It Is All In The Weights: Robust Rotation Averaging Revisited

Chitturi Sidhartha, Venu Madhav Govindu

Abstract: Rotation averaging is the problem of recovering 3D camera rotations from a number of pairwise relative rotation estimates. The state-of-the-art method of [51 involves robust averaging in the Lie-algebra of 3D rotations using an $\ell_{\frac{1}{2}}$ loss function which is carried out using an iteratively reweighted least squares (IRLS) minimization. In this paper we argue that the performance of IRLS-based rotation averaging is intimately connected with two factors: a) the nature of the robust loss function used, and b) the initialization. We make two contributions. Firstly, we analyse the pitfalls associated with the unbounded weights in IRLS minimization of $\ell_{p}(0\lt p\lt 2)$ loss functions in the context of rotation averaging. We elucidate the design choices and modifications implicit to the state-of-the-art method of [5] that overcomes these problems. Secondly, we argue that the $\ell_{\frac{1}{2}}$ -based IRLS method is inflexible in adapting to the specific noise characteristics of individual datasets, leading to poorer performance. We remedy this limitation by means of a Geman-McClure loss function embedded in a graduated optimization framework. We present results on a number of large-scale real-world datasets to demonstrate that our proposed method outpetforms state-of-the-art methods in terms of both efficiency and accuracy.