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Figure 5.1 (a and b) Fractal patterns and fractal dimension D related to the degree of complexity of the patterns. Calculation of the fractal dimension is described in Equation (5.5).

fractal measures as texture descriptors is given in Section 5.1.1. Readers requiring a more detailed description of fractals are referred to Agterberg and Cheng (1999), who introduce a special issue of Computers and Geosciences devoted to the topic of fractals and multifractals; Mandelbrot (1977, 1982); and Feder (1988).

5.1.1 Introduction to fractals

Fractal geometry was first defined and explored by Mandelbrot (1977, 1982). Since then, this novel field has attracted the attention of a number of researchers. The idea of fractals is now widely used in image processing and image compression (Barnsley, 1993; Barnsley and Hurd, 1993). Mandelbrot used the term ‘fractal’ to represent the irregular and fragmented nature of real world objects. The word itself is derived from the Latin word fractus meaning ‘irregular segments’.

A fractal is, by definition, a set for which the Hausdorff-Besicovich dimension is strictly larger than the topological dimension. In other word, the fractal dimension value of a complex object should be larger than our intuitive definition of its dimension, i.e. its Euclidean dimension.

The concept of the fractal dimension of an object can be explained by using the well-known example of a coastline whose length has to be measured on a map using a measuring instrument that has a specific step length, for example a pair of dividers. The step length of the measuring instrument

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Classification Methods for Remotely Sensed Data
Classification Methods for Remotely Sensed Data, Second Edition
ISBN: 1420090720
EAN: 2147483647
Year: 2001
Pages: 354

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