Rotation Averaging in a Split Second: A Primal-Dual Method and a Closed-Form for Cycle Graphs

Gabriel Moreira, Manuel Marques, João Paulo Costeira; Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), 2021, pp. 5452-5460

Abstract

A cornerstone of geometric reconstruction, rotation averaging seeks the set of absolute rotations that optimally explains a set of measured relative orientations between them. In spite of being an integral part of bundle adjustment and structure-from-motion, averaging rotations is both a nonconvex and high-dimensional optimization problem. In this paper, we address it from a maximum likelihood estimation standpoint and make a twofold contribution. Firstly, we set forth a novel initialization-free primal-dual method which we show empirically to converge to the global optimum. Further, we derive what is to our knowledge, the first optimal closed-form solution for rotation averaging in cycle graphs and contextualize this result within spectral graph theory. Our proposed methods achieve a significant gain both in precision and performance.

Related Material

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[bibtex]
@InProceedings{Moreira_2021_ICCV, author = {Moreira, Gabriel and Marques, Manuel and Costeira, Jo\~ao Paulo}, title = {Rotation Averaging in a Split Second: A Primal-Dual Method and a Closed-Form for Cycle Graphs}, booktitle = {Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV)}, month = {October}, year = {2021}, pages = {5452-5460} }