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.
https://github.com/liangzu/ARCS

本文提出了一种新的算法 $	exttt {ARCS+}$，它使用 $	exttt {ARCS}$, 鲁棒子空间学习和区间捅刺来部分重叠的二维数据集中寻找最佳旋转和对应关系，并通过 Riemannian 亚梯度下降方法对其进行精细优化。在实验中，它在大型数据集上实现了最优性能。

ARCS: 精确的旋转和对应点搜索

ARCS: Accurate Rotation and Correspondence Search

We propose 3DSmoothNet, a full workflow to match 3D point clouds with a
siamese deep learning architecture and fully convolutional layers using a
voxelized smoothed density value (SDV) representation. The latter is computed
per interest point and aligned to the local reference frame (LRF) to achieve
rotation invariance. Our compact, learned, rotation invariant 3D point cloud
descriptor achieves 94.9% average recall on the 3DMatch benchmark data set,
outperforming the state-of-the-art by more than 20 percent points with only 32
output dimensions. This very low output dimension allows for near realtime
correspondence search with 0.1 ms per feature point on a standard PC. Our
approach is sensor- and sceneagnostic because of SDV, LRF and learning highly
descriptive features with fully convolutional layers. We show that 3DSmoothNet
trained only on RGB-D indoor scenes of buildings achieves 79.0% average recall
on laser scans of outdoor vegetation, more than double the performance of our
closest, learning-based competitors. Code, data and pre-trained models are
available online at this https URL

提出了一种基于三维点云的全工作流程，利用卷积神经网络和全卷积层来匹配三维点云，利用兴趣点体素化光滑密度值 (SDV) 表示，从而实现旋转不变性，并在 3DMatch 基准数据集上取得了 94.9% 的平均召回率，性能比同类方法提高了 20% 以上，同时实现了高效的近实时的对应点搜索。