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Partial Symmetry in Polynomial Systems and Its Application in Computer Vision

Kuang, Yubin LU ; Zheng, Yinqiang and Åström, Karl LU orcid (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:
author
; and
organization
publishing date
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
2021-09-22 04:28:40
@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},
  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},
}