Rotation Averaging in a Split Second: A Primal-Dual Method and a Closed-Form for Cycle Graphs
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 non-convex 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.
Cite
@article{arxiv.2109.08046,
title = {Rotation Averaging in a Split Second: A Primal-Dual Method and a Closed-Form for Cycle Graphs},
author = {Gabriel Moreira and Manuel Marques and João Paulo Costeira},
journal= {arXiv preprint arXiv:2109.08046},
year = {2023}
}