Polynomial Solvers for Saturated Ideals
(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:
https://lup.lub.lu.se/record/9c5a8ff4-57af-4ffa-820c-cb51ee4c0e65
- author
- Larsson, Viktor
LU
; Åström, Karl
LU
and Oskarsson, Magnus LU
- organization
- publishing date
- 2017-10
- 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
- project
- Semantic Mapping and Visual Navigation for Smart Robots
- 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
- 2022-09-06 09:57:21
@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}}, booktitle = {{2017 IEEE International Conference on Computer Vision (ICCV)}}, isbn = {{978-1-5386-1032-9}}, language = {{eng}}, 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}}, doi = {{10.1109/ICCV.2017.251}}, year = {{2017}}, }