| Title | Fast Optimal Three View Triangulation |
| Authors | Martin Byröd, Klas Josephson, Karl Åström |
| Full-text | Available as PDF |
| Alternative Location | http://dx.doi.org/10.1007/9..., Restricted Access |
| Publication | Lecture Notes in Computer Science |
| Year | 2007 |
| Volume | 4844 |
| Pages | 549 - 559 |
| Document type | Conference paper |
| Conference name | Asian Conference on Computer Vision |
| Conference Date | November 18-22, 2007 |
| Conference Location | Tokyo, Japan |
| Status | Published |
| Quality controlled | Yes |
| Language | eng |
| Publisher | Springer |
| Abstract English | 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. |
| Keywords | Triangulation, Gröbner Basis, Optimal, |
| ISBN/ISSN/Other | ISBN: 978-3-540-76389-5 |
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