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

Forskningsoutput: Kapitel i bok/rapport/Conference proceeding › Konferenspaper i proceeding › Peer review

Sammanfattning

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.

Originalspråk	engelska
Titel på värdpublikation	IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2017
Förlag	IEEE - Institute of Electrical and Electronics Engineers Inc.
Sidor	2383 - 2392
Antal sidor	10
ISBN (elektroniskt)	978-1-5386-0457-1
ISBN (tryckt)	978-1-5386-0458-8
DOI	https://doi.org/10.1109/CVPR.2017.256
Status	Published - 2017 juli
Evenemang	IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2017 - e Hawaii Convention Center Honolulu, Hawaii., Honolulu, USA Varaktighet: 2017 juli 21 → 2017 juli 26 http://cvpr2017.thecvf.com

Konferens

Konferens	IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2017
Förkortad titel	CVPR
Land/Territorium	USA
Ort	Honolulu
Period	2017/07/21 → 2017/07/26
Internetadress	http://cvpr2017.thecvf.com

Ämnesklassifikation (UKÄ)

Datorseende och robotik (autonoma system)

Tillgång till dokument

10.1109/CVPR.2017.256

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

Semantisk kartering & visuell navigering för smarta robotar
Åström, K., Sminchisescu, C., Kahl, F., Robertsson, A., Flood, G., Priisalu, M., Greiff, M. & Sun, Z.
2016/07/01 → 2022/06/30
Projekt: Forskning

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@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. i IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2017. IEEE - Institute of Electrical and Electronics Engineers Inc., s. 2383 - 2392 , IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2017 , Honolulu, Hawaii, USA, 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. s. 2383 - 2392 .

Forskningsoutput: Kapitel i bok/rapport/Conference proceeding › Konferenspaper i proceeding › Peer review

TY - GEN

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

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AU - Åström, Karl

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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

Sammanfattning

Konferens

Ämnesklassifikation (UKÄ)

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Projekt

Semantisk kartering & visuell navigering för smarta robotar

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