Efficient and Robust Large-Scale Rotation Averaging

TLDR: The approach works on the Lie group structure of 3D rotations and solves the problem of large-scale robust rotation averaging in two ways, using modern ℓ1 optimizers to carry out robust averaging of relative rotations that is efficient, scalable and robust to outliers.

Abstract: In this paper we address the problem of robust and efficient averaging of relative 3D rotations. Apart from having an interesting geometric structure, robust rotation averaging addresses the need for a good initialization for large scale optimization used in structure-from-motion pipelines. Such pipelines often use unstructured image datasets harvested from the internet thereby requiring an initialization method that is robust to outliers. Our approach works on the Lie group structure of 3D rotations and solves the problem of large-scale robust rotation averaging in two ways. Firstly, we use modern l1 optimizers to carry out robust averaging of relative rotations that is efficient, scalable and robust to outliers. In addition, we also develop a two step method that uses the l1 solution as an initialisation for an iteratively reweighted least squares (IRLS) approach. These methods achieve excellent results on large-scale, real world datasets and significantly outperform existing methods, i.e. the state-of-the-art discrete-continuous optimization method of [3] as well as the Weiszfeld method of [8]. We demonstrate the efficacy of our method on two large scale real world datasets and also provide the results of the two aforementioned methods for comparison.