Stereology and Stochastic Geometry (Computational Imaging and Vision) Book

This book, written for the scientist-practitioner, presents in a concise, understandable, step-by-step form, the derivations of all the formulas of classical stereology ("quantitative microscopy") along with those of such modern constructs as star volume and the disector. Striving for simplicity, it is an attack on obfuscation by one of the founders of the field of stereology. Anatomists, histologists, materials scientists and geo-scientists will find this work an extremely readable explanation of the theory underlying their procedures. It covers the formulas for methods based on sectioning as well as those based on plane projections as used in transmission electron microscopy and point projections as used in photogrammetry. It reintroduces the useful Cahn-Hilliard estimators for the variances of stereological measurements, originally published by the National Bureau of Standards. To give the reader a perspective on their accuracy, new Monte Carlo bench tests of their performance have been included. It provides a short discussion of the practical aspects of fractal geometry for the stereologist. There has been an increasing interest in the statistical analysis of the geometry of natural and man-made objects such as biological specimens, metals, rocks and patterns of vegetation. Stereology, originally thought of as a tool for microscopists, can be applied on all dimensional scales. Expanding the conventional definition of stereology, the work treats its generalizations into hyperspace and the popular "very large-specimen" techniques developed by geostatisticians, including variograms and kriging. For over thirty years John Hilliard both created stereology and taught it. Earlier versions of this work, privately published, were the standard text on stereology at Northwestern University for two decades. During this period the nature of the subject evolved from an intuitive experimental focus to one based on set and measure theory. Through its historical perspective, the book gently and gradually teaches the rudiments of set and measure theory up through the Minkowski functionals and kinematic measure. Co-author and editor, Lawrence Lawson was one of John Hilliard's students. In completing and editing this volume he has preserved John Hilliard's entertaining "Lewis Carroll" style and has captured the essence of some of the more interesting discussions between John Hilliard and his students. Well-published in the fields of physical metallurgy and X-ray backscatter imaging, Lawrence Lawson has been a quiet advocate of teaching reform aimed at making mathematics accessible to students in the humanities. He has taught mathematics and engineering at several universities and has developed introductory courses based on adaptive teaching for students with "math anxiety".Read More