Singularity Analysis for the Perspective-Four and Five-Line Problems

Fast and Accurate Pose Estimation with Unknown Focal Length Using Line Correspondences

Estimating camera pose is one of the key steps in computer vison, photogrammetry and SLAM (Simultaneous Localization and Mapping). It is mainly calculated based on the 2D-3D correspondences of features, including 2D-3D point and line correspondences. If a zoom lens is equipped, the focal length needs to be estimated simultaneously. In this paper, a new method of fast and accurate pose estimation with unknown focal length using two 2D-3D line correspondences and the camera position is proposed. Our core contribution is to convert the PnL (perspective-n-line) problem with 2D-3D line correspondences into an estimation problem with 3D-3D point correspondences. One 3D line and the camera position in the world frame can define a plane, the 2D line projection of the 3D line and the camera position in the camera frame can define another plane, and actually the two planes are the same plane, which is the key geometric characteristic in this paper's estimation of focal length and pose. We establish the transform between the normal vectors of the two planes with this characteristic, and this transform can be regarded as the camera projection of a 3D point. Then, the pose estimation using 2D-3D line correspondences is converted into pose estimation using 3D-3D point correspondences in intermediate frames, and, lastly, pose estimation can be finished quickly. In addition, using the property whereby the angle between two planes is invariant in both the camera frame and world frame, we can estimate the camera focal length quickly and accurately. Experimental results show that our proposed method has good performance in numerical stability, noise sensitivity and computational speed with synthetic data and real scenarios, and has strong robustness to camera position noise.