A Certifiably Globally Optimal Solution to the Non-Minimal Relative Pose Problem
Abstract
Finding the relative pose between two calibrated views ranks among the most fundamental geometric vision problems. It therefore appears as somewhat a surprise that a globally optimal solver that minimizes a properly defined energy over non-minimal correspondence sets and in the original space of relative transformations has yet to be discovered. This, notably, is the contribution of the present paper. We formulate the problem as a Quadratically Constrained Quadratic Program (QCQP), which can be converted into a Semidefinite Program (SDP) using Shor's convex relaxation. While a theoretical proof for the tightness of this relaxation remains open, we prove through exhaustive validation on both simulated and real experiments that our approach always finds and certifies (a-posteriori) the global optimum of the cost function.
Cite
Text
Briales et al. "A Certifiably Globally Optimal Solution to the Non-Minimal Relative Pose Problem." Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2018. doi:10.1109/CVPR.2018.00023Markdown
[Briales et al. "A Certifiably Globally Optimal Solution to the Non-Minimal Relative Pose Problem." Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2018.](https://mlanthology.org/cvpr/2018/briales2018cvpr-certifiably/) doi:10.1109/CVPR.2018.00023BibTeX
@inproceedings{briales2018cvpr-certifiably,
title = {{A Certifiably Globally Optimal Solution to the Non-Minimal Relative Pose Problem}},
author = {Briales, Jesus and Kneip, Laurent and Gonzalez-Jimenez, Javier},
booktitle = {Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition},
year = {2018},
doi = {10.1109/CVPR.2018.00023},
url = {https://mlanthology.org/cvpr/2018/briales2018cvpr-certifiably/}
}