Beyond Gröbner Bases : Basis Selection for Minimal Solvers
(2018) 31st Meeting of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2018 p.3945-3954- 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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/8d714374-3873-46f2-b63e-0f1e8be715bd
- author
- Larsson, Viktor LU ; Oskarsson, Magnus LU ; Astrom, Kalle LU ; Wallis, Alge ; Pajdla, Tomas and Kukelova, Zuzana
- organization
- publishing date
- 2018-12-14
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- host publication
- Proceedings - 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2018
- article number
- 8578513
- pages
- 10 pages
- publisher
- IEEE Computer Society
- conference name
- 31st Meeting of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2018
- conference location
- Salt Lake City, United States
- conference dates
- 2018-06-18 - 2018-06-22
- external identifiers
-
- scopus:85062852057
- ISBN
- 9781538664209
- DOI
- 10.1109/CVPR.2018.00415
- language
- English
- LU publication?
- yes
- id
- 8d714374-3873-46f2-b63e-0f1e8be715bd
- date added to LUP
- 2019-04-01 09:33:58
- date last changed
- 2022-09-06 09:57:22
@inproceedings{8d714374-3873-46f2-b63e-0f1e8be715bd, abstract = {{<p>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.</p>}}, author = {{Larsson, Viktor and Oskarsson, Magnus and Astrom, Kalle and Wallis, Alge and Pajdla, Tomas and Kukelova, Zuzana}}, booktitle = {{Proceedings - 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2018}}, isbn = {{9781538664209}}, language = {{eng}}, month = {{12}}, pages = {{3945--3954}}, publisher = {{IEEE Computer Society}}, title = {{Beyond Gröbner Bases : Basis Selection for Minimal Solvers}}, url = {{http://dx.doi.org/10.1109/CVPR.2018.00415}}, doi = {{10.1109/CVPR.2018.00415}}, year = {{2018}}, }