Optimized stereo reconstruction of free-form space curves based on a nonuniform rational B-spline model

Analytical reconstruction of 3D curves from their stereo images is an important issue in computer vision. We present an optimization framework for such a problem based on a nonuniform rational B-spline (NURBS) curve model that converts reconstruction of a 3D curve into reconstruction of control points and weights of a NURBS representation of the curve, accordingly bypassing the error-prone point-to-point correspondence matching. Perspective invariance of NURBS curves and constraints deduced on stereo NURBS curves are employed to formulate the 3D curve reconstruction problem into a constrained nonlinear optimization. A parallel rectification technique is then adopted to simplify the constraints, and the Levenberg-Marquardt algorithm is applied to search for the optimal solution of the simplified problem. The results from our experiments show that the proposed framework works stably in the presence of different data samplings, randomly posed noise, and partial loss of data and is potentially suitable for real scenes.     

基于UG平台的截面特征曲线全局约束优化研究

截面曲线是曲面建模过程中的重要特征,将截面特征曲线重建技术与正向设计技术相结合是实现复杂特征曲面模型重建的重要方法。针对这一问题提出了一种基于UG草图的截面特征曲线全局约束优化技术,并对实现该方法的约束表达、全局约束优化模型的建立及求解、基于UG平台的算法实现等关键技术进行了深入研究。应用实例表明,基于UG的截面特征曲线全局约束优化方法可以得到满足约束条件下的与数据点逼近的最优曲线,基于该曲线可以快速、准确地重建出具有复杂特征的曲面模型。     

Investigating the enhancement of three-dimensional diffraction tomography by using multiple illumination planes

The three dimensional (3-D) extension of the two well-known diffraction tomography algorithms, namely, direct Fourier interpolation (DFI) and filtered backpropagation (FBP), are presented and the problem of the data needed for a full 3-D reconstruction is investigated. These algorithms can be used efficiently to solve the inverse scattering problem for weak scatterers in the frequency domain under the first-order Born and Rytov approximations. Previous attempts of 3-D reconstruction with plane-wave illumination have used data obtained with the incident direction restricted at the xy plane. However, we show that this restriction results in the omission of the contribution of certain spatial frequencies near the omegaz axis for the final reconstruction. The effect of this omission is studied by comparing the results of reconstruction with and without data obtained from other incident directions that fill the spatial frequency domain. We conclude that the use of data obtained for incident direction in only the xy plane is sufficient to achieve a satisfactory quality of reconstruction for a class of objects presenting smooth variation along the z axis, while abrupt variations along the z axis cannot be imaged. This result should be taken into account in the process of designing the acquisition geometry of a tomography scanner.     

一类带两个形状参数的类四次三角Bézier曲线

给出了带两个形状参数λ1,λ2的类四次三角多项式Bézier曲线。该曲线不仅具有与四次Bézier曲线类似的性质,而且无需有理形式即可精确表示圆、椭圆、抛物线等二次曲线弧以及高精度近似表示圆柱螺线等超越曲线。利用两个参数的不同取值能够局部或整体调控曲线的形状,并且可以从两侧逼近控制多边形。讨论了两段曲线G2和C4连续的拼接条件。实例表明,该曲线在造型设计方面具有较高的应用价值。     

Topology optimization of compliant mechanisms using pairs of curves

The structural topology optimization approach can be used to generate compliant mechanisms for some desired input–output requirements. The success of the optimization depends on the structural geometry representation scheme used. In this paper, a novel representation scheme is proposed. The representation scheme is characterized by pairs of curves that are used to connect Input/Ouput (I/O) regions of the structure. Each pair of curves includes a normal curve and a fat curve. The areas bounded by the pair of curves define the material distribution between them. All I/O regions are connected to one another (either directly or indirectly) by pairs of curves in order to form one single connected load-bearing structure. A genetic algorithm for constrained and multiobjective optimization is then applied with the representation scheme of the structure in the form of a graph. Simulation results from a displacement inverter and a displacement redirector indicate that the presented representation scheme is appropriate.     

Modified Method for Dynamic Stress‐Strain Curve Determination of Closed‐Cell Foams

The paper presents a modified method for the non‐linear dynamic stress‐strain curve determination with the use of cushion curves provided by the manufacturers of closed‐cell foams. This method consists of two main stages: stage 1 – the cushion curves transformation to the coordinate system of dynamic stress‐energy density, combined with the cubic b‐spline curve approximation, and stage 2 – development of the dynamic stress‐strain curve considering that the area under the curve is equal to the energy density of a collision. The stress‐strain curves are one of the basic parameters of the foam material models used to describe the collision process, in the modelling environments of finite element method (FEM), e.g. LS‐DYNA. Performed verification consisting in the reconstruction of cushion curves using LS‐DYNA showed that the proposed method of the dynamic stress‐strain curves determination is efficient and effective. Taking into account that access to the stress‐strain curves is hindered (cushioning material manufacturers do not publish them), and the access to charts of cushion curves is easier, the proposed method for determining the stress‐strain curves can relevantly shorten the process of preparing the input data, which are required during modelling of spatial structures using FEM. Copyright © 2016 John Wiley & Sons, Ltd.     

A 3D domain decomposition approach for the identification of spatially varying elastic material parameters

The post‐treatment of (3D) displacement fields for the identification of spatially varying elastic material parameters is a large inverse problem that remains out of reach for massive 3D structures. We explore here the potential of the constitutive compatibility method for tackling such an inverse problem, provided an appropriate domain decomposition technique is introduced. In the method described here, the statically admissible stress field that can be related through the known constitutive symmetry to the kinematic observations is sought through minimization of an objective function, which measures the violation of constitutive compatibility. After this stress reconstruction, the local material parameters are identified with the given kinematic observations using the constitutive equation. Here, we first adapt this method to solve 3D identification problems and then implement it within a domain decomposition framework which allows for reduced computational load when handling larger problems. Copyright © 2015 John Wiley & Sons, Ltd.     

橡胶减振器非线性动态特性的试验研究

采用电动振动台对橡胶减振器的非线性动态特性进行了试验研究,利用正逆傅立叶变换对试验数据进行了处理.建立了橡胶减振器的动力学模型,运用Runge-Kutta法和模型曲线重构法论证了模型对单一工况参数识别的有效性.利用该模型对试验工况逐一进行识别,得到了不同工况下橡胶减振器的刚度和阻尼.分析发现识别的刚度和阻尼与振幅和频率之间呈曲面关系,表明橡胶减振器在较大振幅下的动态特性已不能用简单的曲线来描述.     

两类形状可调五次广义Ball曲线

定义了两种带形状参数的曲线。第一种曲线包含了五次Wang-Ball和Said-Ball曲线以及介于这两种曲线之间的无数曲线;第二种曲线包含了五次Said-Ball和Bézier曲线以及介于这两种曲线之间的无数曲线。通过分析这两种曲线与五次Bézier曲线之间的关系,得出了形状参数的几何意义,并给出了这两种曲线的几何作图法。     

Determination of the dispersion curve of the refractive index by the stockwell transform

The determination of dispersion curves by the Stockwell transform (ST) is proposed. The required numerical data for dispersion curves are produced from the transmittance signal by the ST. The obtained data are then used to estimate the unknown dispersion parameters in Cauchy's formula using the genetic algorithm method through the minimisation problem based on the least-squares curve fitting. The results have shown that the dispersion curve obtained from the ST produced more improved outcomes than those obtained from the continuous wavelet transform.     

基于半正交B样条小波的任意控制顶点数曲线光顺

目前,小波分析应用于逆向工程时,对控制顶点有特殊要求,只能处理2j r个控制顶点的图形,为此提出了一种可以光顺任意控制顶点B样条曲线的小波分析新方法。在介绍B样条定义的基础上,从小波分析的定义出发,用严格的数学证明推导了任意控制顶点曲线的小波分解与重构具体算法。最后,该算法成功应用于B样条曲线的小波光顺,实例表明,该算法准确、结果稳定,效率理想。     

An Insightful Marginal Cost Analysis for an Electric Utility Capacity Planning Problem

Given a situation in which a finite number of load curves occur with either known probabilities or over nonoverlapping fractions of time, the problem addressed herein is to conduct a marginal cost analysis for allocating to the various load curves, the capital costs of equipments used in an optimal capacity expansion plan. Such an allocation may be used, for example, in determining a marginal cost time-of-day pricing scheme. A recent paper solves this problem through a formal mathematical programming duality approach. The purpose of the present paper is to first demonstrate that closed form expressions for such marginal cost capital allocations can be readily obtained through an intuitive and insightful perturbation analysis, without any recourse to mathematical programming techniques. Hence, a practitioner can therefore more easily understand and interpret the available duality results. Furthermore, the analysis contained in this paper helps to unify and generalize some existing contributions in the literature, and sheds light on the extent of information contained in the so-called equivalent load duration curve. By way of this analysis, a new set of easier to use and more general capital cost allocation formulae are also obtained.     

Blind-deconvolution analysis of transient curves by the use of a convolved autoregressive model

A new method is proposed for analyzing a transient curve as a multiexponential decay convolved with an instrumental response function and for estimating the decay constants and amplitudes without knowledge of the response function. The method requires a single-exponential reference curve observed with the same response function as that for a sample curve, whereas its decay-constant and amplitude values are not necessary for the estimation. The sample and reference curves are analyzed with a convolved autoregressive model, which is based on a linear least-squares algorithm. This method has the advantage of a short computation time when compared with a conventional nonlinear least-squares fitting technique. Double-exponential curves are also acceptable as the reference, if two curves with different decay parameters can be provided for the analysis.     

The relation between fit and prediction for alternative forms of learning curves and relearning curves

Learning-curve models fitted to initial data are used to predict subsequent performance; however, the model that fits the initial data best may not predict best in future periods - a paradox documented in applications of other prediction models. Little evidence exists about the magnitude of the problem in the domain of learning curves and relearning curves. Using laboratory data, the authors examine the predictive ability of alternative models, examine the strength of the relation between goodness-of-fit and predictive ability, and test whether this relation is the same for both learning curves and relearning curves. Although the correlations between measures of goodness-of-fit and predictive ability are not high, one curve (a log-log-linear model recently introduced to the literature) tended to dominate the rankings on the basis of predictive ability for both learning curves and relearning curves. This curve also tended to provide the best fit in the estimation period as a relearning curve, and the second-best fit as a learning curve.     

Quantitative optical image reconstruction of turbid media by use of direct-current measurements

We present a detailed experimental study concerning quantitative optical property reconstruction of heterogeneous turbid media by use of absolute dc data only. We performed experiments by using tissuelike phantoms in both single-target and multitarget configurations in which variations in target size and optical contrast with the background were explored. Our results show that both scattering and absorption images can be reconstructed quantitatively by use of dc data only, whereas it was impossible to obtain such quantitative information in previously reported studies. We believe that this improvement is primarily a result of the realization of a novel data preprocessing/optimization scheme for accurately determining several critical parameters needed for reconstruction. The use of this data preprocessing/optimization scheme also eliminates the calibration reference measurement previously required for reconstruction. Experimental confirmation of this scheme is given in detail.     

Evaluation of the tensile properties of a material through spherical indentation: definition of an average representative strain and a confidence domain

In the present article, a new method for the determination of the hardening law using the load displacement curve, F–h, of a spherical indentation test is developed. This method is based on the study of the error between an experimental indentation curve and a number of finite elements simulation curves. For the smaller values of these errors, the error distribution shape is a valley, which is defined with an analytic equation. Except for the fact that the identified hardening law is a Hollomon type, no assumption was made for the proposed identification method. A new representative strain of the spherical indentation, called “average representative strain,” ε _aR was defined in the proposed article. In the bottom of the valley, all the stress–strain curves that intersect at a point of abscissa ε _aR lead to very similar indentation curves. Thus, the average representative strain indicates the part of the hardening law that is the better identified from spherical indentation test. The results show that a unique material parameter set (yield stress σ _y, strain hardening exponent n) is identified when using a single spherical indentation curve. However, for the experimental cases, the experimental imprecision and the material heterogeneity lead to different indentation curves, which makes the uniqueness of solution impossible. Therefore, the identified solution is not a single curve but a domain that is called “solution domain” in the yield stress–work hardening exponent diagram, and “confidence domain” in the stress–strain diagram. The confidence domain gives clear answers to the question of uniqueness of the solution and on the sensitivity of the indentation test to the identified hardening laws parameters.     

Effect of interaction between deep impurity traps on thermally stimulated currents in semiconductors

We demonstrate that the problem of determining the concentrations of free and trapped charge carriers in wide-gap semiconductors from their thermally stimulated current (TSC) curves for m interacting levels in an implicit difference scheme for numerically solving differential rate equations of TSCs reduces to finding the roots of an algebraic equation of degree m + 1. For two interacting trap levels of the same nature (electron or hole traps), we present an algorithm for numerically solving differential rate equations of TSCs which allows the concentrations of free and trapped charge carriers to be determined. TSC curves can be divided into four types according to their shape (dependent on trap parameters and experimental conditions): “splitting” (two well-resolved peaks separated by a temperature range), “saddle” (a well-defined minimum between two peaks), shoulder (on the high- or low-energy side), and “coalescence-absorption” (one peak). The modeling results are used to interpret an experimental TSC curve for semiconducting InSe and to demonstrate that, to adequately interpret experimental TSC data, one should use a model for the interaction between levels.