Aide in decision-making: contribution to uncertainties in three-dimensional measurement

The authorities of the standards organization International Organization of Standardization (ISO) advocate mastering any uncertainties in all parts of the industrialization process. In the three-dimensional (3D) measurement process, uncertainty is usually obtained at the end of a battery of tests. It is defined as a whole because it includes several types of errors, known systematic components, unknown systematic components and random components. Automated calculations of uncertainty can be made based on statistics. This method is based on statistical concepts, which are in accordance with “The Guide to the expression of the uncertainty in measurement” (GUM). It also enables us to generate uncertainties on the verification of ISO specifications (or specs in the ISO directives). In the course of this article, a usage will be presented that takes the knowledge of uncertainties into account: this usage will help the operator to take a decision on the conformance of a mechanical part in reference to its conformance to geometric tolerance.     

Combining multiple Large Volume Metrology systems: Competitive versus cooperative data fusion

Large Volume Metrology (LVM) tasks can require the concurrent use of several measuring systems. These systems generally consist of set of sensors measuring the distances and/or angles with respect to a point of interest so as to determine its 3D position. When combining different measuring systems, characterized by sensors of different nature, competitive or cooperative methods can be adopted for fusing data. Competitive methods, which are by far the most diffused in LVM, basically perform a weighted mean of the 3D positions determined by the individual measuring systems. On the other hand, for cooperative methods, distance and/or angular measurements by sensors of different systems are combined together in order to determine a unique 3D position of the point of interest.This paper proposes a novel cooperative approach which takes account of the measurement uncertainty in distance and angular measurements of sensors of different nature. The proposed approach is compared with classical competitive approaches from the viewpoint of the metrological performance. The main advantages of the cooperative approach, with respect to the competitive one, are: (i) it is the only option when the individual LVM systems are not able to provide autonomous position measurements (e.g., laser interferometers or single cameras), (ii) it is the only option when only some of the sensors of autonomous systems work correctly (for instance, a laser tracker in which only distance – not angular – measurements are performed), (iii) when using systems with redundant sensors (i.e. photogrammetric systems with a large number of distributed cameras), point localization tends to be better than that using the competitive fusion approach.     

Efficiency of grid representation and its algorithms for areal 3D scan data

This paper describes the efficiency of a grid representation for an areal 3D scan data and the algorithms for managing measurement data captured by areal 3D scanners. Due to the measurement principles of areal 3D scanners, a measurement point is generated for each pixel of the imaging sensor inside the 3D scanner. Therefore, when the measurement points are perspectively projected on the image plane of the imaging sensor, each point has one-to-one correspondence to the imaging elements of the sensor that has a regular grid structure. By using this property, measurement points are represented by their depth values in a grid representation model. Compared to the conventional representation model, such as triangular mesh and cloud of points, the grid representation uses less memory and allows efficient algorithms for processing the measurement data captured by areal 3D scanners. This paper was recommended for publication in revised form by Associate Editor Soon Hung Han Minho Chang is a Professor at the department of mechanical engineering at Korea University in Seoul Korea. He received a PhD degree in Mechanical Engineering from MIT in 1996. He worked for Korea Institute of Science and Technology. His research interests include mechanical design, three-dimensional measurement, and CAD. Yun Chan Chung is a Professor in the department of die and mold engineering at Seoul National University of Technology, Korea. He worked for Cubictek and DaimlerChrysler, developing CAD/CAM systems mainly in die and mold making. He received PhD in Industrial Engineering from KAIST in 1996. His research interests include digital manufacturing, tool-path generation and verification, and software engineering.     

全站仪测量自行火炮身管指向的方法改进

在实现自行火炮身管指向测量的各类方法中,全站仪测量法综合性能表现良好。但传统全站仪测量身管指向方法存在缺乏北向基准、存在轴线模拟误差的问题,因此提出了一种基于旋转矩阵的全站仪测量自行火炮身管真实指向方法。然后,利用欧拉-罗德里格斯公式推导出标记点连线与真实轴线指向的偏差公式,进而得到了真实指向相对于各观测量的不确定度模型。随后,为了减小测量方法的误差,研究了全站仪最佳布站位置,并基于蒙特卡罗方法原理进行寻优解算。最后,进行了模拟身管实装实验,实验结果表明,最佳布站方式下的测量不确定度在0.1以内,验证了本方法的可行性和准确性,抑制了由于布站方式引起的测量误差。     

An approach to determining the kinematic parameters of biomechanical systems with applications to the wrist.

This paper presents an accurate and robust approach for determining the kinematic parameters of biomechanical systems. A computationally efficient algorithm is given for estimating the translation vector and rotation matrix of a moving body from measurements of the position of at least four spatially distributed points on the body. This algorithm provides an estimation of the spatial location and orientation of the body which is less sensitive to measurement error than other methods. It is indicated how the kinematic parameters can be used to determine the linear translation and angular rotation of the moving body in terms of an anatomically relevant coordinate system. The design, fabrication and calibration of an inexpensive, serial-link, three-dimensional mechanical digitizer for use in data acquisition is described. This device is kinematically optimized and is easy to use for accurate data collection. An implementation of this approach to quantifying certain aspects of the kinematics of the human wrist is discussed.     

Volumetric error modelling of a stereo vision system for error correction in photogrammetric three-dimensional coordinate metrology

Optical three-dimensional coordinate measurement using stereo vision has systematic errors that affect measurement quality. This paper presents a scheme for measuring, modelling and correcting these errors. The position and orientation of a linear stage are measured with a laser interferometer while a stereo vision system tracks target points on the moving stage. With reference to the higher accuracy laser interferometer measurement, the displacement errors of the tracked points are evaluated. Regression using a neural network is used to generate a volumetric error model from the evaluated displacement errors. The regression model is shown to outperform other interpolation methods. The volumetric error model is validated by correcting the three-dimensional coordinates of the point cloud from a photogrammetry instrument that uses the stereo vision system. The corrected points from the measurement of a calibrated spherical artefact are shown to have size and form errors of less than 50 μm and 110 μm respectively. A reduction of up to 30% in the magnitude of the probing size error is observed after error correction is applied.     

Analytical solution for interface stresses due to concentrated surface force

The two-dimensional analytical solution for interface stresses due to concentrated surface force has been deduced, by introducing infinite mirror points which are the images of the load point reflected by the interface and the free surface, and adopting the interchange law of differentiation. The analytical solution can be represented in terms of the summation of the “partial” Goursat's complex stress functions defined in the local coordinate systems with their origins placed at each of the mirror points. It is found that the “partial” stress functions corresponding to a higher order mirror point can be determined from those to the lower one. It is also found that the contribution of the “partial” stress functions to the stress field decreases with the increase of the corresponding mirror point order, therefore, only considering the stress functions corresponding to the first several order mirror points can give the accurate enough solution. Numerical examination by the use of boundary element method has also been carried out to verify the theoretical development.     

基于测地线的躺卧三维颅面模型矫正

三维颅面软组织因受重力影响在躺卧与直立两种姿态下的差异较大,为将躺卧姿态下获取的三维颅面模型矫正为直立姿态下的三维模型,本文提出了一种基于测地线的躺卧三维颅面模型的直立矫正方法。首先利用测地距离的内蕴几何不变性,建立两种姿态下面部特征点的点对应;然后,利用主成分分析建立颅面特征点运动模型;最后,对待矫正的躺卧颅面模型,根据颅面特征点运动模型确定特征点的运动,根据特征点的运动确定躺卧颅面模型到直立颅面模型的变形。所提方法将与直立姿态人脸模型间的平均误差从矫正前的10-2数量级下降到矫正后的10-4数量级。本文利用测地距离的内蕴几何不变性,解决了两种姿态下面部特征点对应的难题;所建立的颅面特征点运动模型,能够较好地表示颅面在两种姿态下发生的形变,从而能够实现有效地模型矫正。     

Sampling uncertainty in coordinate measurement data analysis

There are a number of important software related issues in coordinate metrology. After measurement data are collected in the form of position vectors, the data analysis software must derive the necessary geometric information from the point set, and uncertainty plays an important role in the analysis. When extreme fit approaches (L_−∞ norm estimation approaches) are employed for form error evaluation, the uncertainty is closely related to the sampling process used to gather the data. The measurement points are a subset of the true surface, and, consequently, the extreme fit result differs from the true value. In this paper, we investigate the functional relationship between the uncertainty in an extreme fit and the number of points measured. Two major issues are addressed in this paper. The first addresses and identifies the parameters that affect the functional relationship. The second develops a methodology to apply this relationship to the sampling of measurement points.