Search results for: rating points.

Authors: Niramol Juntarachat, Romain Privat, Jean-Noël Jaubert

Abstract:

In this paper, vapour-liquid critical locus for the binary system acetone + chloroform was determined experimentally over the whole range of composition. The critical property measurements were carried out using a dynamic-synthetic apparatus, employed in the dynamic mode. The critical points are visually determined by observing the critical opalescence and the simultaneous disappearance and reappearance of the meniscus in the middle of a high-pressure view cell which withstands operations up to 673K and 20MPa. The experimental critical points measured in this work were compared to those available in literature.

Keywords: Experimental measurement, critical point, critical locus, negative azeotrope.

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Authors: Safeer Hussain Khan

Abstract:

In this paper, we introduce a two-step iterative algorithm to prove a strong convergence result for approximating common fixed points of three contractive-like operators. Our algorithm basically generalizes an existing algorithm..Our iterative algorithm also contains two famous iterative algorithms: Mann iterative algorithm and Ishikawa iterative algorithm. Thus our result generalizes the corresponding results proved for the above three iterative algorithms to a class of more general operators. At the end, we remark that nothing prevents us to extend our result to the case of the iterative algorithm with error terms.

Keywords: Contractive-like operator, iterative algorithm, fixed point, strong convergence.

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Authors: Qihe Li, Yupin Luo

Abstract:

Camera calibration plays an important role in the domain of the analysis of sports video. Considering soccer video, in most cases, the cross-points can be used for calibration at the center of the soccer field are not sufficient, so this paper introduces a new automatic camera calibration algorithm focus on solving this problem by using the properties of images of the center circle, halfway line and a touch line. After the theoretical analysis, a practicable automatic algorithm is proposed. Very little information used though, results of experiments with both synthetic data and real data show that the algorithm is applicable.

Keywords: Absolute conic, camera calibration, circular points, line at infinity.

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Authors: Barıs Kocer, Ahmet Arslan

Abstract:

Travelling salesman problem (TSP) is a combinational optimization problem and solution approaches have been applied many real world problems. Pure TSP assumes the cities to visit are fixed in time and thus solutions are created to find shortest path according to these point. But some of the points are canceled to visit in time. If the problem is not time crucial it is not important to determine new routing plan but if the points are changing rapidly and time is necessary do decide a new route plan a new approach should be applied in such cases. We developed a route plan transfer method based on transfer learning and we achieved high performance against determining a new model from scratch in every change.

Keywords: genetic algorithms, transfer learning, travellingsalesman problem

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Authors: R. Khaldi, N. Benamrouche, M. Bouheraoua

Abstract:

The ability to predict an accurate temperature distribution requires the knowledge of the losses, the thermal characteristics of the materials, and the cooling conditions, all of which are very difficult to quantify. In this paper, the impact of the effects of iron and copper losses are investigated separately and their effects on the heating in various points of the stator of an induction motor, is highlighted by using two simple tests. In addition, the effect of a defect, such as an open circuit in a phase of the stator, on the heating is also obtained by a no-load test. The squirrel cage induction motor is rated at 2.2 kW; 380 V; 5.2 A; Δ connected; 50 Hz; 1420 rpm and the class of insulation F, has been thermally tested under several load conditions. Several thermocouples were placed in strategic points of the stator.

Keywords: induction motor, temperature, heating, losses

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Authors: Mahmood Reza Shakarami, Reza Sedaghati

Abstract:

Electricity market activities and a growing demand for electricity have led to heavily stressed power systems. This requires operation of the networks closer to their stability limits. Power system operation is affected by stability related problems, leading to unpredictable system behavior. Voltage stability refers to the ability of a power system to sustain appropriate voltage levels through large and small disturbances. Steady-state voltage stability is concerned with limits on the existence of steady-state operating points for the network. FACTS devices can be utilized to increase the transmission capacity, the stability margin and dynamic behavior or serve to ensure improved power quality. Their main capabilities are reactive power compensation, voltage control and power flow control. Among the FACTS controllers, Static Var Compensator (SVC) provides fast acting dynamic reactive compensation for voltage support during contingency events. In this paper, voltage stability assessment with appropriate representations of tap-changer transformers and SVC is investigated. Integrating both of these devices is the main topic of this paper. Effect of the presence of tap-changing transformers on static VAR compensator controller parameters and ratings necessary to stabilize load voltages at certain values are highlighted. The interrelation between transformer off nominal tap ratios and the SVC controller gains and droop slopes and the SVC rating are found. P-V curves are constructed to calculate loadability margins.

Keywords: SVC, voltage stability, P-V curve, reactive power, tap changing transformer.

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Authors: Halil Snopce, Ilir Spahiu, Lavdrim Elmazi

Abstract:

A lot of Scientific and Engineering problems require the solution of large systems of linear equations of the form bAx in an effective manner. LU-Decomposition offers good choices for solving this problem. Our approach is to find the lower bound of processing elements needed for this purpose. Here is used the so called Omega calculus, as a computational method for solving problems via their corresponding Diophantine relation. From the corresponding algorithm is formed a system of linear diophantine equalities using the domain of computation which is given by the set of lattice points inside the polyhedron. Then is run the Mathematica program DiophantineGF.m. This program calculates the generating function from which is possible to find the number of solutions to the system of Diophantine equalities, which in fact gives the lower bound for the number of processors needed for the corresponding algorithm. There is given a mathematical explanation of the problem as well. Keywordsgenerating function, lattice points in polyhedron, lower bound of processor elements, system of Diophantine equationsand : calculus.

Keywords: generating function, lattice points in polyhedron, lower bound of processor elements, system of Diophantine equations and calculus.

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Authors: Mohammad Ali Tabarzad, Caro Lucas, Nassim Jafarzadeh Eslami

Abstract:

After the development of the Internet a suitable discipline for trading goods electronically has been emerged. However, this type of markets is not still mature enough in order to become independent and get closer to seller/buyer-s needs. Furthermore, the buyable and sellable goods in these markets still don-t have essential standards for being well-defined. In this paper, we will present a model for development of a market which can contain goods with variable definitions and we will also investigate its characteristics. Besides, by noticing the fact that people have different discriminations, it-s figured out that the significance of each attribute of a specific product may vary from different people-s view points. Consequently we-ll present a model for weighting and accordingly different people-s view points could be satisfied. These two aspects will be discussed completely throughout this paper.

Keywords: Electronic markets, selection of multi attributegoods, data infusion.

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Authors: Ferenc Kovács, Gábor Hosszú

Abstract:

The paper presents an advanced control system for tennis ball throwing machines to improve their accuracy according to the ball impact points. A further advantage of the system is the much easier calibration process involving the intelligent solution of the automatic adjustment of the stroking parameters according to the ball elasticity, the self-calibration, the use of the safety margin at very flat strokes and the possibility to placing the machine to any position of the half court. The system applies mathematical methods to determine the exact ball trajectories and special approximating processes to access all points on the aimed half court.

Keywords: Control system, robot programming, robot control, sports equipment, throwing machine.

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Authors: Zheng Dian Xun, Cheng Bo, Lin Hetong

Abstract:

This paper focuses on the orbit avoidance strategy of the optical remote sensing satellite. The optical remote sensing satellite, moving along the Sun-synchronous orbit, is equipped with laser warning equipment to alert CCD camera from laser attacks. This paper explores the strategy of satellite avoidance to protect the CCD camera and also the satellite. The satellite could evasive to several target points in the orbital coordinates of virtual satellite. The so-called virtual satellite is a passive vehicle which superposes the satellite at the initial stage of avoidance. The target points share the consistent cycle time and the same semi-major axis with the virtual satellite, which ensures the properties of the satellite’s Sun-synchronous orbit remain unchanged. Moreover, to further strengthen the avoidance capability of satellite, it can perform multi-target-points avoid maneuvers. On occasions of fulfilling the satellite orbit tasks, the orbit can be restored back to virtual satellite through orbit maneuvers. There into, the avoid maneuvers adopts pulse guidance. In addition, the fuel consumption is optimized. The avoidance strategy discussed in this article is applicable to optical remote sensing satellite when it is encountered with hostile attack of space-based laser anti-satellite.

Keywords: Optical remote sensing satellite, satellite avoidance, virtual satellite, avoid target-point, avoid maneuver.

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Authors: Daehwan Kim, Jaemin Kim, Seongwon Cho, Yongsuk Jang, Sun-Tae Chung, Boo-Gyoun Kim

Abstract:

AAM has been successfully applied to face alignment, but its performance is very sensitive to initial values. In case the initial values are a little far distant from the global optimum values, there exists a pretty good possibility that AAM-based face alignment may converge to a local minimum. In this paper, we propose a progressive AAM-based face alignment algorithm which first finds the feature parameter vector fitting the inner facial feature points of the face and later localize the feature points of the whole face using the first information. The proposed progressive AAM-based face alignment algorithm utilizes the fact that the feature points of the inner part of the face are less variant and less affected by the background surrounding the face than those of the outer part (like the chin contour). The proposed algorithm consists of two stages: modeling and relation derivation stage and fitting stage. Modeling and relation derivation stage first needs to construct two AAM models: the inner face AAM model and the whole face AAM model and then derive relation matrix between the inner face AAM parameter vector and the whole face AAM model parameter vector. In the fitting stage, the proposed algorithm aligns face progressively through two phases. In the first phase, the proposed algorithm will find the feature parameter vector fitting the inner facial AAM model into a new input face image, and then in the second phase it localizes the whole facial feature points of the new input face image based on the whole face AAM model using the initial parameter vector estimated from using the inner feature parameter vector obtained in the first phase and the relation matrix obtained in the first stage. Through experiments, it is verified that the proposed progressive AAM-based face alignment algorithm is more robust with respect to pose, illumination, and face background than the conventional basic AAM-based face alignment algorithm.

Keywords: Face Alignment, AAM, facial feature detection, model matching.

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Authors: Hicham Benamirouche, Oum Elkheir Moussi

Abstract:

The purpose of the study is to examine the dynamics of Algeria’s natural gas exports through the Autoregressive Distributed Lag (ARDL) bounds testing approach with break points. The analysis was carried out for the period from 1967 to 2015. Based on imperfect substitution specification, the ARDL approach reveals a long-run equilibrium relationship between Algeria’s Natural gas exports and their determinant factors (Algeria’s gas reserves, Domestic gas consumption, Europe’s GDP per capita, relative prices, the European gas production and the market share of competitors). All the long-run elasticities estimated are statistically significant with a large impact of domestic factors, which constitute the supply constraints. In short term, the elasticities are statistically significant, and almost comparable to those of the long term. Furthermore, the speed of adjustment towards long-run equilibrium is less than one year because of the little flexibility of the long term export contracts. Two break points have been estimated when we employ the domestic gas consumption as a break variable; 1984 and 2010, which reflect the arbitration policy between the domestic gas market and gas exports.

Keywords: Natural gas exports, elasticity, ARDL bounds testing, break points, Algeria.

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Authors: Marc Diesse, Hochschule Heilbronn

Abstract:

We address the question of identifying the configuration space singularities of linkages, i.e., points where the configuration space is not locally a submanifold of Euclidean space. Because the configuration space cannot be smoothly parameterized at such points, these singularity types have a significantly negative impact on the kinematics of the linkage. It is known that Jacobian methods do not provide sufficient conditions for the existence of CS-singularities. Herein, we present several additional algebraic criteria that provide the sufficient conditions. Further, we use those criteria to analyze certain classes of planar linkages. These examples will also show how the presented criteria can be checked using algorithmic methods.

Keywords: Linkages, configuration space singularities, real algebraic geometry, analytic geometry, computer algebra.

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Authors: Chanon Aphirukmatakun, Natasha Dejdumrong

Abstract:

In image processing and visualization, comparing two bitmapped images needs to be compared from their pixels by matching pixel-by-pixel. Consequently, it takes a lot of computational time while the comparison of two vector-based images is significantly faster. Sometimes these raster graphics images can be approximately converted into the vector-based images by various techniques. After conversion, the problem of comparing two raster graphics images can be reduced to the problem of comparing vector graphics images. Hence, the problem of comparing pixel-by-pixel can be reduced to the problem of polynomial comparisons. In computer aided geometric design (CAGD), the vector graphics images are the composition of curves and surfaces. Curves are defined by a sequence of control points and their polynomials. In this paper, the control points will be considerably used to compare curves. The same curves after relocated or rotated are treated to be equivalent while two curves after different scaled are considered to be similar curves. This paper proposed an algorithm for comparing the polynomial curves by using the control points for equivalence and similarity. In addition, the geometric object-oriented database used to keep the curve information has also been defined in XML format for further used in curve comparisons.

Keywords: Bezier curve, Said-Ball curve, Wang-Ball curve, DP curve, CAGD, comparison, geometric object database.

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Authors: Leehter Yao, Kuei-Song Weng, Cherng-Dir Huang

Abstract:

A fuzzy classifier using multiple ellipsoids approximating decision regions for classification is to be designed in this paper. An algorithm called Gustafson-Kessel algorithm (GKA) with an adaptive distance norm based on covariance matrices of prototype data points is adopted to learn the ellipsoids. GKA is able toadapt the distance norm to the underlying distribution of the prototypedata points except that the sizes of ellipsoids need to be determined a priori. To overcome GKA's inability to determine appropriate size ofellipsoid, the genetic algorithm (GA) is applied to learn the size ofellipsoid. With GA combined with GKA, it will be shown in this paper that the proposed method outperforms the benchmark algorithms as well as algorithms in the field.

Keywords: Ellipsoids, genetic algorithm, classification, fuzzyc-means (FCM)

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Authors: M. Kashiripoor

Abstract:

Existing indicators for sustainable urban development do not identify the features of cities’ planning structures and their architecture. Iranian city has special relevance problem of assessing the conformity of their planning and development of the concept of sustainable development. Based on theoretical sources, the author concludes that, despite the existence of common indicators for sustainable development of settlements, specialized evaluation criteria city structure planning has not been developed. He is trying to fill this gap and put forward a system of indicators characterizing the level of development of the architectural-planning structure of the city. The proposed system of indicators is designed based on technical and economic urban standard indicators from different countries. Alternative designing systems and requirements of modern rating systems like LEED-ND comprise a criterion for evaluation of urban structures in accordance with principles of "Green" building and New Urbanism. Urban development trends are close in spirit of sustainable development and developed under its influence. The study allowed concluding that a system of indicators to identify the relevant architectural-planning structure of the city, requirements of sustainable development, should be adapted to the conditions of each country, particularly in Iran. The article attempts typology proposed indicators, which are presented in tabular form and are divided into two types: planning and spatial. This article discusses the known indicators of sustainable development and proposed specific system of indicators characterizing the level of development of architectural-planning structure of the city. This article examines indicators for evaluating level of city' planning structure development. The proposed system of indicators is derived from the urban planning standards and rating systems such as LEED-ND, BREEAM Community and CASBEE-UD.

Keywords: Architectural-planning structure of cities, urban planning indicators, urban space indicators.

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Authors: Hajar Sadeghi, Payman Moallem, S. Amirhassn Monadjemi

Abstract:

This paper presents a new feature based dense stereo matching algorithm to obtain the dense disparity map via dynamic programming. After extraction of some proper features, we use some matching constraints such as epipolar line, disparity limit, ordering and limit of directional derivative of disparity as well. Also, a coarseto- fine multiresolution strategy is used to decrease the search space and therefore increase the accuracy and processing speed. The proposed method links the detected feature points into the chains and compares some of the feature points from different chains, to increase the matching speed. We also employ color stereo matching to increase the accuracy of the algorithm. Then after feature matching, we use the dynamic programming to obtain the dense disparity map. It differs from the classical DP methods in the stereo vision, since it employs sparse disparity map obtained from the feature based matching stage. The DP is also performed further on a scan line, between any matched two feature points on that scan line. Thus our algorithm is truly an optimization method. Our algorithm offers a good trade off in terms of accuracy and computational efficiency. Regarding the results of our experiments, the proposed algorithm increases the accuracy from 20 to 70%, and reduces the running time of the algorithm almost 70%.

Keywords: Chain Correspondence, Color Stereo Matching, Dynamic Programming, Epipolar Line, Stereo Vision.

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Authors: Guixia Lv, Longjun Shen

Abstract:

This paper presents a finite point method based on directional derivatives for diffusion equation on 2D scattered points. To discretize the diffusion operator at a given point, a six-point stencil is derived by employing explicit numerical formulae of directional derivatives, namely, for the point under consideration, only five neighbor points are involved, the number of which is the smallest for discretizing diffusion operator with first-order accuracy. A method for selecting neighbor point set is proposed, which satisfies the solvability condition of numerical derivatives. Some numerical examples are performed to show the good performance of the proposed method.

Keywords: Finite point method, directional derivatives, diffusionequation, method for selecting neighbor point set.

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Authors: K. Chandra Sekaran

Abstract:

This paper describes a paradigmatic approach to develop architecture of secure systems by describing the requirements from four different points of view: that of the owner, the administrator, the user, and the network. Deriving requirements and developing architecture implies the joint elicitation and describing the problem and the structure of the solution. The view points proposed in this paper are those we consider as requirements towards their contributions as major parties in the design, implementation, usage and maintenance of secure systems. The dramatic growth of the technology of Internet and the applications deployed in World Wide Web have lead to the situation where the security has become a very important concern in the development of secure systems. Many security approaches are currently being used in organizations. In spite of the widespread use of many different security solutions, the security remains a problem. It is argued that the approach that is described in this paper for the development of secure architecture is practical by all means. The models representing these multiple points of view are termed the requirements model (views of owner and administrator) and the operations model (views of user and network). In this paper, this multiple view paradigm is explained by first describing the specific requirements and or characteristics of secure systems (particularly in the domain of networks) and the secure architecture / system development methodology.

Keywords: Multiple view paradigms, requirements model, operations model, secure system, owner, administrator, user, network.

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Authors: Souleymane Oumtanaga, Falilu Abudul Kadiri

Abstract:

Internet is without any doubt the fastest and effective mean of communication making it possible to reach a great number of people in the world. It draws its base from exchange points. Indeed exchange points are used to inter-connect various Internet suppliers and operators in order to allow them to exchange traffic and it is with these interconnections that Internet made its great strides. They thus make it possible to limit the traffic delivered via the operators of transits. This limitation allows a significant improvement of the quality of service, a reduction in the latency time just as a reduction of the cost of connection for the final subscriber. Through this article we will show how the installation of an IXP allows an improvement and a diversification of the services just as a reduction of the Internet connection costs.

Keywords: Quality of service, Exchange point, interconnection, Service providers, bandwidth, traffic, routers, routing table.

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Authors: SuGil Choi, SeungWan Han, Chi-Yoon Jeong, TaekYong Nam

Abstract:

This paper proposes a specialized Web robot to automatically collect objectionable Web contents for use in an objectionable Web content classification system, which creates the URL database of objectionable Web contents. It aims at shortening the update period of the DB, increasing the number of URLs in the DB, and enhancing the accuracy of the information in the DB.

Keywords: Web robot, objectionable Web content classification, URL database, URL rating

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Authors: Chansiri Singhtaun

Abstract:

This paper proposes a mathematical model and examines the performance of an exact algorithm for a location– transportation problems in humanitarian relief. The model determines the number and location of distribution centers in a relief network, the amount of relief supplies to be stocked at each distribution center and the vehicles to take the supplies to meet the needs of disaster victims under capacity restriction, transportation and budgetary constraints. The computational experiments are conducted on the various sizes of problems that are generated. Branch and bound algorithm is applied for these problems. The results show that this algorithm can solve problem sizes of up to three candidate locations with five demand points and one candidate location with up to twenty demand points without premature termination.

Keywords: Disaster response, facility location, humanitarian relief, transportation.

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Authors: Adel Bouchakhchoukha, Hakim Akeb

Abstract:

In this work, we propose a hybrid heuristic in order to solve the Team Orienteering Problem (TOP). Given a set of points (or customers), each with associated score (profit or benefit), and a team that has a fixed number of members, the problem to solve is to visit a subset of points in order to maximize the total collected score. Each member performs a tour starting at the start point, visiting distinct customers and the tour terminates at the arrival point. In addition, each point is visited at most once, and the total time in each tour cannot be greater than a given value. The proposed heuristic combines beam search and a local optimization strategy. The algorithm was tested on several sets of instances and encouraging results were obtained.

Keywords: Team Orienteering Problem, Vehicle Routing, Beam Search, Local Search.

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Authors: Reza Mohammadi, Mahdieh Sahebi

Abstract:

We develop a method based on polynomial quintic spline for numerical solution of fourth-order non-homogeneous parabolic partial differential equation with variable coefficient. By using polynomial quintic spline in off-step points in space and finite difference in time directions, we obtained two three level implicit methods. Stability analysis of the presented method has been carried out. We solve four test problems numerically to validate the derived method. Numerical comparison with other methods shows the superiority of presented scheme.

Keywords: Fourth-order parabolic equation, variable coefficient, polynomial quintic spline, off-step points, stability analysis.

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Authors: Kero T., Söderberg R., Andersson M., Lindkvist L.

Abstract:

The introduction of mass-customization has enabled new ways to treat patients within medicine. However, the introduction of industrialized treatments has also meant new obstacles. The purpose of this study was to introduce and theoretically test a method for improving dental crown fit. The optimization method allocates support points in order to check the final variation for dental crowns. Three different types of geometries were tested and compared. The three geometries were also divided into three sub-geometries: Current method, Optimized method and Feasible method. The Optimized method, using the whole surface for support points, provided the best results. The results support the objective of the study. It also seems that the support optimization method can dramatically improve the robustness of dental crown treatments.

Keywords: Bio-medicine, Dentistry, Mass-customization, Optimization and Robust design.

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Authors: Abhijit Mitra, Pranab Kumar Banerjee, C. Ardil

Abstract:

We introduce an effective approach for automatic offline au- thentication of handwritten samples where the forgeries are skillfully done, i.e., the true and forgery sample appearances are almost alike. Subtle details of temporal information used in online verification are not available offline and are also hard to recover robustly. Thus the spatial dynamic information like the pen-tip pressure characteristics are considered, emphasizing on the extraction of low density pixels. The points result from the ballistic rhythm of a genuine signature which a forgery, however skillful that may be, always lacks. Ten effective features, including these low density points and den- sity ratio, are proposed to make the distinction between a true and a forgery sample. An adaptive decision criteria is also derived for better verification judgements.

Keywords: Handwritten document verification, Skilled forgeries, Low density pixels, Adaptive decision boundary.

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Authors: Salam Khalifa, Naveed Ahmed

Abstract:

We present a new method to reconstruct a temporally coherent 3D animation from single or multi-view RGB-D video data using unbiased feature point sampling. Given RGB-D video data, in form of a 3D point cloud sequence, our method first extracts feature points using both color and depth information. In the subsequent steps, these feature points are used to match two 3D point clouds in consecutive frames independent of their resolution. Our new motion vectors based dynamic alignement method then fully reconstruct a spatio-temporally coherent 3D animation. We perform extensive quantitative validation using novel error functions to analyze the results. We show that despite the limiting factors of temporal and spatial noise associated to RGB-D data, it is possible to extract temporal coherence to faithfully reconstruct a temporally coherent 3D animation from RGB-D video data.

Keywords: 3D video, 3D animation, RGB-D video, Temporally Coherent 3D Animation.

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Authors: Xu LiYun, Briand Florent, Fan GuoLiang

Abstract:

The loop-layout design problem (LLDP) aims at optimizing the sequence of positioning of the machines around the cyclic production line. Traffic congestion is the usual criteria to minimize in this type of problem, i.e. the number of additional cycles spent by each part in the network until the completion of its required routing sequence of machines. This paper aims at applying several improvements mechanisms such as a positioned-based crossover operator for the Genetic Algorithm (GA) called a Two Points Crossover (TPC) and an offspring selection process. The performance of the improved GA is measured using well-known examples from literature and compared to other evolutionary algorithms. Good results show that GA can still be competitive for this type of problem against more recent evolutionary algorithms.

Keywords: Crossover, genetic algorithm, layout design problem, loop-layout, manufacturing optimization.

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Authors: Domingo López-Rodríguez, Enrique Mérida-Casermeiro, Juan M. Ortiz-de-Lazcano-Lobato

Abstract:

Hopfield model of associative memory is studied in this work. In particular, two main problems that it possesses: the apparition of spurious patterns in the learning phase, implying the well-known effect of storing the opposite pattern, and the problem of its reduced capacity, meaning that it is not possible to store a great amount of patterns without increasing the error probability in the retrieving phase. In this paper, a method to avoid spurious patterns is presented and studied, and an explanation of the previously mentioned effect is given. Another technique to increase the capacity of a network is proposed here, based on the idea of using several reference points when storing patterns. It is studied in depth, and an explicit formula for the capacity of the network with this technique is provided.

Keywords: Associative memory, Hopfield network, network capacity, spurious patterns.

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Authors: Srijanani Anurag Prasad

Abstract:

The Coalescence Hidden-variable Fractal Interpolation Surface (CHFIS) was built by combining interpolation data from the Iterated Function System (IFS). The interpolation data in a CHFIS comprise a row and/or column of uncertain values when a single point is entered. Alternatively, a row and/or column of additional points are placed in the given interpolation data to demonstrate the node added CHFIS. There are three techniques for inserting new points that correspond to the row and/or column of nodes inserted, and each method is further classified into four types based on the values of the inserted nodes. As a result, numerous forms of node insertion can be found in a CHFIS.

Keywords: Fractal, interpolation, iterated function system, coalescence, node insertion, knot insertion.

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