ML Anthology

Beyond Grobner Bases: Basis Selection for Minimal Solvers

Viktor Larsson, Magnus Oskarsson, Kalle Astrom, Alge Wallis, Zuzana Kukelova, Tomas Pajdla
CVPR 2018
doi:10.1109/CVPR.2018.00415 /cvpr/2018/larsson2018cvpr-beyond/

Abstract

Many computer vision applications require robust estimation of the underlying geometry, in terms of camera motion and 3D structure of the scene. These robust methods often rely on running minimal solvers in a RANSAC framework. In this paper we show how we can make polynomial solvers based on the action matrix method faster, by careful selection of the monomial bases. These monomial bases have traditionally been based on a Grobner basis for the polynomial ideal. Here we describe how we can enumerate all such bases in an efficient way. We also show that going beyond Grobner bases leads to more efficient solvers in many cases. We present a novel basis sampling scheme that we evaluate on a number of problems.

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Cite

Text

Larsson et al. "Beyond Grobner Bases: Basis Selection for Minimal Solvers." Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2018. doi:10.1109/CVPR.2018.00415

Markdown

[Larsson et al. "Beyond Grobner Bases: Basis Selection for Minimal Solvers." Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2018.](https://mlanthology.org/cvpr/2018/larsson2018cvpr-beyond/) doi:10.1109/CVPR.2018.00415

BibTeX

@inproceedings{larsson2018cvpr-beyond,
  title     = {{Beyond Grobner Bases: Basis Selection for Minimal Solvers}},
  author    = {Larsson, Viktor and Oskarsson, Magnus and Astrom, Kalle and Wallis, Alge and Kukelova, Zuzana and Pajdla, Tomas},
  booktitle = {Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition},
  year      = {2018},
  doi       = {10.1109/CVPR.2018.00415},
  url       = {https://mlanthology.org/cvpr/2018/larsson2018cvpr-beyond/}
}