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Other titles in the Wiley Series in Probability & Mathematical Statistics series:
Fractals, Random Shapes and Point Fields: Methods of Geometrical Statistics (Wiley Series in Probability & Mathematical Statistics)by Dietrich Stoyan and Helga Stoyan
Synopses & Reviews
There has been an increasing interest in the statistical analysis of geometric objects and structures in many branches of science and engineering in recent years. The aim of this book is to present these statistical methods for practical use by non-mathematicians by outlining the mathematical ideas rather than concentrating on detailed proofs. The clarity of exposition ensures that the book will be a valuable resource for researchers and practitioners in many scientific disciplines who wish to use these methods in their work. In particular, the book is suited to materials scientists, geologists, environmental scientists, and biologists.
Book News Annotation:
Presents statistical analysis methods of geometric objects and structures for practical use by non-mathematicians, outlining the mathematical ideas rather than concentrating on detailed proofs. Introduces the theory of fractals and methods of measuring fractal dimensions, describes modern methods for the statistical analysis of random shapes, and presents an introduction to the statistical theory of point fields. Of interest to materials scientists, geologists, environmental scientists, and biologists.
Annotation c. Book News, Inc., Portland, OR (booknews.com)
An exposition of fractals, shape and form, and point processes, which analyzes the current theoretical information. The organization of the text is such that each part can be read independently. Many case studies and true examples are used to illustrate the text.
In Part I the reader is introduced to the methods of measuring the fractal dimension of irregular geometric structures. Part II demonstrates important modern methods for the statistical analysis of random shapes. The statistical theory of point fields, with and without marks, is introduced in Part III. Each of the three sections concentrates on the mathematical ideas, rather than detailed proofs, and can be read independently.
Table of Contents
FRACTALS AND METHODS FOR THE DETERMINATION OF FRACTAL DIMENSIONS.
Hausdorff Measure and Dimension.
Methods for the Empirical Determination of Fractal Dimension.
THE STATISTICS OF SHAPES AND FORMS.
Representation of Contours.
Set Theoretic Analysis.
Point Description of Figures.
POINT FIELD STATISTICS.
Finite Point Fields.
Poisson Point Fields.
Fundamentals of the Theory of Point Fields.
Statistics for Homogeneous Point Fields.
Point Field Models.
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