Practical Stereology

by John C. Russ

Overview

vi on geometric probability is included, students can be expected to create a few simple programs like those shown, but for other geometries. I am indebted to Tom Hare for critical reviews of the material and an endless enthusiasm to debate and derive stereological relationships; to John Matzka at Plenum Press for patiently instructing me in the intricacies of typesetting; to Chris Russ for helping to program many of these measurement techniques; and especially to Helen Adams, both for her patience with my creative fever to write yet another book, and for pointing out that the title, which I had intended to contrast to "theoretical stereology," can also be understood as the antonym of "impractical stereology." John C. Russ Raleigh, NC July, 1986 Chapter 1: Statistics 1 Accuracy and precision 1 The mean and standard deviation 5 Distributions 7 Comparison 13 Correlation 18 Nonlinear fitting 19 Chapter 2: Image Types 23 Planar sections 23 Projected images 25 Finite sections 28 Space-filling structures and dispersed phases 29 Types of images and contrast mechanisms 31 Sampling 32 Chapter 3: Manual Methods 35 Volume fraction 35 Surface density 38 Contiguity 41 Mean intercept length 42 Line density 43 Grain size determination 55 Curvature 48 Reticles to aid counting 49 Magnification and units 51 Chapter4: Size Distributions 53 Intercept length in spheres 53 Nonspherical shapes 57 Corrections for finite section thickness 59 Lamellae 61 Measurement of profile size 62 Nonspherical particles 69 vii Contents viii Chapter 5: Computer Metlwds 73

Product Details

ISBN-13:	9781489935359
Publisher:	Springer US
Publication date:	08/07/2013
Edition description:	Softcover reprint of the original 1st ed. 1986
Pages:	188
Product dimensions:	6.10(w) x 9.25(h) x 0.02(d)

Table of Contents

1: Introduction.- Elements of microstucture.- Geometric properties of features.- Typical stereological procedures.- Fundamental relationships.- Intercept length and grain size.- Curvature.- Second order stereology.- Stereology of single objects.- 2: Basic Stereological Procedures.- What stereology is.- How stereology works.- Why stereology works.- Ground rules for applying stereology.- 3: Geometry of Microstructures.- The qualitative microstructural state.- The quantitative microstructural state.- The topographic microstructural state.- 4: Classical Stereological Measures.- Two-dimensional structures; area fraction from the point count.- Volume fraction from the point count.- Two-dimensional structures; feature perimeter from the line intercept count.- Three-dimensional structures: surface area and the line intercept count.- Three-dimensional microstructures; line length and the area point count.- 5: Less Common Stereological Measures.- Three-dimensional features: topological properties and the volume tangent count.- Three-dimensional features: the mean caliper diameter.- Mean surface curvature and its integral.- The sweeping line probe in two dimensions.- Edges in three-dimensional Microstructures.- 6: Sample Design in Stereology.- Population of point probes.- Population of lines in two dimensions.- Line probes in three dimensions.- Planes in three-dimensional space.- Disectors in three-dimensional space.- Sampling strategies in 3D.- 7: Procedures for IUR Sampling.- Volume fraction.- Sampling planes.- Isotropic planes.- Isotropic line probes.- Volume probes—the Disector.- Networks.- 8: Statistical Interpretation of Data.- Sources of variability in measurement.- Distributions of values.- The mean, median and mode.- The central limit theorem and the Gaussiandistribution.- Variance and standard deviation.- Testing distributions for normality—skew and kurtosis.- Some other common distributions.- Comparing sets of measurements—the T-test.- Nonparametric comparisons.- Linear regression.- Nonlinear regression.- 9: Computer-Assisted Methods.- Getting the image to the computer.- Display and storage.- Image processing.- Overlaying grids onto images.- Basic stereological calculations.- 10: Computer Measurement of Images.- Measurement using grids.- Measuring area with pixels.- Measurement parameters—size.- Other feature measurements: shape and position.- Image processing to enable thresholding and measurement.- Image processing to extract measurable information.- Combining multiple images.- 11: Geometric Modeling.- Methods: analytic and sampling.- Sphere intercepts.- Intercept lengths in other bodies.- Intercept lengths in three dimensions.- Intersections of planes with objects.- Bertrand’s paradox.- The Buffon needle problem.- 12: Unfolding Size Distributions.- Linear intercepts in spheres.- Plane intersections.- Other shapes.- Simpler methods.- Lamellae.- 13: Anisotropy and Gradients.- Grain structures in rolled metals.- Boundary orientation.- Gradients and neighbor relationships.- Distances and irregular gradients.- Alignment.- 14: Finite Section Thickness.- Projected images.- Bias in stereological measurements.- Measurements within sections.- 15: Three-Dimensional Imaging.- Limitations of stereology.- Serial methods for acquiring 3D image data.- Inversion to obtain 3D data.- Stereoscopy as a 3D technique.- Visualization.- Processing.- Measurement.- References.