An efficient solution to the perspective-three-point pose problem

In this paper, we present a new algebraic method to solve the perspective-three-point (P3P) problem, which directly computes the rotation and position of a camera in the world frame without the intermediate derivation of the points in the camera frame. Unlike other online methods, the proposed method uses an object coordinate frame, in which the known 3D coordinates are sparse, facilitating formulations of the P3P problem. Additionally, two auxiliary variables are introduced to parameterize the rotation and position matrix, and then a closed-form solution for the camera pose is obtained from subsequent substitutions. This algebraic approach makes the processes more easily followed and significantly improves the performance. Experimental results demonstrated that our method offers accuracy and precision comparable to the existing state-of-the art methods but it has better computational efficiency.