Search results for: Interhemispheric conjugate points

Authors: Jing Li, Quan Pan, Stan. Z. Li, Tao Yang

Abstract:

A novel algorithm for construct a seamless video mosaic of the entire panorama continuously by automatically analyzing and managing feature points, including management of quantity and quality, from the sequence is presented. Since a video contains significant redundancy, so that not all consecutive video images are required to create a mosaic. Only some key images need to be selected. Meanwhile, feature-based methods for mosaicing rely on correction of feature points? correspondence deeply, and if the key images have large frame interval, the mosaic will often be interrupted by the scarcity of corresponding feature points. A unique character of the method is its ability to handle all the problems above in video mosaicing. Experiments have been performed under various conditions, the results show that our method could achieve fast and accurate video mosaic construction. Keywords?video mosaic, feature points management, homography estimation.

Keywords: Video mosaic, feature points management, homography estimation.

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Authors: O. Poleshchuk, E. Komarov

Abstract:

The paper presents the method developed to assess rating points of objects with qualitative indexes. The novelty of the method lies in the fact that the authors use linguistic scales that allow to formalize the values of the indexes with the help of fuzzy sets. As a result it is possible to operate correctly with dissimilar indexes on the unified basis and to get stable final results. The obtained rating points are used in decision making based on fuzzy expert opinions.

Keywords: complete orthogonal semantic space, qualitativecharacteristic, rating points.

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Authors: Ahmet Tekcan

Abstract:

Let p ≥ 5 be a prime number and let Fp be a finite field. In this work, we determine the number of rational points on singular curves Ea : y2 = x(x - a)2 over Fp for some specific values of a.

Keywords: Singular curve, elliptic curve, rational points.

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Authors: Maria Hussin, Malik Zawwar Hussain, Mubashrah Saddiqa

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We present a trigonometric scheme to approximate a circular arc with its two end points and two end tangents/unit tangents. A rational cubic trigonometric Bézier curve is constructed whose end control points are defined by the end points of the circular arc. Weight functions and the remaining control points of the cubic trigonometric Bézier curve are estimated by variational approach to reproduce a circular arc. The radius error is calculated and found less than the existing techniques.

Keywords: Control points, rational trigonometric Bézier curves, radius error, shape measure, weight functions.

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Authors: Rachid Ahdid, Khaddouj Taifi, Said Safi, Bouzid Manaut

Abstract:

Automatic detection of facial feature points plays an important role in applications such as facial feature tracking, human-machine interaction and face recognition. The majority of facial feature points detection methods using two-dimensional or three-dimensional data are covered in existing survey papers. In this article chosen approaches to the facial features detection have been gathered and described. This overview focuses on the class of researches exploiting facial feature points detection to represent facial surface for two-dimensional or three-dimensional face. In the conclusion, we discusses advantages and disadvantages of the presented algorithms.

Keywords: Facial feature points, face recognition, facial feature tracking, two-dimensional data, three-dimensional data.

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Authors: Vitaliy Tayanov

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In this paper we present the algorithm which allows us to have an object tracking close to real time in Full HD videos. The frame rate (FR) of a video stream is considered to be between 5 and 30 frames per second. The real time track building will be achieved if the algorithm can follow 5 or more frames per second. The principle idea is to use fast algorithms when doing preprocessing to obtain the key points and track them after. The procedure of matching points during assignment is hardly dependent on the number of points. Because of this we have to limit pointed number of points using the most informative of them.

Keywords: video tracking, real-time, Hungarian algorithm, Full HD video.

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Authors: Muhammad F. Yaqub, Iqbal Gondal, Joarder Kamruzzaman

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Occurrence of a multiple-points fault in machine operations could result in exhibiting complex fault signatures, which could result in lowering fault diagnosis accuracy. In this study, a multiple-points defect model (MPDM) is proposed which can simulate fault signature-s dynamics for n-points bearing faults. Furthermore, this study identifies that in case of multiple-points fault in the rotary machine, the location of the dominant component of defect frequency shifts depending upon the relative location of the fault points which could mislead the fault diagnostic model to inaccurate detections. Analytical and experimental results are presented to characterize and validate the variation in the dominant component of defect frequency. Based on envelop detection analysis, a modification is recommended in the existing fault diagnostic models to consider the multiples of defect frequency rather than only considering the frequency spectrum at the defect frequency in order to incorporate the impact of multiple points fault.

Keywords: Envelop detection, machine defect frequency, multiple faults, machine health monitoring.

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Authors: Yi Xu, Zexiang Li

Abstract:

In inspection and workpiece localization, sampling point data is an important issue. Since the devices for sampling only sample discrete points, not the completely surface, sampling size and location of the points will be taken into consideration. In this paper a method is presented for determining the sampled points size and location for achieving efficient sampling. Firstly, uncertainty analysis of the localization parameters is investigated. A localization uncertainty model is developed to predict the uncertainty of the localization process. Using this model the minimum size of the sampled points is predicted. Secondly, based on the algebra theory an eigenvalue-optimal optimization is proposed. Then a freeform surface is used in the simulation. The proposed optimization is implemented. The simulation result shows its effectivity.

Keywords: eigenvalue-optimal optimization, freeform surface inspection, sampling size and location, sampled points.

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Authors: V.Rezaie, M.Khanmohammady

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An original DEA model is to evaluate each DMU optimistically, but the interval DEA Model proposed in this paper has been formulated to obtain an efficiency interval consisting of Evaluations from both the optimistic and the pessimistic view points. DMUs are improved so that their lower bounds become so large as to attain the maximum Value one. The points obtained by this method are called ideal points. Ideal PPS is calculated by ideal of efficiency DMUs. The purpose of this paper is to rank DMUs by this ideal PPS. Finally we extend the efficiency interval of a DMU under variable RTS technology.

Keywords: Data envelopment analysis (DEA), Decision makingunit (DMU), Interval DEA, Ideal points, Ideal PPS, Return to scale(RTS).

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Authors: Hiroaki Hirose, Hiroshi Ikeda, Isao Takeda

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The Japanese version of the SF-36 has been employed to assess individuals’ health-related QOL (HRQOL). This study aimed to clarify the HRQOL of motorists with a spinal cord injury, in order to compare these individuals' SF-36 scores and national standard values. A total of 100 motorists with a spinal cord injury participated in this study. Participants’ HRQOL was evaluated using the Japanese version of the SF-36 (second edition). The score for each subscale was standardized based on data on the Japanese population. The average scores for NPF, NRP, NBP, NGH, NVT, NSF, NRE, and NMH were 10.9, 41.8, 45.9, 47.1, 46.1, 46.7, 46.0, and 47.4 points, respectively. Subjects showed significantly lower scores for NPF and NRP compared with national standard values, which were both ≤ 45.0 points, but relatively normal scores for the other items: NBP, NGH, NVT, NSF, NRE and NMH (> 45.0 points). The average scores for PCS, MCS and RCS were 21.9, 56.0, and 50.0 points, respectively. Subjects showed a significantly lower PCS score (≤ 20.0 points); however, the MCS score was higher (> 55.0 points) along with a relatively normal RCS score in these individuals (= 50.0 points).

Keywords: Health-related QOL (HRQOL), SF-36, motorist, spinal cord injury, Japan.

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Authors: Xi Pei, Ruifen Cao, Hui Liu, Chufeng Jin, Mengyun Cheng, Huaqing Zheng, Yican Wu, FDS Team

Abstract:

In intensity modulated radiation therapy (IMRT) treatment planning, beam angles are usually preselected on the basis of experience and intuition. Therefore, getting an appropriate beam configuration needs a very long time. Based on the present situation, the paper puts forward beam orientation optimization using ant colony optimization (ACO). We use ant colony optimization to select the beam configurations, after getting the beam configuration using Conjugate Gradient (CG) algorithm to optimize the intensity profiles. Combining with the information of the effect of pencil beam, we can get the global optimal solution accelerating. In order to verify the feasibility of the presented method, a simulated and clinical case was tested, compared with dose-volume histogram and isodose line between target area and organ at risk. The results showed that the effect was improved after optimizing beam configurations. The optimization approach could make treatment planning meet clinical requirements more efficiently, so it had extensive application perspective.

Keywords: intensity modulated radiation therapy, ant colonyoptimization, Conjugate Gradient algorithm

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Authors: A. Jamal, M. A. I. El-Shaarawi, E. M. A. Mokheimer

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Combined conduction-free convection heat transfer in vertical eccentric annuli is numerically investigated using a finitedifference technique. Numerical results, representing the heat transfer parameters such as annulus walls temperature, heat flux, and heat absorbed in the developing region of the annulus, are presented for a Newtonian fluid of Prandtl number 0.7, fluid-annulus radius ratio 0.5, solid-fluid thermal conductivity ratio 10, inner and outer wall dimensionless thicknesses 0.1 and 0.2, respectively, and dimensionless eccentricities 0.1, 0.3, 0.5, and 0.7. The annulus walls are subjected to thermal boundary conditions, which are obtained by heating one wall isothermally whereas keeping the other wall at inlet fluid temperature. In the present paper, the annulus heights required to achieve thermal full development for prescribed eccentricities are obtained. Furthermore, the variation in the height of thermal full development as function of the geometrical parameter, i.e., eccentricity is also investigated.

Keywords: Conjugate natural convection, eccentricity, heat transfer, vertical eccentric annuli.

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Authors: Musa Demirci, Nazlı Yıldız İkikardeş, Gökhan Soydan, İsmail Naci Cangül

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In this work, we consider the rational points on elliptic curves over finite fields Fp. We give results concerning the number of points Np,a on the elliptic curve y2 ≡ x3 +a3(mod p) according to whether a and x are quadratic residues or non-residues. We use two lemmas to prove the main results first of which gives the list of primes for which -1 is a quadratic residue, and the second is a result from [1]. We get the results in the case where p is a prime congruent to 5 modulo 6, while when p is a prime congruent to 1 modulo 6, there seems to be no regularity for Np,a.

Keywords: Elliptic curves over finite fields, rational points, quadratic residue.

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Authors: Svetlana Pushkar

Abstract:

The Leadership in Energy and Environmental Design (LEED) green building rating system is recognized in Europe. LEED uses regional priority (RP) points that are adapted to different environmental conditions. However, the appropriateness of the RP points is still a controversial question. To clarify this issue, two different parts of Europe: northern Europe (Finland and Sweden) and southern Europe (Turkey and Spain) were considered. Similarities and differences in the performances of LEED 2009-new construction (LEED-NC 2009) in these four countries were analyzed. It was found that LEED-NC 2009 performances in northern and southern parts of Europe in terms of Sustainable Sites (SS), Water Efficiency (WE), Materials and Resources (MR), and Indoor Environmental Quality (EQ) were similar, whereas in Energy and Atmosphere (EA), their performances were different. WE and SS revealed high performances (70-100%); EA and EQ demonstrated intermediate performance (40-60%); and MR displayed low performance (20-40%). It should be recommended introducing the following new RP points: for Turkey - water-related points and for all four observed countries - green power-related points for improving the LEED adaptation in Europe.

Keywords: Green building, Europe, LEED, regional priority points.

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Authors: Boonyarat Chaleephay

Abstract:

The purpose of this research paper was to describe the relationship of acupressure points on the anterior surface of the upper limb in accordance with Applied Thai Traditional Massage (ATTM) and the deep structures located at those acupressure points. There were 2 population groups; normal subjects and cadaver specimens. Eighteen males with age ranging from 20-40 years old and seventeen females with ages ranging from 30-97 years old were studies. This study was able to obtain a fundamental knowledge concerning acupressure point and the deep structures that related to those acupressure points. It might be used as the basic knowledge for clinically applying and planning treatment as well as teaching in ATTM.

Keywords: Acupressure point (AP), Applie Thai Traditional Medicine (ATTM), Paresthesia, Numbness.

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Authors: Ahmet Tekcan

Abstract:

Let p be a prime number, Fp be a finite field and t ∈ F*p= Fp- {0}. In this paper we obtain some properties of ellipticcurves Ep,t: y2= y2= x3- t2x over Fp. In the first sectionwe give some notations and preliminaries from elliptic curves. In the second section we consider the rational points (x, y) on Ep,t. Wegive a formula for the number of rational points on Ep,t over Fnp for an integer n ≥ 1. We also give some formulas for the sum of x?andy?coordinates of the points (x, y) on Ep,t. In the third section weconsider the rank of Et: y2= x3- t2x and its 2-isogenous curve Et over Q. We proved that the rank of Etand Etis 2 over Q. In the last section we obtain some formulas for the sums Σt∈F?panp,t for an integer n ≥ 1, where ap,t denote the trace of Frobenius.

Keywords: Elliptic curves over finite fields, rational points onelliptic curves, rank, trace of Frobenius.

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Authors: К. R. Aida–Zade, C. Ardil, S. S. Rustamov

Abstract:

Statement of the automatic speech recognition problem, the assignment of speech recognition and the application fields are shown in the paper. At the same time as Azerbaijan speech, the establishment principles of speech recognition system and the problems arising in the system are investigated. The computing algorithms of speech features, being the main part of speech recognition system, are analyzed. From this point of view, the determination algorithms of Mel Frequency Cepstral Coefficients (MFCC) and Linear Predictive Coding (LPC) coefficients expressing the basic speech features are developed. Combined use of cepstrals of MFCC and LPC in speech recognition system is suggested to improve the reliability of speech recognition system. To this end, the recognition system is divided into MFCC and LPC-based recognition subsystems. The training and recognition processes are realized in both subsystems separately, and recognition system gets the decision being the same results of each subsystems. This results in decrease of error rate during recognition. The training and recognition processes are realized by artificial neural networks in the automatic speech recognition system. The neural networks are trained by the conjugate gradient method. In the paper the problems observed by the number of speech features at training the neural networks of MFCC and LPC-based speech recognition subsystems are investigated. The variety of results of neural networks trained from different initial points in training process is analyzed. Methodology of combined use of neural networks trained from different initial points in speech recognition system is suggested to improve the reliability of recognition system and increase the recognition quality, and obtained practical results are shown.

Keywords: Speech recognition, cepstral analysis, Voice activation detection algorithm, Mel Frequency Cepstral Coefficients, features of speech, Cepstral Mean Subtraction, neural networks, Linear Predictive Coding.

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Authors: Sanjib Kr Pal, S. Bhattacharyya

Abstract:

Mixed convection of Cu-water nanofluid in an enclosure with thick wavy bottom wall has been investigated numerically. A co-ordinate transformation method is used to transform the computational domain into an orthogonal co-ordinate system. The governing equations in the computational domain are solved through a pressure correction based iterative algorithm. The fluid flow and heat transfer characteristics are analyzed for a wide range of Richardson number (0.1 ≤ Ri ≤ 5), nanoparticle volume concentration (0.0 ≤ ϕ ≤ 0.2), amplitude (0.0 ≤ α ≤ 0.1) of the wavy thick- bottom wall and the wave number (ω) at a fixed Reynolds number. Obtained results showed that heat transfer rate increases remarkably by adding the nanoparticles. Heat transfer rate is dependent on the wavy wall amplitude and wave number and decreases with increasing Richardson number for fixed amplitude and wave number. The Bejan number and the entropy generation are determined to analyze the thermodynamic optimization of the mixed convection.

Keywords: Entropy generation, mixed convection, conjugate heat transfer, numerical, nanofluid, wall waviness.

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Authors: Neelam Bawane nee' Singhal, C. V. Srikrishna

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Many metrics were proposed to evaluate the characteristics of the analysis and design model of a given product which in turn help to assess the quality of the product. Function point metric is a measure of the 'functionality' delivery by the software. This paper presents an analysis of a set of programs of a project developed in Cµ through Function Points metric. Function points are measured for a Data Flow Diagram (DFD) of the case developed at initial stage. Lines of Codes (LOCs) and possible errors are calculated with the help of measured Function Points (FPs). The calculations are performed using suitable established functions. Calculated LOCs and errors are compared with actual LOCs and errors found at the time of analysis & design review, implementation and testing. It has been observed that actual found errors are more than calculated errors. On the basis of analysis and observations, authors conclude that function point provides useful insight and helps to analyze the drawbacks in the development process.

Keywords: Function Points, Data Flow Diagram, Lines ofCodes.

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Authors: Ali Mohammadi Torkashvand, Hamid Reza Alipour

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This study investigates the possibility providing gully erosion map by the supervised classification of satellite images (ETM+) in two mountainous and plain land types. These land types were the part of Varamin plain, Tehran province, and Roodbar subbasin, Guilan province, as plain and mountain land types, respectively. The position of 652 and 124 ground control points were recorded by GPS respectively in mountain and plain land types. Soil gully erosion, land uses or plant covers were investigated in these points. Regarding ground control points and auxiliary points, training points of gully erosion and other surface features were introduced to software (Ilwis 3.3 Academic). The supervised classified map of gully erosion was prepared by maximum likelihood method and then, overall accuracy of this map was computed. Results showed that the possibility supervised classification of gully erosion isn-t possible, although it need more studies for results generalization to other mountainous regions. Also, with increasing land uses and other surface features in plain physiography, it decreases the classification of accuracy.

Keywords: Supervised classification, Gully erosion, Map.

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Authors: Hadi Seyedarabi, Ali Aghagolzadeh, Sohrab Khanmohammadi

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Face and facial expressions play essential roles in interpersonal communication. Most of the current works on the facial expression recognition attempt to recognize a small set of the prototypic expressions such as happy, surprise, anger, sad, disgust and fear. However the most of the human emotions are communicated by changes in one or two of discrete features. In this paper, we develop a facial expressions synthesis system, based on the facial characteristic points (FCP's) tracking in the frontal image sequences. Selected FCP's are automatically tracked using a crosscorrelation based optical flow. The proposed synthesis system uses a simple deformable facial features model with a few set of control points that can be tracked in original facial image sequences.

Keywords: Deformable face model, facial animation, facialcharacteristic points, optical flow.

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Authors: Sanghoon Kim, Sun-Tae Chung, Souhwan Jung, Seoungseon Jeon, Jaemin Kim, Seongwon Cho

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In this paper, we propose a face recognition algorithm using AAM and Gabor features. Gabor feature vectors which are well known to be robust with respect to small variations of shape, scaling, rotation, distortion, illumination and poses in images are popularly employed for feature vectors for many object detection and recognition algorithms. EBGM, which is prominent among face recognition algorithms employing Gabor feature vectors, requires localization of facial feature points where Gabor feature vectors are extracted. However, localization method employed in EBGM is based on Gabor jet similarity and is sensitive to initial values. Wrong localization of facial feature points affects face recognition rate. AAM is known to be successfully applied to localization of facial feature points. In this paper, we devise a facial feature point localization method which first roughly estimate facial feature points using AAM and refine facial feature points using Gabor jet similarity-based facial feature localization method with initial points set by the rough facial feature points obtained from AAM, and propose a face recognition algorithm using the devised localization method for facial feature localization and Gabor feature vectors. It is observed through experiments that such a cascaded localization method based on both AAM and Gabor jet similarity is more robust than the localization method based on only Gabor jet similarity. Also, it is shown that the proposed face recognition algorithm using this devised localization method and Gabor feature vectors performs better than the conventional face recognition algorithm using Gabor jet similarity-based localization method and Gabor feature vectors like EBGM.

Keywords: Face Recognition, AAM, Gabor features, EBGM.

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Authors: Said M. Easa, Ahmed Shaker

Abstract:

The hidden-point bar method is useful in many surveying applications. The method involves determining the coordinates of a hidden point as a function of horizontal and vertical angles measured to three fixed points on the bar. Using these measurements, the procedure involves calculating the slant angles, the distances from the station to the fixed points, the coordinates of the fixed points, and then the coordinates of the hidden point. The propagation of the measurement errors in this complex process has not been fully investigated in the literature. This paper evaluates the effect of the bar geometry on the position accuracy of the hidden point which depends on the measurement errors of the horizontal and vertical angles. The results are used to establish some guidelines regarding the inclination angle of the bar and the location of the observed points that provide the best accuracy.

Keywords: Hidden point, accuracy, error propagation, surveying, evaluation, simulation, geometry.

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Authors: Sujit Kumar Sardar Manasi Mandal Samit Kumar Majumder

Abstract:

The notion of intuitionistic fuzzy sets was introduced by Atanassov as a generalization of the notion of fuzzy sets. Y.B. Jun and S.Z. Song introduced the notion of intuitionistic fuzzy points. In this paper we find some relations between the intuitionistic fuzzy ideals of a semigroup S and the set of all intuitionistic fuzzy points of S.

Keywords: Semigroup, Regular(intra-regular) semigroup, Intuitionistic fuzzy point, Intuitionistic fuzzy subsemigroup, Intuitionistic fuzzy ideal, Intuitionistic fuzzy interior ideal, Intuitionistic fuzzy semiprime ideal, Intuitionistic fuzzy prime ideal.

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Authors: Seongchan Kang, Hongsik Yun, Hyukgil Kim, Minwoo Park

Abstract:

For this study, this researcher conducted a precision network adjustment with QOCA, the precision network adjustment software developed by Jet Propulsion Laboratory, to perform an integrated network adjustment on the Unified Control Points managed by the National Geographic Information Institute. Towards this end, 275 Unified Control Points observed in 2008 were selected before a network adjustment is performed on those 275 Unified Control Points. The RMSE on the discrepancies of coordinates as compared to the results of GLOBK was ±6.07mm along the N axis, ±2.68mm along the E axis and ±6.49mm along the U axis.

Keywords: Network adjustment, QOCA, unified control point.

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Authors: Benshi Zhu

Abstract:

In this paper, multiple positive solutions for semipositone discrete eigenvalue problems are obtained by using a three critical points theorem for nondifferentiable functional.

Keywords: Discrete eigenvalue problems, positive solutions, semipositone, three critical points theorem

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Authors: Abdulrahman S. Alturki, John S. Loomis

Abstract:

This paper discusses a corner detection algorithm for camera calibration. Calibration is a necessary step in many computer vision and image processing applications. Robust corner detection for an image of a checkerboard is required to determine intrinsic and extrinsic parameters. In this paper, an algorithm for fully automatic and robust X-corner detection is presented. Checkerboard corner points are automatically found in each image without user interaction or any prior information regarding the number of rows or columns. The approach represents each X-corner with a quadratic fitting function. Using the fact that the X-corners are saddle points, the coefficients in the fitting function are used to identify each corner location. The automation of this process greatly simplifies calibration. Our method is robust against noise and different camera orientations. Experimental analysis shows the accuracy of our method using actual images acquired at different camera locations and orientations.

Keywords: Camera Calibration, Corner Detector, Saddle Points, X-Corners.

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Authors: Md. Zahangir Alom, Mei-Lan Piao, Md. Shariful Islam, Nam Kim, Jae-Hyeung Park

Abstract:

The evaluation and measurement of human body dimensions are achieved by physical anthropometry. This research was conducted in view of the importance of anthropometric indices of the face in forensic medicine, surgery, and medical imaging. The main goal of this research is to optimization of facial feature point by establishing a mathematical relationship among facial features and used optimize feature points for age classification. Since selected facial feature points are located to the area of mouth, nose, eyes and eyebrow on facial images, all desire facial feature points are extracted accurately. According this proposes method; sixteen Euclidean distances are calculated from the eighteen selected facial feature points vertically as well as horizontally. The mathematical relationships among horizontal and vertical distances are established. Moreover, it is also discovered that distances of the facial feature follows a constant ratio due to age progression. The distances between the specified features points increase with respect the age progression of a human from his or her childhood but the ratio of the distances does not change (d = 1 .618 ) . Finally, according to the proposed mathematical relationship four independent feature distances related to eight feature points are selected from sixteen distances and eighteen feature point-s respectively. These four feature distances are used for classification of age using Support Vector Machine (SVM)-Sequential Minimal Optimization (SMO) algorithm and shown around 96 % accuracy. Experiment result shows the proposed system is effective and accurate for age classification.

Keywords: 3D Face Model, Face Anthropometrics, Facial Features Extraction, Feature distances, SVM-SMO

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Authors: Ahmet Tekcan, Arzu Özkoç, Hatice Alkan

Abstract:

In this work, we consider the number of integer solutions of Diophantine equation D : y2 - 2yx - 3 = 0 over Z and also over finite fields Fp for primes p ≥ 5. Later we determine the number of rational points on curves Ep : y2 = Pp(x) = yp 1 + yp 2 over Fp, where y1 and y2 are the roots of D. Also we give a formula for the sum of x- and y-coordinates of all rational points (x, y) on Ep over Fp.

Keywords: Diophantine equation, Pell equation, quadratic form.

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Authors: Nitima Aschariyaphotha, Pratan Sakkaplangkul, Anirut Luadsong

Abstract:

The study of the Andaman Sea can be studied by using the oceanic model; therefore the grid covering the study area should be generated. This research aims to generate grid covering the Andaman Sea, situated between longitudes 90◦E to 101◦E and latitudes 1◦N to 18◦N. A horizontal grid is an orthogonal curvilinear with 87 × 217 grid points. The methods used in this study are cubic spline and bilinear interpolations. The boundary grid points are generated by spline interpolation while the interior grid points have to be specified by bilinear interpolation method. A vertical grid is sigma coordinate with 15 layers of water column.

Keywords: Sigma Coordinate, Curvilinear Coordinate, AndamanSea.

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