Set Of Sample Points Research Articles

A new kind of regional importance measure of the input variable and its state dependent parameter solution

To further analyze the effect of different regions within input variable on the variance and mean of the model output, two new regional importance measures (RIMs) are proposed, which are the “contribution to variance of conditional mean (CVCM)” and the “contribution to mean of conditional mean (CMCM)”. The properties of the two RIMs are analyzed and their relationships with the existing contribution to sample variance (CSV) and contribution to sample mean (CSM) are derived. Based on their characteristics, the highly efficient state dependent parameter (SDP) method is introduced to estimate them. By virtue of the advantages of the SDP-based method, the same set of sample points utilized for solving CSM and CSV is enough to estimate CVCM and CMCM. Several examples demonstrate that CVCM can provide further information on the existing CSV, which can effectively instruct the engineer on how to achieve a targeted reduction of the main effect of each input variable. CMCM can act as effectively as the CSM, but the convergence and stability for estimating CMCM by numerical simulation is better than those for estimating CSM. Besides, the efficiency and accuracy of the SDP-based method are also testified by the examples.

Using shape contexts method for registration of contra lateral breasts in thermal images.

To achieve symmetric boundaries for left and right breasts boundaries in thermal images by registration. The proposed method for registration consists of two steps. In the first step, shape context, an approach as presented by Belongie and Malik was applied for registration of two breast boundaries. The shape context is an approach to measure shape similarity. Two sets of finite sample points from shape contours of two breasts are then presented. Consequently, the correspondences between the two shapes are found. By finding correspondences, the sample point which has the most similar shape context is obtained. In this study, a line up transformation which maps one shape onto the other has been estimated in order to complete shape. The used of a thin plate spline permitted good estimation of a plane transformation which has capability to map unselective points from one shape onto the other. The obtained aligning transformation of boundaries points has been applied successfully to map the two breasts interior points. Some of advantages for using shape context method in this work are as follows: (1) no special land marks or key points are needed; (2) it is tolerant to all common shape deformation; and (3) although it is uncomplicated and straightforward to use, it gives remarkably powerful descriptor for point sets significantly upgrading point set registration. Results are very promising. The proposed algorithm was implemented for 32 cases. Boundary registration is done perfectly for 28 cases. We used shape contexts method that is simple and easy to implement to achieve symmetric boundaries for left and right breasts boundaries in thermal images.

Energy-Minimizing Curve Fitting for High-Order Surface Mesh Generation

We investigate different techniques for fitting Bézier curves to surfaces in context of high-order curvilinear mesh generation. Starting from distance-based least-squares fitting we develop an incremental algorithm, which incorporates approximations of stretch and bending energy. In the process, the algorithm reduces the energy weight in favor of accuracy, leading to an optimized set of sampling points. This energy-minimizing fitting strategy is applied to analytically defined as well as triangulated surfaces. The results confirm that the proposed method straightens and shortens the curves efficiently. Moreover the method preserves the accuracy and convergence behavior of distance-based fitting. Preliminary application to surface mesh generation shows a remarkable improvement of patch quality in high curvature regions.

High Dimensional Model Representation With Principal Component Analysis

In engineering design, spending excessive amount of time on physical experiments or expensive simulations makes the design costly and lengthy. This issue exacerbates when the design problem has a large number of inputs, or of high dimension. High dimensional model representation (HDMR) is one powerful method in approximating high dimensional, expensive, black-box (HEB) problems. One existing HDMR implementation, random sampling HDMR (RS-HDMR), can build an HDMR model from random sample points with a linear combination of basis functions. The most critical issue in RS-HDMR is that calculating the coefficients for the basis functions includes integrals that are approximated by Monte Carlo summations, which are error prone with limited samples and especially with nonuniform sampling. In this paper, a new approach based on principal component analysis (PCA), called PCA-HDMR, is proposed for finding the coefficients that provide the best linear combination of the bases with minimum error and without using any integral. Several benchmark problems of different dimensionalities and one engineering problem are modeled using the method and the results are compared with RS-HDMR results. In all problems with both uniform and nonuniform sampling, PCA-HDMR built more accurate models than RS-HDMR for a given set of sample points.

An efficient optimum Latin hypercube sampling technique based on sequencing optimisation using simulated annealing

This paper proposes a new optimal Latin hypercube sampling method (OLHS) for design of a computer experiment. The new method is based on solving sequencing and continuous optimisation using simulated annealing. There are two sets of design variables used in the optimisation process: sequencing and real number variables. The special mutation operator is developed to deal with such design variables. The performance of the proposed numerical strategy is tested and compared with three established OLHS methods, namely genetic algorithm (GA), enhanced stochastic evolutionary algorithm (ESEA) and successive local enumeration (SLE). Based on 30 test problems with various design dimensions and numbers of sampling points, the proposed method gives the best results. The method can generate an optimum set of sampling points within reasonable computing time; therefore, it can be considered as a powerful tool for design of computer experiments.

An Area‐Preserving Parametrization for Spherical Rectangles

AbstractWe present an area‐preserving parametrization for spherical rectangles which is an analytical function with domain in the unit rectangle [0, 1]2 and range in a region included in the unit‐radius sphere. The parametrization preserves areas up to a constant factor and is thus very useful in the context of rendering as it allows to map random sample point sets in [0, 1]2 onto the spherical rectangle. This allows for easily incorporating stratified, quasi‐Monte Carlo or other sampling strategies in algorithms that compute scattering from planar rectangular emitters.

Minimizing edge length to connect sparsely sampled unstructured point sets

Most methods for interpolating unstructured point clouds handle densely sampled point sets quite well but get into trouble when the point set contains regions with much sparser sampling, a situation often encountered in practice. In this paper, we present a new method that provides a better interpolation of sparsely sampled features.We pose the surface construction problem as finding the triangle mesh which minimizes the sum of all triangles’ longest edge. Since searching for matching umbrellas among sparsely sampled points to yield a closed manifold shape is a difficult problem, we introduce suitable heuristics. Our algorithm first connects the points by triangles chosen in order of their longest edge and with the requirement that all edges must have at least two incident triangles. This yields a closed non-manifold shape which we call the Boundary Complex. Then we transform it into a manifold triangulation using topological operations. We show that in practice, runtime is linear to that of the Delaunay triangulation of the points. Source code is available online.

Hexagonal honeycomb cell optimisation by way of meta-model techniques

This paper presents the result of an optimisation study by linear, quadratic, Kriging and radial basis meta-models in order to augment the crashworthiness characteristic of cellular structures. Thin-walled cellular structures (honeycomb) have the ability to absorb impact energy during crashing, thus it is important to enhance the crushing efficiency and optimise the structural reliability. The optimisation carried out in this study is aimed at maximising the energy absorption characteristics using meta-models while considering some limitation on the maximum force as a constraint. Achieving these characteristics is an important factor in crashworthiness analysis, which minimises the damage in dynamic performance. The objective of using various meta-models is to qualify the meta-model in crashworthiness analysis using different point selection schemes and different number of points. The optimisation is performed in two stages; through experimental design methods in which a set of sampling points is selected from design space and polynomial fitting in order to optimise the objective. It is concluded that D-optimal best suits response surface method for model approximation. Kriging performed best by space filling and the best point selection scheme for radial basis surrogate is latin hypercube design. The results show that for optimising the crashworthiness characteristics of honeycomb, Kriging and quadratic response surface (RS) are best, in terms of accuracy and robustness point of view and the radial basis neural network would be the second best. During this optimisation, the RS was combined with detailed geometrically simplified finite element model of honeycomb cell using ANSYS/LS-DYNA, LS-DYNA and LS-opt packages. Approximated functions combined with the finite element analysis were an effective tool to optimise highly non-linear impact problems. This has led to the development of validated algorithm that enabled the development of the optimised solutions.

Explicit reduced‐order models for the stabilized finite element approximation of the incompressible Navier–Stokes equations

SUMMARYIn this paper, we present an explicit formulation for reduced‐order models of the stabilized finite element approximation of the incompressible Navier–Stokes equations. The basic idea is to build a reduced‐order model based on a proper orthogonal decomposition and a Galerkin projection and treat all the terms in an explicit way in the time integration scheme, including the pressure. This is possible because the reduced model snapshots do already fulfill the continuity equation. The pressure field is automatically recovered from the reduced‐order basis and solution coefficients. The main advantage of this explicit treatment of the incompressible Navier–Stokes equations is that it allows for the easy use of hyper‐reduced order models, because only the right‐hand side vector needs to be recovered by means of a gappy data reconstruction procedure. A method for choosing the optimal set of sampling points at the discrete level in the gappy procedure is also presented. Numerical examples show the performance of the proposed strategy. Copyright © 2013 John Wiley & Sons, Ltd.

Matching Cost Filtering for Dense Stereo Correspondence

Dense stereo correspondence enabling reconstruction of depth information in a scene is of great importance in the field of computer vision. Recently, some local solutions based on matching cost filtering with an edge-preserving filter have been proved to be capable of achieving more accuracy than global approaches. Unfortunately, the computational complexity of these algorithms is quadratically related to the window size used to aggregate the matching costs. The recent trend has been to pursue higher accuracy with greater efficiency in execution. Therefore, this paper proposes a new cost-aggregation module to compute the matching responses for all the image pixels at a set of sampling points generated by a hierarchical clustering algorithm. The complexity of this implementation is linear both in the number of image pixels and the number of clusters. Experimental results demonstrate that the proposed algorithm outperforms state-of-the-art local methods in terms of both accuracy and speed. Moreover, performance tests indicate that parameters such as the height of the hierarchical binary tree and the spatial and range standard deviations have a significant influence on time consumption and the accuracy of disparity maps.

Crust and skeleton approximation from samples

Samples of shape boundary carry the information of the shape for a sufficiently dense sampling. There is not any connectivity information between sample points and the geometry or topology of the original shape is not known. These samples are used for crust and skeleton approximation. In this article, we focus on the Voronoi-based methods which the shape is defined by a set of sample points on the shape boundary and then the shape and its skeleton is approximated with the Voronoi diagram of these points. These methods are extremely sensitive to noise and boundary perturbation. To overcome the problems of crust and skeleton extraction, we propose a new method by labeling the sample points. The conceptual structure and the results illustrate that our method are stable, easy to implement, robust and able to handle sharp corners and open curves, even in the presence of significant noise and perturbations.

Adaptive manifolds for real-time high-dimensional filtering

We present a technique for performing high-dimensional filtering of images and videos in real time. Our approach produces high-quality results and accelerates filtering by computing the filter's response at a reduced set of sampling points, and using these for interpolation at all N input pixels. We show that for a proper choice of these sampling points, the total cost of the filtering operation is linear both in N and in the dimension d of the space in which the filter operates. As such, ours is the first high-dimensional filter with such a complexity. We present formal derivations for the equations that define our filter, as well as for an algorithm to compute the sampling points. This provides a sound theoretical justification for our method and for its properties. The resulting filter is quite flexible, being capable of producing responses that approximate either standard Gaussian, bilateral, or non-local-means filters. Such flexibility also allows us to demonstrate the first hybrid Euclidean-geodesic filter that runs in a single pass. Our filter is faster and requires less memory than previous approaches, being able to process a 10-Megapixel full-color image at 50 fps on modern GPUs. We illustrate the effectiveness of our approach by performing a variety of tasks ranging from edge-aware color filtering in 5-D, noise reduction (using up to 147 dimensions), single-pass hybrid Euclidean-geodesic filtering, and detail enhancement, among others.

Adaptive manifolds for real-time high-dimensional filtering

We present a technique for performing high-dimensional filtering of images and videos in real time. Our approach produces high-quality results and accelerates filtering by computing the filter's response at a reduced set of sampling points, and using these for interpolation at all N input pixels. We show that for a proper choice of these sampling points, the total cost of the filtering operation is linear both in N and in the dimension d of the space in which the filter operates. As such, ours is the first high-dimensional filter with such a complexity. We present formal derivations for the equations that define our filter, as well as for an algorithm to compute the sampling points. This provides a sound theoretical justification for our method and for its properties. The resulting filter is quite flexible, being capable of producing responses that approximate either standard Gaussian, bilateral, or non-local-means filters. Such flexibility also allows us to demonstrate the first hybrid Euclidean-geodesic filter that runs in a single pass. Our filter is faster and requires less memory than previous approaches, being able to process a 10-Megapixel full-color image at 50 fps on modern GPUs. We illustrate the effectiveness of our approach by performing a variety of tasks ranging from edge-aware color filtering in 5-D, noise reduction (using up to 147 dimensions), single-pass hybrid Euclidean-geodesic filtering, and detail enhancement, among others.

Area-to-Point Kriging of Soil Phosphorus Composite Samples

Mapping of phosphorus (P) is based on sampling and laboratory analysis. Although laboratory analysis is costly, the number of samples is restricted in practice. In zone sampling, areas of the field are used to composite samples from sets of sampling points to reduce efforts. This study introduces area-to-point (ATP) kriging for downscaling composite samples with different sizes and shapes of the sampling areas. ATP kriging makes use of the coordinates of the sampling points of the composite samples. The applicability was tested on a simulated data set as well as on a spatially dense sample set of P measurements. Validation shows that ATP kriging outperforms point kriging with centroid interpolation. The root mean square error (RMSE) is reduced from 39.5 to 33.5 mg kg−1. ATP kriging predictions were better at retaining the P value of the sampling area. The smoothing effect of interpolation and the aggregation effect of compositing the samples were reduced.

An new immune genetic algorithm based on uniform design sampling

The deficiencies of keeping population diversity, prematurity and low success rate of searching the global optimal solution are the shortcomings of genetic algorithm (GA). Based on the bias of samples in the uniform design sampling (UDS) point set, the crossover operation in GA is redesigned. Using the concentrations of antibodies in artificial immune system (AIS), the chromosomes concentration in GA is defined and the clonal selection strategy is designed. In order to solve the maximum clique problem (MCP), an new immune GA (UIGA) is presented based on the clonal selection strategy and UDS. The simulation results show that the UIGA provides superior solution quality, convergence rate, and other various indices to those of the simple and good point GA when solving MCPs.

Preserving geometric properties in reconstructing regions from internal and nearby points

The problem of reconstructing a region from a set of sample points is common in many geometric applications, including computer vision. It is very helpful to be able to guarantee that the reconstructed region “approximates” the true region, in some sense of approximation. In this paper, we study a general category of reconstruction methods, called “locally-based reconstruction functions of radius α,” and we consider two specific functions, Jα(S) and Fα(S), within this category. We consider a sample S, either finite or infinite, that is specified to be within a given Hausdorff distance δ of the true region R, and we prove a number of theorems which give conditions on R, δ that are sufficient to guarantee that the reconstructed region is an approximation of the true region. Specifically, we prove:1.For any R, if F is any locally-based reconstruction method of radius α where α is small enough, and if the Hausdorff distance from S to R is small enough, then the dual-Hausdorff distance from F(S) to R, the Hausdorff distance between their boundaries, and the measure of their symmetric difference are guaranteed to be small.2.If R is r-regular, then for any ϵ,ϕ>0, if α is small enough, and the Hausdorff distance from S to R is small enough, then each of the regions Jα(S) and Fα(S) is ϵ-similar to R and is an (ϵ,ϕ)-approximation in tangent of R.

Tracking Moving Object via Unscented Particle Filter in Sensor Network

Moving object tracking is one of the typical applications in wireless sensor network (WSN). As a result, a lot of important solutions have been proposed in the last decade, toward addressing different aspects of object tracking in WSN settings. This work describes an Unscented particle filter (UPF) based Moving Object Tracking algorithm, UMOT, in WSN settings, where the sensor nodes are clustered dynamically to provide sensing and data fusion tasks. The key idea of UPF is to capture accurately the posterior mean and covariance of non-linear Gaussian variable up to the second order, through propagating a set of sample points in the state system. It has been demonstrated that UPF addresses the deficiency of using transition prior as the proposal distribution, which results in biased posterior estimation due to excluding the recent observations. We present the design and implementation of UMOT, together with comprehensive simulations, conducted to evaluate the proposed methods. The simulation results show that UMOT achieves significant improvement over existing schemes in various network settings.

How to define a locally adaptive sampling criterion for topologically correct reconstruction of multiple regions

Volume-based boundary reconstruction processes often have to deal with non-manifold shapes. Even though many reconstruction algorithms have been proposed for non-manifold surfaces, they usually do not preserve topological properties. Only recently, methods were presented which—given a finite set of surface sample points—result in a mesh representation of the original boundary preserving all or certain neighborhood relations, even if the sampling is sparse and highly noise corrupted. We show that the required sampling conditions of the algorithm called “refinement reduction” limit the guaranteed correctness of the outcome to a small class of shapes. We define new locally adaptive sampling conditions that depend on our new pruned medial axis and finally prove without any restriction on shapes that under these new conditions, the result of “refinement reduction” corresponds to a refinement of a topologically correct mesh in cases where the previous sampling criteria failed. Based on our results we propose a new criterion for locally adaptive point set decimation. We also discuss why our sampling conditions can only lead to a refinement of a correct reconstruction but not necessarily to a correct reconstruction itself.

A tropical cyclone-based method for global optimization

This paper proposes a new heuristic, Tropical Cyclone-based Method (TCM), for solving global optimization problems with box constraints. TCM mimics the formation process of tropical cyclones in the atmosphere to move a set of sample points towards optimality. The formation of a tropical cyclone in nature is still not completely understood by people. Nevertheless, inspired by the known formation factors of a tropical cyclone, TCM is designed to seek optimal solutions by considering airflow, disturbance, and convection in order to traverse the solution space. Experimental results on some well-known nonlinear test functions are included. Compared with the well-known Electromagnetism-like Mechanism (EM), TCM is both effective and efficient for solving the reported test functions.

Bending-Invariant Correspondence Matching on 3-D Human Bodies for Feature Point Extraction

In this paper, we present an automatic approach to match correspondences on 3-D human bodies in various postures so that feature points can be automatically extracted. The feature points are very important to the establishment of volumetric parameterization around human bodies for the human-centered customization of soft-products (Trans. Autom. Sci. Eng., vol. 4, issue no. 1, pp. 11-21, 2007). For a given template human model with a set of predefined feature points, we first down-sample the input model into a set of sample points. Then, the corresponding points of these samples on the human model are identified by minimizing the distortion with the help of a series of transformations regardless of their differences in postures, scales or positions. The basic idea of our algorithm is to transform the template human body to the shape of the input model iteratively. To generate a bending invariant mapping, the initial correspondence/transformation is computed in a multidimensional scaling (MDS) embedding domain of 3-D human models, where the Euclidean distance between two samples on a 3-D model in the MDS domain corresponds to the geodesic distance between them in ℜ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> . As the posture change (i.e., the body bending) of a human model can be considered as approximately isometric in the intrinsic 3-D shape, the initial correspondences established in the MDS domain can greatly enhance the robustness of our approach in body bending. Once the correspondences between the surface samples on the template model and the input model are determined after iterative transformations, we have essentially found the corresponding feature points on the input model. Finally, the locations of the based local matching step.