Description

Book Synopsis
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 FRACTALDIMENSIONS.

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.

Fractals Random Shapes and Point Fields

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    A Hardback by Dietrich Stoyan, Helga Stoyan

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      Book details

      Publisher John Wiley & Sons Inc
      Published 16 August 1994
      ISBN-13 9780471937579
      978-0471937579
      ISBN-10 0471937576
      Also in:
      Mathematics Topology

      Description

      Book Synopsis
      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 FRACTALDIMENSIONS.

      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.

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