Search results for: binary system

Authors: Fahad Alhussein, Huaping Liu

Abstract:

This paper compares the multipath mitigation performance of code correlation reference waveform receivers with variable and fixed window width, for binary offset carrier and multiplexed binary offset carrier signals typically used in global navigation satellite systems. In the variable window width method, such width is iteratively reduced until the distortion on the discriminator with multipath is eliminated. This distortion is measured as the Euclidean distance between the actual discriminator (obtained with the incoming signal), and the local discriminator (generated with a local copy of the signal). The variable window width have shown better performance compared to the fixed window width. In particular, the former yields zero error for all delays for the BOC and MBOC signals considered, while the latter gives rather large nonzero errors for small delays in all cases. Due to its computational simplicity, the variable window width method is perfectly suitable for implementation in low-cost receivers.

Keywords: Correlation reference waveform receivers, binary offset carrier, multiplexed binary offset carrier, global navigation satellite systems.

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Authors: Mehran Yazdi, Zahra Adelpour, Batoul Bahraini, Yasaman Keshtkar Jahromi

Abstract:

In this paper we use the property of co-occurrence matrix in finding parallel lines in binary pictures for fingerprint identification. In our proposed algorithm, we reduce the noise by filtering the fingerprint images and then transfer the fingerprint images to binary images using a proper threshold. Next, we divide the binary images into some regions having parallel lines in the same direction. The lines in each region have a specific angle that can be used for comparison. This method is simple, performs the comparison step quickly and has a good resistance in the presence of the noise.

Keywords: Parallel lines detection, co-occurrence matrix, fingerprint identification.

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Authors: Panos Kotsas, Tony Dodd

Abstract:

This paper presents the application of a signal intensity independent similarity criterion for rigid and non-rigid body registration of binary objects. The criterion is defined as the weighted ratio image of two images. The ratio is computed on a voxel per voxel basis and weighting is performed by setting the raios between signal and background voxels to a standard high value. The mean squared value of the weighted ratio is computed over the union of the signal areas of the two images and it is minimized using the Chebyshev polynomial approximation.

Keywords: rigid and non-rigid body registration, binary objects

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Authors: S Kalyani, K Shanti Swarup

Abstract:

Power System Security is a major concern in real time operation. Conventional method of security evaluation consists of performing continuous load flow and transient stability studies by simulation program. This is highly time consuming and infeasible for on-line application. Pattern Recognition (PR) is a promising tool for on-line security evaluation. This paper proposes a Support Vector Machine (SVM) based binary classification for static and transient security evaluation. The proposed SVM based PR approach is implemented on New England 39 Bus and IEEE 57 Bus systems. The simulation results of SVM classifier is compared with the other classifier algorithms like Method of Least Squares (MLS), Multi- Layer Perceptron (MLP) and Linear Discriminant Analysis (LDA) classifiers.

Keywords: Static Security, Transient Security, Pattern Recognition, Classifier, Support Vector Machine.

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Authors: S. Hma Salah, H. Du, N. Al-Jawad

Abstract:

Ethnicity identification of face images is of interest in many areas of application, but existing methods are few and limited. This paper presents a fusion scheme that uses block-based uniform local binary patterns and Haar wavelet transform to combine local and global features. In particular, the LL subband coefficients of the whole face are fused with the histograms of uniform local binary patterns from block partitions of the face. We applied the principal component analysis on the fused features and managed to reduce the dimensionality of the feature space from 536 down to around 15 without sacrificing too much accuracy. We have conducted a number of preliminary experiments using a collection of 746 subject face images. The test results show good accuracy and demonstrate the potential of fusing global and local features. The fusion approach is robust, making it easy to further improve the identification at both feature and score levels.

Keywords: Ethnicity identification, fusion, local binary patterns, wavelet.

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Authors: O. Kadri, M. D. Mouss, L.H. Mouss, F. Merah

Abstract:

This paper proposes a novel hybrid algorithm for feature selection based on a binary ant colony and SVM. The final subset selection is attained through the elimination of the features that produce noise or, are strictly correlated with other already selected features. Our algorithm can improve classification accuracy with a small and appropriate feature subset. Proposed algorithm is easily implemented and because of use of a simple filter in that, its computational complexity is very low. The performance of the proposed algorithm is evaluated through a real Rotary Cement kiln dataset. The results show that our algorithm outperforms existing algorithms.

Keywords: Binary Ant Colony algorithm, Support VectorMachine, feature selection, classification.

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Authors: M. Chumburidze, N. Salia, T. Namchevadze

Abstract:

This work deals with case processing problems in business. The task of strategic credit requirements management of cases portfolio is discussed. The information model of credit requirements in a binary tree diagram is considered. The algorithms to solve issues of prioritizing clusters of cases in business have been investigated. An implementation of priority queues to support case management operations has been presented. The corresponding pseudo codes for the programming application have been constructed. The tools applied in this development are based on binary tree ordering algorithms, optimization theory, and business management methods.

Keywords: Credit network, case portfolio, binary tree, priority queue, stack.

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Authors: V. Venkatachalam, S. Selvan

Abstract:

The security of computer networks plays a strategic role in modern computer systems. Intrusion Detection Systems (IDS) act as the 'second line of defense' placed inside a protected network, looking for known or potential threats in network traffic and/or audit data recorded by hosts. We developed an Intrusion Detection System using LAMSTAR neural network to learn patterns of normal and intrusive activities, to classify observed system activities and compared the performance of LAMSTAR IDS with other classification techniques using 5 classes of KDDCup99 data. LAMSAR IDS gives better performance at the cost of high Computational complexity, Training time and Testing time, when compared to other classification techniques (Binary Tree classifier, RBF classifier, Gaussian Mixture classifier). we further reduced the Computational Complexity of LAMSTAR IDS by reducing the dimension of the data using principal component analysis which in turn reduces the training and testing time with almost the same performance.

Keywords: Binary Tree Classifier, Gaussian Mixture, IntrusionDetection System, LAMSTAR, Radial Basis Function.

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Authors: Qiu Chen, Koji Kotani, Feifei Lee, Tadahiro Ohmi

Abstract:

In this paper, we propose an improved face recognition algorithm using histogram-based features in spatial and frequency domains. For adding spatial information of the face to improve recognition performance, a region-division (RD) method is utilized. The facial area is firstly divided into several regions, then feature vectors of each facial part are generated by Binary Vector Quantization (BVQ) histogram using DCT coefficients in low frequency domains, as well as Local Binary Pattern (LBP) histogram in spatial domain. Recognition results with different regions are first obtained separately and then fused by weighted averaging. Publicly available ORL database is used for the evaluation of our proposed algorithm, which is consisted of 40 subjects with 10 images per subject containing variations in lighting, posing, and expressions. It is demonstrated that face recognition using RD method can achieve much higher recognition rate.

Keywords: Face recognition, Binary vector quantization (BVQ), Local Binary Patterns (LBP), DCT coefficients.

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Authors: Christian Arcos, Marley Vellasco, Abraham Alcaim

Abstract:

In this paper, we present a wavelet coefficients masking based on Local Binary Patterns (WLBP) approach to enhance the temporal spectra of the wavelet coefficients for speech enhancement. This technique exploits the wavelet denoising scheme, which splits the degraded speech into pyramidal subband components and extracts frequency information without losing temporal information. Speech enhancement in each high-frequency subband is performed by binary labels through the local binary pattern masking that encodes the ratio between the original value of each coefficient and the values of the neighbour coefficients. This approach enhances the high-frequency spectra of the wavelet transform instead of eliminating them through a threshold. A comparative analysis is carried out with conventional speech enhancement algorithms, demonstrating that the proposed technique achieves significant improvements in terms of PESQ, an international recommendation of objective measure for estimating subjective speech quality. Informal listening tests also show that the proposed method in an acoustic context improves the quality of speech, avoiding the annoying musical noise present in other speech enhancement techniques. Experimental results obtained with a DNN based speech recognizer in noisy environments corroborate the superiority of the proposed scheme in the robust speech recognition scenario.

Keywords: Binary labels, local binary patterns, mask, wavelet coefficients, speech enhancement, speech recognition.

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Authors: Mehdi Hosseinzadeh, Amir Sabbagh Molahosseini, Keivan Navi

Abstract:

In this paper, a new reverse converter for the moduli set {2n, 2n–1, 2n–1–1} is presented. We improved a previously introduced conversion algorithm for deriving an efficient hardware design for reverse converter. Hardware architecture of the proposed converter is based on carry-save adders and regular binary adders, without the requirement for modular adders. The presented design is faster than the latest introduced reverse converter for moduli set {2n, 2n–1, 2n–1–1}. Also, it has better performance than the reverse converters for the recently introduced moduli set {2n+1–1, 2n, 2n–1}

Keywords: Residue arithmetic, Residue number system, Residue-to-Binary converter, Reverse converter

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Authors: Tun Myat Aung, Ni Ni Hla

Abstract:

This paper begins by describing basic properties of finite field and elliptic curve cryptography over prime field and binary field. Then we discuss the discrete logarithm problem for elliptic curves and its properties. We study the general common attacks on elliptic curve discrete logarithm problem such as the Baby Step, Giant Step method, Pollard’s rho method and Pohlig-Hellman method, and describe in detail experiments of these attacks over prime field and binary field. The paper finishes by describing expected running time of the attacks and suggesting strong elliptic curves that are not susceptible to these attacks.c

Keywords: Discrete logarithm problem, general attacks, elliptic curves, strong curves, prime field, binary field, attack experiments.

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Authors: Ellips Masehian, Golnaz Habibi

Abstract:

This paper presents a novel algorithm for path planning of mobile robots in known 3D environments using Binary Integer Programming (BIP). In this approach the problem of path planning is formulated as a BIP with variables taken from 3D Delaunay Triangulation of the Free Configuration Space and solved to obtain an optimal channel made of connected tetrahedrons. The 3D channel is then partitioned into convex fragments which are used to build safe and short paths within from Start to Goal. The algorithm is simple, complete, does not suffer from local minima, and is applicable to different workspaces with convex and concave polyhedral obstacles. The noticeable feature of this algorithm is that it is simply extendable to n-D Configuration spaces.

Keywords: 3D C-space, Binary Integer Programming (BIP), Delaunay Tessellation, Robot Motion Planning.

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Authors: M. Petchsangsai, N. Wonglertnirant, T. Rojanarata, P. Opanasopit, T. Ngawhirunpat

Abstract:

The objective of the present study was to evaluate the potential of hollow microneedles for enhancing the transdermal delivery of Bovine Serum Albumin (MW~66,000 Da)-Fluorescein Isothiocyanate (BSA-FITC) conjugate, a hydrophilic large molecular compound. Moreover, the effect of different formulations was evaluated. The series of binary mixtures composed of propylene glycol (PG) and pH 7.4 phosphate buffer solution (PBS) was prepared and used as a medium for BSA-FITC. The results showed that there was no permeation of BSA-FITC solution across the neonatal porcine skin without using hollow microneedles, whereas the cumulative amount of BSA-FITC released at 8 h through the neonatal porcine skin was about 60-70% when using hollow microneedles. Furthermore, the results demonstrated that the higher volume of PG in binary mixtures injected, the lower cumulative amount of BSA-FITC released and release rate of BSA-FITC from skin. These release profiles of BSA-FITC in binary mixtures were expressed by Fick-s law of diffusion. These results suggest the utilization of hollow microneedle to enhance transdermal delivery of protein and provide useful information for designing an effective hollow microneedle system.

Keywords: Hydrophilic macromolecules, Microneedles, Propylene glycol, Transdermal drug delivery

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Authors: Wei-Jong Yang, Wei-Hau Du, Pau-Choo Chang, Jar-Ferr Yang, Pi-Hsia Hung

Abstract:

The demands of smart visual thing recognition in various devices have been increased rapidly for daily smart production, living and learning systems in recent years. This paper proposed a visual thing recognition system, which combines binary scale-invariant feature transform (SIFT), bag of words model (BoW), and support vector machine (SVM) by using color information. Since the traditional SIFT features and SVM classifiers only use the gray information, color information is still an important feature for visual thing recognition. With color-based SIFT features and SVM, we can discard unreliable matching pairs and increase the robustness of matching tasks. The experimental results show that the proposed object recognition system with color-assistant SIFT SVM classifier achieves higher recognition rate than that with the traditional gray SIFT and SVM classification in various situations.

Keywords: Color moments, visual thing recognition system, SIFT, color SIFT.

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Authors: A. Khelassi, R. Bendib

Abstract:

The paper considers the effect of feed plate location on the interactions in a seven plate binary distillation column. The mathematical model of the distillation column is deduced based on the equations of mass and energy balances for each stage, detailed model for both reboiler and condenser, and heat transfer equations. The Dynamic Relative Magnitude Criterion, DRMC is used to assess the interactions in different feed plate locations for a seven plate (Benzene-Toluene) binary distillation column ( the feed plate is originally at stage 4). The results show that whenever we go far from the optimum feed plate position, the level of interaction augments.

Keywords: Distillation column, assessment of interactions, feedplate location, DRMC.

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Authors: Elsayed A. Habib Elamir

Abstract:

In social network analysis the mean nodal degree and density of the graph can be considered as a measure of the activity of all actors in the network and this is an important property of a graph and for making comparisons among networks. Since subjects in a family or organization are subject to common environment factors, it is prime interest to study the association between responses. Therefore, we study the distribution of the mean nodal degree and density of the graph under correlated binary units. The cross product ratio is used to capture the intra-units association among subjects. Computer program and an application are given to show the benefits of the method.

Keywords: Correlated Binary data, cross product ratio, densityof the graph, multiplicative binomial distribution.

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Authors: Mallappa A. Devani, John U. Kennedy Oubagaranadin, Basudeb Munshi

Abstract:

In this preliminary work, locally available husk of Cajanus cajan (commonly known in India as Tur or Arhar), a bio-waste, has been used in its physically treated and chemically activated form for the removal of binary Cu (II) and Zn(II) ions from the real waste water obtained from an electroplating industry in Bangalore, Karnataka, India and from laboratory prepared binary solutions having almost similar composition of the metal ions, for comparison. The real wastewater after filtration and dilution for five times was used for biosorption studies at the normal pH of the solutions at room temperature. Langmuir's binary model was used to calculate the metal uptake capacities of the biosorbents. It was observed that Cu(II) is more competitive than Zn(II) in biosorption. In individual metal biosorption, Cu(II) uptake was found to be more than that of the Zn(II) and a similar trend was observed in the binary metal biosorption from real wastewater and laboratory prepared solutions. FTIR analysis was carried out to identify the functional groups in the industrial wastewater and EDAX for the elemental analysis of the biosorbents after experiments.

Keywords: Biosorption, Cajanus cajan, multi metal remediation, wastewater.

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Authors: K. Akilandeswari, G. M. Nasira

Abstract:

Brain-Computer Interfaces (BCIs) measure brain signals activity, intentionally and unintentionally induced by users, and provides a communication channel without depending on the brain’s normal peripheral nerves and muscles output pathway. Feature Selection (FS) is a global optimization machine learning problem that reduces features, removes irrelevant and noisy data resulting in acceptable recognition accuracy. It is a vital step affecting pattern recognition system performance. This study presents a new Binary Particle Swarm Optimization (BPSO) based feature selection algorithm. Multi-layer Perceptron Neural Network (MLPNN) classifier with backpropagation training algorithm and Levenberg-Marquardt training algorithm classify selected features.

Keywords: Brain-Computer Interfaces (BCI), Feature Selection (FS), Walsh–Hadamard Transform (WHT), Binary Particle Swarm Optimization (BPSO), Multi-Layer Perceptron (MLP), Levenberg–Marquardt algorithm.

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Authors: Serkan Narlı, Ahmet Z. Ozcelik

Abstract:

The theory of rough sets is generalized by using a filter. The filter is induced by binary relations and it is used to generalize the basic rough set concepts. The knowledge representations and processing of binary relations in the style of rough set theory are investigated.

Keywords: Rough set, fuzzy set, membership function, knowledge representation and processing, information theory

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Authors: Toshihiko Sasama, Takahide Yanaka, Kazunori Sugahara, Hiroshi Masuyama

Abstract:

In order to monitor for traffic traversal, sensors can be deployed to perform collaborative target detection. Such a sensor network achieves a certain level of detection performance with the associated costs of deployment and routing protocol. This paper addresses these two points of sensor deployment and routing algorithm in the situation where the absolute quantity of sensors or total energy becomes insufficient. This discussion on the best deployment system concluded that two kinds of deployments; Normal and Power law distributions, show 6 and 3 times longer than Random distribution in the duration of coverage, respectively. The other discussion on routing algorithm to achieve good performance in each deployment system was also addressed. This discussion concluded that, in place of the traditional algorithm, a new algorithm can extend the time of coverage duration by 4 times in a Normal distribution, and in the circumstance where every deployed sensor operates as a binary model.

Keywords: binary sensor, coverage rate, power energy consumption, routing algorithm, sensor deployment

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Authors: H. Mahboubi, B. Moshiri, A. Khaki Seddigh

Abstract:

Recently, a great amount of interest has been shown in the field of modeling and controlling hybrid systems. One of the efficient and common methods in this area utilizes the mixed logicaldynamical (MLD) systems in the modeling. In this method, the system constraints are transformed into mixed-integer inequalities by defining some logic statements. In this paper, a system containing three tanks is modeled as a nonlinear switched system by using the MLD framework. Comparing the model size of the three-tank system with that of a two-tank system, it is deduced that the number of binary variables, the size of the system and its complexity tremendously increases with the number of tanks, which makes the control of the system more difficult. Therefore, methods should be found which result in fewer mixed-integer inequalities.

Keywords: Hybrid systems, mixed-integer inequalities, mixed logical dynamical systems, multi-tank system.

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Authors: Seema Kapoor, Baljinder K. Gill, V. K. Rattan

Abstract:

Isobaric vapor-liquid equilibrium measurements are reported for the binary mixture of Methyl acetate and Isopropylbenzene at 97.3 kPa. The measurements have been performed using a vapor recirculating type (modified Othmer's) equilibrium still. The mixture shows positive deviation from ideality and does not form an azeotrope. The activity coefficients have been calculated taking into consideration the vapor phase nonideality. The data satisfy the thermodynamic consistency tests of Herington and Black. The activity coefficients have been satisfactorily correlated by means of the Margules, NRTL, and Black equations. A comparison of the values of activity coefficients obtained by experimental data with the UNIFAC model has been made.

Keywords: Binary mixture, Isopropylbenzene, Methyl acetate, Vapor-liquid equilibrium.

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Authors: Mohammad Amin Safi, Mahmud Ashrafizaadeh, Amir Ali Ashrafizaadeh

Abstract:

A highly optimized implementation of binary mixture diffusion with no initial bulk velocity on graphics processors is presented. The lattice Boltzmann model is employed for simulating the binary diffusion of oxygen and nitrogen into each other with different initial concentration distributions. Simulations have been performed using the latest proposed lattice Boltzmann model that satisfies both the indifferentiability principle and the H-theorem for multi-component gas mixtures. Contemporary numerical optimization techniques such as memory alignment and increasing the multiprocessor occupancy are exploited along with some novel optimization strategies to enhance the computational performance on graphics processors using the C for CUDA programming language. Speedup of more than two orders of magnitude over single-core processors is achieved on a variety of Graphical Processing Unit (GPU) devices ranging from conventional graphics cards to advanced, high-end GPUs, while the numerical results are in excellent agreement with the available analytical and numerical data in the literature.

Keywords: Lattice Boltzmann model, Graphical processing unit, Binary mixture diffusion, 2D flow simulations, Optimized algorithm.

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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: Herti Utami, Sutijan, Roto, Wahyudi Budi Sediawan

Abstract:

α-Pinene is the main component of the most turpentine oils. The hydration of α-pinene with acid catalysts leads to a complex mixture of monoterpenes. In order to obtain more valuable products, the α-pinene in the turpentine can be hydrated in dilute mineral acid solutions to produce α-terpineol. The design of separation processes requires information on phase equilibrium and related thermodynamic properties. This paper reports the results of study on liquid-liquid equilibrium (LLE) of system containing α- pinene + water and α-terpineol + water. Binary LLE for α-pinene + water system, and α-terpineol + water systems were determined by experiment at 301K and atmospheric pressure. The two component mixture was stirred for about 30min, then the mixture was left for about 2h for complete phase separation. The composition of both phases was analyzed by using a Gas Chromatograph. The experimental data were correlated by considering both NRTL and UNIQUAC activity coefficient models. The LLE data for the system of α-pinene + water and α-terpineol + water were correlated successfully by the NRTL model. The experimental data were not satisfactorily fitted by the UNIQUAC model. The NRTL model (α =0.3) correlates the LLE data for the system of α-pinene + water at 301K with RMSD of 0.0404%. And the NRTL model (α =0.61) at 301K with RMSD of 0.0058 %. The NRTL model (α =0.3) correlates the LLE data for the system of α- terpineol + water at 301K with RMSD of 0.1487% and the NRTL model (α =0.6) at 301K with RMSD of 0.0032%, between the experimental and calculated mole fractions.

Keywords: α-Pinene, α-Terpineol, Liquid-liquid Equilibrium, NRTL model, UNIQUAC model

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Authors: R. Krishnamoorthi, N. Kannan

Abstract:

In this paper, a new algorithm for generating codebook is proposed for vector quantization (VQ) in image coding. The significant features of the training image vectors are extracted by using the proposed Orthogonal Polynomials based transformation. We propose to generate the codebook by partitioning these feature vectors into a binary tree. Each feature vector at a non-terminal node of the binary tree is directed to one of the two descendants by comparing a single feature associated with that node to a threshold. The binary tree codebook is used for encoding and decoding the feature vectors. In the decoding process the feature vectors are subjected to inverse transformation with the help of basis functions of the proposed Orthogonal Polynomials based transformation to get back the approximated input image training vectors. The results of the proposed coding are compared with the VQ using Discrete Cosine Transform (DCT) and Pairwise Nearest Neighbor (PNN) algorithm. The new algorithm results in a considerable reduction in computation time and provides better reconstructed picture quality.

Keywords: Orthogonal Polynomials, Image Coding, Vector Quantization, TSVQ, Binary Tree Classifier

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Authors: Shagufta Tabassum, V. P. Pawar

Abstract:

The study of static dielectric properties in a binary mixture of 1,2 dichloroethane (DE) and n,n dimethylformamide (DMF) polar liquids has been carried out in the frequency range of 10 MHz to 30 GHz for 11 different concentration using time domain reflectometry technique at 10ºC temperature. The dielectric relaxation study of solute-solvent mixture at microwave frequencies gives information regarding the creation of monomers and multimers as well as interaction between the molecules of the binary mixture. The least squares fit method is used to determine the values of dielectric parameters such as static dielectric constant (ε₀), dielectric constant at high frequency (ε_∞) and relaxation time (τ).

Keywords: Excess parameters, relaxation time, static dielectric constant, time domain reflectometry.

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Authors: Qiong Wang

Abstract:

One of the most important problems to solve is eye location for a driver fatigue monitoring system. This paper presents an efficient method to achieve fast and accurate eye location in grey level images obtained in the real-word driving conditions. The structure of eye region is used as a robust cue to find possible eye pairs. Candidates of eye pair at different scales are selected by finding regions which roughly match with the binary eye pair template. To obtain real one, all the eye pair candidates are then verified by using support vector machines. Finally, eyes are precisely located by using binary vertical projection and eye classifier in eye pair images. The proposed method is robust to deal with illumination changes, moderate rotations, glasses wearing and different eye states. Experimental results demonstrate its effectiveness.

Keywords: eye location, structure feature, driver fatiguemonitoring

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Authors: John Mark Lampos, Virgilio Sison

Abstract:

Two constructions of unit-memory binary convolutional codes from linear block codes over the finite semi-local ring F2r +vF2r , where v2 = v, are presented. In both cases, if the linear block code is systematic, then the resulting convolutional encoder is systematic, minimal, basic and non-catastrophic. The Hamming free distance of the convolutional code is bounded below by the minimum Hamming distance of the block code. New examples of binary convolutional codes that meet the Heller upper bound for systematic codes are given.

Keywords: Convolutional codes, semi-local ring, free distance, Heller bound.

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