  Correspondences between 3D lines and their 2D images captured by a camera are
often used to determine position and orientation of the camera in space. In
this work, we propose a novel algebraic algorithm to estimate the camera pose.
We parameterize 3D lines using Pl\"ucker coordinates that allow linear
projection of the lines into the image. A line projection matrix is estimated
using Linear Least Squares and the camera pose is then extracted from the
matrix. An algebraic approach to handle mismatched line correspondences is also
included. The proposed algorithm is an order of magnitude faster yet comparably
accurate and robust to the state-of-the-art, it does not require
initialization, and it yields only one solution. The described method requires
at least 9 lines and is particularly suitable for scenarios with 25 and more
lines, as also shown in the results.

Computer Vision and Pattern Recognition