An efficient and globally optimal method for camera pose estimation using line features

The accurate estimation of camera pose using numerous line correspondences in real time is a challenging task. This paper presents a non-iterative approach to solve the Perspective-n-Line (PnL) problem. The method can provide high speed and global optimality, as well as linear complexity. A nonlinear least squares (non-LLS) objective function is first formulated by parameterizing the rotation matrix with Cayley representation. A system of three third-order equations is then derived from its optimality conditions, and then, it is solved directly based on the Gröbner basis technique. Finally, the camera pose can be easily obtained by back-substitution. A major advantage of the proposed method lies in scalability, as the size of the elimination template used in the Gröbner basis technique is independent to the number of line correspondences. Extensive and detailed experiments on synthetic data and real images are conducted, demonstrating that the proposed method achieves an accuracy that is equivalent or superior to the leading methods, but with reduced computational requirements. The source code is available at https://github.com/dannyshin1/danny/tree/master/OPnL1.