Design and implementation of an estimator of fractal dimension using fuzzytechniques

This paper presents a new method for estimating the fractal dimension of on e-dimensional profiles. In this approach, the real fractal dimension D is c onsidered as an implicit continuous function of the estimated fractal dimen sion D-e, the resolution and several other elements. By approximating this function from a number of experimental data, we can obtain more precise est imates 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 a ssociated with values of D, resolution, trends of profiles, and etc. (2) st ochastic errors, which are mainly caused by the choice of the sequence {eps ilon (k)} representing the sizes of structuring elements corresponding to d ifferent scales. The effectiveness of this method is shown by estimating fr actal dimensions for two sample functions and a number of natural and synth etic fibers. (C) 2000 Pattern Recognition Society. Published by Elsevier Sc ience Ltd. All rights reserved.