3D Images of Materials Structures

PERFACEINTRODUCTIONPRELIMINARIESGeneral NotationCharacteristics of SetsRandom SetsFourier AnalysisLATTICES, ADJACENCY OF LATTICE POINTS, AND IMAGESIntroductionPoint Lattices, Digitizations and Pixel ConfigurationsAdjacency and Euler NumberThe Euler Number of Microstructure ConstituentsImage DataRenderingIMAGE PROCESSINGFourier Transform of an ImageFilteringSegmentationMEASUREMENT OF INTRINSIC VOLUMES AND RELATED QUANTITIESIntroductionIntrinsic VolumesIntrinsic Volume DensitiesDirectional AnalysisDistances Between Random Sets and Distance DistributionsSPECTRAL ANALYSISIntroductionSecond-Order Characteristics of a Random Volume MeasureCorrelations Between Random StructuresSecond-Order Characteristics of Random SurfacesSecond-Order Characteristics of Random Point FieldsMODEL-BASED IMAGE ALANYSISIntroduction,MotivationPoint Field ModelsMacroscopicallyHomogeneous Systems of Non-overlapping ParticlesMacroscopically Homogeneous Systems of Overlapping ParticlesMacroscopically HomogeneousFibre SystemsTessellationsSIMULATION OF MATERIAL PROPERTIESIntroductionEffective Conductivity of Polycrystals by StochasticHomogenizationComputation of Effective Elastic Moduli of Porous Media by FEM SimulationREFERENCESINDEX

Dr. Katja Schladitz is with Fraunhofer-Institut für 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.