Fast(er) Robust Point Cloud Alignment Using Lie Algebra

We present a novel Lie algebra based Iterative Reweighted Least Squares (IRLS) algorithm for robust 3D point cloud alignment. We reformulate the optimal update computation to a compact form which requires only one pass through the data. Although this reformulation does not alter the asymptotic computational complexity, it is well suited for contemporary hardware architectures, yielding significant practical speedups. In extensive experiments on challenging benchmark datasets with added correspondence corruption, the method is consistently at least four times faster than previous literature whilst being mathematically equivalent, demonstrating it is well suited for time-critical applications.