Fractals, Random Shapes and Point Fields

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. 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.

Dietrich Stoyan, Professor a the Insitut fur Stochastik, University of Freiberg, Germany.