基于Moore-Penrose广义逆修正的摄像机标定方法

摄像机标定的四步法，具有快速和高精度特点，适合实时性强的场合。但其非线性优化过程中，所使用的Levenberg- Marquardt算法在精度要求很高的条件下，表现出不稳定性;且其增量方程中的[JTJ]计算量较大，导致内存消耗大、耗费时间长。针对四步法中非线性优化算法存在的不足，提出一种利用Moore-Penrose 广义逆修正的高斯-牛顿算法，对摄像机标定参数进行非线性优化。该方法无需考虑雅可比矩阵的奇异性，在合理选择初始值的条件下，比Levenberg-Marquardt算法更稳定，速度更快。实验表明该方法收敛速度较快，精度和稳定性较高，将为实际应用中的摄像机标定参数优化提供一种更为有效的方法。

Camera calibration method based on modified by Moore-Penrose inversion

The four-step camera calibration with a fast and high-precision features,is suitable for strong real-time situation. However, during its non-linear optimization proccss, the Levenberg-Marquardt algorithm which is used in condition of high precision, shows instability; and its increment equations for the calculation is so complex that may result in large mcmory and more time consuming.In order to make up for the shortages of the four-step non-linear optimization algorithm, this paper proposes an algorithm which based on a Moore-Penrose generalized inverse modified Gauss-Newton algorithm, is uscd for the camera calibration parameters of non-linear optimization.There is no need to consider the singularity of Jacobian matrix.Under the conditions of the reasonable initial value, it＇s more stable and faster than the Levenberg-Marquardt algorithm. Experiments show that this algorithm has rapid convergence speed, high accuracy and stability, it will bc more efficient in the practical application of camera calibration parameters optimization.