加权最小二乘算法在机器视觉系统中的应用

Application of weighted least square method to machine vision system

为了进一步提高机器视觉的重建精度,对相机站位和重建精度之间的关系进行了分析,并在此基础上估计权值,将加权的最小二乘算法应用于机器视觉系统的三维重建算法中。利用参数方程描述了机器视觉系统,推导了空间点三维重建的参数方程解法。利用误差传递原理,分析了从相机像平面上协方差到物空间协方差的传递过程,给出了误差传递和相机布局的直接关系。然后,利用得到的物空间协方差估计加权最小二乘算法的权值,最后进行解算。仿真和实验结果表明:加权最小二乘算法总体上优于普通的最小二乘法,当噪声方差比较小时,两种算法的区别不大。但是当噪声方差>0.5时,拍摄像片数量少于30幅的情况下有更优的精度;对距离为37.0310,24.9704,26.0153cm的测量中,和普通最小二乘算法比较,加权最小二乘算法提高的精度平均为0.4cm。

In order to improve the accuracy of a recovered object by machine vision system, the relationship between the camera position and the accuracy of the recovered object is analyzed and the weighted values based on the relationship are evaluated. Then, the weighted least square method is used in the machine vision system. After expressing the machine vision model by parameter equations, a recovering equation for 3D space point recovering is deduced based on the parameter equation. Then, according to the error transmission principle, the transmission from the uncertainty of a camera image plane to the uncertainty of an observe space is analyzed, and the relationship between the error transmission and the camera position is obtained. Finally, the covariance of the observed object is used to evaluate the weighted value for the weighted least square method. Experimental results indicate that the accuracy of the weighted least square method is better than that of the general least square method. When the noise variance is bigger than 0. 5 and the number of the photos is less than 30, this method can offer a very good measuring accuracy. According to the experiment, when the measurement distances are 37. 031 0 cm, 24. 970 4 cm and 26. 015 3 cm, the weighted least square method can improve the accuracy by 0. 4 cm.