未标定摄像机非共面P4P问题的一种解析解

An Analytic Solution for the Noncoplanar P4P 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.文中针对未标定二参数针孔摄像机,首次研究了非共面P4P问题解的个数,同时提出了一种解析解.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14个变量构造出了14个约束方程,然后通过消元推导出只含一个未知数的8次多项式方程,分析证实一般情况下未标定摄像机非共面P4P问题最多有8组实解,而且解的上限可以达到.大量的仿真和真实图像实验表明,该算法在确定摄像机内外参上精度很高,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.This paper researches firstly the number of solutions of the noncoplanar P4P problem with an uncalibrated two-parameter pinhole camera,and proposes an analytic solution.The analytic solution can obtain the position and orientation of a camera with respect to world coordinate frame and intrinsic parameter of the camera simultaneously.According to projection equations of four control points and properties of rotation matrix,the analysis is performed first by writing a suitable fourteen equations in fourteen unknowns.Then,by a specifically-developed elimination scheme,the equation set that was consisted of the fourteen equations reduces to an 8th polynomial equation with only one unknown.Last,it is confirmed that the noncoplanar P4P problem with an uncalibrated two-parameter pinhole camera has at most 8 solutions,generally,and also attainable.A large number of synthetic experiments as well as experiments with real images show that the robustness of this method is very strong,and the results are very accurate for fast determination of intrinsic and extrinsic parameters.The algorithm might well be used for object pose estimation,hand-eye coordination and landmark-guided navigation.