A Polynomial-time Solution for Robust Registration with Extreme Outlier Rates

Abstract

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.