We propose the first fast and certifiable algorithm for the registration of two sets of 3D points in the presence of large amounts of outlier correspondences. We first reformulate the registration problem using a Truncated Least Squares (TLS) cost that is insensitive to a large fraction of spurious correspondences. Then, we provide a general graph-theoretic framework to decouple scale, rotation, and translation estimation, which allows solving in cascade for the three transformations. Despite the fact that each subproblem is still non-convex and combinatorial in nature, we show that (i) TLS scale and (component-wise) translation estimation can be solved in polynomial time via adaptive voting, (ii) TLS rotation estimation can be relaxed to a semidefinite program (SDP) and the relaxation is tight, even in the presence of extreme outlier rates, and (iii) the graph-theoretic framework allows drastic pruning of outliers by finding the maximum clique. We name the resulting algorithm TEASER (Truncated least squares Estimation And SEmidefinite Relaxation). While solving large SDP relaxations is typically slow, we develop a second fast and certifiable algorithm, named TEASER++, that uses graduated non-convexity to solve the rotation subproblem and leverages Douglas-Rachford Splitting to efficiently certify global optimality. For both algorithms, we provide theoretical bounds on the estimation errors, which are the first of their kind for robust registration problems. Moreover, we test their performance on standard, object detection, and the 3DMatch benchmarks, and show that (i) both algorithms dominate the state of the art and are robust to more than 99% outliers, (ii) TEASER++ can run in milliseconds, and (iii) TEASER++ is so robust it can also solve problems without correspondences, where it largely outperforms ICP and it is more accurate than Go-ICP while being orders of magnitude faster.

中文翻译：

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TEASER：快速且可认证的点云注册

我们提出了第一个快速且可认证的算法，用于在存在大量异常值对应的情况下注册两组 3D 点。我们首先使用对大部分虚假对应不敏感的截断最小二乘法 (TLS) 成本重新制定配准问题。然后，我们提供了一个通用的图论框架来解耦尺度、旋转和平移估计，这允许对三个变换进​​行级联求解。尽管每个子问题本质上仍然是非凸和组合的，但我们表明（i）TLS 尺度和（组件方式）平移估计可以通过自适应投票在多项式时间内解决，（ii）TLS 旋转估计可以放宽到半定程序 (SDP) 并且放宽很紧，即使存在极端异常率，(iii) 图论框架允许通过找到最大集团来大幅修剪异常值。我们将结果算法命名为 TEASER（截断最小二乘估计和半定松弛）。虽然解决大型 SDP 松弛通常很慢，但我们开发了第二种快速且可证明的算法，名为 TEASER++，它使用分级非凸性来解决旋转子问题，并利用 Douglas-Rachford 分裂来有效地证明全局最优性。对于这两种算法，我们都提供了估计误差的理论界限，这是同类算法中第一个解决鲁棒配准问题的方法。此外，我们在标准、对象检测和 3DMatch 基准测试中测试了它们的性能，并表明 (i) 两种算法都主导了现有技术并且对超过 99% 的异常值具有鲁棒性，