Taking and analyzing images of materials' microstructures is essential for quality control, choice and design of all kind of products. Today, the standard method still is to analyze 2D microscopy images. But, insight into the 3D geometry of the microstructure of materials and measuring its characteristics become more and more prerequisites in order to choose and design advanced materials according to desired product properties.
This first book on processing and analysis of 3D images of materials structures describes how to develop and apply efficient and versatile tools for geometric analysis and contains a detailed description of the basics of 3d image analysis.

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