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Title: Fast Optimal Three View Triangulation
Authors: Byröd, Martin and Josephson, Klas and Åström, Kalle
Editors: Yagi, Yasushi and Kweon, In So and Kang, Sing Bing and Zha, Hongbin
Year: 2007
Document Type:Conference Paper
Conference: Asian Conference on Computer Vision
Conference location: Tokyo, Japan
Status: In Press
Refereed: Yes
Keywords: Triangulation, Optimal, Gröbner Basis, polynomial equations
BibTeX item:BibTeX
Extra: Code available
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.




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