Boundary Correction Research Articles

Video object tracking with feedback of performance measures

Presents a scalable object tracking framework, which is capable of tracking the contour of nonrigid objects in the presence of occlusion. The framework consists of open-loop boundary prediction and closed-loop boundary correction parts. The open-loop prediction block adaptively divides the object contour into subcontours, and estimates the mapping parameters for each subsegment. The closed-loop boundary correction block employs a suitably weighted combination of low-level features such as color edge, color segmentation, motion models, and motion segmentation for each subcontour. Performance evaluation measures are used in a feedback loop to evaluate the goodness of the segmentation/tracking in order to adjust the weights assigned to each of these low-level features for each subcontour at each frame. The framework is scalable because it can be adapted to track a coarse estimate of the boundary of selected objects in real-time, as well as pixel-accurate boundary tracking in off-line mode. The proposed method does not depend on any single motion or shape model, and does not need training. Experimental results demonstrate that the algorithm is able to track the object boundaries under significant occlusion and background clutter.

Nearest-Neighbor Variance Estimation (NNVE)

Robust covariance estimation commonly proceeds by downweighting outliers. In this article we measure the “outlyingness” of a data point by the standardized distance between the point and its Kth nearest neighbor. The appropriate weights for robust estimation are found by a model-based mixture modeling approach that follows from considering the data cloud as a realization of a high-dimensional point process. To correct a potential bias when there are no outliers, we introduce a boundary correction procedure that artificially adds in extra outlying points; the resulting methodology is called nearest-neighbor variance estimation (NNVE). The strength of NNVE is its robustness against a large proportion of noise points and against deviation from normality of the signal. A consistency result for the method is established. Under some reasonable assumptions, it is shown that the covariance estimate is bounded and that each point has only bounded influence on the final estimates. NNVE outperformed the popular minimum volume ellipsoid (MVE) estimator in simulation studies, with a big improvement when the proportion of outliers was very large (> 50%). In our simulation study, when the proportion of outliers was ≥ 50%, the mean squared error of the NNVE estimator of variance was at least 100 times smaller than that of the MVE estimator. The proposed estimator also outperformed MVE in cases where the underlying data distribution was not normal. Good performance of NNVE in several real examples is demonstrated. A potential drawback of NNVE is that data points condensed in moderate-sized clusters would be classified as signal. Even though we do not support approaches discarding moderate-sized clusters as outliers without checking, this feature of NNVE could be problematic, particularly when only the main data cloud is of interest. A simple diagnostic tool built on existing model-based clustering procedure is proposed. This procedure allows us to check whether there is more than one separate data cloud in the data after cleaning. It also supplies the central locations of the separated moderate-sized clusters, which allows further investigation. Finally, because NNVE reduces the problem of finding the robustness weights to a one-dimensional problem, it may be useful in high-dimensional problems, such as those encountered in data mining.

A semiparametric method of boundary correction for kernel density estimation

We propose a new estimator for boundary correction for kernel density estimation. Our method is based on local Bayes techniques of Hjort (Bayesian Statist. 5 (1996) 223). The resulting estimator is semiparametric type estimator: a weighted average of an initial guess and the ordinary reflection method estimator. The proposed estimator is seen to perform quite well compared to other existing well-known estimators for densities which have the shoulder condition at the endpoints.

Wigner functions with boundaries

We consider the general Wigner function for a particle confined to a finite interval and subject to Dirichlet boundary conditions. We derive the boundary corrections to the “stargenvalue” equation and to the time evolution equation. These corrections can be cast in the form of a boundary potential contributing to the total Hamiltonian which together with a subsidiary boundary condition is responsible for the discretization of the energy levels. We show that a completely analogous formulation (in terms of boundary potentials) is also possible in standard operator quantum mechanics and that the Wigner and the operator formulations are also in one-to-one correspondence in the confined case. In particular, we extend Baker’s converse construction to bounded systems. Finally, we elaborate on the applications of the formalism to the subject of Wigner trajectories, namely in the context of collision processes and quantum systems displaying chaotic behavior in the classical limit.

On robust local polynomial estimation with long-memory errors

Prediction in time series models with a trend requires reliable estimation of the trend function at the right end of the observed series. Local polynomial smoothing is a suitable tool because boundary corrections are included implicitly. However, outliers may lead to unreliable estimates, if least-squares regression is used. In this paper, local polynomial smoothing based on M-estimation is considered for the case where the error process exhibits long-range dependence. In contrast to the iid case, all M-estimators are asymptotically equivalent to the least-square solution, under the (ideal) Gaussian model. The potential usefulness of the proposal for forecasting is illustrated by practical and simulated examples. A simulation study shows that outliers have a major effect on nonrobust bandwidth selection, in particular due to the change of the dependence structure.

Boundary and Bias Correction in Kernel Hazard Estimation

A new class of local linear hazard estimators based on weighted least square kernel estimation is considered. The class includes the kernel hazard estimator of Ramlau‐Hansen (1983), which has the same boundary correction property as the local linear regression estimator (see Fan & Gijbels, 1996). It is shown that all the local linear estimators in the class have the same pointwise asymptotic properties. We derive the multiplicative bias correction of the local linear estimator. In addition we propose a new bias correction technique based on bootstrap estimation of additive bias. This latter method has excellent theoretical properties. Based on an extensive simulation study where we compare the performance of competing estimators, we also recommend the use of the additive bias correction in applied work.

Boundary corrections in fractal analysis of galaxy surveys

The analysis of redshift surveys with fractal tools requires one to apply some form of statistical correction for galaxies lying near the geometric boundary of the sample. In this paper we compare three different methods of performing such a correction upon estimates of the correlation integral in order to assess the extent to which estimates may be biased by boundary terms. We apply the corrections illustrative examples, including a simple fractal set (L\'{e}vy flight), a random $\beta$-model, and a subset of the CfA2 Southern Cap survey. This study shows that the new ``angular'' correction method we present is more generally applicable than the other methods used to date: the conventional ``capacity'' correction imposes a bias towards homogeneity, and the ``deflation'' method discards large-scale information, and consequently reduces the statistical usefulness of data sets. The ``angular'' correction method is effective at recovering true fractal dimensions, although the extent to which boundary corrections are important depends on the form of fractal distribution assumed as well as the details of the survey geometry. We also show that the CfA2 Southern sample does not show any real evidence of a transition to homogeneity. We then revisit the IRAS PSCz survey and ``mock'' PSCz catalogues made using N-body simulations of two different cosmologies. The results we obtain from the PSCz survey are not significantly affected by the form of boundary correction used, confirming that the transition from fractal to homogeneous behaviour reported by Pan & Coles (2000) is real.

Comparison of boundary correction factor solutions for two symmetric cracks in a straight-shank hole

This paper compares the mode I boundary correction factor solutions for two symmetric elliptical cracks emanating from a straight-shank hole. A variety of methods were used to generate the solutions. A global–intermediate–local hierarchical approach was developed using the finite element method (FEM). Comparisons were made with the following methods: the FEM with the equivalent domain integral, semi-empirical stress-intensity factor (SIF) equations, the finite element alternating method, the boundary element method (BEM) with the crack opening displacement approach, the BEM using special crack-tip elements, and the three-dimensional weight function method. The SIF solutions were within a band of ±3% about the average solution.

Clarification of the Mirage Method for Boundary Correction, with Possible Bias in Plot and Point Sampling

Abstract While the mirage method of boundary overlap correction has been shown to be unbiased, an emphasis on the case of circular inclusion zones has led to an ambiguity in its presentation in much of the literature. We present a clarification of the method and show that its incorrect application leads to bias. We further show that depending on the method of slope correction, the potential for bias extends to variable radius plot sampling. Correct application of the mirage method has implications for when plots should be reflected, and how borderline trees should be handled on the reflected plots. FOR. SCI. 47(2):242–245.

Boundary Correction Factors for Elliptical Surface Cracks Emanating from Countersunk Rivet Holes

To predict the crack growth and residual strength of riveted joints subjected to widespread fatigue damage, accurate stress and fracture analyses of corner and surface cracks at a rivet hole are needed. The results presented focus on the calculation of stress-intensity factor (SIF) solutions for cracks at countersunk rivet holes for tension, bending, and wedge load conditions. A wide range of configuration parameters were varied, including the crack size, crack shape, crack location, and length of the straight shank hole. A finite-element-based global-intermediatelocal hierarchical approach was used. The results are expressed as boundary correction factors (BCFs), which are nondimensional representations of the SIF. The BCFs were determined along the crack front in terms of the physical angle, which was measured from the inner surface of the plate to a point on the hole boundary or on the outer surface of the plate. In general, the values of BCFs increased along the crack front, moving from the inner surface of the plate toward the hole boundary or the outer surface. The values of the BCFs were highest for the crack fronts closest to the hole boundary. The trends in the solutions were the same for the three loading conditions.

Nonparametric Regression and Spline Smoothing

Provides a unified account of the most popular approaches to nonparametric regression smoothing. This edition contains discussions of boundary corrections for trigonometric series estimators; detailed asymptotics for polynomial regression; testing goodness-of-fit; estimation in partially linear models; practical aspects, problems and methods for co

Hydrogen atom in a spherical well: linear approximation

We discuss the boundary effects on a quantum system by examiningthe problem of a hydrogen atom in a spherical well. Using an approximation method which is linear in energy we calculate the boundary corrections to the ground-state energy and wavefunction.We obtain the asymptotic dependence of the ground-state energy on the radius of the well.

Boundary correction factors for elliptical surface cracks emanating from countersunk rivet holes

Boundary correction factors for elliptical surface cracks emanating from countersunk rivet holes

RAPID ROUGHENING OF Mo2C FILM SURFACE

The roughness of Mo2C film surface is measured and the results are gi ven.By introduction of crystalline boundary correction,the rapid roughening phen omenon is explained theoretically.

An Improved Estimator of the Density Function at the Boundary

We propose a new method of boundary correction for kernel density estimation. The technique is a kind of generalized reflection method involving reflecting a transformation of the data. The transformation depends on a pilot estimate of the logarithmic derivative of the density at the boundary. In simulations, the new method is seen to clearly outperform an earlier generalized reflection idea. It also has overall advantages over boundary kernel methods and a nonnegative adaptation thereof, although the latter are competitive in some situations. We also present the theory underlying the new methodology.

A simple smoothing spline, II

A simple derivation is given for a kernel-type approximation of the weight function for a linear smoothing spline that explicitly includes boundary corrections. As an application, asymptotic approximations are obtained for the estimator's pointwise and integrated mean squared errors.

Finite element modelling of fatigue crack growth of surface cracked plates: Part III: Stress intensity factor and fatigue crack growth life

Stress intensity factors (SIFs) and fatigue crack growth lives, obtained by a numerical simulation technique which is based on a multiple degree of freedom model, are presented. The results include those for both semi-elliptical static cracks and propagating cracks that are not necessarily semi-elliptical. Comparisons are made between the present results and the predictions from a two degree of freedom model based on the Newman and Raju closed-form SIF equation. The results show that the widely used Newman and Raju equation might be of relatively worse accuracy for cracks whose depth is larger than 90% of the plate thickness; that the present SIF predictions during crack growth are generally in good agreement with those obtained by the two degree of freedom method; and that most of the cracks approach, but cannot subsequently maintain, an iso- K profile because of the presence of both the front and back surfaces of the plate, or the bending component of the load. The free surface correction is also considered in both the multiple and two degree of freedom methods. The results show that the free boundary correction seems to have little influence on fatigue crack growth curves; and that agreement between the fatigue crack growth curves estimated from the present technique and the Newman and Raju ‘two-point plus semi-ellipse’ method, assuming the relation of C C =0.9 m C A , is excellent for pure tension, while it becomes slightly worse for pure bending.

Finite element modelling of fatigue crack growth of surface cracked plates: Part II: Crack shape change

Investigations into the shape change of surface fatigue cracks are made by using the multiple degree of freedom model described in Part I. Three combinations of tension and bending loads are considered, i.e. DOB = 0 (pure tension), 0.5 and 1 (pure bending). Analyses of the shape of propagating crack fronts show that the semi-elliptical profile is approximately maintained during crack growth for all loading cases. Generally, the trend of aspect ratio changes predicted agrees with that from the Newman and Raju method for all three loading cases. However, for pure tension, as the crack closely approaches the plate back surface, a slight rise of aspect ratio was calculated, an effect which is absent in the predictions using the Newman and Raju method. The free boundary correction produces a slight effect on aspect ratio variations but seems to have extremely little influence on fatigue crack growth curves. The present predictions are in good agreement with limited experimental results on surface crack shape changes found in the literature.

Material compressibility effects for the squeeze of very thin films

The purpose of the present work is the study and clarification of the essential role played by the material compressibility of very thin solid layers such as for instance appear in surface force experiments. For the sake of simplicity, attention will be focused on an elastic film squeezed between rigid surfaces. The starting point is the classical lubrication theory reformulated within the framework of linear elasticity (Incompressible Reynolds Model). This model is then extended to include compressibility effects. This extension is based on a phenomenological analysis of the stress and strain fields obtained in some simple model cases and which are shown to correspond to an oedometric squeeze inside the contact with boundary corrections. This results in the oedometric Reynolds model which is then applied to two special cases: a uniform film of constant thickness under plane strain condition and the interfacial film occurring in the sphere/plane contact. These two problems confirm the fact that compressibility cannot be neglected for very thin films and show that the governing adimensional parameters combine compressibility and thinness.

Analysis of sound generated by free shear flows using direct numerical simulations

The sound produced by large-scale structures in free shear flows is investigated using direct numerical simulations (DNS). Both temporal and spatial DNS approaches are investigated, with special attention given to the former due to its lower computational cost. It is shown that the temporal approach can be used to investigate Mach-wave generation but not the general sound emitted by large-scale subsonic sources. Consequently, temporal DNS data of supersonic mixing layers undergoing transition to turbulence are analyzed. Two dominant Mach waves are found, each of which is identified with vortical features in the flow. The spatial DNS approach is then investigated to study the effect of the computational box size on the sound calculation. A large-scale model is used to show that the low-subsonic case is more restrictive in that sense than the supersonic one. The first case is further investigated by calculating the basic radiation emitted by axisymmetric jets, using the compact Lighthill and Mohring–Kambe formulations. Boundary corrections are developed and tested to reduce the box size effect and to improve the agreement between the two formulations. Finally, the effect of the retarded-time variation along the jet is discussed.