Stochastic geometry involves the statistical analysis of complicated geometrical patterns which occur in many areas of science and technology. This book aims to make the results and methods of stochastic geometry accessible to non-theoreticians, while at the same time serving as an introduction to the subject for mathematicians. The exposition is mathematically exact and takes into account the latest results, but in most cases proofs are omitted, and it is intended that applied scientists who may not wish to follow the mathematical arguments in detail will still be able to interpret and use the formulae. Topics covered include the basic theories of point processes, random sets, fibre processes, tessellations, stereology and the statistical theory of shape. The theory is illustrated by many examples drawn from different branches of science; actual data in the form of images are presented, and their analysis is discussed. The book is a greatly revised and enlarged version of the original German edition by Stoyan and Mecke, with a new chapter on random processes of geometrical objects. It is the first treatment available in English of the important East German school of stochastic geometry. As well as being of great interest to statisticians, this treatment of the subject should prove useful to applied scientists working in fields such as geology, biology, microscopy and metallurgy and to pure mathematicians working in geometry.
Foreword to the German Edition; Foreword to the English Edition; Mathematical Foundations; Point Processes I: The Poisson Point Process; Random Closed Sets I: The Boolean Model; Point Processes II: General Theory; Point Processes III: Construction of Models; Random Closed Sets II: The General Case; Random Measures; Random Processes of Geometrical Objects; Fibre and Surface Processes; Random Tessellations; Stereology.