In this work, we present a novel algebraic method to the perspective-three-line (P3L) problem for determining the position and attitude of a calibrated camera from features of three known reference lines. Unlike other methods, the proposed method uses an intermediate camera frame F and an intermediate world frame E, with sparse known line coordinates, facilitating formulations of the P3L problem. Additionally, the rotation matrix between the frame E and the frame F is parameterized by using its orthogonality, and then a closed-form solution for the P3L pose problem is obtained from subsequent substitutions. This algebraic method makes the processes more easily followed and significantly improves the performance. The experimental results show that the proposed method offers numerical stability, accuracy and efficiency comparable or better than that of state-of-the-art method.

在这项工作中，我们提出了一种新颖的代数方法，用于解决三线透视图（P3L）问题，以便根据三条已知参考线的特征确定校准相机的位置和姿态。与其他方法不同，所提出的方法使用中间相机框架F和中间世界框架E以及稀疏的已知线坐标，从而简化了P3L问题的表述。另外，通过使用框架E和框架F的正交性参数化框架E和框架F之间的旋转矩阵，然后从后续替换中获得P3L姿势问题的闭式解。这种代数方法使处理过程更容易遵循，并显着提高了性能。实验结果表明，该方法具有数值稳定性，