Partial Symmetry in Polynomial Systems and Its Application in Computer Vision
Kuang, Yubin LU ; Zheng, Yinqiang and Åström, Karl LU
(2014)
IEEE Conference on Computer Vision and Pattern Recognition (CVPR 2014), 2014
p.438-445
- Abstract
- Algorithms for solving systems of polynomial equations
are key components for solving geometry problems in computer
vision. Fast and stable polynomial solvers are essential
for numerous applications e.g. minimal problems or
finding for all stationary points of certain algebraic errors.
Recently, full symmetry in the polynomial systems has been
utilized to simplify and speed up state-of-the-art polynomial
solvers based on Gr¨obner basis method. In this paper, we
further explore partial symmetry (i.e. where the symmetry
lies in a subset of the variables) in the polynomial systems.
We develop novel numerical schemes to utilize such partial
... (More) - Algorithms for solving systems of polynomial equations
are key components for solving geometry problems in computer
vision. Fast and stable polynomial solvers are essential
for numerous applications e.g. minimal problems or
finding for all stationary points of certain algebraic errors.
Recently, full symmetry in the polynomial systems has been
utilized to simplify and speed up state-of-the-art polynomial
solvers based on Gr¨obner basis method. In this paper, we
further explore partial symmetry (i.e. where the symmetry
lies in a subset of the variables) in the polynomial systems.
We develop novel numerical schemes to utilize such partial
symmetry. We then demonstrate the advantage of our
schemes in several computer vision problems. In both synthetic
and real experiments, we show that utilizing partial
symmetry allow us to obtain faster and more accurate polynomial
solvers than the general solvers. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/4590468
- author
- Kuang, Yubin
LU
; Zheng, Yinqiang
and Åström, Karl
LU
- organization
- publishing date
- 2014
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- keywords
- Systems of polynomial equations, computer vision, algebraic geometry, minimal solvers
- host publication
- [Host publication title missing]
- pages
- 8 pages
- publisher
- Computer Vision Foundation
- conference name
- IEEE Conference on Computer Vision and Pattern Recognition (CVPR 2014), 2014
- conference location
- Columbus, Ohio, United States
- conference dates
- 2014-06-24 - 2014-06-27
- external identifiers
-
- wos:000361555600056
- scopus:84911451653
- ISSN
- 1063-6919
- DOI
- 10.1109/CVPR.2014.63
- language
- English
- LU publication?
- yes
- additional info
- All papers presented at CVPR 2014 are freely available the CVF site http://www.cv-foundation.org/openaccess/CVPR2014.py The Authorative versions of these papers will be posted at IEEE Xplore.
- id
- 4ec7cfdb-127e-4151-acb0-08319266c30f (old id 4590468)
- alternative location
- http://www.cv-foundation.org/openaccess/content_cvpr_2014/html/Kuang_Partial_Symmetry_in_2014_CVPR_paper.html
- date added to LUP
- 2016-04-01 13:24:16
- date last changed
- 2022-02-11 20:57:48
@inproceedings{4ec7cfdb-127e-4151-acb0-08319266c30f,
abstract = {{Algorithms for solving systems of polynomial equations<br/><br>
are key components for solving geometry problems in computer<br/><br>
vision. Fast and stable polynomial solvers are essential<br/><br>
for numerous applications e.g. minimal problems or<br/><br>
finding for all stationary points of certain algebraic errors.<br/><br>
Recently, full symmetry in the polynomial systems has been<br/><br>
utilized to simplify and speed up state-of-the-art polynomial<br/><br>
solvers based on Gr¨obner basis method. In this paper, we<br/><br>
further explore partial symmetry (i.e. where the symmetry<br/><br>
lies in a subset of the variables) in the polynomial systems.<br/><br>
We develop novel numerical schemes to utilize such partial<br/><br>
symmetry. We then demonstrate the advantage of our<br/><br>
schemes in several computer vision problems. In both synthetic<br/><br>
and real experiments, we show that utilizing partial<br/><br>
symmetry allow us to obtain faster and more accurate polynomial<br/><br>
solvers than the general solvers.}},
author = {{Kuang, Yubin and Zheng, Yinqiang and Åström, Karl}},
booktitle = {{[Host publication title missing]}},
issn = {{1063-6919}},
keywords = {{Systems of polynomial equations; computer vision; algebraic geometry; minimal solvers}},
language = {{eng}},
pages = {{438--445}},
publisher = {{Computer Vision Foundation}},
title = {{Partial Symmetry in Polynomial Systems and Its Application in Computer Vision}},
url = {{https://lup.lub.lu.se/search/files/3347700/4590472.pdf}},
doi = {{10.1109/CVPR.2014.63}},
year = {{2014}},
}