Fast Optimal Three View Triangulation
Byröd, Martin LU ; Josephson, Klas LU and Åström, Karl LU
(2008)
Swedish Symposium on Image Analysis (SSBA) 2008
p.95-98
- Abstract
- We consider the problem of L2-optimal triangulation from three separate views. Triangulation is an important part of numerous computer vision systems. Under gaussian noise, minimizing the L2 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 Gröbner 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... (More)
- We consider the problem of L2-optimal triangulation from three separate views. Triangulation is an important part of numerous computer vision systems. Under gaussian noise, minimizing the L2 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 Gröbner 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/1050640
- author
- Byröd, Martin
LU
; Josephson, Klas
LU
and Åström, Karl
LU
- organization
- publishing date
- 2008
- type
- Contribution to conference
- publication status
- published
- subject
- pages
- 4 pages
- conference name
- Swedish Symposium on Image Analysis (SSBA) 2008
- conference location
- Lund, Sweden
- conference dates
- 2008-03-13 - 2008-03-14
- language
- English
- LU publication?
- yes
- id
- 7c6256b7-82ce-4b76-81ad-757167f964b1 (old id 1050640)
- alternative location
- http://www.maths.lth.se/vision/publications/publications/view_paper.php?paper_id=400
- date added to LUP
- 2016-04-04 13:23:43
- date last changed
- 2020-12-22 02:16:06
@misc{7c6256b7-82ce-4b76-81ad-757167f964b1,
abstract = {{We consider the problem of L2-optimal triangulation from three separate views. Triangulation is an important part of numerous computer vision systems. Under gaussian noise, minimizing the L2 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 Gröbner 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}},
language = {{eng}},
pages = {{95--98}},
title = {{Fast Optimal Three View Triangulation}},
url = {{https://lup.lub.lu.se/search/files/6109307/1245444.pdf}},
year = {{2008}},
}