论文标题
弧：准确的旋转和对应搜索
ARCS: Accurate Rotation and Correspondence Search
论文作者
论文摘要
本文是关于旧的wahba问题的更一般形式，我们称之为“同时旋转和信函搜索”。在此概括中，我们需要找到最能使两个部分重叠的$ 3 $ d点集的旋转，分别是$ m $和$ n $的$ 3 $ d点。我们首先提出一个求解器，$ \ texttt {arcs} $，i）假设一般职位的无噪声点集，ii）仅需要$ 2 $ inlliers，iii），iii）使用$ o（m \ log m）$时间和$ o（m）$（m）$ space和iv）可以成功解决问题，例如，$ m，$ m，n $ n。接下来，我们将$ \ texttt {arcs} $鲁棒化为噪声，为此，我们使用强大的子空间学习和间隔刺伤中的想法大致解决了共识最大化问题。第三，我们完善了在单位四元空间中通过riemannian sublatient下降方法确定的大致共识，我们在$ o（\ varepsilon^{ - 4}）$迭代或本地迭代的$ o（\ varepsilon^{ - 4}）中的$ \ varepsilon $ stationartion commented commented complience。我们将这些算法组合到$ \ texttt {arcs+} $中，以同时搜索旋转和对应关系。实验表明，$ \ texttt {arcs+} $在大规模数据集上达到了最先进的性能，其$ 10^6 $点，$ 10^4 $ $ $ $ $ $ $速度在替代方法上。 \ url {https://github.com/liangzu/arcs}
This paper is about the old Wahba problem in its more general form, which we call "simultaneous rotation and correspondence search". In this generalization we need to find a rotation that best aligns two partially overlapping $3$D point sets, of sizes $m$ and $n$ respectively with $m\geq n$. We first propose a solver, $\texttt{ARCS}$, that i) assumes noiseless point sets in general position, ii) requires only $2$ inliers, iii) uses $O(m\log m)$ time and $O(m)$ space, and iv) can successfully solve the problem even with, e.g., $m,n\approx 10^6$ in about $0.1$ seconds. We next robustify $\texttt{ARCS}$ to noise, for which we approximately solve consensus maximization problems using ideas from robust subspace learning and interval stabbing. Thirdly, we refine the approximately found consensus set by a Riemannian subgradient descent approach over the space of unit quaternions, which we show converges globally to an $\varepsilon$-stationary point in $O(\varepsilon^{-4})$ iterations, or locally to the ground-truth at a linear rate in the absence of noise. We combine these algorithms into $\texttt{ARCS+}$, to simultaneously search for rotations and correspondences. Experiments show that $\texttt{ARCS+}$ achieves state-of-the-art performance on large-scale datasets with more than $10^6$ points with a $10^4$ time-speedup over alternative methods. \url{https://github.com/liangzu/ARCS}
