Fast Optimal Three View Triangulation
Byröd, Martin LU ; Josephson, Klas LU and Åström, Karl LU
(2007)
Asian Conference on Computer Vision (ACCV 2007), 2007
4844.
p.549-559
- Abstract
- We consider the problem of $L_2$-optimal triangulation from three separate views. Triangulation is an important part of numerous computer vision systems. Under gaussian noise, minimizing the $L_2$ norm of the reprojection error gives a statistically optimal estimate. This has been solved for two views. However, for three or more views, it is not clear how this should be done. A previously proposed, but computationally impractical, method draws on Gr{"o}bner basis techniques to solve for the complete set of stationary points of the cost function. We show how this method can be modified to become significantly more stable and hence given a fast implementation in standard IEEE double precision. We evaluate the precision and speed of the new... (More)
- We consider the problem of $L_2$-optimal triangulation from three separate views. Triangulation is an important part of numerous computer vision systems. Under gaussian noise, minimizing the $L_2$ norm of the reprojection error gives a statistically optimal estimate. This has been solved for two views. However, for three or more views, it is not clear how this should be done. A previously proposed, but computationally impractical, method draws on Gr{"o}bner basis techniques to solve for the complete set of stationary points of the cost function. We show how this method can be modified to become significantly more stable and hence given a fast implementation in standard IEEE double precision. We evaluate the precision and speed of the new method on both synthetic and real data. The algorithm has been implemented in a freely available software package which can be downloaded from the Internet. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/787775
- author
- Byröd, Martin
LU
; Josephson, Klas
LU
and Åström, Karl
LU
- organization
- publishing date
- 2007
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- keywords
- Triangulation, Gröbner Basis, Optimal
- host publication
- Lecture Notes in Computer Science
- editor
- Yagi, Yasushi ; Kweon, In So ; Kang, Sing Bing and Zha, Hongbin
- volume
- 4844
- pages
- 549 - 559
- publisher
- Springer
- conference name
- Asian Conference on Computer Vision (ACCV 2007), 2007
- conference location
- Tokyo, Japan
- conference dates
- 2007-11-18 - 2007-11-22
- external identifiers
-
- wos:000252603100054
- scopus:38149087651
- ISBN
- 978-3-540-76389-5
- DOI
- 10.1007/978-3-540-76390-1_54
- language
- English
- LU publication?
- yes
- id
- 8b6dce46-a43c-469b-b8a8-478c4fb90706 (old id 787775)
- date added to LUP
- 2016-04-04 11:07:15
- date last changed
- 2022-03-15 22:48:26
@inproceedings{8b6dce46-a43c-469b-b8a8-478c4fb90706,
abstract = {{We consider the problem of $L_2$-optimal triangulation from three separate views. Triangulation is an important part of numerous computer vision systems. Under gaussian noise, minimizing the $L_2$ norm of the reprojection error gives a statistically optimal estimate. This has been solved for two views. However, for three or more views, it is not clear how this should be done. A previously proposed, but computationally impractical, method draws on Gr{"o}bner basis techniques to solve for the complete set of stationary points of the cost function. We show how this method can be modified to become significantly more stable and hence given a fast implementation in standard IEEE double precision. We evaluate the precision and speed of the new method on both synthetic and real data. The algorithm has been implemented in a freely available software package which can be downloaded from the Internet.}},
author = {{Byröd, Martin and Josephson, Klas and Åström, Karl}},
booktitle = {{Lecture Notes in Computer Science}},
editor = {{Yagi, Yasushi and Kweon, In So and Kang, Sing Bing and Zha, Hongbin}},
isbn = {{978-3-540-76389-5}},
keywords = {{Triangulation; Gröbner Basis; Optimal}},
language = {{eng}},
pages = {{549--559}},
publisher = {{Springer}},
title = {{Fast Optimal Three View Triangulation}},
url = {{https://lup.lub.lu.se/search/files/5698996/1245435.pdf}},
doi = {{10.1007/978-3-540-76390-1_54}},
volume = {{4844}},
year = {{2007}},
}