Fast Optimal Three View Triangulation
(2007) Asian Conference on Computer Vision (ACCV 2007), 2007 In Lecture Notes in Computer Science 4844. p.549559 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:
http://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
 in
 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
 external identifiers

 WOS:000252603100054
 Scopus:38149087651
 ISBN
 9783540763895
 DOI
 10.1007/9783540763901_54
 language
 English
 LU publication?
 yes
 id
 8b6dce46a43c469bb8a8478c4fb90706 (old id 787775)
 date added to LUP
 20080108 16:30:15
 date last changed
 20161013 04:44:02
@misc{8b6dce46a43c469bb8a8478c4fb90706, 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}, editor = {Yagi, Yasushi and Kweon, In So and Kang, Sing Bing and Zha, Hongbin}, isbn = {9783540763895}, keyword = {Triangulation,Gröbner Basis,Optimal}, language = {eng}, pages = {549559}, publisher = {ARRAY(0xa110a48)}, series = {Lecture Notes in Computer Science}, title = {Fast Optimal Three View Triangulation}, url = {http://dx.doi.org/10.1007/9783540763901_54}, volume = {4844}, year = {2007}, }