| Title | A Column-Pivoting Based Strategy for Monomial Ordering in Numerical Gröbner Basis Calculations |
| 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 | 2008 |
| Volume | 5305 |
| Pages | 130 - 143 |
| Document type | Conference paper |
| Conference name | The 10th European Conference on Computer Vision |
| Conference Date | 2008-10-12/2008-10-18 |
| Conference Location | Marseille, France |
| Status | Published |
| Quality controlled | Yes |
| Language | eng |
| Publisher | Springer |
| Abstract English | This paper presents a new fast approach to improving stability in polynomial equation solving. Gröbner basis techniques for equation solving have been applied successfully to several geometric computer vision problems. However, in many cases these methods are plagued by numerical problems. An interesting approach to stabilising the computations is to study basis selection for the quotient space Cx/I . In this paper, the exact matrix computations involved in the solution procedure are clarified and using this knowledge we propose a new fast basis selection scheme based on QR-factorization with column pivoting. We also propose an adaptive scheme for truncation of the Gröbner basis to further improve stability. The new basis selection strategy is studied on some of the latest reported uses of Gröbner basis methods in computer vision and we demonstrate a fourfold increase in speed and nearly as good overall precision as the previous SVD-based method. Moreover, we get typically get similar or better reduction of the largest errors. |
| ISBN/ISSN/Other | ISSN: 0302-9743 |
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