基于非线性优化的摄像机2D标定法

基于平面靶标，利用不同的非线性优化方法精确标定摄像机的线性参数以及畸变参数。基于绝对二次曲线的图像（IAC）构成约束方程，线性求解线性模型内外参数的初始值，在此基础上充分考虑非线性模型中的径向畸变和切向畸变，利用Rodrigues旋转公式减小优化参数的个数，分别采用最速下降法和LM最优化方法求解精确参数。实验结果表明，基于非线性优化的2D标定法能够简化初始值的计算，获得精确的非线性参数，最速下降法具有较快的收敛速度，LM算法能够获得更小的投影误差，且利用优化工具箱可以显著减小计算难度。可以根据实际需要选择不同的优化算法，实现摄像机的快速精确标定。

Nonlinear optimization algorithms for camera calibration based on 2D pattern

Based on 2D pattern, different nonlinear optimization algorithms are used to calibrate the camera parameters including the linear parameters and distortions. Two basic restrictions are deduced from the characteristics of homography based on image of the absolute conic. By establishing the corresponding relationship between elements in IAC matrix and intrinsic parameters, the initial values of intrinsic parameters are solved linearly while the initial extrinsic parameters are obtained through the relationship between homography and linear parameters. By analyzing radial and tangential distortions and using Rodrigues＇ rotation formula to decrease the number of optimization parameters, two optimiztion algorithms, namely the steepest descent algorithm and the Levenberg-Marquad algorithm are used to obtain the accurate parameters. The results show that nonlinear optimization algorithms for camera calibration based on 2D pattern can simplify the calculation of initial parameter and steepest descent algorithm while Levenberg-Marquad algorithm obtains projection with smaller errors. The latter can be performed with optimization toolbox to reduce the calculation difficulty obviously. Optimization algorithms should be chosen depending on practical conditions to obtain accurate the camera parameters quickly.