Efficient Solution of Point-Line Absolute Pose
Petr Hruby, Timothy Duff, Marc Pollefeys
TL;DR
The paper tackles absolute pose estimation from mixed 3D-2D correspondences comprising points and lines, introducing two algebraically optimal minimal solvers for P2P1L and P1P2L. By leveraging special reference frames and problem structure, the authors reduce the necessary polynomial degrees to $2$ and $4$ respectively, achieving significant speedups while preserving numerical stability. They also address coplanar degeneracies and provide stabilization strategies, along with extensive synthetic and real-data experiments demonstrating up to roughly 6x faster runtimes than state-of-the-art methods without sacrificing accuracy. The work contributes practical, theoretically informed solvers that enhance RANSAC-based pose estimation in mixed-feature environments, with publicly available code at the provided repository.
Abstract
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}