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Энэ илтгэлд бид тэг биш g(x)-тэй (1) системийг авч үзэх замаар [8]-д олж авсан үр дүнг өргөтгөсөн болно. Бид f(x) ба g(x) коэффициент функцүүдийн хоорондын хамаарлыг судалж, Ли бүлгийн бүрэн ангиллыг болон (1)-ийн инфинитесимал симметрүүдээр үүсгэгдсэн Ли алгебруудын бүтцийг тодорхойлсон. Үүний үр дүнд бид харгалзах оптимал системүүд болон ердийн дифференциал тэгшитгэлийн reduced системийг гаргаж авсан. Цаашлаад Миттаг-Леффлерийн функц, өргөтгөсөн Райттын функц, Фокс-Н функц зэрэг тусгай функцүүдээр reduced ердийн дифференциал тэгшитгэлийн шийдүүдийг тодорхой өгсөн. Эндээс эдгээр шийдүүдийг ашиглан бид (1) системийн бүлгийн инвариант шийдүүдийг илэрхийлсэн болно.
Fast and efficient integer factorization algorithms are crucial in analyzing, designing and breaking cryptographic schemes. In this paper, we propose an efficient algorithm for counting the non-trivial as well as trivial solutions.
Spatial tracking technologies are necessary to design usable 3D (three-dimensional) user interfaces. Traditionally, 6-DOF (degree of freedom) trackers are widely used in 3D user interfaces by detecting the 3D location and orientation of the object. Conventionally, 3D user interfaces extracted from image sequences require additional devices for their 3D input to sense 3D motion. In this regard, our approach to converting motion parameters into 3D input using a monocular camera is unique. In this study, we introduce the development of 3D input through 6-DOF motion estimations. Finally, 3D input could be provided through motion estimations using a monocular camera. To improve existing motion estimations, they could be applied in real-time to provide 3D input of 3D interaction. They were robust to provide 3D input. Keywords: 3D input, 3D user interface, motion estimation, 6-DOF
Last decades, selecting for optimal location of a new organization has been an essential component in all kinds of businesses, including manufacturing and service organizations. The most significant difficulty to address the location selection problems is finding how to measure the considered criteria. Multicriteria decision-making (MCDM) methods are most suitable for solving the facility location selection problems for these reasons. In this work, we applied AHP, PROMETHEE, and TOPSIS methods of the MCDM technique. When we are employing these methods to solve location selection problems of one organization, these methods prove their applicability to deal with such types of decision-making problems with multiple criteria and facility alternatives.
Сүүлийн жилүүдэд төрийн болон хувийн бүх төрлийн бизнес, тэр дундаа үйлдвэрлэл, үйлчилгээний байгууллагуудын хувьд байршлыг зохистой сонгох хэрэгцээ шаардлага маш их болсон байна. Байгууламжийн байршлын оновчтой шийдвэр гаргахын тулд олон шалгуурт шийдвэр гаргах (Multi Criteria Decision making-MCDM) техникийн төрлүүд болох AHP, PROMETHEE, TOPSIS аргуудыг дэлхийн улс орнуудад хот болон бүс нутагтаа хэрэглэж байгааг олон судалгааны ажлуудад харуулжээ. Энэхүү судалгааны ажлаар бид эдгээр аргуудыг ашиглан нэгэн байгууллагын хувьд хэрэгцээт байгууламжаа өөрийн сонгосон хувилбаруудаас оновчтой сонгоход тусалсан үр дүнг гаргаж, аргуудын харьцуулалт хийж харуулсан болно.
This study presents Kalman filtering based motion correction. Motion of a moving object in image sequences is estimated from phase correlation that is applied to sub-images. To smooth noisy motion, characterized as translation, rotation and scale, Kalman filtering was applied after phase correlation. Experimentally, we observed that Kalman filtered rotation and scale were comparatively lower than originally estimated values. Also, Kalman filtered rotation and scale parameters considerably improved the visual appearance of tracking in the real scene.
We aimed a tracking algorithm which works robustly in the presence of large scale, rotation, and translation of a moving object. To recover 2D rotation and scale between an object in a template and an object in next frames of the video sequence, we applied the phase correlation method as frequency matching. Since the changes in scale and rotation in the Cartesian coordinates are transformed into translations in log-polar coordinate system, we applied frequency matching in log-polar domain. Translation motion is acquired through template matching technique by dynamically updating template for each frame based on feature matching. An original method for motion estimation in frequency domain was mostly introduced in image registration task [1-5]. We introduced our algorithm different from previous applications. The original method had limitations in that a sub-image was selected for every position in the target image and was compared against the sub-image from template. We overcome this problem by combining feature matching into frequency matching. The proposed method finds the feature correspondences in the template and subsequence frames. Feature points are used to reduce the computational time. Results, experiments, and test datasets to check accuracy of the estimated motion parameters from the proposed method is presented.
Active contour models with fractional order derivative has studied in last few years due to the object detection becoming more accurate than integer order derivative. In this work, we consider the energy functional consists of two terms : fitting term and regularization term. Fractional order fitting term and global fitting term can describe the original image more accurately. We use Grunwald-Letnikov fractional order differentiation. Moreover, we present the two-dimensional fractional order differentiation, that was acquired through the extension of the one-dimensional fractional order differentiation. Finally, we present some experimental results which are compared to base model with integer order derivative.
While working with a three dimensional (3D) user interface, professional users can interact with virtual 3D space in more intuitive way by positioning their 3D model or viewing, and providing access to their favorite applications than with a 2D mouse. To contribute its importance, we review approaches for providing input of 3D user interface by determining motion of a moving object in image sequences taken by a single camera without using additional devices to sense 3D motion. We also summarized technical and application difference between estimation approaches of the object motion in frequency and spatial domain. In frequency domain, we proposed a method for providing inputs of 3D interaction between physical and virtual 3D space based on log-polar transformation and phase correlation using two dimensional (2D) to 2D point correspondences. The estimated motion parameters were providing four degrees of freedom (4-DOF) input to the interaction system. In spatial domain, firstly, the relative pose estimation methods developed in computer vision and photogrammetric field was carried out. We implemented approaches for 3D motion estimation in both fields by using 2D to 2D point correspondences, and performed an analysis for their results. The estimated motion parameters were providing up to 6-DOF input to the interaction system. In spatial domain, secondly, we present an approach for providing input of 3D interaction by determining 3D motion of an object based on 2D to 3D point correspondences. To estimate motion parameters as characterized by 3D rotation and 3D translation, non-linear equations based on rigid transformation have been formulated in least square. Good initial values of this non-linear system were provided from para-perspective projection model to overcome ill-conditioned convergence problem of the equations. The estimated motion parameters were providing 6-DOF input to the interaction system.
Determining three-dimensional (3D) motion parameters from image sequences has been challenging task in a variety of applications for a long time. Motion parameters are determined through linear and non-linear algorithms by establishing point correspondences extracted from two or more views. Generally, non-linear algorithms solve problem of non-linear least squares iteratively. Iterative methods may converge to a local but not global minimum with a good initial guess, or may diverge at all. In a number of cases, linear algorithms have formulated with given eight or more correspondences. Linear algorithms solve linear equations that give the unique solution except in degenerate cases. In all practical situation, non-linear and linear algorithms fail to find the unique solution for many situations such as initialization, degenerate spatial configuration, noisy data, any relative motion between the camera and the scene. We present an analytical result on how estimation error depends on motion characteristics of the moving object in image sequences taken from single camera. First, non- linear and linear algorithms are described that determines motion parameters from point correspondences between perspective views. The relationship between errors and the motion of the moving object are analyzed. The results of the analysis show that when the algorithms are failed with which motion of the moving object. Simulations are demonstrated performance of the algorithms as well as the relationships between errors and motion of the object in the image sequences.
Motion estimation from point correspondences is an important task in computer vision. Generally, computation of nonlinear equations in this field require good initial value, while computation of linear equations require additional constraint to choose correct solution for recovering motion parameters. In this work, we demonstrate main differences for computation of the linear and nonlinear equations in motion estimation. The main contribution of this study is that the result can be help to understand the computation technique on motion estimation from point correspondences.
Abstract: Most of the image processing techniques use edge detection function. Traditional edge detection operator computes the first order derivative, it produces thicker edges of image, and the second order derivative results more sensitive to noise. In this work, we discuss an image segmentation algorithm using global and local image fitting energy based on fractional derivative. This method can preserve more low frequency contour feature, keep high frequency marginal feature and also enhance medium frequency texture details. Furthermore, segmentation algorithm yields good visual effects for various images. We test our method on various images and compare them to other existing methods.
We present a new algorithm for determining 3D motion of a moving rigid object in the image sequences relative to a single camera. In the case where features are two-dimensional (2D), they are obtained usually by projective transformations of the 3D features on the object surface under perspective model. The perspective model has formulated in non-linear least square problem to determine 3D motions as characterized by rotation and translation iteratively. In practice, it is numerically ill-conditioned and may converge slowly or even fail to converge, if it starts with not good enough initial guess. However, since paraperspective projection model closely approximates perspective projection for recovering the 3D motion and shape of the object in Euclidean space, we used the results provided from paraperspective projection model as an initial value of non-linear optimization refinement under perspective camera model equations.
We present a new algorithm for determining 3D motion of a moving rigid object in the image sequences relative to a single camera. In the case where features are two-dimensional (2D), they are obtained usually by projective transformations of the 3D features on the object surface under perspective model. The perspective model has formulated in non-linear least square problem to determine 3D motions as characterized by rotation and translation iteratively. In practice, it is numerically ill-conditioned and may converge slowly or even fail to converge, if it starts with not good enough initial guess. However, since paraperspective projection model closely approximates perspective projection for recovering the 3D motion and shape of the object in Euclidean space, we used the results provided from paraperspective projection model as an initial value of non-linear optimization refinement under perspective camera model equations.
3D tracking plays a vital role in 3D projects by enhancing optimal control in 3D environments to reduce the time and cost of it. We present various real-time 3D motion estimation approaches developed in computer vision field and compare their performance. The methods developed in computer vision estimates 3D motion of a moving object relative to a camera or equivalently moving camera relative to the object in an image sequence when its corresponding features are known at different times. We reviewed 3D motion models formulated by different methods related to their geometric properties. We implemented two different methods and analyzed their performance results. Comparison from test datasets from image sequences demonstrated that homography based approach were more accurate than essential matrix based approach under noisy situations.
3D tracking plays a vital role in 3D projects by enhancing optimal control in 3D environments to reduce the time and cost of it. We present various real-time 3D motion estimation approaches developed in computer vision field and compare their performance. The methods developed in computer vision estimates 3D motion of a moving object relative to a camera or equivalently moving camera relative to the object in an image sequence when its corresponding features are known at different times. We reviewed 3D motion models formulated by different methods related to their geometric properties. We implemented two different methods and analyzed their performance results. Comparison from test datasets from image sequences demonstrated that homography based approach were more accurate than essential matrix based approach under noisy situations.
