基于瑞利原理摄像机标定的精度研究

Precision of Camera Calibration Based on Rayleigh Principle

在摄像机标定时，由于所采用的数学模型（针孔模型）只是一种近似的模型，而且由于干扰及图像处理时所产生的噪声，使得在求解投影矩阵时会形成较大的误差。根据瑞利原理，通过求取法方程的最小特征值所对应的特征向量来得到摄像机的投影矩阵，以提高标定精度。然后根据标定块特征点在世界坐标系的坐标与投影矩阵求得其投影点的坐标，以其与相对应的实际图像坐标的残差的均方值作为标定精度的性能指标，进行精度分析。这种方法能够满足较多场合的精度要求。

Because of mathematical model of camera which is pin - hole model being approximate, and the perturbation and noises caused by image-processing, all that will lead to larger errors during solving projection matrixes during camera calibration. In order to improve calibration precision, projection matrixes of camera can be obtained by solving eigenvectors of minimum eigenvalue of normal equations on the basis of Rayleigh principle. Finally, coordination of projection points in image coordination systems can be solved in accordance with feature points coordination in world coordination systems and the projection matrixes of camera, and the mean square values of errors between projection points coordination and their actual image＇s is taken as performance index of calibration precision for precision analysis.