This paper introduces a method for modification of the formula of the fractal box counting dimension. The method is based on the utilization of the probability distribution formula in the fractal box count. The purpose of this method is to use it for the discrimination of oil spill areas from the surrounding features e.g. sea surface and look-alikes in RADARSAT-1 SAR data. The result showed that the new formula of the fractal box counting dimension was able to discriminate between oil spills and look-alike areas. The low wind area had the highest fractal dimension peak of 2.9, as compared to the oil slick and the surrounding rough sea. The maximum error standard deviation of the low wind area was 0.68 which performed with a 2.9 fractal dimension value.
Studies conducted on the various geometric properties of skeletons of water bodies have shown highly promising results. However, these studies were made under the assumption that water bodies were static objects and that they remained constant over time. Water bodies are actually dynamic objects; they go through significant spatio-temporal changes due to drought and flood. In this study, the characterization of skeletons of simulated drought and flood of water bodies was performed. It was observed that as the drought level increased from 1 to 9, the average length of the skeletons decreased due to reduction in the size of the water bodies and increase in the number of water bodies. As the drought level increased from 9 to 15, the average length of the skeletons increased further due to vanishing of small water bodies. Flood caused an increase in the average length of the skeletons due to merging of adjacent water bodies. Power law relationships were observed between the average length of the skeletons of the simulated drought/flood and the level of drought/flood. The scaling exponent of these power laws which was named as a fractal dimension, indicated the rate of change of the average length of the skeletons of simulated drought/flood of water bodies over varying levels of drought/flood. However, errors observed in the goodness of fit of the plots indicated that monofractals were not sufficient to characterise the skeletons of simulated drought and flood of water bodies. Multifractals and lacunarity analysis were required for more accurate characterisation.
Natural gamma ray well logging technique is used to characterize the radioactivity (GR) laterally and vertically in Banting district, SW of Malaysia. Seven drilled boreholes, along N-S profile with their natural gamma ray records are utilized to compute the heat production (HP) parameter, based on the Bucker and Rybach relationship.The analysis of 3467 measured points in those boreholes indicates that GR varies between 6.24 API and 358.4 API with an average of 79.95 API, while HP varies between 0.086 and 5.65 μw/m3 with an average of 1.25 μw/m3.The multi-fractal Concentration-Number (C-N) is used to characterize the radioactivity and heat production variations and to isolate different GR and HP populations in the study region. The high radioactivity and heat production ranges are mainly related to the silty clay layers, accompanied by uranium and thorium.
Understanding the relationship between microbial community and mechanism of aerobic granulation could enable wider applications of granules for high-strength wastewater treatment. The majority of granulation studies principally determine the engineering aspects of granules formation with little emphasis on the microbial diversity. In this study, three identical reactors namely R1, R2 and R3 were operated using POME at volumetric loadings of 1.5, 2.5 and 3.5 kg COD m(-3) d(-1), respectively. Aeration was provided at a volumetric flow rate of 2.5 cms(-1). Aerobic granules were successfully developed in R2 and R3 while bioflocs dominated R1 until the end of experiments. Fractal dimension (D(f)) averaged at 1.90 suggesting good compactness of granules. The PCR-DGGE results indicated microbial evolutionary shift throughout granulation despite different operating OLRs based on decreased Raup and Crick similarity indices upon mature granule formation. The characteristics of aerobic granules treating high strength agro-based wastewater are determined at different volumetric loadings.
The structural and hydrodynamic features for granules were characterized using settling experiments, predefined mathematical simulations and ImageJ-particle analyses. This study describes the rheological characterization of these biologically immobilized aggregates under non-Newtonian flows. The second order dimensional analysis defined as D2=1.795 for native clusters and D2=1.099 for dewatered clusters and a characteristic three-dimensional fractal dimension of 2.46 depicts that these relatively porous and differentially permeable fractals had a structural configuration in close proximity with that described for a compact sphere formed via cluster-cluster aggregation. The three-dimensional fractal dimension calculated via settling-fractal correlation, U∝l(D) to characterize immobilized granules validates the quantitative measurements used for describing its structural integrity and aggregate complexity. These results suggest that scaling relationships based on fractal geometry are vital for quantifying the effects of different laminar conditions on the aggregates' morphology and characteristics such as density, porosity, and projected surface area.
Cancer starts when cells in a part of the body start to grow out of control. In fact cells become cancer cells because of DNA damage. A DNA walk of a genome represents how the frequency of each nucleotide of a pairing nucleotide couple changes locally. In this research in order to study the cancer genes, DNA walk plots of genomes of patients with lung cancer were generated using a program written in MATLAB language. The data so obtained was checked for fractal property by computing the fractal dimension using a program written in MATLAB. Also, the correlation of damaged DNA was studied using the Hurst exponent measure. We have found that the damaged DNA sequences are exhibiting higher degree of fractality and less correlation compared with normal DNA sequences. So we confirmed this method can be used for early detection of lung cancer. The method introduced in this research not only is useful for diagnosis of lung cancer but also can be applied for detection and growth analysis of different types of cancers.
Human brain response is the result of the overall ability of the brain in analyzing different internal and external stimuli and thus making the proper decisions. During the last decades scientists have discovered more about this phenomenon and proposed some models based on computational, biological, or neuropsychological methods. Despite some advances in studies related to this area of the brain research, there were fewer efforts which have been done on the mathematical modeling of the human brain response to external stimuli. This research is devoted to the modeling and prediction of the human EEG signal, as an alert state of overall human brain activity monitoring, upon receiving external stimuli, based on fractional diffusion equations. The results of this modeling show very good agreement with the real human EEG signal and thus this model can be used for many types of applications such as prediction of seizure onset in patient with epilepsy.
Digital image processing is one of the most widely used computer vision technologies in biomedical engineering. In the present modern ophthalmological practice, biomarkers analysis through digital fundus image processing analysis greatly contributes to vision science. This further facilitates developments in medical imaging, enabling this robust technology to attain extensive scopes in biomedical engineering platform. Various diagnostic techniques are used to analyze retinal microvasculature image to enable geometric features measurements such as vessel tortuosity, branching angles, branching coefficient, vessel diameter, and fractal dimension. These extracted markers or characterized fundus digital image features provide insights and relates quantitative retinal vascular topography abnormalities to various pathologies such as diabetic retinopathy, macular degeneration, hypertensive retinopathy, transient ischemic attack, neovascular glaucoma, and cardiovascular diseases. Apart from that, this noninvasive research tool is automated, allowing it to be used in large-scale screening programs, and all are described in this present review paper. This paper will also review recent research on the image processing-based extraction techniques of the quantitative retinal microvascular feature. It mainly focuses on features associated with the early symptom of transient ischemic attack or sharp stroke.
Coronary Artery Disease (CAD), caused by the buildup of plaque on the inside of the coronary arteries, has a high mortality rate. To efficiently detect this condition from echocardiography images, with lesser inter-observer variability and visual interpretation errors, computer based data mining techniques may be exploited. We have developed and presented one such technique in this paper for the classification of normal and CAD affected cases. A multitude of grayscale features (fractal dimension, entropies based on the higher order spectra, features based on image texture and local binary patterns, and wavelet based features) were extracted from echocardiography images belonging to a huge database of 400 normal cases and 400 CAD patients. Only the features that had good discriminating capability were selected using t-test. Several combinations of the resultant significant features were used to evaluate many supervised classifiers to find the combination that presents a good accuracy. We observed that the Gaussian Mixture Model (GMM) classifier trained with a feature subset made up of nine significant features presented the highest accuracy, sensitivity, specificity, and positive predictive value of 100%. We have also developed a novel, highly discriminative HeartIndex, which is a single number that is calculated from the combination of the features, in order to objectively classify the images from either of the two classes. Such an index allows for an easier implementation of the technique for automated CAD detection in the computers in hospitals and clinics.
Cardiovascular diseases (CVDs) are the leading cause of deaths worldwide. The rising mortality rate can be reduced by early detection and treatment interventions. Clinically, electrocardiogram (ECG) signal provides useful information about the cardiac abnormalities and hence employed as a diagnostic modality for the detection of various CVDs. However, subtle changes in these time series indicate a particular disease. Therefore, it may be monotonous, time-consuming and stressful to inspect these ECG beats manually. In order to overcome this limitation of manual ECG signal analysis, this paper uses a novel discrete wavelet transform (DWT) method combined with nonlinear features for automated characterization of CVDs. ECG signals of normal, and dilated cardiomyopathy (DCM), hypertrophic cardiomyopathy (HCM) and myocardial infarction (MI) are subjected to five levels of DWT. Relative wavelet of four nonlinear features such as fuzzy entropy, sample entropy, fractal dimension and signal energy are extracted from the DWT coefficients. These features are fed to sequential forward selection (SFS) technique and then ranked using ReliefF method. Our proposed methodology achieved maximum classification accuracy (acc) of 99.27%, sensitivity (sen) of 99.74%, and specificity (spec) of 98.08% with K-nearest neighbor (kNN) classifier using 15 features ranked by the ReliefF method. Our proposed methodology can be used by clinical staff to make faster and accurate diagnosis of CVDs. Thus, the chances of survival can be significantly increased by early detection and treatment of CVDs.
Cross-sectional view echocardiography is an efficient non-invasive diagnostic tool for characterizing Myocardial Infarction (MI) and stages of expansion leading to heart failure. An automated computer-aided technique of cross-sectional echocardiography feature assessment can aid clinicians in early and more reliable detection of MI patients before subsequent catastrophic post-MI medical conditions. Therefore, this paper proposes a novel Myocardial Infarction Index (MII) to discriminate infarcted and normal myocardium using features extracted from apical cross-sectional views of echocardiograms. The cross-sectional view of normal and MI echocardiography images are represented as textons using Maximum Responses (MR8) filter banks. Fractal Dimension (FD), Higher-Order Statistics (HOS), Hu's moments, Gabor Transform features, Fuzzy Entropy (FEnt), Energy, Local binary Pattern (LBP), Renyi's Entropy (REnt), Shannon's Entropy (ShEnt), and Kapur's Entropy (KEnt) features are extracted from textons. These features are ranked using t-test and fuzzy Max-Relevancy and Min-Redundancy (mRMR) ranking methods. Then, combinations of highly ranked features are used in the formulation and development of an integrated MII. This calculated novel MII is used to accurately and quickly detect infarcted myocardium by using one numerical value. Also, the highly ranked features are subjected to classification using different classifiers for the characterization of normal and MI LV ultrasound images using a minimum number of features. Our current technique is able to characterize MI with an average accuracy of 94.37%, sensitivity of 91.25% and specificity of 97.50% with 8 apical four chambers view features extracted from only single frame per patient making this a more reliable and accurate classification.
One of the most recent non-invasive technologies to examine the gastrointestinal tract is wireless capsule endoscopy (WCE). As there are thousands of endoscopic images in an 8-15 h long video, an evaluator has to pay constant attention for a relatively long time (60-120 min). Therefore the possibility of the presence of pathological findings in a few images (displayed for evaluation for a few seconds only) brings a significant risk of missing the pathology with all negative consequences for the patient. Hence, manually reviewing a video to identify abnormal images is not only a tedious and time consuming task that overwhelms human attention but also is error prone. In this paper, a method is proposed for the automatic detection of abnormal WCE images. The differential box counting method is used for the extraction of fractal dimension (FD) of WCE images and the random forest based ensemble classifier is used for the identification of abnormal frames. The FD is a well-known technique for extraction of features related to texture, smoothness, and roughness. In this paper, FDs are extracted from pixel-blocks of WCE images and are fed to the classifier for identification of images with abnormalities. To determine a suitable pixel block size for FD feature extraction, various sizes of blocks are considered and are fed into six frequently used classifiers separately, and the block size of 7×7 giving the best performance is empirically determined. Further, the selection of the random forest ensemble classifier is also done using the same empirical study. Performance of the proposed method is evaluated on two datasets containing WCE frames. Results demonstrate that the proposed method outperforms some of the state-of-the-art methods with AUC of 85% and 99% on Dataset-I and Dataset-II respectively.
Myocardial infarction (MI), also referred to as heart attack, occurs when there is an interruption of blood flow to parts of the heart, due to the acute rupture of atherosclerotic plaque, which leads to damage of heart muscle. The heart muscle damage produces changes in the recorded surface electrocardiogram (ECG). The identification of MI by visual inspection of the ECG requires expert interpretation, and is difficult as the ECG signal changes associated with MI can be short in duration and low in magnitude. Hence, errors in diagnosis can lead to delay the initiation of appropriate medical treatment. To lessen the burden on doctors, an automated ECG based system can be installed in hospitals to help identify MI changes on ECG. In the proposed study, we develop a single-channel single lead ECG based MI diagnostic system validated using noisy and clean datasets. The raw ECG signals are taken from the Physikalisch-Technische Bundesanstalt database. We design a novel two-band optimal biorthogonal filter bank (FB) for analysis of the ECG signals. We present a method to design a novel class of two-band optimal biorthogonal FB in which not only the product filter but the analysis lowpass filter is also a halfband filter. The filter design problem has been composed as a constrained convex optimization problem in which the objective function is a convex combination of multiple quadratic functions and the regularity and perfect reconstruction conditions are imposed in the form linear equalities. ECG signals are decomposed into six subbands (SBs) using the newly designed wavelet FB. Following to this, discriminating features namely, fuzzy entropy (FE), signal-fractal-dimensions (SFD), and renyi entropy (RE) are computed from all the six SBs. The features are fed to the k-nearest neighbor (KNN). The proposed system yields an accuracy of 99.62% for the noisy dataset and an accuracy of 99.74% for the clean dataset, using 10-fold cross validation (CV) technique. Our MI identification system is robust and highly accurate. It can thus be installed in clinics for detecting MI.
The fractal dimension is a global measure of complexity and is useful for quantifying anatomical structures, including the retinal vascular network. A previous study found a linear declining trend with aging on the retinal vascular fractal dimension (DF); however, it was limited to the older population (49 years and older). This study aimed to investigate the possible models of the fractal dimension changes from young to old subjects (10-73 years). A total of 215 right-eye retinal samples, including those of 119 (55%) women and 96 (45%) men, were selected. The retinal vessels were segmented using computer-assisted software, and non-vessel fragments were deleted. The fractal dimension was measured based on the log-log plot of the number of grids versus the size. The retinal vascular DF was analyzed to determine changes with increasing age. Finally, the data were fitted to three polynomial models. All three models are statistically significant (Linear: R2 = 0.1270, 213 d.f., p
Walking is an everyday activity in our daily life. Because walking affects heart rate variability, in this research, for the first time, we analyzed the coupling among the alterations of the complexity of walking paths and heart rate. We benefited from the fractal theory and sample entropy to evaluate the influence of the complexity of paths on the complexity of heart rate variability (HRV) during walking. We calculated the fractal exponent and sample entropy of the R-R time series for nine participants who walked on four paths with various complexities. The findings showed a strong coupling among the alterations of fractal dimension (an indicator of complexity) of HRV and the walking paths. Besides, the result of the analysis of sample entropy also verified the obtained results from the fractal analysis. In further studies, we can analyze the coupling among the alterations of the complexities of other physiological signals and walking paths.
Training methodology of the Back Propagation Network (BPN) is well documented. One aspect of BPN that requires investigation is whether or not the BPN would get trained for a given training data set and architecture. In this paper the behavior of the BPN is analyzed during its training phase considering convergent and divergent training data sets. Evolution of the weights during the training phase was monitored for the purpose of analysis. The evolution of weights was plotted as return map and was characterized by means of fractal dimension. This fractal dimensional analysis of the weight evolution trajectories is used to provide a new insight to understand the behavior of BPN and dynamics in the evolution of weights.
Alumina powder was synthesized from an aluminum precursor and studied using small angle neutron scattering (SANS) technique and complemented with transmission electron microscope (TEM). XRD measurement confirmed that the alumina produced was of high purity and highly crystalline D-phase. SANS examination indicates the formation of mass fractals microstructures with fractal dimension of about 2.8 on the alumina powder.
Voice disorders are associated with irregular vibrations of vocal folds. Based on the source filter theory of speech production, these irregular vibrations can be detected in a non-invasive way by analyzing the speech signal. In this paper we present a multiband approach for the detection of voice disorders given that the voice source generally interacts with the vocal tract in a non-linear way. In normal phonation, and assuming sustained phonation of a vowel, the lower frequencies of speech are heavily source dependent due to the low frequency glottal formant, while the higher frequencies are less dependent on the source signal. During abnormal phonation, this is still a valid, but turbulent noise of source, because of the irregular vibration, affects also higher frequencies. Motivated by such a model, we suggest a multiband approach based on a three-level discrete wavelet transformation (DWT) and in each band the fractal dimension (FD) of the estimated power spectrum is estimated. The experiments suggest that frequency band 1-1562 Hz, lower frequencies after level 3, exhibits a significant difference in the spectrum of a normal and pathological subject. With this band, a detection rate of 91.28 % is obtained with one feature, and the obtained result is higher than all other frequency bands. Moreover, an accuracy of 92.45 % and an area under receiver operating characteristic curve (AUC) of 95.06 % is acquired when the FD of all levels is fused. Likewise, when the FD of all levels is combined with 22 Multi-Dimensional Voice Program (MDVP) parameters, an improvement of 2.26 % in accuracy and 1.45 % in AUC is observed.
Stroke survivors are more prone to developing cognitive impairment and dementia. Dementia detection is a challenge for supporting personalized healthcare. This study analyzes the electroencephalogram (EEG) background activity of 5 vascular dementia (VaD) patients, 15 stroke-related patients with mild cognitive impairment (MCI), and 15 control healthy subjects during a working memory (WM) task. The objective of this study is twofold. First, it aims to enhance the discrimination of VaD, stroke-related MCI patients, and control subjects using fuzzy neighborhood preserving analysis with QR-decomposition (FNPAQR); second, it aims to extract and investigate the spectral features that characterize the post-stroke dementia patients compared to the control subjects. Nineteen channels were recorded and analyzed using the independent component analysis and wavelet analysis (ICA-WT) denoising technique. Using ANOVA, linear spectral power including relative powers (RP) and power ratio were calculated to test whether the EEG dominant frequencies were slowed down in VaD and stroke-related MCI patients. Non-linear features including permutation entropy (PerEn) and fractal dimension (FD) were used to test the degree of irregularity and complexity, which was significantly lower in patients with VaD and stroke-related MCI than that in control subjects (ANOVA; p ˂ 0.05). This study is the first to use fuzzy neighborhood preserving analysis with QR-decomposition (FNPAQR) dimensionality reduction technique with EEG background activity of dementia patients. The impairment of post-stroke patients was detected using support vector machine (SVM) and k-nearest neighbors (kNN) classifiers. A comparative study has been performed to check the effectiveness of using FNPAQR dimensionality reduction technique with the SVM and kNN classifiers. FNPAQR with SVM and kNN obtained 91.48 and 89.63% accuracy, respectively, whereas without using the FNPAQR exhibited 70 and 67.78% accuracy for SVM and kNN, respectively, in classifying VaD, stroke-related MCI, and control patients, respectively. Therefore, EEG could be a reliable index for inspecting concise markers that are sensitive to VaD and stroke-related MCI patients compared to control healthy subjects.
One of the main areas of behavioural neuroscience is forecasting the human behaviour. Epilepsy is a central nervous system disorder in which nerve cell activity in the brain becomes disrupted, causing seizures or periods of unusual behaviour, sensations and sometimes loss of consciousness. An estimated 5% of the world population has epileptic seizure but there is not any method to cure it. More than 30% of people with epilepsy cannot control seizure. Epileptic seizure prediction, refers to forecasting the occurrence of epileptic seizures, is one of the most important but challenging problems in biomedical sciences, across the world. In this research we propose a new methodology which is based on studying the EEG signals using two measures, the Hurst exponent and fractal dimension. In order to validate the proposed method, it is applied to epileptic EEG signals of patients by computing the Hurst exponent and fractal dimension, and then the results are validated versus the reference data. The results of these analyses show that we are able to forecast the onset of a seizure on average of 25.76 seconds before the time of occurrence.