clustered and regular patterns, 4.5 Ripley+/-Kelly Markov point processes, 5 Topics in Voronoi and Johnson-Mehl tessellations, 5.1 Introduction, 5.2 Geometric structure, 5.3 Stationary Voronoi and Johnson-Mehl tessellations, 5.4 Poisson models, 5.5 A special class of Poisson models, 6 Mathematical morphology, 6.1 Introduction, 6.2 Brief review of mathematical morphology, 6.3 Advanced morphological segmentation techniques, 6.4 Granulometries: applications and algorithms, 6.5 Conclusion, 7 Random closed sets, 7.1 Introduction, 7.2 Distributions of random sets, 7.3 Convergence of random set distributions, 7.4 Limit theorems, 7.5 Statistical inference for random sets, 7.6 Concluding remarks, 8 General shape and registration analysis, 8.1 Introduction, 8.2 Matching with regression, 8.3 Estimation by matching, 8.4 Distributions and inference, 8.5 Robust matching, 8.6 Smoothed matching, 8.7 Discussion, 9 Nash inequalities, 9.1 Introduction, 9.2 Poincare inequalities, 9.3 Nash inequalities, 9.4 Conclusion, Index