Sidhartha Chitturi and Venu Madhav Govindu

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 [5] involves robust averaging in the Lie-algebra of 3D rotations using an ` 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 `p(0 < p < 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 ` 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 outperforms state-of-the-art methods in terms of both efficiency and accuracy.