Efficient Solution of Point-Line Absolute Pose

TL;DR

This paper introduces simplified and faster solutions for pose estimation problems involving points and lines, reducing polynomial degrees and improving computational stability and speed.

Contribution

It presents elementary methods that lower polynomial degrees in minimal pose estimation problems, enabling more efficient and stable solutions compared to prior approaches.

Findings

Reduced polynomial degrees from 4 to 2 and from 8 to 4.

Achieved nearly tenfold speedup over previous methods.

Solutions are numerically stable and practical for real-world use.

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}