研究了基于二维(QR)码识别的P4P算法,提出利用QR码中存储的四个共面顶点的坐标和QR码图像中的像素坐标进行定位。通过相机标定和图像校正得到校正的QR码四个共面顶点的像素坐标,通过译码程序解析得到四个共面顶点的实际位置坐标,将P4P算法解算输出的旋转矩阵和平移向量作为下一步算法的迭代初始值。在透视N点投影算法中,借助李群和李代数之间的局部同构关系,将流形上的寻优转化为切空间中的寻优,利用线性空间中的最优化手段对目标值进行优化。在切空间的任何梯度方向,参数值都在该空间内,即所求矩阵都在流形上。实验结果表明,在导航运动过程中,相机坐标位置误差小于±2 mm,旋转角度误差小于±0.5°,算法具有较高的定位精度及稳定性。

This paper studies P4P localization algorithm based on quick response (QR) code recognition, and proposes to use the coordinates of the four coplanar vertices stored in the QR code and the pixel coordinate in the QR code images to locate. The pixel coordinates of the four coplanar vertices of the corrected QR code are obtained through camera calibration and image correction, and the actual position coordinates of the four coplanar vertices are obtained through decoding program analysis. The rotation matrix and translation vector output by the P4P algorithm are used as the following iterative initial values of the next algorithm. In perspective N points projection algorithm, the optimization on manifold is converted into optimization in tangent space by means of local isomorphism between Lie group and Lie algebra, and the optimization method in linear space is used to optimize the target value. In any gradient direction of the tangent space, the parameter value is in the space, that is, the matrix is all on the manifold. Experimental results show that during the navigation movement, the camera coordinate position error is less than ±2 mm, and the rotation angle error is less than ±0.5°, showing that the algorithm has high positioning accuracy and stability.