# It Is All in the Weights: Robust Rotation Averaging Revisited

Sidhartha, C and Govindu, VM (2021) It Is All in the Weights: Robust Rotation Averaging Revisited. In: 9th International Conference on 3D Vision, 1-3 Dec 2021, Virtual, Online, pp. 1134-1143.

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Official URL: https://doi.org/10.1109/3DV53792.2021.00121

## 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-\frac12 -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. Â© 2021 IEEE.

Item Type: Conference Paper Proceedings - 2021 International Conference on 3D Vision, 3DV 2021 Institute of Electrical and Electronics Engineers Inc. The copyright for this article belongs to Institute of Electrical and Electronics Engineers Inc. Algebra; Cameras; Computer vision; Iterative methods; Large dataset; Least squares approximations, 3D camera; 3D rotation; Camera rotations; Iteratively reweighted least-squares; Least squares minimization; Lie Algebra; Loss functions; Performance; Relative rotation; State-of-the-art methods, Rotation Division of Electrical Sciences > Electrical Engineering 09 Mar 2022 10:29 09 Mar 2022 10:29 http://eprints.iisc.ac.in/id/eprint/71538