面向位姿测量的摄像机标定方法及应用研究

在工业、航天、医疗等许多领域中，经常需要测量两个空间物体坐标系间的相对位姿。位姿测量方法一般包括声纳或激光测距、GPS、视觉方法等多种方法，其中视觉方法由于其信息量大、处理速度快等特点发挥了越来越重要的作用。在基于模型的单目视觉位姿测量中，位姿测量系统的测量精度与摄像机标定误差、图像坐标的检测误差、目标模型的测量误差等许多因素有关，而摄像机标定误差是影响位姿测量精度的一个主要误差来源，是测量系统内在的不可避免的误差。 实际应用中，提高整个系统的测量精度是三维视觉测量的一项重要任务，而摄像机标定精度的提高将有效地提高位姿测量精度。针对传统的摄像机标定方法在实际工程应用中存在的问题，以提高基于模型的单目视觉位姿测量系统的测量精度为目标，利用理论推导和仿真实验相结合的方法，首先通过从几何意义求解摄像机内外参数，深刻理解摄像机各参数的物理意义；然后在此基础上，重点研究摄像机标定空间的选择、标定参数误差与位姿测量误差之间以及标定参数误差与测量空间之间的关系分析；最后在理论研究的基础上，针对工程应用提出摄像机标定的相应策略，以提高整个系统的测量精度。 首先，在基于几何意义的摄像机内外参数求解方法研究中，从摄像机投影变换矩阵出发，通过几何思路求解摄像机内外参数；同时在此求解过程中，从几何意义推导得到描述透视投影变换的 矩阵必须满足的约束条件。这对深刻理解摄像机各参数的物理意义及其几何关系，对从直观几何方面分析摄像机参数对位姿精度的影响有着一定的意义。 其次，针对标定空间对位姿测量精度的影响，首先推导出标定空间与标定参数误差之间的关系，在此基础上，再给出标定参数误差和位姿测量结果误差之间的关系。实验结果表明：不管测试目标的成像范围如何，在满视场范围内标定时标定误差最小，从而可以得到更高的位姿测量精度。研究结果可为实际工程应用中测量系统的摄像机标定提供理论依据，对标定点的布置和摆放具有指导意义。 最后，在摄像机标定参数误差对位姿测量精度的影响研究中，通过理论推导结合仿真实验及几何解释说明，使用误差传播的方法，建立了位姿测量误差受摄像机标定参数误差影响的数学模型，分析了摄像机标定参数误差与位姿测量误差的关系，得到如下结论：测量距离方向位置精度主要受焦比误差和摄像机外参数光轴方向平移量误差的影响；姿态角精度主要受主点误差和摄像机外参数旋转角误差的影响。在标定参数误差与测量空间之间的关系方面，摄像机内外参数的误差在不同测量距离有着不同的影响。近距离时，应主要考虑外参数光轴方向平移量误差的影响；而远距离时，应主要考虑内参数焦比误差的影响。该结论可以指导摄像机标定方法的选择，根据不同的情况采用不同的算法以满足实际精度需求，从而达到优化系统设计，提高整个定位系统性能的目的，对于指导视觉位姿测量系统的工程应用具有一定的意义。

基于EIV模型的点线位姿估计研究

位姿估计是计算机视觉的一个重要的研究内容，它在目标定位、摄像机标定、手眼系统、移动机器人及三维重建等领域有着广泛的应用。常用的确定目标位姿的视觉方法包括基于模型的单目视觉方法和双目视觉方法。目前，单目视觉方法大多采取点特征和线特征，这是因为点线特征的提取比较容易，而且具有数学上的简易性。在实现目标位姿测量时，像素量化引起的特征点的图像坐标噪声是不可避免的问题，它必将引起物体的位姿计算值的误差。同时，为了充分利用图像处理中提取的点线特征，我们希望能将这些特征在一个统一的数学模型下进行位姿估计。针对上述问题，本文取得了如下研究成果： 首先，采用双重四元数同时表示旋转和平移，从而将点线特征约束统一成二次型约束的形式。这种形式利于采用伪线性化方法简化问题，进而通过迭代算法求解位姿参数。 然后，为了在位姿估计中考虑到量化误差的影响，引入了EIV模型描述影响点线特征投影的量化误差。同时，给出了优化目标函数，提出了基于奇异值分解的迭代算法来估计位姿参数，并在迭代算法中通过增加一条收敛规则解决了实现过程中遇到的振荡问题，保证了算法的收敛。和传统的迭代算法相比，该算法具有以下两个特点：第一，受初始值的影响小，实验中采用随机初值依然可以收敛；第二，迭代过程不是采用传统的步长搜索，收敛速度快。此外，本文还研究了位姿参数估计值的统计特性，证明了估计值的无偏性。 最后，考虑到量化误差、点线特征数目和目标相对摄像机的距离等影响位姿估计结果的几个因素，本文设计了仿真实验和实际实验分别对点特征和线特征的位姿估计进行测试。结果表明：该算法可以应用于任意三个以上点特征和线特征的情况，受初值影响小，收敛快，提高了位姿估计结果的精度和鲁棒性。

一种基于旋转体的摄像机定位方法

基于旋转体的摄像机定位是单目合作目标定位领域中的涉及较少并且较为困难的一个问题,传统的基于点基元、直线基元及曲线基元的定位方法在用于旋转体定位过程中都存在相应的问题.文中设计了一种由4个相切椭圆构成的几何模型,该模型环绕于圆柱体表面,利用二次曲线的投影仍然是二次曲线的特性和椭圆的相应性质能够得到唯一确定模型位置的3个坐标点,从而将旋转体定位问题转化为P3P问题.在对P3P的解模式区域进行分析后,推导了根据模型上可视曲线的弯曲情况来确定P3P问题解模式的判别方法,并给出证明过程.仿真实验表明了这种模型定位方法的有效性.最后利用这个模型引导机械手完成目标定位的实验.

基于模型的位姿估计中优化方法研究

介绍了基于模型的位姿估计中所使用的一些优化方法。为了提高位姿估计的精度,摄像机的标定参数必须足够精确,这就对标定过程的非线性优化算法提出了很高的要求,采用了一种新的优化目标函数,用来最小化控制点间的三维重建误差,从而使标定参数是全局最优;在双像机位姿估计中,引入了实时遗传算法进行全局搜索,加快了算法的收敛速度。最后的实验证明了这些方法的正确性并显示出这些方法在精度上比传统方法有了较大程度的提高。

Influence of threshold stress on the estimation of the Weibull statistics

The influence of threshold stress on the estimation of the Weibull statistics is discussed in terms of the Akaike information criterion. Numerical simulations show that, if sample data are limited in number and threshold stress is not too large, the two-parameter Weibull distribution is still a preferred choice. For example, the fit of strength data of glass and ceramics to the two- and three-parameter Weibull distributions is compared.

Parameter-estimation of a spherical top inductively-coupled plasma source with global-model

Using spatially averaged global model, we succeed in obtaining some plasma parameters for a low pressure inductively coupled plasma source of our laboratory. As far as the global balance is concerned, the models can give reasonable results of the parameters, such as the global electron temperature and the ion impacting energy, etc. It is found that the ion flow is hardly affected by the neutral gas pressure. Finally, the magnetic effects are calculated by means of the method. The magnetic field can play an important role to increase plasma density and ion current.

The fatigue life estimation of notched specimens under random loading

The LY12-cz aluminium alloy sheet specimens with a central hole were tested under constant amplitude loading, Rayleigh narrow band random loading and a typical fighter broad band random loading. The fatigue life was estimated by means of the nominal stress and the Miner's rule. The stress cycles were distinguished by the rainflow count, range count and peak value count, respectively. The comparison between the estimated results and the test results was made. The effects of random loading sequence and small load cycles on fatigue life were also studied.

Estimation of Correlation Distance of Soil Properties by Geostatistics

Random field theory has been used to model the spatial average soil properties, whereas the most widely used, geostatistics, on which also based a common basis (covariance function) has been successfully used to model and estimate natural resource since 1960s. Therefore, geostistics should in principle be an efficient way to model soil spatial variability Based on this, the paper presents an alternative approach to estimate the scale of fluctuation or correlation distance of a soil stratum by geostatistics. The procedure includes four steps calculating experimental variogram from measured data, selecting a suited theoretical variogram model, fitting the theoretical one to the experimental variogram, taking the parameters within the theoretical model obtained from optimization into a simple and finite correlation distance 6 relationship to the range a. The paper also gives eight typical expressions between a and b. Finally, a practical example was presented for showing the methodology.

An Instrumented Indentation Method for Young's Modulus Measurement with Accuracy Estimation

The relationships between indentation responses and Young's modulus of an indented material were investigated by employing dimensional analysis and finite element method. Three representative tip bluntness geometries were introduced to describe the shape of a real Berkovich indenter. It was demonstrated that for each of these bluntness geometries, a set of approximate indentation relationships correlating the ratio of nominal hardness/reduced Young's modulus H (n) /E (r) and the ratio of elastic work/total work W (e)/W can be derived. Consequently, a method for Young's modulus measurement combined with its accuracy estimation was established on basis of these relationships. The effectiveness of this approach was verified by performing nanoindentation tests on S45C carbon steel and 6061 aluminum alloy and microindentation tests on aluminum single crystal, GCr15 bearing steel and fused silica.

Algorithm of far-field centre estimation based on phase-only matched filter

Estimation of the far-field centre is carried out in beam auto-alignment. In this paper, the features of the far-field of a square beam are presented. Based on these features, a phase-only matched filter is designed, and the algorithm of centre estimation is developed. Using the simulated images with different kinds of noise and the 40 test images that are taken in sequence, the accuracy of this algorithm is estimated. Results show that the error is no more than one pixel for simulated noise images with a 99% probability, and the stability is restricted within one pixel for test images. Using the improved algorithm, the consumed time is reduced to 0.049 s.