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Design and implementation of an estimator of fractal dimension using fuzzy techniques

โœ Scribed by X. Zeng; L. Koehl; C. Vasseur

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
615 KB
Volume
34
Category
Article
ISSN
0031-3203

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โœฆ Synopsis

This paper presents a new method for estimating the fractal dimension of one-dimensional pro"les. In this approach, the real fractal dimension D is considered as an implicit continuous function of the estimated fractal dimension D , the resolution and several other elements. By approximating this function from a number of experimental data, we can obtain more precise estimates of the fractal dimension D. This approximation is done using a fuzzy logic controller and an averaging procedure, permitting to, respectively, decrease two kinds of estimation errors: (1) systematic errors, which are associated with values of D, resolution, trends of pro"les, and etc. (2) stochastic errors, which are mainly caused by the choice of the sequence + I , representing the sizes of structuring elements corresponding to di!erent scales. The e!ectiveness of this method is shown by estimating fractal dimensions for two sample functions and a number of natural and synthetic "bers.

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