Efficient Solution of Point-Line Absolute Pose

We revisit certain problems of pose estimation based on 3D–2D correspondences between features which may be points or lines. Specifically, we address the two previously-studied minimal problems of estimating camera extrinsics from \(p \in \{ 1, 2 \}\) point–point correspondences and \(l=3-p\) line–line correspondences. To the best of our knowledge, all of the previously-known practical solutions to these problems required computing the roots of degree \(\ge 4\) (univariate) polynomials when \(p=2\), or degree \(\ge 8\) polynomials when \(p=1.\) We describe and implement two elementary solutions which reduce the degrees of the needed polynomials from $4$ to $2$ and from $8$ to $4$, respectively. We show experimentally that the resulting solvers are numerically stable and fast: when compared to the previous state-of-the art, we may obtain nearly an order of magnitude speedup. The code is available at \url{https://github.com/petrhruby97/efficient\_absolute}