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Beyond Gröbner Bases : Basis Selection for Minimal Solvers

Larsson, Viktor LU ; Oskarsson, Magnus LU ; Astrom, Kalle LU ; Wallis, Alge ; Pajdla, Tomas and Kukelova, Zuzana (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.

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author
; ; ; ; and
organization
publishing date
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
2020-12-29 03:22:59
@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},
}