Oczeretko Edward, Kitlas Agnieszka, Swiatecka Jolanta, Laudański Tadeusz
Institute of Computer Science, University of Białystok, Poland.
Riv Biol. 2004 Aug-Dec;97(3):499-504.
The fractal dimension D may be calculated in many ways, since its strict definition, the Hausdorff definition is too complicated for practical estimation. In this paper we perform a comparative study often methods of fractal analysis of time series. In Benoit, a commercial program for fractal analysis, five methods of computing fractal dimension of time series (rescaled range analysis, power spectral analysis, roughness-length, variogram methods and wavelet method) are available. We have implemented some other algorithms for calculating D: Higuchi's fractal dimension, relative dispersion analysis, running fractal dimension, method based on mathematical morphology and method based on intensity differences. For biomedical signals results obtained by means of different algorithms are different, but consistent.
分形维数D可以通过多种方式计算,因为其严格定义,即豪斯多夫定义对于实际估计来说过于复杂。在本文中,我们对时间序列的十种分形分析方法进行了比较研究。在Benoit(一个用于分形分析的商业程序)中,可以使用五种计算时间序列分形维数的方法(重标极差分析、功率谱分析、粗糙度长度、变差函数法和小波法)。我们还实现了一些其他计算D的算法: Higuchi分形维数、相对离散度分析、滑动分形维数、基于数学形态学的方法和基于强度差异的方法。对于生物医学信号,通过不同算法获得的结果不同,但具有一致性。