A note on fractal dimensions of biomedical waveforms

Department of Electrical Communication Engineering, Indian Institute of Science, Bangalore 560 012, India.
Computers in Biology and Medicine (Impact Factor: 1.24). 09/2009; 39(11):1006-12. DOI: 10.1016/j.compbiomed.2009.08.001
Source: PubMed


In this paper, we study performance of Katz method of computing fractal dimension of waveforms, and its estimation accuracy is compared with Higuchi's method. The study is performed on four synthetic parametric fractal waveforms for which true fractal dimensions can be calculated, and real sleep electroencephalogram. The dependence of Katz's fractal dimension on amplitude, frequency and sampling frequency of waveforms is noted. Even though the Higuchi's method has given more accurate estimation of fractal dimensions, the study suggests that the results of Katz's based fractal dimension analysis of biomedical waveforms have to be carefully interpreted.

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    • "The value of this index is usually a non-integer, fractional number; hence, the designation of a fractal dimension. There are many notions of FD, and various algorithms have been proposed to compute them (Raghavendra and Dutt, 2009). None of these methods, however, should be considered as universal, which justifies an empirical comparison of their abilities as feature extractors from EMG signals. "
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    ABSTRACT: Abstract The study of electromyographic (EMG) signals has gained increased attention in the last decades since the proper analysis and processing of these signals can be instrumental for the diagnosis of neuromuscular diseases and the adaptive control of prosthetic devices. As a consequence, various pattern recognition approaches, consisting of different modules for feature extraction and classification of EMG signals, have been proposed. In this paper, we conduct a systematic empirical study on the use of Fractal Dimension (FD) estimation methods as feature extractors from EMG signals. The usage of FD as feature extraction mechanism is justified by the fact that EMG signals usually show traces of self-similarity and by the ability of FD to characterize and measure the complexity inherent to different types of muscle contraction. In total, eight different methods for calculating the FD of an EMG waveform are considered here, and their performance as feature extractors is comparatively assessed taking into account nine well-known classifiers of different types and complexities. Results of experiments conducted on a dataset involving seven distinct types of limb motions are reported whereby we could observe that the normalized version of the Katz׳s estimation method and the Hurst exponent significantly outperform the others according to a class separability measure and five well-known accuracy measures calculated over the induced classifiers.
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    • "In addition to the standard box-counting, circle-counting, or yardstick methods, more effective methods were developed, such as the methods by Katz [6], Higuchi [7], Sevcik [8], and Raghavendra and Dutt (multiresolution box-counting MRBC and multiresolution length-based MRL methods [9]). The choice of mathematical methods gained fresh momentum when Raghavendra and Dutt [9, 10] compared existing methods and found Katz' method [6] to be highly inaccurate. They also demonstrated the bad correlation of a hypnogram with the corresponding sleep EEG's fractal dimensions calculated with Katz' method, whereas Higuchi's method provided a good correlation [10]. "
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