Search results for: fractal gray level image

Authors: Eman A. Al-Hilo, Hawraa H. Al-Waelly

Abstract:

In this work, fractal compression (FIC) technique is introduced based on using moment features to block indexing the zero-mean range-domain blocks. The moment features have been used to speed up the IFS-matching stage. Its moments ratio descriptor is used to filter the domain blocks and keep only the blocks that are suitable to be IFS matched with tested range block. The results of tests conducted on Lena picture and Cat picture (256 pixels, resolution 24 bits/pixel) image showed a minimum encoding time (0.89 sec for Lena image and 0.78 of Cat image) with appropriate PSNR (30.01dB for Lena image and 29.8 of Cat image). The reduction in ET is about 12% for Lena and 67% for Cat image.

Keywords: fractal gray level image, fractal compression technique, iterated function system, moments feature, zero-mean range-domain block

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Authors: S. Sushma, S. Balasubramanian, K. C. Latha, R. Sridhar

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Structural texture measures are used to address the aspect of breast cancer risk assessment in screening mammograms. The current study investigates whether texture properties characterized by local Fractal Dimension (FD) and lacunarity contribute to assess breast cancer risk. Fractal Dimension represents the complexity while the lacunarity characterize the gap of a fractal dimension. In this paper, we present our result confirming that the lacunarity value resulted in algorithm using mammogram images states that level of lacunarity will be low when the Fractal Dimension value will be high.

Keywords: breast cancer, fractal dimension, image analysis, lacunarity, mammogram

Procedia PDF Downloads 350

Authors: Ali Abdrhman M. Ukasha

Abstract:

Data security needed in data transmission, storage, and communication to ensure the security. The single step parallel contour extraction (SSPCE) method is used to create the edge map as a key image from the different Gray level/Binary image. Performing the X-OR operation between the key image and each bit plane of the original image for image pixel values change purpose. The Arnold transform used to changes the locations of image pixels as image scrambling process. Experiments have demonstrated that proposed algorithm can fully encrypt 2D Gary level image and completely reconstructed without any distortion. Also shown that the analyzed algorithm have extremely large security against some attacks like salt & pepper and JPEG compression. Its proof that the Gray level image can be protected with a higher security level. The presented method has easy hardware implementation and suitable for multimedia protection in real time applications such as wireless networks and mobile phone services.

Keywords: SSPCE method, image compression-salt- peppers attacks, bitplanes decomposition, Arnold transform, lossless image encryption

Procedia PDF Downloads 395

Authors: Md. Enamul Haque, Abdullah Al Kaisan, Mahmudur R. Saniat, Aminur Rahman

Abstract:

In this paper, we have implemented both sequential and parallel version of fractal image compression algorithms using CUDA (Compute Unified Device Architecture) programming model for parallelizing the program in Graphics Processing Unit for medical images, as they are highly similar within the image itself. There is several improvements in the implementation of the algorithm as well. Fractal image compression is based on the self similarity of an image, meaning an image having similarity in majority of the regions. We take this opportunity to implement the compression algorithm and monitor the effect of it using both parallel and sequential implementation. Fractal compression has the property of high compression rate and the dimensionless scheme. Compression scheme for fractal image is of two kinds, one is encoding and another is decoding. Encoding is very much computational expensive. On the other hand decoding is less computational. The application of fractal compression to medical images would allow obtaining much higher compression ratios. While the fractal magnification an inseparable feature of the fractal compression would be very useful in presenting the reconstructed image in a highly readable form. However, like all irreversible methods, the fractal compression is connected with the problem of information loss, which is especially troublesome in the medical imaging. A very time consuming encoding process, which can last even several hours, is another bothersome drawback of the fractal compression.

Keywords: accelerated GPU, CUDA, parallel computing, fractal image compression

Procedia PDF Downloads 296

Authors: Ali A. Ukasha

Abstract:

Data security needed in data transmission, storage, and communication to ensure the security. The single step parallel contour extraction (SSPCE) method is used to create the edge map as a key image from the different Gray level/Binary image. Performing the X-OR operation between the key image and each bit plane of the original image for image pixel values change purpose. The Arnold transform used to changes the locations of image pixels as image scrambling process. Experiments have demonstrated that proposed algorithm can fully encrypt 2D Gary level image and completely reconstructed without any distortion. Also shown that the analyzed algorithm have extremely large security against some attacks like salt & pepper and JPEG compression. Its proof that the Gray level image can be protected with a higher security level. The presented method has easy hardware implementation and suitable for multimedia protection in real time applications such as wireless networks and mobile phone services.

Keywords: SSPCE method, image compression, salt and peppers attacks, bitplanes decomposition, Arnold transform, lossless image encryption

Procedia PDF Downloads 454

Authors: O. Boussoufi, K. Lamrini Uahabi, M. Atounti

Abstract:

The main purpose of this paper is to calculate the fractal dimension of some Julia Sets and Mandelbrot Set in the Misiurewicz Points. Using Matlab to generate the Julia Sets images that match the Misiurewicz points and using a Fractal software, we were able to find different measures that characterize those fractals in textures and other features. We are actually focusing on fractal dimension and the error calculated by the software. When executing the given equation of regression or the log-log slope of image a Box Counting method is applied to the entire image, and chosen settings are available in a FracLAc Program. Finally, a comparison is done for each image corresponding to the area (boundary) where Misiurewicz Point is located.

Keywords: box counting, FracLac, fractal dimension, Julia Sets, Mandelbrot Set, Misiurewicz Points

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Authors: Adnan H. M. Al-Helali, Hamza A. Ali

Abstract:

Growth of censorship and pervasive monitoring on the Internet, Steganography arises as a new means of achieving secret communication. Steganography is the art and science of embedding information within electronic media used by common applications and systems. Generally, hiding information of multimedia within images will change some of their properties that may introduce few degradation or unusual characteristics. This paper presents a new image steganography approach for hiding information of multimedia (images, text, and audio) using generated Mandelbrot Fractal image as a cover. The proposed technique has been extensively tested with different images. The results show that the method is a very secure means of hiding and retrieving steganographic information. Experimental results demonstrate that an effective improvement in the values of the Peak Signal to Noise Ratio (PSNR), Mean Square Error (MSE), Normalized Cross Correlation (NCC) and Image Fidelity (IF) over the previous techniques.

Keywords: fractal image, information hiding, Mandelbrot et fractal, steganography

Procedia PDF Downloads 507

Authors: Adnan H. M. Al-Helali, Hamza A. Ali

Abstract:

The growth of censorship and pervasive monitoring on the Internet, Steganography arises as a new means of achieving secret communication. Steganography is the art and science of embedding information within electronic media used by common applications and systems. Generally, hiding information of multimedia within images will change some of their properties that may introduce few degradation or unusual characteristics. This paper presents a new image steganography approach for hiding information of multimedia (images, text, and audio) using generated Mandelbrot Fractal image as a cover. The proposed technique has been extensively tested with different images. The results show that the method is a very secure means of hiding and retrieving steganographic information. Experimental results demonstrate that an effective improvement in the values of the Peak Signal to Noise Ratio (PSNR), Mean Square Error (MSE), Normalized Cross Correlation (NCC), and Image Fidelity (IF) over the pervious techniques.

Keywords: fractal image, information hiding, Mandelbrot set fractal, steganography

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Authors: R. K. Pateriya, Jyoti Bharti

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This paper presents an approach for data hiding methods which provides a secret communication between sender and receiver. The data is hidden in gray-scale images and the boundary of gray-scale image is used to store the mapping information. In this an approach data is in ASCII format and the mapping is in between ASCII value of hidden message and pixel value of cover image, since pixel value of an image as well as ASCII value is in range of 0 to 255 and this mapping information is occupying only 1 bit per character of hidden message as compared to 8 bit per character thus maintaining good quality of stego image.

Keywords: ASCII value, cover image, PSNR, pixel value, stego image, secret message

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Authors: Khalid Salhi, El Miloud Jaara, Mohammed Talibi Alaoui

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In this paper, we present a neural approach for unsupervised natural color-texture image segmentation, which is based on both Kohonen maps and mathematical morphology, using a combination of the texture and the image color information of the image, namely, the fractal features based on fractal dimension are selected to present the information texture, and the color features presented in RGB color space. These features are then used to train the network Kohonen, which will be represented by the underlying probability density function, the segmentation of this map is made by morphological watershed transformation. The performance of our color-texture segmentation approach is compared first, to color-based methods or texture-based methods only, and then to k-means method.

Keywords: segmentation, color-texture, neural networks, fractal, watershed

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Authors: Abraham Terán Salcedo, Didier Samayoa Ochoa

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This work presents a numerical implementation of a method for estimating the box-counting dimension of self-avoiding curves on a planar space, fractal objects captured on digital images; this method is named fractioning estimator. Classical methods of digital image processing, such as noise filtering, contrast manipulation, and thresholding, among others, are used in order to obtain binary images that are suitable for performing the necessary computations of the fractioning estimator. A user interface is developed for performing the image processing operations and testing the fractioning estimator on different captured images of real-life fractal objects. To analyze the results, the estimations obtained through the fractioning estimator are compared to the results obtained through other methods that are already implemented on different available software for computing and estimating the box-counting dimension.

Keywords: box-counting, digital image processing, fractal dimension, numerical method

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Authors: M. A. Alqahtani, D. P. Coleman, N. D. Pugh, L. D. M. Nokes

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In diagnostic ultrasound, the echo graphic B-scan texture is an important area of investigation since it can be analyzed to characterize the histological state of internal tissues. An important factor requiring consideration when evaluating ultrasonic tissue texture is the depth. The effect of attenuation with depth of ultrasound, the size of the region of interest, gain, and dynamic range are important variables to consider as they can influence the analysis of texture features. These sources of variability have to be considered carefully when evaluating image texture as different settings might influence the resultant image. The aim of this study is to investigate the effect of depth on the texture features in-vivo using a 3D ultrasound probe. The left leg medial head of the gastrocnemius muscle of 10 healthy subjects were scanned. Two regions A and B were defined at different depth within the gastrocnemius muscle boundary. The size of both ROI’s was 280*20 pixels and the distance between region A and B was kept constant at 5 mm. Texture parameters include gray level, variance, skewness, kurtosis, co-occurrence matrix; run length matrix, gradient, autoregressive (AR) model and wavelet transform were extracted from the images. The paired t –test was used to test the depth effect for the normally distributed data and the Wilcoxon–Mann-Whitney test was used for the non-normally distributed data. The gray level, variance, and run length matrix were significantly lowered when the depth increased. The other texture parameters showed similar values at different depth. All the texture parameters showed no significant difference between depths A and B (p > 0.05) except for gray level, variance and run length matrix (p < 0.05). This indicates that gray level, variance, and run length matrix are depth dependent.

Keywords: ultrasound image, texture parameters, computational biology, biomedical engineering

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Authors: V. V. Reddy, N. V. Sarma

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A circularly polarized fractal boundary microstrip antenna is presented. The sides of a square patch along x-axis, y-axis are replaced with Minkowski and Koch curves correspondingly. By using the fractal curves as edges, asymmetry in the structure is created to excite two orthogonal modes for circular polarization (CP) operation. The indentation factors of the fractal curves are optimized for pure CP. The simulated results of the novel poly fractal antenna are demonstrated.

Keywords: fractal, circular polarization, Minkowski, Koch

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Authors: Yousif Mohamed Y. Abdallah, Eltayeb Wagallah

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Image enhancement allows the observer to see details in images that may not be immediately observable in the original image. Image enhancement is the transformation or mapping of one image to another. The enhancement of certain features in images is accompanied by undesirable effects. To achieve maximum image quality after denoising, a new, low order, local adaptive Gaussian scale mixture model and median filter were presented, which accomplishes nonlinearities from scattering a new nonlinear approach for contrast enhancement of bones in bone scan images using both gamma correction and negative transform methods. The usual assumption of a distribution of gamma and Poisson statistics only lead to overestimation of the noise variance in regions of low intensity but to underestimation in regions of high intensity and therefore to non-optional results. The contrast enhancement results were obtained and evaluated using MatLab program in nuclear medicine images of the bones. The optimal number of bins, in particular the number of gray-levels, is chosen automatically using entropy and average distance between the histogram of the original gray-level distribution and the contrast enhancement function’s curve.

Keywords: bone scan, nuclear medicine, Matlab, image processing technique

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Authors: Rhea Kapoor

Abstract:

Fractal dimension provides a way to characterize non-geometric shapes like those found in nature. The purpose of this research is to estimate Minkowski fractal dimension of human lung images for early detection of lung cancer. Lung cancer is the leading cause of death among all types of cancer and an early histopathological analysis will help reduce deaths primarily due to late diagnosis. A Python application program, PathoPy2.0, was developed for analyzing medical images in pixelated format and estimating Minkowski fractal dimension using a new box-counting algorithm that allows windowing of images for more accurate calculation in the suspected areas of cancerous growth. Benchmark geometric fractals were used to validate the accuracy of the program and changes in fractal dimension of lung images to indicate the presence of issues in the lung. The accuracy of the program for the benchmark examples was between 93-99% of known values of the fractal dimensions. Fractal dimension values were then calculated for lung images, from National Cancer Institute, taken over time to correctly detect the presence of cancerous growth. For example, as the fractal dimension for a given lung increased from 1.19 to 1.27 due to cancerous growth, it represents a significant change in fractal dimension which lies between 1 and 2 for 2-D images. Based on the results obtained on many lung test cases, it was concluded that fractal dimension of human lungs can be used to diagnose lung cancer early. The ideas behind PathoPy2.0 can also be applied to study patterns in the electrical activity of the human brain and DNA matching.

Keywords: fractals, histopathological analysis, image processing, lung cancer, Minkowski dimension

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Authors: Katsuhiro Narikiyo, Shota Hashikawa

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This paper proposes a way of removing noises and reducing the number of colors contained in a JPEG image. Main purpose of this project is to convert color images to monochrome images for the color-blind. We treat the crispy color images like the Tokyo subway map. Each color in the image has an important information. But for the color blinds, similar colors cannot be distinguished. If we can convert those colors to different gray values, they can distinguish them. Therefore we try to convert color images to monochrome images.

Keywords: color-blind, JPEG, monochrome image, denoise

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Authors: A. El Hamdouni, J. Zbitou, A. Tajmouati, L. El Abdellaoui, A. Errkik, A. Tribak, M. Latrach

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This paper presents a novel fractal antenna structure proposed for UWB (Ultra – Wideband) applications. The frequency band 3.1-10.6 GHz released by FCC (Federal Communication Commission) as the commercial operation of UWB has been chosen as frequency range for this antenna based on coplanar waveguide (CPW) feed and circular shapes fulfilled according to fractal geometry. The proposed antenna is validated and designed by using an FR4 substrate with overall area of 34 x 43 mm2. The simulated results performed by CST-Microwave Studio and compared by ADS (Advanced Design System) show good matching input impedance with return loss less than -10 dB between 2.9 GHz and 11 GHz.

Keywords: Fractal antenna, Fractal Geometry, CPW Feed, UWB, FCC

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Authors: Khaled Harrar, Rachid Jennane

Abstract:

The purpose of this study is the discrimination of 28 postmenopausal with osteoporotic femoral fractures from an age-matched 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.

Keywords: osteoporosis, fractal dimension, fractal signature, bone mineral density

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Authors: S. Sushma, S. Balasubramanian, K. C. Latha

Abstract:

The mammographic image of breast cancer compressed and synthesized to get co-efficient values which will be converted (5x5) matrix to get ROI image where we get the highest value of effected region and with the same ideology the technique has been extended to differentiate between Calcification and normal cell image using mean value derived from 5x5 matrix values

Keywords: texture analysis, mammographic image, partitioned gray scale co-oocurance matrix, co-efficient

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Authors: Yun-Xuan Tang, Pei-Yuan Liu, Kun-Mu Lu, Min-Tsung Tseng, Liang-Kuang Chen, Yuh-Feng Tsai, Ching-Wen Lee, Jay Wu

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Breast cancer is predominant of malignant tumors in females. The increase in the glandular density increases the risk of breast cancer. BI-RADS is a frequently used density indicator in mammography; however, it significantly overestimates the glandularity. Therefore, it is very important to accurately and quantitatively assess the glandularity by mammography. In this study, 20%, 30% and 50% glandularity phantoms were exposed using a mammography machine at 28, 30 and 31 kVp, and 30, 55, 80 and 105 mAs, respectively. The regions of interest (ROIs) were drawn to assess the gray level. The relationship between the glandularity and gray level under various compression thicknesses, kVp, and mAs was established by the multivariable linear regression. A phantom verification was performed with automatic exposure control (AEC). The regression equation was obtained with an R-square value of 0.928. The average gray levels of the verification phantom were 8708, 8660 and 8434 for 0.952, 0.963 and 0.985 g/cm3, respectively. The percent differences of glandularity to the regression equation were 3.24%, 2.75% and 13.7%. We concluded that the proposed method could be clinically applied in mammography to improve the glandularity estimation and further increase the importance of breast cancer screening.

Keywords: mammography, glandularity, gray value, BI-RADS

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Authors: Te-Jen Chang, I-Hui Pan, Kuang-Hsiung Tan, Shan-Jen Cheng, Chien-Wu Lan, Chih-Chan Hu

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With the event of multimedia age in order to protect data not to be tampered, damaged, and faked, information hiding technologies are proposed. Information hiding means important secret information is hidden into cover multimedia and then camouflaged media is produced. This camouflaged media has the characteristic of natural protection. Under the undoubted situation, important secret information is transmitted out.Reversible information hiding technologies for high capacity is proposed in this paper. The gray images are as cover media in this technology. We compress gray images and compare with the original image to produce the estimated differences. By using the estimated differences, expression information hiding is used, and higher information capacity can be achieved. According to experimental results, the proposed technology can be approved. For these experiments, the whole capacity of information payload and image quality can be satisfied.

Keywords: cover media, camouflaged media, reversible information hiding, gray image

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Authors: Fuad M. Alkoot

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The main component of a machine learning system is the classifier. Classifiers are mathematical models that can perform classification tasks for a specific application area. Additionally, many classifiers are combined using any of the available methods to reduce the classifier error rate. The benefits gained from the combination of multiple classifier designs has motivated the development of diverse approaches to multiple classifiers. We aim to investigate using fractal geometry to develop an improved classifier combiner. Initially we experiment with measuring the fractal dimension of data and use the results in the development of a combiner strategy.

Keywords: fractal geometry, machine learning, classifier, fractal dimension

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Authors: Zerroug Abdelhamid, Danielle Chassoux

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Various models are given to simulate homogeneous or heterogeneous cancerous tumors and extract in each case the boundary. The fractal dimension is then estimated by least squares method and compared to some previous methods.

Keywords: simulation, cancerous tumor, Markov fields, fractal dimension, extraction, recovering

Procedia PDF Downloads 335

Authors: Beibit Karibayev, Akmaral Imanbayeva, Timur Namazbayev

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Currently, the small spacecraft (SSC) industry is experiencing a big boom in popularity. This is primarily due to ease of use, low cost and mobility. In addition, these programs can be implemented not only at the state level but also at the level of companies, universities and other organizations. For remote sensing of the Earth (ERS), small spacecraft with an orientation system is used. It is important to take into account here that a remote sensing device, for example, a camera for photographing the Earth's surface, must be directed at the Earth's surface. But this, at first glance, the limitation can be turned into an advantage using a patch antenna. This work proposed to use a patch antenna based on a unidirectional fractal in the SSC. The CST Microwave Studio software package was used for simulation and research. Copper (ε = 1.0) was chosen as the emitting element and reflector. The height of the substrate was 1.6 mm, the type of substrate material was FR-4 (ε = 4.3). The simulation was performed in the frequency range of 0 – 6 GHz. As a result of the research, a patch antenna based on fractal geometry was developed for ERS nanosatellites. The capabilities of these antennas are modeled and investigated. A method for calculating and modeling fractal geometry for patch antennas has been developed.

Keywords: antenna, earth remote sensing, fractal, small spacecraft

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Authors: Roza Afarin, Saeed Mozaffari

Abstract:

The aim of this paper is image encryption using Genetic Algorithm (GA). The proposed encryption method consists of two phases. In modification phase, pixels locations are altered to reduce correlation among adjacent pixels. Then, pixels values are changed in the diffusion phase to encrypt the input image. Both phases are performed by GA with binary chromosomes. For modification phase, these binary patterns are generated by Local Binary Pattern (LBP) operator while for diffusion phase binary chromosomes are obtained by Bit Plane Slicing (BPS). Initial population in GA includes rows and columns of the input image. Instead of subjective selection of parents from this initial population, a random generator with predefined key is utilized. It is necessary to decrypt the coded image and reconstruct the initial input image. Fitness function is defined as average of transition from 0 to 1 in LBP image and histogram uniformity in modification and diffusion phases, respectively. Randomness of the encrypted image is measured by entropy, correlation coefficients and histogram analysis. Experimental results show that the proposed method is fast enough and can be used effectively for image encryption.

Keywords: correlation coefficients, genetic algorithm, image encryption, image entropy

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Authors: Hamidreza Namazi

Abstract:

Fractal analysis is assessing fractal characteristics of data. It consists of several methods to assign fractal characteristics to a dataset which may be a theoretical dataset or a pattern or signal extracted from phenomena including natural geometric objects, sound, market fluctuations, heart rates, digital images, molecular motion, networks, etc. Fractal analysis is now widely used in all areas of science. An important limitation of fractal analysis is that arriving at an empirically determined fractal dimension does not necessarily prove that a pattern is fractal; rather, other essential characteristics have to be considered. For this purpose a Visual C++ based software called FRATSAN (FRActal Time Series ANalyser) was developed which extract information from signals through three measures. These measures are Fractal Dimensions, Jeffrey’s Measure and Hurst Exponent. After computing these measures, the software plots the graphs for each measure. Besides computing three measures the software can classify whether the signal is fractal or no. In fact, the software uses a dynamic method of analysis for all the measures. A sliding window is selected with a value equal to 10% of the total number of data entries. This sliding window is moved one data entry at a time to obtain all the measures. This makes the computation very sensitive to slight changes in data, thereby giving the user an acute analysis of the data. In order to test the performance of this software a set of EEG signals was given as input and the results were computed and plotted. This software is useful not only for fundamental fractal analysis of signals but can be used for other purposes. For instance by analyzing the Hurst exponent plot of a given EEG signal in patients with epilepsy the onset of seizure can be predicted by noticing the sudden changes in the plot.

Keywords: EEG signals, fractal analysis, fractal dimension, hurst exponent, Jeffrey’s measure

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Authors: T. Benyetho, L. El Abdellaoui, J. Terhzaz, H. Bennis, N. Ababssi, A. Tajmouati, A. Tribak, M. Latrach

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This work presents a new planar multiband antenna based on fractal geometry. This structure is optimized and validated into simulation by using CST-MW Studio. To feed this antenna we have used a CPW line which makes it easy to be incorporated with integrated circuits. The simulation results presents a good matching input impedance and radiation pattern in the GSM band at 900 MHz and ISM band at 2.4 GHz. The final structure is a dual band fractal antenna with 70 x 70 mm² as a total area by using an FR4 substrate.

Keywords: Antenna, CPW, fractal, GSM, multiband

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Authors: Manish Kumar Thakur, Subrata Kumar Ghosh

Abstract:

Various types of particles found in lubricant may be characterized by their fractal dimension. Some of the available methods are: yard-stick method or structured walk method, box-counting method. This paper presents a review of the developments and progress in fractal dimension computing methods as applied to characteristics the surface of wear particles. An overview of these methods, their implementation, their advantages and their limits is also present here. It has been accepted that wear particles contain major information about wear and friction of materials. Morphological analysis of wear particles from a lubricant is a very effective way for machine condition monitoring. Fractal dimension methods are used to characterize the morphology of the found particles. It is very useful in the analysis of complexity of irregular substance. The aim of this review is to bring together the fractal methods applicable for wear particles.

Keywords: fractal dimension, morphological analysis, wear, wear particles

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Authors: Marsden Jacques, Dennis Wong

Abstract:

A weak order is a way to rank n objects where ties are allowed. In this talk, we present a recursive framework to generate Gray codes for weak orders. We then describe a simple algorithm based on the framework that generates 2-Gray codes for weak orders in constant amortized time per string. This framework can easily be modified to generate other Gray codes for weak orders. We provide an example on using the framework to generate the first Shift Gray code for weak orders, also in constant amortized time, where consecutive strings differ by a shift or a symbol change.

Keywords: weak order, Cayley permutation, Gray code, shift Gray code

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Authors: Gülşen Akın Evingür, Önder Pekcan

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The fractal analysis is a bridge between the microstructure and macroscopic properties of gels. Fractal structure is usually provided to define the complexity of crosslinked molecules. The complexity in gel systems is described by the fractal dimension (Df). In this study, polyacrylamide- graphene oxide (GO) composite gels were prepared by free radical crosslinking copolymerization. The fractal analysis of polyacrylamide- graphene oxide (GO) composite gels were analyzed in various GO contents during gelation and were investigated by using Fluorescence Technique. The analysis was applied to estimate Df s of the composite gels. Fractal dimension of the polymer composite gels were estimated based on the power law exponent values using scaling models. In addition, here we aimed to present the geometrical distribution of GO during gelation. And we observed that as gelation proceeded GO plates first organized themselves into 3D percolation cluster with Df=2.52, then goes to diffusion limited clusters with Df =1.4 and then lines up to Von Koch curve with random interval with Df=1.14. Here, our goal is to try to interpret the low conductivity and/or broad forbidden gap of GO doped PAAm gels, by the distribution of GO in the final form of the produced gel.

Keywords: composite gels, fluorescence, fractal, scaling

Procedia PDF Downloads 280