大尺寸视觉测量精度的理论和实验研究
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摘要
随着制造业的发展,对测量任务提出了大范围、高精度、现场测量,甚至动态测量的要求。传统的三维测量技术无法满足这一要求,在这种背景下,视觉测量技术得以产生并成为一个重要的研究方向。视觉测量技术以图像为信息的载体,和计算机技术紧密的结合,具有非接触、快速测量、高精度等特点,已被广泛应用于各种测量任务中。视觉测量系统的精度直接决定着该系统的价值,因此研究视觉测量的精度理论及实验有重要的意义。
本文在相关项目的资助下,较系统的研究了大尺寸视觉测量精度的理论,具体涵盖了测量的误差源、误差传递分析、精度的评价、摄像机标定等方面。论文主要针对以下几个关键问题展开了研究并取得相应成果：
(1)为了推导重建点的不确定度、投影矩阵和像点不确定度的数学关系,提出了利用参数方程重新描述投影过程的新思路。文中改变了视觉测量系统的原有解算方程,利用参数方程描述投影过程,并重新推导了三维重建点的解算方程。该方法克服了原有分析方法过于繁杂的不足,简化了误差传递分析,给出了明确的重建点不确定度的数学公式。同时,利用该数学公式估计权值,提出了视觉测量系统的加权最小二乘算法,仿真和实验结果表明,该算法在摄像机数量较少的条件下解算精度优于原有方法,在摄像机数量较多的条件下解算精度不次于原有方法。
(2)针对视觉测量系统样本量小,误差非典型分布,以及并非所有的影响因素都可以建立明确的数学公式的问题,将灰色系统理论用于视觉测量系统。文中首先改进了灰色系统理论,提出利用灰色系数向量来描述测量数据的不确定度,在此基础上利用灰色系统关联分析方法,研究因素对视觉测量系统精度的影响,该方法弥补了采用数理统计方法作系统分析导致的不足,给出了影响因素和测量精度之间的关联度,为视觉测量方案的设计提供了参考依据。
(3)针对大尺寸视觉测量的精度评价问题,提出了以距离约束为基础,进行点的拟合,利用拟合点估计偏差和不确定度的评定方法,并定义为拟合点的偏差和离散度。该方法首先在视场内建立多个基准距离；利用距离和坐标系的选取无关的性质,在视觉测量系统中,基于距离约束对点的偏差进行拟合。由于存在误差,使得该点的拟合存在离散度,从而将多个控制点的不确定度传递到拟合点上,利用该点的拟合不确定度来表示整个视觉测量的不确定度。实验中,偏差估计达到了设定的置信水平,不确定度的估计也符合实际值。
(4)摄像机参数标定是视觉测量的关键环节,本文针对大尺寸视觉测量系统的摄像机标定问题,提出了二维柔性拼接标定方法。该方法基于多个子标定板,各子标定板分为扩展区和识别区,其中识别区由编码点组成,通过编码点的匹配使得多个子标定板拼接成一个虚拟的母标定板,从而构成一个大面积的二维标定板。该方法可以随意布置标定板,在视场内随意的扩展母标定板的面积,并且标定板制备非常方便,可以很好的适用于大尺寸视觉测量系统的摄像机标定。实验结果表明,该方法的标定精度较高。
Measurement is an important method for human beings to understand the world and is the basis of science development. With the development of manufacturing industries, the large-scale, high accuracy, even all attitude and dynamical measurement are required. The traditional three-dimensional measurement technology (CMM) can not meet these requirements. In this context, the vision measurement technology emerges and is becoming more important. Based on the rigorous theory and modern software and hardware facilities, vision measurement system has been closely combined with computer. The vision measurement technology as a non-contact, high accuracy, rapid measurement method has been applied widely. Accuracy is the core indicator of any measurement task, so it is significance to study the accuracy theory of vision measurement.
Supported by relevant fund project, the accuracy theory of vision measurement is studied. In this paper, the research covered measurement error sources, error propagation analysis, accuracy evaluation and camera calibration. The dissertation conducts researches on the following issues:
(1)In order to derive mathematical formulas from the uncertainty of reconstructing points, projection matrix and the uncertainty of image points, the vision measurement theory based on the parameter equations is proposed. In this paper, the original projective equations are substituted by parameter equations, and the solved fomulas are rederived. This method overcomes the original disadvantages. By this method the error propagation analysis is simplified and the mathematical formulas of uncertainty of reconstructing points are provided clearly. Based on the formulas, the weighted least square algorithm for vision measurement is proposed. Simulation and experiment results show that the method in the conditions of small number cameras is better than the original method, and in the conditions of large number cameras is not worse than the original method.
(2) For the small sample size of vision measurement, error atypical distribution, and not all factors can be expressed by formulas, the grey system theory is used to vision measurement system analysis. Firstly, some part of the grey theory is researched and improved in this paper. The grey coefficient vector is proposed to describe the uncertainty of vision measurement that increases the stability. Then the grey system relation analysis method is used to study the impact of those factors. The grey theory is used to research the vision measurement system to make up some shortcoming of the statistical method and the correlation between the measurement accuracy and factors is described. This method provides a reference for the vision measurement plan design.
(3) In order to evaluate the measurement accuracy of large scale vision measurement system, the method named "the variance of fitting point" based on distance constraints was proposed. Firstly, several line segments of known length with common vertex were placed in the view field and these length values were considered as true values. In vision measurement system coordinate, these line segments could not cross one point because of the error existence. According to the length constraint, a point would be fitted by the least error square algorithm. Finally, the measurement accuracy was denoted by the variance of the fitting point. In the experiment, bias estimation for 88 points has one point bias beyond the limit deviation, and the uncertainty evaluation is consistent.
(4) The camera calibration is key factor of vision measurement. Focusing on the camera calibration of the large scale vision measurement system, the calibrating method based on two-dimensional connectible flexible object is proposed by this paper. The method based on many two-dimensional objects that include extending part and discriminative part. The discriminative part composed by encoded points. Many sub-objects connected by those encode points that make up of a large size two-dimensional object. This method can connect sub-object without errors, then calibrating the camera with high precision. The method can extend the two-dimensional object area enough large, and it is flexible and convenience. The method can accomplish the camera calibration task of the large scale vision measurement system.
本文在相关项目的资助下,较系统的研究了大尺寸视觉测量精度的理论,具体涵盖了测量的误差源、误差传递分析、精度的评价、摄像机标定等方面。论文主要针对以下几个关键问题展开了研究并取得相应成果：
(1)为了推导重建点的不确定度、投影矩阵和像点不确定度的数学关系,提出了利用参数方程重新描述投影过程的新思路。文中改变了视觉测量系统的原有解算方程,利用参数方程描述投影过程,并重新推导了三维重建点的解算方程。该方法克服了原有分析方法过于繁杂的不足,简化了误差传递分析,给出了明确的重建点不确定度的数学公式。同时,利用该数学公式估计权值,提出了视觉测量系统的加权最小二乘算法,仿真和实验结果表明,该算法在摄像机数量较少的条件下解算精度优于原有方法,在摄像机数量较多的条件下解算精度不次于原有方法。
(2)针对视觉测量系统样本量小,误差非典型分布,以及并非所有的影响因素都可以建立明确的数学公式的问题,将灰色系统理论用于视觉测量系统。文中首先改进了灰色系统理论,提出利用灰色系数向量来描述测量数据的不确定度,在此基础上利用灰色系统关联分析方法,研究因素对视觉测量系统精度的影响,该方法弥补了采用数理统计方法作系统分析导致的不足,给出了影响因素和测量精度之间的关联度,为视觉测量方案的设计提供了参考依据。
(3)针对大尺寸视觉测量的精度评价问题,提出了以距离约束为基础,进行点的拟合,利用拟合点估计偏差和不确定度的评定方法,并定义为拟合点的偏差和离散度。该方法首先在视场内建立多个基准距离；利用距离和坐标系的选取无关的性质,在视觉测量系统中,基于距离约束对点的偏差进行拟合。由于存在误差,使得该点的拟合存在离散度,从而将多个控制点的不确定度传递到拟合点上,利用该点的拟合不确定度来表示整个视觉测量的不确定度。实验中,偏差估计达到了设定的置信水平,不确定度的估计也符合实际值。
(4)摄像机参数标定是视觉测量的关键环节,本文针对大尺寸视觉测量系统的摄像机标定问题,提出了二维柔性拼接标定方法。该方法基于多个子标定板,各子标定板分为扩展区和识别区,其中识别区由编码点组成,通过编码点的匹配使得多个子标定板拼接成一个虚拟的母标定板,从而构成一个大面积的二维标定板。该方法可以随意布置标定板,在视场内随意的扩展母标定板的面积,并且标定板制备非常方便,可以很好的适用于大尺寸视觉测量系统的摄像机标定。实验结果表明,该方法的标定精度较高。
Measurement is an important method for human beings to understand the world and is the basis of science development. With the development of manufacturing industries, the large-scale, high accuracy, even all attitude and dynamical measurement are required. The traditional three-dimensional measurement technology (CMM) can not meet these requirements. In this context, the vision measurement technology emerges and is becoming more important. Based on the rigorous theory and modern software and hardware facilities, vision measurement system has been closely combined with computer. The vision measurement technology as a non-contact, high accuracy, rapid measurement method has been applied widely. Accuracy is the core indicator of any measurement task, so it is significance to study the accuracy theory of vision measurement.
Supported by relevant fund project, the accuracy theory of vision measurement is studied. In this paper, the research covered measurement error sources, error propagation analysis, accuracy evaluation and camera calibration. The dissertation conducts researches on the following issues:
(1)In order to derive mathematical formulas from the uncertainty of reconstructing points, projection matrix and the uncertainty of image points, the vision measurement theory based on the parameter equations is proposed. In this paper, the original projective equations are substituted by parameter equations, and the solved fomulas are rederived. This method overcomes the original disadvantages. By this method the error propagation analysis is simplified and the mathematical formulas of uncertainty of reconstructing points are provided clearly. Based on the formulas, the weighted least square algorithm for vision measurement is proposed. Simulation and experiment results show that the method in the conditions of small number cameras is better than the original method, and in the conditions of large number cameras is not worse than the original method.
(2) For the small sample size of vision measurement, error atypical distribution, and not all factors can be expressed by formulas, the grey system theory is used to vision measurement system analysis. Firstly, some part of the grey theory is researched and improved in this paper. The grey coefficient vector is proposed to describe the uncertainty of vision measurement that increases the stability. Then the grey system relation analysis method is used to study the impact of those factors. The grey theory is used to research the vision measurement system to make up some shortcoming of the statistical method and the correlation between the measurement accuracy and factors is described. This method provides a reference for the vision measurement plan design.
(3) In order to evaluate the measurement accuracy of large scale vision measurement system, the method named "the variance of fitting point" based on distance constraints was proposed. Firstly, several line segments of known length with common vertex were placed in the view field and these length values were considered as true values. In vision measurement system coordinate, these line segments could not cross one point because of the error existence. According to the length constraint, a point would be fitted by the least error square algorithm. Finally, the measurement accuracy was denoted by the variance of the fitting point. In the experiment, bias estimation for 88 points has one point bias beyond the limit deviation, and the uncertainty evaluation is consistent.
(4) The camera calibration is key factor of vision measurement. Focusing on the camera calibration of the large scale vision measurement system, the calibrating method based on two-dimensional connectible flexible object is proposed by this paper. The method based on many two-dimensional objects that include extending part and discriminative part. The discriminative part composed by encoded points. Many sub-objects connected by those encode points that make up of a large size two-dimensional object. This method can connect sub-object without errors, then calibrating the camera with high precision. The method can extend the two-dimensional object area enough large, and it is flexible and convenience. The method can accomplish the camera calibration task of the large scale vision measurement system.
引文
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