3D Images of Materials Structures Processing and Analysis 1st Edition by Joachim Ohser, Katja Schladitz 352731203X 9783527312030

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Product details:

ISBN 10: 352731203X

ISBN 13: 9783527312030

Author: Joachim Ohser, Katja Schladitz

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.

Table of contents:

1 Introduction
2.1.1 Points and Sets in Euclidean Spaces
2.1.2 Curvatures
2.1.3 Measures and Measurable Spaces
2.2.1 The Euler Number and the Integral of Gaussian Curvature
2.2.2 The Mean Width and the Integral of the Mean Curvature
2.2.3 Intrinsic Volumes of Convex Bodies
2.2.4 Additive Extensions on the Convex Ring
2.2.5 The Principal Kinematic Formulae of Integral Geometry
2.3 Random Sets
2.3.1 Definition of Random Sets
2.3.2 Characteristics of Random Closed Sets
2.3.3 Random Point Fields
2.3.4 Random Tessellations
2.4.1 Measurable Functions
2.4.2 Fourier Transform
2.4.3 Bochner’s Theorem
3.2 Point Lattices, Digitizations and Pixel Configurations
3.2.1 Homogeneous Lattices
3.2.2 Digitization
3.2.3 Pixel Configurations
3.3 Adjacency and Euler Number
3.3.1 Adjacency Systems
3.3.2 Discretization of Sets with Respect to Adjacency
3.3.3 Euler Number
3.3.4 Complementarity
3.3.5 Multi-grid Convergence
3.4.1 Counting Nodes in Open Foams
3.4.2 Connectivity of the Fibres in Non-woven Materials
3.5 Image Data
3.5.1 The Inverse Lattice
3.5.2 The Nyquist–Shannon Sampling Theorem
3.6.1 Volume Rendering
3.6.2 Surface Rendering
4.1.1 The Discrete Fourier Transform of a Discrete One-Dimensional Signal
4.1.2 Fast Fourier Transform
4.1.3 Extensions to Higher Dimensions
4.2.1 Morphological Transforms of Sets
4.2.2 Linear Filters
4.2.3 Morphological Filters
4.2.4 Rank Value Filters
4.2.5 Diffusion Filters
4.2.6 Geodesic Morphological Transforms
4.2.7 Distance Transforms
4.2.8 Skeletonization
4.3 Segmentation
4.3.1 Binarization
4.3.2 Connectedness, Connected Components and Labelling
4.3.3 Watershed Transform
4.3.4 Further Segmentation Methods
5.1 Introduction
5.2 Intrinsic Volumes
5.2.1 Section Lattices and Translation Lattices
5.2.2 Measurement of Intrinsic Volumes
5.2.3 Discretization of the Translative Integral
5.2.4 Discretization of the Integral over all Subspaces
5.2.5 Shape Factors
5.2.6 Edge Correction
5.3 Intrinsic Volume Densities
5.3.1 Estimation of Intrinsic Volume Densities for Macroscopically Homogeneous Random Sets
5.3.2 Characterization of Anisotropy
5.3.3 Mean Chord Length
5.3.4 Structure Model Index
5.3.5 Estimation of the Intrinsic Volume Densities for Macroscopically Homogeneous and Isotropic Random Sets
5.3.6 Intrinsic Volume Densities of the Solid Matter of Two Natural Porous Structures
5.4 Directional Analysis
5.4.1 Inverse Cosine Transform
5.4.2 Use of Pixel Configurations Carrying Directional Information
5.4.3 Gradient and Hessian Matrix
5.4.4 Maximum Filter Response
5.5 Distances Between Random Sets and Distance Distributions
5.5.1 Spherical Contact Distribution Function and Related Quantities
5.5.2 Stochastic Dependence of Constituents of Metallic Foams
6.1 Introduction
6.2 Second-Order Characteristics of a Random Volume Measure
6.2.1 Covariance Function and Bartlett Spectrum
6.2.2 Power Spectrum
6.2.3 Measurement of the Covariance and the Power Spectrum
6.2.4 Macroscopic Homogeneity and Isotropy
6.2.5 Mean Face Width of an Open Foam
6.2.6 Random Packing of Balls
6.2.7 Particle Rearrangement During Sintering Processes
6.3 Correlations Between Random Structures
6.3.1 The Cross-Covariance Function
6.3.3 Spatial Cross-Correlation Between Constituents of Metallic Foams
6.4 Second-Order Characteristics of Random Surfaces
6.4.1 The Random Surface Measure
6.4.2 The Bartlett Spectrum
6.4.3 Power Spectrum
6.4.4 Measurement of the Power Spectrum with Respect to the Surface Measure
6.5 Second-Order Characteristics of Random Point Fields
6.5.1 Point Fields and Associated Random Functions
6.5.2 A Wiener–Khintchine Theorem for Point Fields
6.5.3 Estimation of the Pair Correlation Function
6.5.4 The Power Spectra of the Centres of Balls in Dense Packings
7.1 Introduction, Motivation
7.2.1 The Poisson Point Field
7.2.3 Finite Point Fields Defined by a Probability Density
7.3 Macroscopically Homogeneous Systems of Non-overlapping Particles
7.4 Macroscopically Homogeneous Systems of Overlapping Particles
7.4.1 Intrinsic Volumes of Boolean Models in Rn
7.4.2 Intrinsic Volumes of Boolean Models in R3
7.4.3 Structure Model Index for Boolean Models in R3
7.5.1 Boolean Cylinder Model
7.5.2 PET Stacked Fibre Non-woven Materials
7.5.3 Carbon Paper
7.6.1 Geometric Properties of Tessellations of R3
7.6.2 Voronoï Tessellations
7.6.3 Laguerre Tessellations
7.6.4 The Weaire–Phelan Foam
7.6.5 Mean Values of Geometric Characteristics of Open Foams
7.6.6 Modelling a Closed Polymer Foam
7.6.7 Modelling an Open Ceramic Foam
8.1 Introduction
8.2 Effective Conductivity of Polycrystals by Stochastic Homogenization
8.3.1 Fundamentals of Linear Elasticity
8.3.2 Finite Element Method
8.3.3 Effective Stiffness Tensor Random Sets
8.3.4 Effective Elastic Moduli of a Porous Alumina Material

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Tags: Joachim Ohser, Katja Schladitz, Images, Structures, Processing