- Keywords: perception, point_cloud, sdp
- Abstract: We propose TEASER, the first fast and certifiable algorithm, for 3D point cloud registration with large amounts of outlier correspondences. We decouple scale, rotation, and translation estimation, and adopt a Truncated Least Squares (TLS) formulation for each subproblem. Despite being non-convex and combinatorial, we show that (i) TLS scale and translation estimation can be solved exactly in polynomial time via adaptive voting, (ii) TLS rotation estimation can be solved by a tight semidefinite programming (SDP) relaxation, with a certifiable global optimality guarantee. We also develop a second certifiable algorithm, named TEASER++, that circumvents solving an SDP and runs in milliseconds. We provide theoretical bounds on the estimation errors for both algorithms. Experiments show that both algorithms dominate the state of the art and are robust against 99% outliers. We release a fast open-source C++ implementation of TEASER++ at https://github.com/MIT-SPARK/TEASER-plusplus.