PERFACE
INTRODUCTION
PRELIMINARIES
General Notation
Characteristics of Sets
Random Sets
Fourier Analysis
LATTICES, ADJACENCY OF LATTICE POINTS, AND IMAGES
Introduction
Point Lattices, Digitizations and Pixel Configurations
Adjacency and Euler Number
The Euler Number of Microstructure Constituents
Image Data
Rendering
IMAGE PROCESSING
Fourier Transform of an Image
Filtering
Segmentation
MEASUREMENT OF INTRINSIC VOLUMES AND RELATED QUANTITIES
Introduction
Intrinsic Volumes
Intrinsic Volume Densities
Directional Analysis
Distances Between Random Sets and Distance Distributions
SPECTRAL ANALYSIS
Introduction
Second-Order Characteristics of a Random Volume Measure
Correlations Between Random Structures
Second-Order Characteristics of Random Surfaces
Second-Order Characteristics of Random Point Fields
MODEL-BASED IMAGE ALANYSIS
Introduction,Motivation
Point Field Models
MacroscopicallyHomogeneous Systems of Non-overlapping Particles
Macroscopically Homogeneous Systems of Overlapping Particles
Macroscopically Homogeneous Fibre Systems
Tessellations
SIMULATION OF MATERIAL PROPERTIES
Introduction
Effective Conductivity of Polycrystals by StochasticHomogenization
Computation of Effective Elastic Moduli of Porous Media by FEM Simulation
REFERENCES
INDEX
