Fractals, Random Shapes and Point Fields: Methods of Geometrical Statistics / Edition 1

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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.

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Editorial Reviews

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 (
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Product Details

Table of Contents


Hausdorff Measure and Dimension.

Deterministic Fractals.

Random Fractals.

Methods for the Empirical Determination of Fractal Dimension.


Fundamental Concepts.

Representation of Contours.

Set Theoretic Analysis.

Point Description of Figures.




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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