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

摘要

This paper presents a new method for estimating the fractal dimension of one-dimensional profiles. In this approach, the real fractal dimension D is considered as an implicit continuous function of the estimated fractal dimension De, 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 profiles, and etc. (2) stochastic errors, which are mainly caused by the choice of the sequence {εk} representing the sizes of structuring elements corresponding to different scales. The effectiveness of this method is shown by estimating fractal dimensions for two sample functions and a number of natural and synthetic fibers.