未标定摄像机P5P问题的一种解析解

An Analytic Solution for the P5P Problem with an Uncalibrated Camera

经典PnP问题是以摄像机内参已知为前提条件的,然而对未标定摄像机PnP问题的研究更具有实际意义．文中对未标定四参数针孔摄像机P5P问题的解析解进行了研究,不仅可以求出摄像机相对于世界坐标系的位姿,而且还能得到摄像机的内参．首先根据投影方程和旋转矩阵的性质,利用16个变量构造出了16个约束方程,然后通过消元推导出只含一个未知数的4次多项式方程,分析证实一般情况下未标定摄像机P5P问题最多有4组解．大量的仿真实验表明该算法在确定摄像机位姿上精度很高,且鲁棒性很强．该算法在物体定位、手眼定标、路标导航等领域具有比较重要的实际应用价值．

Classical PnP problem is based on an important precondition that the intrinsic parameters of a camera are known. But it is more valuable in real applications to investigate the PnP problem with an uncalibrated camera. In this paper, an analytic solution for the PSP problem with an uncalibrated four-parameter pinhole camera is proposed. The position and orientation of a camera with respect to world coordinate frame and intrinsic parameter of the camera can be obtained together by solving this problem. According to projection equations of five control points and properties of rotation matrix, the analysis is performed first by writing a suitable sixteen equations in sixteen unknowns. Then, by a specifically-developed elimination scheme, the equa- tion set that is consisted of the sixteen equations is reduced to a biquadratic polynomial equation with only one unknown. Last, we confirm the PSP problem with an uncalibrated four-parameter pinhole camera has at most 4 solutions, generally. A large number of synthetic experiments show that on the one hand the robustness of this method is very strong, on the other hand the results are very accurate for fast determination of extrinsic parameters. The algorithm might well be used for object pose estimation, hand-eye coordination and landmark-guided navigation.