Using higuchis method higuchi, 1988 the fractal dimension was calculated using custom written software in matlab the mathworks inc. Why should gaussian noise have fractal dimension of 1. The fractal dimension was calculated over the entire. Nalecz institute of biocybernetics and biomedical engineering polish academy of sciences 4 trojdena st.
Computeraided diagnosis of neural diseases from eeg signals or other physiological signals that can be treated as time series, e. The three papers using a multifractal approach applied the generalized sandbox method doubal et al. A 32segment quadric fractal scaled and viewed through boxes of different sizes. Application of higuchi fractal dimension in analysis of heart. Using fractal analysis in modeling trends in the national. Fractal dimension analysis of the magnetic time series. Extracting features is a key component in the analysis of eeg signals. The higuchis method is a method of analysis that is being increasingly used for the analysis of time series 2,3, it is a very ef. Fractal dimension, higuchi, katz, multiresolution boxcounting, eeg waveforms. Select the rgb threshold to convert the image into binary data and its automatic extraction.
Mar 10, 2020 higuchi fractal dimension hfd following. A fractal is a shape that retains its structural detail despite scaling and this is the reason why complex objects can be described with the help of fractal dimension. Fractal dimensions are used to characterize a broad spectrum of objects ranging from the abstract to practical phenomena, including. Higuchi s fractal dimension originates from chaos theory and for almost thirty years it has been successfully applied as a complexity measure of artificial, natural or. The term fractal was first introduced in 1975 by mandelbrot and was described as a set of points that when looked at smaller scales, resembles the whole set. Box fractal dimension, katz fractal dimension, higuchi fractal. Jan 28, 2020 the only paper calculating monofractal dimension using all three techniques, however, identified higuchi s fd as a better predictor of stroke aliahmad et al. Higuchi and katz fractal dimension measures file exchange. We found significant decreases in the fractal dimension between healthy volunteers n 15, patients in a minimally conscious state n 10, and patients in a vegetative state n 8, regardless of the. Complete higuchi fractal dimension algorithm file exchange.
Methods and data higuchi fractal dimension 20 is a method developed for estimating the amount of selfsimilarity of the data. In2012 20th telecommunications forum telfor 1 2012. Higuchi fractal dimension provided us very useful information about more or less chaotic disposed inspace by the number of companies, the profit, the number of employees and the turnover. Compared with petrosian s algorithm, higuchi s one does not depend on a binary sequence and, in many cases, it is less sensitive to noise 30. The machine learning techniques classifiers with multichannel eeg data input were used for classification in these studies 20, 21. Nonlinear phenomena, volume 31, issue 2, june 1988, pages 277283. Measuring the fractal dimension of quiet stance to. In this study, the selfsimilar method was used to determine the fractal dimension of fesem images, which. Fractal dimension algorithms and their application. Higuchi fractal dimension hfd katz fractal dimension kfd the source code is properly commented.
Since living systems are nonlinear, evaluation of ans activity is difficult by means of linear methods. Higuchi s fractal dimension is a widely used index for evaluating fractality in brain activity, but temporalscalespecific characteristics are lost due to its requirement of averaging over the. In our previous works, we have implemented many eeg feature extraction functions in the python programming language. In the tdfd, dfd, and ds methods, the fractal dimensions were estimated using the fractal dimension estimation method of the methodology with the best performance. A method for calculating 2d higuchis fractal dimension. Higuchi fractal dimension of heart rate variability during percutaneous auricular vagus nerve stimulation in healthy and diabetic subjects. Frontiers complexity analysis of eeg data in persons with. The fractal dimension is an important characteristic of systems, because it contains information about their geometrical structure at multiple scales. Fractal dimension estimator the fractal lab fractal. Higuchi showed that this method provides a precise estimate of the fractal dimension, even for a small number of data.
In this paper we study the effect of higuchi fractal dimension for different phonemes. Higuchis fractal dimension originates from chaos theory and for almost thirty years it has been successfully applied as a complexity measure of artificial, natural or. We propose to apply the higuchi fractal dimension hfd method for assessment of ans activity. Use of the higuchis fractal dimension for the analysis of. Jan 21, 2010 that is, the more homogeneous the texture in the image is, the more homogeneous the fractal dimension becomes, and thus the lower the standard deviation. Higuchi fractal dimension of the electroencephalogram as a. Higuchi fractal analysis of heart rate variability is. Classification of 7 arrhythmias from ecg using fractal dimensions. Discriminating between elderly and young using a fractal. The classification was performed using weka software weka v. Analysis of heart rate variability hrv can be applied to assess the autonomic nervous system ans sympathetic and parasympathetic activity.
Best results were obtained using a kmax value of 60 for ap analysis and 30 for ml analysis cf. Effects of exergames on heart rate variability of women. Higuchi fractal analysis of heart rate variability is sensitive during. Jul 10, 2008 boxcountc,slope also shows the semilog plot of the local slope df dlnndlnr as a function of r. The ilf image landscapes fractal dimension method and d f 2 d method obtained by a 2d generalization of higuchis algorithm were applied to a set of 120 digital histological images of anal intraepithelial neoplasia ain.
Is there any algorithm to select the k max in higuchis. Our idea on generalization is based on higuchis method for estimating fractal dimension values of a planar curve. To check, try to apply the script to images with different textures e. Higuchi, approach to an irregular time series on the. A fractal dimension is an index for characterizing fractal patterns or sets by quantifying their complexity as a ratio of the change in detail to the change in scale 1 several types of fractal dimension can be measured theoretically and empirically. In katzs method, higuchis method, and the method, the fractal dimension of the samples from selected electrodes were concatenated into feature vectors. The use of hfd has evolved from eeg and single neuron activity analysis to the most recent application in automated assessments of different clinical conditions. For instance, fraclac will determine the fractal dimension of a 400 x 400 pixel square as a perfect 1. Measuring the fractal dimension of quiet stance to understand. A fractal dimension fd is a measure of signal complexity. Higuchis method and multiresolution box count that can perform much better for time series data.
Higuchi s fractal dimension hfd is an appropriate method for analysing the fd of biomedical signals 9, as meg recordings, due to the following reasons. Signal pattern recognition based on fractal features and machine. Higuchi, approach to an irregular time series on the basis of the fractal theory, physica d, 1988. The theoretical fractal dimension for this fractal is log32log8 1. The mistake is in the formula for lm,k or lmk as in some papers. All details concerning the originally proposed higuchis method are described in appendix 1. Mar 27, 2015 in the file i offer the source code of. Mathworks is the leading developer of mathematical computing software for engineers and scientists. Among other measures of complexity, the fractal dimension is emerging as being sensitive to neuronal damage secondary to neurological and psychiatric diseases. Fractal properties and morphological investigation of nano. To test whether brain activity is fractal in time as well as space, we used the higuchi temporal fractal dimension on bold timeseries. This study was aimed to compare two electroencephalogram eeg analysis methods, spectral asymmetry index sasi and higuchis fractal dimension hfd, for detection of depression. Higuchi, approach to an irregular time series on basis of fractal dimension, physica d.
Hrv analysis was performed by higuchi fractal dimension technique. Evaluation of methods for estimating fractal dimension in. Using fractal analysis in modeling trends in the national economy. Background and objective for more than 20 years, higuchi s fractal dimension hfd, as a nonlinear method, has occupied an important place in the analysis of biological signals.
It is fastest for powers of two over each dimension. Our idea on generalization is based on higuchi s method for estimating fractal dimension values of a planar curve. Electroencephalographic fractal dimension in healthy ageing. Tikkuhirvi tietavainen and probably corrected by mr. This method for calculating the fractal dimension is designed specifically for use with time series data such as cop data. Simple higuchi fractal dimension implementation file. If df is contant in a certain range of r, then df is the fractal dimension of the set c. Classification of 7 arrhythmias from ecg using fractal. Applications of higuchis fractal dimension in the analysis of biological signals. The following matlab project contains the source code and matlab examples used for complete higuchi fractal dimension algorithm. All parameters of higuchi fractal dimension analysis. In this work, three algorithms are applied to nonlinear time series.
All details concerning the originally proposed higuchi s method are described in appendix 1. During recovery from exercise the poincare plot indices sd1 and sd1sd2 decreased while sd2 and sd2sd1 increased p higuchi fractal method among the various fractal dimension methods, the higuchi fractal method is well suited for studying signal fluctuation in one dimension 10. Higuchis fractal dimension and fractal analysis higuchis fractal dimension is used as a nonlinear measure of signal complexity in the time domain higuchi, 1988. Complete higuchi fractal dimension algorithm in matlab. Electroencephalographic fractal dimension in healthy. Sep 28, 2018 a fractal dimension fd is a measure of signal complexity. This method was developed as an alternative to spectral analysis because although there is a relation between d and.
Application of higuchi fractal dimension in analysis of. Sliding window gen and usage with higuchi fractal dimension windowed hfd discover live editor create scripts with code, output, and formatted text in a single executable document. Pdf application of higuchis fractal dimension from basic to clinical. Background and objective for more than 20 years, higuchis fractal dimension hfd, as a nonlinear method, has occupied an important place in the analysis of biological signals. The higuchi fractal dimension was estimated by calculating the overall mean of the rows and columns eq. Higuchi fractal dimension applied to rr intervals in children with. The source code and files included in this project are listed in the project files section, please make sure whether the listed source code meet your needs there. Hfd 48 was calculated using the algorithm described by khoa, et al. On 2d generalization of higuchis fractal dimension. Gomolka rs 1, kampusch s 2, kaniusas e 2, thurk f 2, szeles jc 3, klonowski w 1. Mathworks is the leading developer of mathematical computing software for engineers and.
I present an example of higuchi fractal dimension analysis in assessing the response of the. Higuchi 20 used his method for magnetic field data and in 21, 2325 higuchis method was used for electroencephalography. Linear sasi method is based on evaluation of the balance of powers in two eeg frequency bands in one channel selected higher and lower than the alpha band spectrum maximum. Fractal analysis was performed by an fd calculating of electrophysiological signals from br neurons using higuchis method. The main goal of this research was to examine accuracy that means sensitivity and specificity of these methods and compare the applicability of both methods in the. Eye fundus retinopathy disease manifestation in retina. Eeg machine learning with higuchis fractal dimension and. The main result is that higuchis algorithm allows a direction dependent as well as direction independent analysis. Fd is estimated by means of the boxcounting method. Higuchi fractal dimension hfd katz fractal dimension kfd the source code is properly commented in english. Higuchi fractal dimension of heart rate variability during. The numerical sequence i could be used to generate a difference series ijii for different lags. In proceedings of the ieee international conference on software quality, reliability and. A method for calculating 2d higuchi s fractal dimension.
Frontiers complexity analysis of eeg data in persons. Heart rate variability with artificial and natural noise michal pierzchalski m. The following describes how to apply the higuchis method to a time series. Here, we calculated higuchis fractal dimension hfd in restingstate eyesclosed electroencephalography eeg recordings from 41 healthy controls. Spectral asymmetry and higuchis fractal dimension measures. Using higuchis algorithm 7 the fractal dimension was calculated using custom written software in matlab the mathworks inc. There are many available algorithms to calculate fd, one of them is higuchis fractal dimension hfd, which is defined.
334 1193 806 1373 1308 1157 80 264 1405 462 358 382 1345 463 453 733 53 1303 185 1400 268 1123 1456 595 1109 832 1221 1288 93 1391 1306 950 1452 1206 67 260