Set Of Initial Points Research Articles

Matching Approach Based on Cross-Correlation and Affine Transformation

A method for image matching based on feature point is proposed on the case of unknown epipolar geometry and unavailable epipolar constraint in a single scene. Firstly, corners of the image as feature points are detected by Harris corner detector, which can participate in the image matching, and using the normalized grayscale cross-correlation coefficient establishes the initial matching of feature points. So the difference between two matching images is not great, using affine transformation deletes mismatching points of set of initial points. Finally, for set of every pair of initial available points, using reliable matching points as the control point estimate affine transformation parameters by the leastsquares method. According to the projection of points from one image onto another image calculate distance difference of corresponding point. The corresponding points whose distances are higher than a given threshold are deleted, so as to obtain correct match. Experimental results show that the approach is simple and can delete most mismatching points effectively.

SpeedSeg: A technique for segmenting pen strokes using pen speed

We present SpeedSeg, a technique for segmenting pen strokes into lines and arcs. The technique uses pen speed information to help infer the segmentation intended by the drawer. To begin, an initial set of candidate segment points is identified. This set includes speed minima below a threshold, and curvature maxima at which the pen speed is also below a threshold. The ink between each pair of consecutive segment points is then classified as either a line or an arc, depending on which fits best. Next, a feedback process is employed, and segments are judiciously merged and split as necessary to improve the quality of the segmentation. In user studies, SpeedSeg performed accurately for new users. The studies also demonstrated that SpeedSeg's accuracy is surprisingly insensitive to the values of many of the empirical parameters used by the technique. However, it is still possible to quickly tune the system to optimize performance for a given user. Finally, SpeedSeg outperformed a state-of-the-art segmentation algorithm.

Fractal boundaries of basin of attraction of Newton–Raphson method in helicopter trim

A key problem in helicopter aeroelastic analysis is the enormous computational time required for a numerical solution of the nonlinear system of algebraic equations required for trim, particularly when free wake models are used. Trim requires calculation of the main rotor and tail rotor controls and the vehicle attitude which leads to the six steady forces and moments about the helicopter center of gravity to be zero. An appropriate initial estimate of the trim state is needed for successful helicopter trim. This study aims to determine the control inputs that can have considerable effect on the convergence of trim solution in the aeroelastic analysis of helicopter rotors by investigating the basin of attraction of the nonlinear equations (set of initial guess points from which the nonlinear equations converge). It is illustrated that the three main rotor pitch controls of collective pitch, longitudinal cyclic pitch and lateral cyclic pitch have a significant contribution to the convergence of the trim solution. Trajectories of the Newton iterates are shown and some ideas for accelerating the convergence of a trim solution in the aeroelastic analysis of helicopters are proposed. It is found that the basins of attraction can have fractal boundaries.

An unstructured CVFEM and moving interface algorithm for non‐Newtonian Hele‐Shaw flows in injection molding

Purpose – The purpose of this paper is to develop a novel unstructured simulation approach for injection molding processes described by the Hele‐Shaw model.Design/methodology/approach – The scheme involves dual dynamic meshes with active and inactive cells determined from an initial background pointset. The quasi‐static pressure solution in each timestep for this evolving unstructured mesh system is approximated using a control volume finite element method formulation coupled to a corresponding modified volume of fluid method. The flow is considered to be isothermal and non‐Newtonian.Findings – Supporting numerical tests and performance studies for polystyrene described by Carreau, Cross, Ellis and Power‐law fluid models are conducted. Results for the present method are shown to be comparable to those from other methods for both Newtonian fluid and polystyrene fluid injected in different mold geometries.Research limitations/implications – With respect to the methodology, the background pointset infers a m...

Polygonal Approximation of Digital Curves to Preserve Original Shapes

In this letter, we propose a novel polygonal approximation of digital curves that preserve original shapes. The proposed method first detects break points, which have two different consecutive vectors, and sets an initial dominant point set. The approximation is then performed iteratively by deleting a dominant point using a novel distance, which can measure both the distance and the angle acuteness. The experimental results show that the proposed method can preserve original shapes and is appropriate for various shapes, including slabsided shapes.

The TCP Split Handshake: Practical Effects on Modern Network Equipment

Many network engineers might presume that the TCP three way handshake is the one, inviolate method of establishing TCP connections. A smaller percentage of engineers are also familiar with the little-used "simultaneous-open" connection method of establishing TCP connections. Researchers have discovered a third means to initiate TCP sessions, dubbed the "split handshake" method, which blends features of both the three way handshake and the simultaneous-open connection. Popular TCP/IP networking stacks respect this novel handshaking method, including Microsoft, Apple, and Linux stacks, with no modification. However, the effects of the split handshake method of session establishment on session aware devices, such as NAT gateways, intrusion detection devices, firewalls, and port scanners are largely unknown. We have provided an initial set of data points which shows that these devices can exhibit a high degree of unreliability and unexpected behavior when a split handshake session is executed by a standard client and a specially-modified server.

Extended hierarchies of invariant fiber bundles for dynamic equations on measure chains

If a linear autonomous ordinary differential of difference equation possesses a coefficient operator, which is (pseudo-) hyperbolic or allows a more specific splitting of its spectrum into appropriate spectral sets, then this gives rise to a so-called hierarchy of invariant linear subspaces of X related to the ranges to the corresponding spectral projections. Together with the intersections of these invariant subspaces, we get an extended hierarchy. Each member of the hierarchy can be characterized dynamically as set of initial points for orbits with a certain asymptotic growth rate in forward or backward time. In this paper we show that such a scenario persists under perturbations w.r.t. two points of view: In the first instance, the invariant linear spaces become an “extended hierarchy” of invariant manifolds, if the linear part is perturbed by a globally Lipschitzian (or smooth) mapping on X. This will be done in the nonautonomous context of dynamic equations on measure chains or time scales, where the time-varying invariant manifolds are called invariant fiber bundles. Secondly, we derive perturbation results well-suited for up-coming applications in analytical discretization theory.

PARAMETRIC OPTIMIZATION METHODS FOR THE TOKAMAK PLASMA CONTROL PROBLEM

Mathematical models of the structural parametric optimization of plasma dynamics are discussed. Optimization approach to plasma dynamic is based on the consideration of trajectory ensemble. This ensemble describes transient process in tokamak subject to the initial data and external disturbances. In the framework of this approach the optimization of dynamics of the trajectory ensemble in ITER tokamak is given. The trajectories of this ensemble are perturbed at the initial point set and the set of external disturbances.

Asymptotic Growth of Spatial Derivatives of Isotropic Flows

It is known from the multiplicative ergodic theorem that the norm of the derivative of certain stochastic flows at a previously fixed point grows exponentially fast in time as the flows evolves. We prove that this is also true if one takes the supremum over a bounded set of initial points. We give an explicit bound for the exponential growth rate which is far different from the lower bound coming from the Multiplicative Ergodic Theorem.

Non-uniform surface sampling techniques for three-dimensional object inspection

While the uniform sampling method is quite popular for point- wise measurement of manufactured parts, we present three novel sam- pling strategies that emphasize 3D non-uniform inspection capability. They are direct and indirect adaptive sampling and local adjustment sampling. The adaptive sampling strategy is based on a recursive sur- face subdivision process that applies two different approaches. One uses the direct triangular patch subdivision while the other uses the in- direct sectional adaptive approach. The direct adaptive sampling ap- proach can distribute points more closely around edges, corners, and vertices as found on the class of machined products. The indirect adap- tive sampling techniques extend optimum 2D sampling methods to 3D applications. The modified 2D adaptive sampling techniques are used sequentially twice; first, the critical cross sections are optimally selected, and then each section is optimally sampled to develop an accurate geo- metric description using a small number of sampling points. Beyond the practical application value of a technique to inspect curved surface ob- jects, this kind of technique is also of value in understanding the principle of optimum sampling in a 3D sense. The local adjustment sampling strat- egy uses a set of predefined starting points and then finds the local optimum position of each nodal point. This method approximates the object by moving the points toward object edges and corners. The pre- defined starting points sets include uniform and non-uniform sampling distribution generated by the direct adaptive sampling approach. The results show that the initial point sets, when preprocessed by the adap- tive sampling using triangular patches, are moved the shortest distance to edges and corners for global optimum approximation, again showing this method's superiority. The performance comparisons of applying uni- form sampling and adaptive sampling are made based on the MSE mean square error value between the real object surfaces and their approximating surfaces. The adaptive sampling methods exhibit better performance than the uniform sampling methods in reducing the MSE values with fewer sample points. In addition to the performance advan- tage over uniform sampling, the non-uniform sampling techniques we propose also proved to be integratable with view planning for the inspec- tion of products by different manufacturing processes. © 2008 Society of

Local complexity functions of interval exchange transformations

We studied numerically complexity functions for interval exchange transformations. We have shown that they grow linearly in time as well as the ϵ-complexity function. Moreover, we found out that they depend also linearly on ϵ where ϵ is the Lebesgue measure of a set of initial points. This allows us to hypothesize that the dimension of the measure related to the ϵ-complexity function could be determined by studying the dependence of local complexity functions on ϵ.

Node placement algorithm and application based on the centroidal Voronoi tessellation

Based on the Voronoi tessellation of initial points, an algorithm with centroidal Voronoi tessellation for construction of nodes used in meshless discretization is proposed. Voronoi tessellations are constructed corresponding to a given set of initial points on the domain. By using natural coordinates of triangles, the centroids of Voronoi tessellations are determined, and the cost function is used as convergence theorem. If the centroids of Voronoi tessellations meet the convergence theorem, those centroids are final obtained nodes placed in the domain and on the boundary. Then by cutting boundary technique, points can be placed in arbitrary do- mains. Uniform and non-uniform nodal arrangements can be realized by this algorithm. A numerical example of cylinder with hole subjected to uniform internal pressure is presented by using the natural neighbour Petrov-Galerkin method and the proposed algo- rithm. The numerical results are in great agreement with the exact solutions, which indicates that the proposed algorithm is very ac- curate and reliable in meshless methods.

Partition of the probability-assigned space in probability density evolution analysis of nonlinear stochastic structures

Based on a partition of probability-assigned space, a strategy for determining the representative point set and the associated weights for use in the probability density evolution method (PDEM) is developed. The PDEM, which is capable of capturing the instantaneous probability density function of responses of linear and nonlinear stochastic systems, was developed in the past few years. The determination of the representative point set and the assigned probabilities is of paramount importance in this approach. In the present paper, a partition of probability-assigned space related to the representative points and the assigned probabilities are first examined. The error in the resulting probability density function of the stochastic responses is then analyzed, leading to two criteria on strategies for determining the representative points and a set of indices in terms of discrepancy of the point sets. A two-step algorithm is proposed, in which an initial uniformly scattered point set is mapped to an optimal set. The implementation of the algorithm is elaborated. Two methods for generating the initial point set are outlined. These are the lattice point sets and the Number-Theoretical nets. A density-related transformation yielding the final point set is then analyzed. Numerical examples are investigated, where the results are compared to those obtained from the standard Monte Carlo simulation and the Latin hyper-cube sampling, demonstrating the accuracy and efficiency of the proposed approach.

Dominant point detection by reverse polygonization of digital curves

A polygonal approximation technique using reverse polygonization is presented in this paper. The reverse polygonization starts from an initial set of dominant points i.e. break points. In that, dominant points are deleted (one in each iteration) such that the maximal perpendicular distance of approximating straight line from original curve is minimal. A comparative study with some commonly referred algorithms is also presented, which shows that this technique can produce better approximation results. The algorithm has additional advantages like simplicity, polygonal approximation with any number of dominant points and up to any error value, and computational efficiency.

A novel approach to polygonal approximation of digital curves

A new approach to polygonal approximation is presented in this paper. It starts from an initial set of dominant points (break points), where the integral square error from a given shape is zero. The proposed algorithm iteratively deletes most redundant dominant points till required approximation is achieved. Stabilization algorithm after elimination of each dominant point ensures high quality of approximation. Results of proposed algorithm are compared with classical algorithms. The proposed algorithm has additional benefits like polygonal approximation with any number of dominant points and up to any error value and robustness of results.

Multiminima Heuristic Methods for Antenna Optimization

Two general approaches to multiminima optimization are considered. The first approach is based on repetition of a single minima method (e.g., the Nelder-Mead simplex applied to the best solution in a set of random trials). The second approach is based on a coarse estimation of local minima using initial set of points and local optimization starting from these local minima (e.g., random search as a generator of the initial set of points and Nelder-Mead simplex as a local optimizer). A comparison of various optimization algorithms has been done on one analytical problem and two well-known examples of antenna design. It is found that: a) the multiminima method based on coarse estimation enables finding more minima with smaller number of iterations than that based on repetition, b) the best multiminima methods are comparable with the best single minima methods in a number of iterations needed for finding the global minima, and c) the multiminima method based on coarse estimation restarted with different weighting coefficients of multiobjective cost function enables efficient Pareto optimization

Markov model fuzzy-reasoning based algorithm for fast block motion estimation

This paper presents a Markov model fuzzy-reasoning based algorithm for fast block motion estimation. To reduce computational complexity, the existing fast search algorithms move iteratively toward the winning point based only on a finite set of search points in every stage. Despite the efficiency of these algorithms, the search process is easily trapped into local minima, especially for high activity video sequences. To overcome this difficulty, we propose a three-states Markov model based algorithm that invokes the fuzzy-reasoning to provide the search an acceptance probability of being able to move out of local minima. Two schemes are employed to further enhance the performance of the algorithm. First, a set of initial search points that exploit high correlations among the motion vectors of the temporally and spatially adjacent blocks as well as their surrounding points are used. Second, an alternate search strategy is addressed to cover more area without increasing computations. Simulation results show that the new algorithm offers superior performance with lower computational complexity and picture quality increase in terms of search points/block and MSE/pel, respectively, compared with the previous works in various scenarios.

Apparent Fractal Dimensions in the HMF Model

We show that recent observations of fractal dimensions in the μ‐space of N‐body Hamiltonian systems with long‐range interactions are due to finite N and finite resolution effects. We provide strong numerical evidence that, in the continuum (Vlasov) limit, a set which initially is not a fractal (e.g., a line in 2D) remains such for all finite times. We perform this analysis for the Hamiltonian mean field (HMF) model, which describes the motion of a system of N fully coupled rotors. The analysis can be indirectly confirmed by studying the evolution of a large set of initial points for the Chirikov standard map.

Variable Resolution Spatial Interpolation Using the Simple Recursive Point Voronoi Diagram

This article introduces a procedure for progressively increasing the density of an initial point set that can be used as a basis for interpolating surfaces of variable resolution from sparse samples of data sites. The procedure uses the Simple Recursive Point Voronoi Diagram in which Voronoi concepts are used to tessellate space with respect to a given set of generator points. The construction is repeated every time with a new generator set, which comprises members selected from the previous generator set plus features of the current tessellation. We show how this procedure can be implemented in Arc/Info and present an illustration of its application using three known surfaces and alternative generator point configurations. Initial results suggest that the procedure has considerable potential and we discuss further methods for evaluating and extending it.

Degenerate resonances in Hamiltonian systems with 3/2 degrees of freedom.

Hamiltonian systems with 3/2 degrees of freedom close to autonomous systems are considered. Special attention is focused on the case of degenerate resonances. In this case, an averaged system in the first approximation reduces to an area-preserving mapping of a cylinder whose rotation number is a nonmonotonic function of the action variable. Behavior of the trajectories of such a map is similar to that of the trajectories of a Poincare map. Three regions: B(+/-) in the upper and lower parts of the cylinder and an additional region A which contains separatrices of fixed points for the corresponding resonance are distinguished on the cylinder. It is shown that there is a nonempty set of initial points corresponding to walking trajectories in B(+/-) and, hence, there are no closed invariant curves that are homotopically nontrivial on the cylinder. Cells limited by a "stochastic network" can exist in region A. The number of cells is the greater the higher the order of degeneration of the resonance. Possible types of orbit behavior in region A are described. (c) 2002 American Institute of Physics.