Abstract: Osteoporosis is a common disease characterized by low bone mass and deterioration of micro-architectural bone tissue, which provokes an increased risk of fracture. This work treats the texture characterization of trabecular bone radiographs. The aim was to analyze according to clinical research a group of 174 subjects: 87 osteoporotic patients (OP) with various bone fracture types and 87 control cases (CC). To characterize osteoporosis, Fractal and MultiFractal (MF) methods were applied to images for features (attributes) extraction. In order to improve the results, a new method of MF spectrum based on the q-stucture function calculation was proposed and a combination of Fractal and MF attributes was used. The Support Vector Machines (SVM) was applied as a classifier to distinguish between OP patients and CC subjects. The features fusion (fractal and MF) allowed a good discrimination between the two groups with an accuracy rate of 96.22%.
Abstract: The purpose of this study is the discrimination of 28
postmenopausal with osteoporotic femoral fractures from an agematched
control group of 28 women using texture analysis based on
fractals. Two pre-processing approaches are applied on radiographic
images; these techniques are compared to highlight the choice of the
pre-processing method. Furthermore, the values of the fractal
dimension are compared to those of the fractal signature in terms of
the classification of the two populations. In a second analysis, the
BMD measure at proximal femur was compared to the fractal
analysis, the latter, which is a non-invasive technique, allowed a
better discrimination; the results confirm that the fractal analysis of
texture on calcaneus radiographs is able to discriminate osteoporotic
patients with femoral fracture from controls. This discrimination was
efficient compared to that obtained by BMD alone. It was also
present in comparing subgroups with overlapping values of BMD.
Abstract: Optic disk segmentation plays a key role in the mass
screening of individuals with diabetic retinopathy and glaucoma
ailments. An efficient hardware-based algorithm for optic disk
localization and segmentation would aid for developing an automated
retinal image analysis system for real time applications. Herein,
TMS320C6416DSK DSP board pixel intensity based fractal analysis
algorithm for an automatic localization and segmentation of the optic
disk is reported. The experiment has been performed on color and
fluorescent angiography retinal fundus images. Initially, the images
were pre-processed to reduce the noise and enhance the quality. The
retinal vascular tree of the image was then extracted using canny
edge detection technique. Finally, a pixel intensity based fractal
analysis is performed to segment the optic disk by tracing the origin
of the vascular tree. The proposed method is examined on three
publicly available data sets of the retinal image and also with the data
set obtained from an eye clinic. The average accuracy achieved is
96.2%. To the best of the knowledge, this is the first work reporting
the use of TMS320C6416DSK DSP board and pixel intensity based
fractal analysis algorithm for an automatic localization and
segmentation of the optic disk. This will pave the way for developing
devices for detection of retinal diseases in the future.
Abstract: Mammography has been one of the most reliable
methods for early detection of breast cancer. There are different
lesions which are breast cancer characteristic such as
microcalcifications, masses, architectural distortions and bilateral
asymmetry. One of the major challenges of analysing digital
mammogram is how to extract efficient features from it for accurate
cancer classification. In this paper we proposed a hybrid feature
extraction method to detect and classify all four signs of breast
cancer. The proposed method is based on multiscale surrounding
region dependence method, Gabor filters, multi fractal analysis,
directional and morphological analysis. The extracted features are
input to self adaptive resource allocation network (SRAN) classifier
for classification. The validity of our approach is extensively
demonstrated using the two benchmark data sets Mammographic
Image Analysis Society (MIAS) and Digital Database for Screening
Mammograph (DDSM) and the results have been proved to be
progressive.
Abstract: Shot boundary detection is a fundamental step for the organization of large video data. In this paper, we propose a new method for video gradual shots detection and classification, using advantages of fractal analysis and AIS-based classifier. Proposed features are “vertical intercept" and “fractal dimension" of each frame of videos which are computed using Fourier transform coefficients. We also used a classifier based on Clonal Selection Algorithm. We have carried out our solution and assessed it according to the TRECVID2006 benchmark dataset.
Abstract: This paper investigates the fractals generated by the dynamical system of intuitionistic fuzzy contractions in the intuitionistic
fuzzy metric spaces by generalizing the Hutchinson-Barnsley theory. We prove some existence and uniqueness theorems of fractals in the
standard intuitionistic fuzzy metric spaces by using the intuitionistic fuzzy Banach contraction theorem. In addition to that, we analyze
some results on intuitionistic fuzzy fractals in the standard intuitionistic fuzzy metric spaces with respect to the Hausdorff intuitionistic
fuzzy metrics.
Abstract: Semiconductor nanomaterials like TiO2 nanoparticles
(TiO2-NPs) approximately less than 100 nm in diameter have become
a new generation of advanced materials due to their novel and
interesting optical, dielectric, and photo-catalytic properties. With the
increasing use of NPs in commerce, to date few studies have
investigated the toxicological and environmental effects of NPs.
Motivated by the importance of TiO2-NPs that may contribute to the
cancer research field especially from the treatment prospective
together with the fractal analysis technique, we have investigated the
effect of TiO2-NPs on colony morphology in the dark condition
using fractal dimension as a key morphological characterization
parameter. The aim of this work is mainly to investigate the cytotoxic
effects of TiO2-NPs in the dark on the growth of human cervical
carcinoma (HeLa) cell colonies from morphological aspect. The in
vitro studies were carried out together with the image processing
technique and fractal analysis. It was found that, these colonies were
abnormal in shape and size. Moreover, the size of the control
colonies appeared to be larger than those of the treated group. The
mean Df +/- SEM of the colonies in untreated cultures was
1.085±0.019, N= 25, while that of the cultures treated with TiO2-NPs
was 1.287±0.045. It was found that the circularity of the control
group (0.401±0.071) is higher than that of the treated group
(0.103±0.042). The same tendency was found in the diameter
parameters which are 1161.30±219.56 μm and 852.28±206.50 μm
for the control and treated group respectively. Possible explanation of
the results was discussed, though more works need to be done in
terms of the for mechanism aspects. Finally, our results indicate that
fractal dimension can serve as a useful feature, by itself or in
conjunction with other shape features, in the classification of cancer
colonies.
Abstract: The objective of this paper is to characterize the spontaneous Electroencephalogram (EEG) signals of four different motor imagery tasks and to show hereby a possible solution for the present binary communication between the brain and a machine ora Brain-Computer Interface (BCI). The processing technique used in this paper was the fractal analysis evaluated by the Critical Exponent Method (CEM). The EEG signal was registered in 5 healthy subjects,sampling 15 measuring channels at 1024 Hz.Each channel was preprocessed by the Laplacian space ltering so as to reduce the space blur and therefore increase the spaceresolution. The EEG of each channel was segmented and its Fractaldimension (FD) calculated. The FD was evaluated in the time interval corresponding to the motor imagery and averaged out for all the subjects (each channel). In order to characterize the FD distribution,the linear regression curves of FD over the electrodes position were applied. The differences FD between the proposed mental tasks are quantied and evaluated for each experimental subject. The obtained results of the proposed method are a substantial fractal dimension in the EEG signal of motor imagery tasks and can be considerably utilized as the multiple-states BCI applications.
Abstract: The colonic tissue is a complicated dynamic system
and the colonic activities it generates are composed of irregular
segmental waves, which are referred to as erratic fluctuations or spikes.
They are also highly irregular with subunit fractal structure. The
traditional time-frequency domain statistics like the averaged
amplitude, the motility index and the power spectrum, etc. are
insufficient to describe such fluctuations. Thus the fractal
box-counting dimension is proposed and the fractal scaling behaviors
of the human colonic pressure activities under the physiological
conditions are studied. It is shown that the dimension of the resting
activity is smaller than that of the normal one, whereas the clipped
version, which corresponds to the activity of the constipation patient,
shows with higher fractal dimension. It may indicate a practical
application to assess the colonic motility, which is often indicated by
the colonic pressure activity.
Abstract: A nucleotide sequence can be expressed as a numerical sequence when each nucleotide is assigned its proton number. A resulting gene numerical sequence can be investigated for its fractal dimension in terms of evolution and chemical properties for comparative studies. We have investigated such nucleotide fluctuation in the 16S rRNA gene of archaea thermophiles. The studied archaea thermophiles were archaeoglobus fulgidus, methanothermobacter thermautotrophicus, methanocaldococcus jannaschii, pyrococcus horikoshii, and thermoplasma acidophilum. The studied five archaea-euryarchaeota thermophiles have fractal dimension values ranging from 1.93 to 1.97. Computer simulation shows that random sequences would have an average of about 2 with a standard deviation about 0.015. The fractal dimension was found to correlate (negative correlation) with the thermophile-s optimal growth temperature with R2 value of 0.90 (N =5). The inclusion of two aracheae-crenarchaeota thermophiles reduces the R2 value to 0.66 (N = 7). Further inclusion of two bacterial thermophiles reduces the R2 value to 0.50 (N =9). The fractal dimension is correlated (positive) to the sequence GC content with an R2 value of 0.89 for the five archaea-euryarchaeota thermophiles (and 0.74 for the entire set of N = 9), although computer simulation shows little correlation. The highest correlation (positive) was found to be between the fractal dimension and di-nucleotide Shannon entropy. However Shannon entropy and sequence GC content were observed to correlate with optimal growth temperature having an R2 of 0.8 (negative), and 0.88 (positive), respectively, for the entire set of 9 thermophiles; thus the correlation lacks species specificity. Together with another correlation study of bacterial radiation dosage with RecA repair gene sequence fractal dimension, it is postulated that fractal dimension analysis is a sensitive tool for studying the relationship between genotype and phenotype among closely related sequences.
Abstract: Biological reactions of individuals of a testing animal
to toxic substance are unique and can be used as an indication of the
existing of toxic substance. However, to distinguish such phenomenon
need a very complicate system and even more complicate to analyze
data in 3 dimensional. In this paper, a system to evaluate in vitro
biological activities to acute toxicity of stochastic self-affine
non-stationary signal of 3D goldfish swimming by using fractal
analysis is introduced. Regular digital camcorders are utilized by
proposed algorithm 3DCCPC to effectively capture and construct 3D
movements of the fish. A Critical Exponent Method (CEM) has been
adopted as a fractal estimator. The hypothesis was that the swimming
of goldfish to acute toxic would show the fractal property which
related to the toxic concentration. The experimental results supported
the hypothesis by showing that the swimming of goldfish under the
different toxic concentration has fractal properties. It also shows that
the fractal dimension of the swimming related to the pH value of FD Ôëê
0.26pH + 0.05. With the proposed system, the fish is allowed to swim
freely in all direction to react to the toxic. In addition, the trajectories
are precisely evaluated by fractal analysis with critical exponent
method and hence the results exhibit with much higher degree of
confidence.
Abstract: All the geophysical phenomena including river
networks and flow time series are fractal events inherently and fractal
patterns can be investigated through their behaviors. A non-linear
system like a river basin can well be analyzed by a non-linear
measure such as the fractal analysis. A bilateral study is held on the
fractal properties of the river network and the river flow time series.
A moving window technique is utilized to scan the fractal properties
of them. Results depict both events follow the same strategy
regarding to the fractal properties. Both the river network and the
time series fractal dimension tend to saturate in a distinct value.
Abstract: In this paper, Zinc Oxide (ZnO) thin films are deposited on glass substrate by sol-gel method. The ZnO thin films with well defined orientation were acquired by spin coating of zinc acetate dehydrate monoethanolamine (MEA), de-ionized water and isopropanol alcohol. These films were pre-heated at 275°C for 10 min and then annealed at 350°C, 450°C and 550°C for 80 min. The effect of annealing temperature and different thickness on structure and surface morphology of the thin films were verified by Atomic Force Microscopy (AFM). It was found that there was a significant effect of annealing temperature on the structural parameters of the films such as roughness exponent, fractal dimension and interface width. Thin films also were characterizied by X-ray Diffractometery (XRD) method. XRD analysis revealed that the annealed ZnO thin films consist of single phase ZnO with wurtzite structure and show the c-axis grain orientation. Increasing annealing temperature increased the crystallite size and the c-axis orientation of the film after 450°C. Also In this study, ZnO thin films in different thickness have been prepared by sol-gel method on the glass substrate at room temperature. The thicknesses of films are 100, 150 and 250 nm. Using fractal analysis, morphological characteristics of surface films thickness in amorphous state were investigated. The results show that with increasing thickness, surface roughness (RMS) and lateral correlation length (ξ) are decreased. Also, the roughness exponent (α) and growth exponent (β) were determined to be 0.74±0.02 and 0.11±0.02, respectively.
Abstract: Natural resources management including water resources requires reliable estimations of time variant environmental parameters. Small improvements in the estimation of environmental parameters would result in grate effects on managing decisions. Noise reduction using wavelet techniques is an effective approach for preprocessing of practical data sets. Predictability enhancement of the river flow time series are assessed using fractal approaches before and after applying wavelet based preprocessing. Time series correlation and persistency, the minimum sufficient length for training the predicting model and the maximum valid length of predictions were also investigated through a fractal assessment.
Abstract: The linear methods of heart rate variability analysis
such as non-parametric (e.g. fast Fourier transform analysis) and
parametric methods (e.g. autoregressive modeling) has become an
established non-invasive tool for marking the cardiac health, but their
sensitivity and specificity were found to be lower than expected with
positive predictive value