TEASER: Fast and Certifiable Point Cloud Registration

We propose the first fast and certifiable algorithm for registration of two sets three-dimensional (3-D) points in presence large amounts outlier correspondences. A certifiable algorithm is one that attempts to solve an intractable optimization problem (e.g., robust estimation with outliers) provides readily checkable conditions verify if returned solution optimal produced most accurate estimate face or bound its suboptimality accuracy. Toward this goal, we reformulate using a xmlns:xlink="http://www.w3.org/1999/xlink">truncated least squares (TLS) cost makes insensitive fraction spurious Then, provide general graph-theoretic framework decouple scale, rotation, translation estimation, which allows solving cascade three transformations. Despite fact each subproblem (scale, estimation) still nonconvex combinatorial nature, show 1) TLS scale (component-wise) can be solved polynomial time via xmlns:xlink="http://www.w3.org/1999/xlink">adaptive voting scheme, 2) rotation relaxed semidefinite program (SDP) relaxation tight, even extreme rates, 3) drastic pruning outliers by finding maximum clique. name resulting TEASER ( xmlns:xlink="http://www.w3.org/1999/xlink">Truncated squares Estimation And SEmidefinite Relaxation ). While SDP relaxations typically slow, develop second algorithm, named TEASER++, uses xmlns:xlink="http://www.w3.org/1999/xlink">graduated nonconvexity leverages xmlns:xlink="http://www.w3.org/1999/xlink">Douglas-Rachford Splitting efficiently certify global optimality. For both algorithms, theoretical bounds on errors, are their kind problems. Moreover, test performance standard benchmarks, object detection datasets, xmlns:xlink="http://www.w3.org/1999/xlink"/> 3DMatch scan matching dataset, algorithms dominate state-of-the-art RANSAC, branch-&-bound, heuristics) more than $\text{99}\%$ when known, TEASER++ run milliseconds it currently fastest so also problems without correspondences hypothesizing all-to-all correspondences), where largely outperforms ICP Go-ICP while being orders magnitude faster. release open-source C++ implementation TEASER++.