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 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.

Cite

Text

Moreira et al. "Rotation Averaging in a Split Second: A Primal-Dual Method and a Closed-Form for Cycle Graphs." International Conference on Computer Vision, 2021. doi:10.1109/ICCV48922.2021.00540

Markdown

[Moreira et al. "Rotation Averaging in a Split Second: A Primal-Dual Method and a Closed-Form for Cycle Graphs." International Conference on Computer Vision, 2021.](https://mlanthology.org/iccv/2021/moreira2021iccv-rotation/) doi:10.1109/ICCV48922.2021.00540

BibTeX

@inproceedings{moreira2021iccv-rotation,
  title     = {{Rotation Averaging in a Split Second: A Primal-Dual Method and a Closed-Form for Cycle Graphs}},
  author    = {Moreira, Gabriel and Marques, Manuel and Costeira, João Paulo},
  booktitle = {International Conference on Computer Vision},
  year      = {2021},
  pages     = {5452-5460},
  doi       = {10.1109/ICCV48922.2021.00540},
  url       = {https://mlanthology.org/iccv/2021/moreira2021iccv-rotation/}
}