Fractals, Random Shapes and Point Fields : Methods of Geometrical Statistics (Wiley Series in Probability and Statistics)

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Fractals, Random Shapes and Point Fields : Methods of Geometrical Statistics (Wiley Series in Probability and Statistics)

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  • 製本 Hardcover:ハードカバー版/ページ数 389 p.
  • 言語 ENG
  • 商品コード 9780471937579
  • DDC分類 519.2

Full Description


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.
Deterministic Fractals.
Random Fractals.
Methods for the Empirical Determination of
Fractal Dimension.
THE STATISTICS OF SHAPES AND FORMS.
Fundamental Concepts.
Representation of Contours.
Set Theoretic Analysis.
Point Description of Figures.
Examples.
POINT FIELD STATISTICS.
Fundamentals.
Finite Point Fields.
Poisson Point Fields.
Fundamentals of the Theory of Point Fields.
Statistics for Homogeneous Point Fields.
Point Field Models.
Appendices.
References.
Index.