Preface nAcknowledgmentsnn1: Preliminaries n1.1 Geometry and measure in the Euclidean spacen1.2 Probability and statisticsnn2: Random Measures and Point Processesn2.1 Basic definitions n2.2 Palm distributions n2.3 Poisson process n2.4 Finite point processes n2.5 Stationary random measures on Rdn2.6 Application of point processes in epidemiology n2.7 Weighted random measures, marked point processesn2.8 Stationary processes of particlesn2.9 Flat processesnn3: Random Fibre And Surface Systemsn3.1 Geometric modelsn3.2 Intensity estimatorsn3.3 Projection measure estimationn3.4 Best unbiased estimators of intensity nn4: Vertical Sampling Schemesn4.1 Randomized samplingn4.2 Design-based approach nn5: Fibre and Surface Anisotropyn5.1 Introductionn5.2 Analytical approach n5.3 Convex geometry approachn5.4 Orientation-dependent direction distributionnn6: Particle Systemsn6.1 Stereological unfolding n6.2 Bivariate unfoldingn6.3 Trivariate unfoldingn6.4 Stereology of extremesnnReferencesnIndex
Stochastic geometry, based on current developments in geometry, probability and measure theory, makes possible modeling of two- and three-dimensional random objects with interactions as they appear in the microstructure of materials, biological tissues, macroscopically in soil, geological sediments etc. In combination with spatial statistics it is used for the solution of practical problems such as the description of spatial arrangements and the estimation of object characteristics. A related field is stereology, which makes possible inference on the structures, based on lower-dimensional observations. Unfolding problems for particle systems and extremes of particle characteristics are studied. The reader can learn about current developments in stochastic geometry with mathematical rigor on one hand and find applications to real microstructure analysis in natural and material sciences on the other hand.