Scalable 3D Registration via Truncated Entry-wise Absolute Residuals
Authors: Tianyu Huang, Liangzu Peng, Rene Vidal, Yun-Hui Liu

Given an input set of 3D point pairs the goal of outlier-robust 3D registration is to compute some rotation and translation that align as many point pairs as possible. This is an important problem in computer vision for which many highly accurate approaches have been recently proposed. Despite their impressive performance these approaches lack scalability often overflowing the 16GB of memory of a standard laptop to handle roughly 30000 point pairs. In this paper we propose a 3D registration approach that can process more than ten million (10^7) point pairs with over 99% random outliers. Moreover our method is efficient entails low memory costs and maintains high accuracy at the same time. We call our method TEAR as it involves minimizing an outlier-robust loss that computes Truncated Entry-wise Absolute Residuals. To minimize this loss we decompose the original 6-dimensional problem into two subproblems of dimensions 3 and 2 respectively solved in succession to global optimality via a customized branch-and-bound method. While branch-and-bound is often slow and unscalable this does not apply to TEAR as we propose novel bounding functions that are tight and computationally efficient. Experiments on various datasets are conducted to validate the scalability and efficiency of our method.