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Polynomial Solvers for Saturated Ideals

Larsson, Viktor LU ; Åström, Karl LU and Oskarsson, Magnus LU (2017) international conference on computer vision, 2017
Abstract
In this paper we present a new method for creating polynomial
solvers for problems where a (possibly infinite) subset
of the solutions are undesirable or uninteresting. These
solutions typically arise from simplifications made during
modeling, but can also come from degeneracies which are
inherent to the geometry of the original problem.
The proposed approach extends the standard action matrix
method to saturated ideals. This allows us to add constraints
that some polynomials should be non-zero on the
solutions. This does not only offer the possibility of improved
performance by removing superfluous solutions, but
makes a larger class of problems tractable. Previously,
problems with... (More)
In this paper we present a new method for creating polynomial
solvers for problems where a (possibly infinite) subset
of the solutions are undesirable or uninteresting. These
solutions typically arise from simplifications made during
modeling, but can also come from degeneracies which are
inherent to the geometry of the original problem.
The proposed approach extends the standard action matrix
method to saturated ideals. This allows us to add constraints
that some polynomials should be non-zero on the
solutions. This does not only offer the possibility of improved
performance by removing superfluous solutions, but
makes a larger class of problems tractable. Previously,
problems with infinitely many solutions could not be solved
directly using the action matrix method as it requires a
zero-dimensional ideal. In contrast we only require that
after removing the unwanted solutions only finitely many
remain. We evaluate our method on three applications, optimal
triangulation, time-of-arrival self-calibration and optimal
vanishing point estimation. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
host publication
2017 IEEE International Conference on Computer Vision (ICCV)
pages
10 pages
publisher
IEEE--Institute of Electrical and Electronics Engineers Inc.
conference name
international conference on computer vision, 2017
conference location
Venice, Italy
conference dates
2017-10-22 - 2017-10-29
external identifiers
  • scopus:85041894297
ISBN
978-1-5386-1032-9
DOI
10.1109/ICCV.2017.251
language
English
LU publication?
yes
id
9c5a8ff4-57af-4ffa-820c-cb51ee4c0e65
alternative location
http://openaccess.thecvf.com/content_ICCV_2017/papers/Larsson_Polynomial_Solvers_for_ICCV_2017_paper.pdf
date added to LUP
2018-01-26 09:22:33
date last changed
2019-02-20 11:05:52
@inproceedings{9c5a8ff4-57af-4ffa-820c-cb51ee4c0e65,
  abstract     = {In this paper we present a new method for creating polynomial<br/>solvers for problems where a (possibly infinite) subset<br/>of the solutions are undesirable or uninteresting. These<br/>solutions typically arise from simplifications made during<br/>modeling, but can also come from degeneracies which are<br/>inherent to the geometry of the original problem.<br/>The proposed approach extends the standard action matrix<br/>method to saturated ideals. This allows us to add constraints<br/>that some polynomials should be non-zero on the<br/>solutions. This does not only offer the possibility of improved<br/>performance by removing superfluous solutions, but<br/>makes a larger class of problems tractable. Previously,<br/>problems with infinitely many solutions could not be solved<br/>directly using the action matrix method as it requires a<br/>zero-dimensional ideal. In contrast we only require that<br/>after removing the unwanted solutions only finitely many<br/>remain. We evaluate our method on three applications, optimal<br/>triangulation, time-of-arrival self-calibration and optimal<br/>vanishing point estimation.},
  author       = {Larsson, Viktor and Åström, Karl and Oskarsson, Magnus},
  isbn         = {978-1-5386-1032-9},
  language     = {eng},
  location     = {Venice, Italy},
  pages        = {10},
  publisher    = {IEEE--Institute of Electrical and Electronics Engineers Inc.},
  title        = {Polynomial Solvers for Saturated Ideals},
  url          = {http://dx.doi.org/10.1109/ICCV.2017.251},
  year         = {2017},
}