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.
Dr. Katja Schladitz is with Fraunhofer-Institut fur Techno- und Wirtschaftsmathematik in Kaiserslautern, Germany, where she coordinates the group working on analysis of 3D images and modelling of microstructures within the image processing department. She has been involved in a number of industrial and academic projects. Her research focuses on application of methods from stochastic geometry to image analysis and modelling materials microstructures. Professor Joachim Ohser holds a Chair at University of Applied Sciences, Darmstadt, Germany, where he is teaching in the field of image processing. He has long experience with characterization and geometric modelling of microstructures. Since 1999 he heads the working group on quantitative microstructural analysis of the German Materials Society (DGM). His research focuses on stochastic and discrete geometry, image analysis and simulation of materials properties.
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