Electroencephalography (EEG) was widely investigated in brain status detection and disease diagnosis, in which the fractal analysis played an important role. In this paper, the roughness scaling extraction (RSE) algorithm proposed in our previous study on surface morphologies was applied to calculate the fractal dimensions (FDs) of artificial profiles and EEG signals. Fractal profiles with ideal FDs ranging from 1.01 to 1.99 were generated through the Weierstrass-Mandelbrot function. The RSE algorithm and the traditional algorithms, including the Higuchi algorithm, the Katz algorithm, and the box counting algorithm, were compared by analyzing the artificial profiles. Based on the mean relative errors and mean square errors, it was found that the RSE algorithm was more accurate than the traditional algorithms. To investigate the influence of noise on FD calculation, noise with different levels was added to the fractal profiles. The RSE and Higuchi algorithms were found reliable at signal-to-noise ratios of 50 and 40 dB, while the accuracy of RSE was also superior to that of the Higuchi. The RSE, Higuchi, and Katz algorithms were utilized to analyze the EEG signals of epilepsy events. The significant FD increasing, which corresponded to the seizure onset, could be detected, and the overlapping between the seizure and non-seizure statuses was small by using the RSE algorithm, indicating its feasibility for the EEG fractal analysis.
In this study, the scaling characteristics of root-mean-squared roughness ([Formula: see text]) was investigated for both fractal and non-fractal profiles by using roughness scaling extraction (RSE) method proposed in our previous work. The artificial profiles generated through Weierstrass–Mandelbrot (W–M) function and the actual profiles, including surface contours of silver thin films and electroencephalography signals, were analyzed. Based on the relationship curves between [Formula: see text] and scale, it was found that there was a continuous variation of the dimension value calculated with RSE method ([Formula: see text]) across the fractal and non-fractal profiles. In the range of fractal region, [Formula: see text] could accurately match with the ideal fractal dimension ([Formula: see text]) input for W–M function. In the non-fractal region, [Formula: see text] values could characterize the complexity of the profiles, similar to the functionality of [Formula: see text] value for fractal profiles, thus enabling the detection of certain incidents in signals such as an epileptic seizure. Moreover, the traditional methods (Box-Counting and Higuchi) of [Formula: see text] calculation failed to reflect the complexity variation of non-fractal profiles, because their [Formula: see text] was generally 1. The feasibility of abnormal implementation of W–M function and the capability of RSE method were discussed according to the analysis on the properties of W–M function, which would be promising to make more understandings of the nonlinear behaviors of both theoretical and practical features.
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