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{this https URL\_absolute}
Abstract (translated)
我们回顾了基于3D--2D对应关系的某些姿态估计问题，这些问题可能是个点或线。具体来说，我们解决了之前研究过的最小问题：从{1,2}点--点对应关系中估计相机外项，以及从$l=3-p$线--线对应关系中估计相机外项。据我们所知，所有之前已知的问题解决方案都需要在$p=2$时计算次数$\ge 4$（单变量）多项式的根，或者在$p=1$时计算次数$\ge 8$多项式的根。我们描述并实现了两种简化解决方案，它们分别将需要的多项式的次数从4降低到2，从8降低到4。我们证明了这些求解器在数值稳定性和速度方面都是快速的：与之前的先进水平相比，我们可能可以实现近一个数量级的速度提升。代码可在此处下载：https://this URL_absolute
URL
https://arxiv.org/abs/2404.16552
