照相站空间基准标定方法及测量误差分析

根据相机内外参数标定方法的结论与性质，通过对阴影成像系统成像原理的分析，利用泰勒级数对图像坐标拾取偏差引起的空间坐标测量误差进行研究，获得了阴影成像系统空间坐标测量误差的数学模型。假定图像坐标拾取误差满足独立同分布，得到测量误差一次矩和二次矩的数学表达式，并进一步分析相机位于标定面同侧且与标定面等距时测量误差的概率特性。符号分析及数值验证结果表明：阴影成像系统坐标测量误差的各个分量非独立；图像识别误差以因子的形式影响测量误差；文中标定方法测量误差的均值与物点到标定面的距离相关且呈线性变化，而测量误差的自协方差则在空间呈非线性分布；物点靠近相机有利于减小测量误差的均值和协方差。

Calibration of Shadowgraphy System and Analysis of Measuring Error

Based on the shadowgraphy system and the calibration of camera intrinsic and extrinsic parameters, the measuring errors associated by image recognition errors are studied, and an error model is built by using Taylor series expansion. Assuming that the image recognition errors are of independent identical distribution (IID), the mathematical expressions of the first moment and the second moment are presented for the measuring errors. Furthermore, the probabilistic properties of the measuring errors are studied according to the hypothesis that the distance between the cameras and the calibration surface are equal. The symbolic analysis and the numerical validation results show that each component of the measuring error is not independent; the recognition errors act as a factor to influence the measuring error; the first moment coefficient of measuring error changes linearly with the distance from object point to calibration surface, but there exists a nonlinear relationship between the auto-covariance coefficient of measuring error and the coordinate of the object point; and both the first moment coefficient and the auto-covariance coefficient are decreased if the object point is close to camera.