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TEASER: Fast and Certifiable Point Cloud Registration

by   Heng Yang, et al.

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. Towards this goal, we first reformulate the registration problem using a Truncated Least Squares (TLS) cost that makes the estimation insensitive to 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 an adaptive voting scheme, (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. 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 certifiable algorithm, named TEASER++, that circumvents the need to solve an SDP and runs in milliseconds. 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 benchmarks, object detection datasets, and the 3DMatch scan matching dataset, and show that (i) both algorithms dominate the state of the art (e.g., RANSAC, branch- -bound, heuristics) and are robust to more than 99 (ii) TEASER++ can run in milliseconds and it is currently the fastest robust registration algorithm, (iii) TEASER++ is so robust it can also solve problems without correspondences (e.g., hypothesizing all-to-all correspondences) where it largely outperforms ICP. We release a fast open-source C++ implementation of TEASER++.


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