Stoyan D., Stoyan H. Fractals, Random Shapes and Point Fields. Methods of Geometrical Statistics

Chichester: John Wiley & Sons, 1994. — 389 p. — ISBN: 0-471-93757-6In 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 fractal dimensionsHausdorff Measure and Dimension
Deterministic Fractals
Random Fractals
Methods for the Empirical Determination of Fractal DimensionThe statistics of shapes and forms
Fundamental Concepts
Representation of Contours
Set Theoretic Analysis
Point Description of Figures
ExamplesPoint field statistics
Fundamentalss
Finite Point Fields
Poisson Point Fields
Fundamentals of the Theory of Point Fields
Statistics for Homogeneous Point Fields
Point Field ModelsAppendices
Measure and Content
sup and inf, lim sup and lim inf
Basic Ideas in Topology
Set Operations
The Euclidean and Hausdorff Metrics
Boolean Models
The Convex Hull
Random Lines and Line Fields
The Dirichlet Mosaic and the Delaunay Triangulation
Germ-Grain Models
The Area of Intersection of Two Discs
Kernel Estimators for Density Functions