旋转矩阵表达方法对相机检校的影响

Camera Calibration Effects of Rotation Matrix Expression

在大倾角像片的相机检校中,经典共线方程是采用欧拉角(φ,ω,κ)描述旋转矩阵的,该方法受限于无法获取位置与姿态的初始值,结果可能导致迭代不收敛。共线方程中的旋转矩阵还可以直接利用方向余弦或单位四元数来描述,相机检校时可以无需依赖位置与姿态的初始值。在相同实验数据、初始值和收敛条件的实验中,直接利用方向余弦描述旋转矩阵的方法明显优于单位四元数方法,主要体现在收敛情况和计算结果接近欧拉角方法两个方面。建议在非量测相机检校时,最好选用直接利用方向余弦描述旋转矩阵的共线方程方法。

Because the initial values of the position and attitude are unable to get, in the big inclination angle images of camera calibration, it may lead to non-convergence iterations by classical collinearity equation of rotation matrix of Euler angle. In collinearity equation, rotation matrix can also be expressed by the direction cosine or unit quaternion. Then the camera calibration can not rely on the initial values of the posi- tion and attitude. This paper uses the same data, the same initial values and the same convergence conditions. The experi- mental results show that the direction cosine method is better than the unit quaternion method. It mainly reflected in the con- vergence case and the calculate value corresponds closely to the method of Euler angle. In the non-metric camera calibration, we recommend that the best choice is the rotation matrix expressed by direction cosine in collinearity equation.