  We propose a robust approach for the registration of two sets of 3D points in
the presence of a large amount of outliers. Our first contribution is to
reformulate the registration problem using a Truncated Least Squares (TLS) cost
that makes the estimation insensitive to a large fraction of spurious
point-to-point correspondences. The second contribution is a general framework
to decouple rotation, translation, and scale estimation, which allows solving
in cascade for the three transformations. Since each subproblem (scale,
rotation, and translation estimation) is still non-convex and combinatorial in
nature, out third contribution is to show that (i) TLS scale and
(component-wise) translation estimation can be solved exactly and in polynomial
time via an adaptive voting scheme, (ii) TLS rotation estimation can be relaxed
to a semidefinite program and the relaxation is tight in practice, even in the
presence of an extreme amount of outliers. We validate the proposed algorithm,
named TEASER (Truncated least squares Estimation And SEmidefinite Relaxation),
in standard registration benchmarks showing that the algorithm outperforms
RANSAC and robust local optimization techniques, and favorably compares with
Branch-and-Bound methods, while being a polynomial-time algorithm. TEASER can
tolerate up to 99% outliers and returns highly-accurate solutions.
