Design and implementation of an estimator of fractal dimension using fuzzy techniques. (English) Zbl 0970.68748
Summary: 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 \(D_e\) 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 \(\{\varepsilon_k\}\) 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.
MSC:
| 68U99 | Computing methodologies and applications |
| 68T10 | Pattern recognition, speech recognition |
| 68U05 | Computer graphics; computational geometry (digital and algorithmic aspects) |
Keywords:
fractal dimension; one-dimensional profiles; model-free estimator; approximation; fuzzy logic controllerSoftware:
GenocopReferences:
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