Efficient Solvers for Minimal Problems by Syzygy-based Reduction

Viktor Larsson; Karl Åström; Magnus Oskarsson

doi:10.1109/CVPR.2017.256

Efficient Solvers for Minimal Problems by Syzygy-based Reduction

Viktor Larsson, Karl Åström, Magnus Oskarsson

Research output: Chapter in Book/Report/Conference proceeding › Paper in conference proceeding › peer-review

Abstract

In this paper we study the problem of automatically generating
polynomial solvers for minimal problems. The main
contribution is a new method for finding small elimination
templates by making use of the syzygies (i.e. the polynomial
relations) that exist between the original equations. Using
these syzygies we can essentially parameterize the set
of possible elimination templates.
We evaluate our method on a wide variety of problems
from geometric computer vision and show improvement
compared to both handcrafted and automatically generated
solvers. Furthermore we apply our method on two previously
unsolved relative orientation problems.

Original language	English
Title of host publication	IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2017
Publisher	IEEE - Institute of Electrical and Electronics Engineers Inc.
Pages	2383 - 2392
Number of pages	10
ISBN (Electronic)	978-1-5386-0457-1
ISBN (Print)	978-1-5386-0458-8
DOIs	https://doi.org/10.1109/CVPR.2017.256
Publication status	Published - 2017 Jul
Event	IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2017 - e Hawaii Convention Center Honolulu, Hawaii., Honolulu, United States Duration: 2017 Jul 21 → 2017 Jul 26 http://cvpr2017.thecvf.com

Conference

Conference	IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2017
Abbreviated title	CVPR
Country/Territory	United States
City	Honolulu
Period	2017/07/21 → 2017/07/26
Internet address	http://cvpr2017.thecvf.com

Subject classification (UKÄ)

Computer graphics and computer vision

Access to Document

10.1109/CVPR.2017.256

http://openaccess.thecvf.com/content_cvpr_2017/papers/Larsson_Efficient_Solvers_for_CVPR_2017_paper.pdf

Semantic Mapping and Visual Navigation for Smart Robots
Åström, K. (PI), Sminchisescu, C. (PI), Kahl, F. (PI), Robertsson, A. (PI), Flood, G. (Research student), Priisalu, M. (Research student), Greiff, M. (Research student) & Sun, Z. (Researcher)
2016/07/01 → 2022/06/30
Project: Research

Cite this

@inproceedings{e10f73813eeb43e8b1385c3f8c2cde74,

title = "Efficient Solvers for Minimal Problems by Syzygy-based Reduction",

abstract = "In this paper we study the problem of automatically generatingpolynomial solvers for minimal problems. The maincontribution is a new method for finding small eliminationtemplates by making use of the syzygies (i.e. the polynomialrelations) that exist between the original equations. Usingthese syzygies we can essentially parameterize the setof possible elimination templates.We evaluate our method on a wide variety of problemsfrom geometric computer vision and show improvementcompared to both handcrafted and automatically generatedsolvers. Furthermore we apply our method on two previouslyunsolved relative orientation problems.",

author = "Viktor Larsson and Karl {\AA}str{\"o}m and Magnus Oskarsson",

year = "2017",

month = jul,

doi = "10.1109/CVPR.2017.256",

language = "English",

isbn = "978-1-5386-0458-8 ",

pages = "2383 -- 2392 ",

booktitle = "IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2017",

publisher = "IEEE - Institute of Electrical and Electronics Engineers Inc.",

address = "United States",

note = "IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2017 , CVPR ; Conference date: 21-07-2017 Through 26-07-2017",

url = "http://cvpr2017.thecvf.com",

}

Larsson, V , Åström, K & Oskarsson, M 2017, Efficient Solvers for Minimal Problems by Syzygy-based Reduction. in IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2017. IEEE - Institute of Electrical and Electronics Engineers Inc., pp. 2383 - 2392 , IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2017 , Honolulu, Hawaii, United States, 2017/07/21. https://doi.org/10.1109/CVPR.2017.256

Efficient Solvers for Minimal Problems by Syzygy-based Reduction. / Larsson, Viktor ; Åström, Karl ; Oskarsson, Magnus.
IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2017. IEEE - Institute of Electrical and Electronics Engineers Inc., 2017. p. 2383 - 2392 .

Research output: Chapter in Book/Report/Conference proceeding › Paper in conference proceeding › peer-review

TY - GEN

T1 - Efficient Solvers for Minimal Problems by Syzygy-based Reduction

AU - Larsson, Viktor

AU - Åström, Karl

AU - Oskarsson, Magnus

PY - 2017/7

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N2 - In this paper we study the problem of automatically generatingpolynomial solvers for minimal problems. The maincontribution is a new method for finding small eliminationtemplates by making use of the syzygies (i.e. the polynomialrelations) that exist between the original equations. Usingthese syzygies we can essentially parameterize the setof possible elimination templates.We evaluate our method on a wide variety of problemsfrom geometric computer vision and show improvementcompared to both handcrafted and automatically generatedsolvers. Furthermore we apply our method on two previouslyunsolved relative orientation problems.

AB - In this paper we study the problem of automatically generatingpolynomial solvers for minimal problems. The maincontribution is a new method for finding small eliminationtemplates by making use of the syzygies (i.e. the polynomialrelations) that exist between the original equations. Usingthese syzygies we can essentially parameterize the setof possible elimination templates.We evaluate our method on a wide variety of problemsfrom geometric computer vision and show improvementcompared to both handcrafted and automatically generatedsolvers. Furthermore we apply our method on two previouslyunsolved relative orientation problems.

U2 - 10.1109/CVPR.2017.256

DO - 10.1109/CVPR.2017.256

M3 - Paper in conference proceeding

SN - 978-1-5386-0458-8

SP - 2383

EP - 2392

BT - IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2017

PB - IEEE - Institute of Electrical and Electronics Engineers Inc.

T2 - IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2017

Y2 - 21 July 2017 through 26 July 2017

ER -

Efficient Solvers for Minimal Problems by Syzygy-based Reduction

Abstract

Conference

Subject classification (UKÄ)

Access to Document

Fingerprint

Projects

Semantic Mapping and Visual Navigation for Smart Robots

Cite this