Improving numerical accuracy of Gröbner basis polynomial equation solvers

Proceedings of the IEEE International Conference on Computer Vision

Volumn , Issue , 2007, Pages

  Byröd, Martin ^a   Josephson, Klas ^a   Åström, Kalle ^a  

^a LUND UNIVERSITY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

ARTIFICIAL INTELLIGENCE; COMPUTER NETWORKS; COMPUTER VISION; EQUATIONS OF MOTION; IMAGE PROCESSING; MATHEMATICAL PROGRAMMING; POLYNOMIAL APPROXIMATION; POLYNOMIALS; STRUCTURAL OPTIMIZATION;

POLYNOMIAL EQUATIONS;

NUMERICAL METHODS;

EID: 50649098598     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ICCV.2007.4408885     Document Type: Conference Paper

References (20)

1. S. Agarwal, M. K. Chandraker, F. Kahl, D. J. Kriegman, and S. Belongie. Practical global optimization for multiview geometry. In Proc. 9th European Conf. on Computer Vision, Graz, Austria, pages 592-605, 2006.
2. M. Chasles. Question 296. Nouv. Ann. Math., 14(50), 1855.
3. D. Cox, J. Little, and D. O'Shea. Using Algebraic Geometry. Springer Verlag, 1998.
4. M. Demazure. Sur deux problemes de reconstruction. Technical Report 882, INRIA, Rocquencourt, France, 1988.
5. M. A. Fischler and R. C. Bolles. Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography. Communications of the ACM, 24(6):381-95, 1981.
6. D. Grayson and M. Stillman. Macaulay 2. Available at http://www.math. uiuc.edu/Macaulay2/, 1993-2002. An open source computer algebra software.
7. ∞ minimization in geometric reconstruction problems. In Proc. Conf. Computer Vision and Pattern Recognition, Washington DC, pages 504-509, Washington DC, USA, 2004.
8. R. Hartley and P. Sturm. Triangulation. Computer Vision and Image Understanding, 68:146-157, 1997.
9. M. T. Heath. Scientific Computing : An introductory Survey. McGraw-Hill, 1996.
10. ∞-norm. In ICCV, pages 1002-1009, 2005.
11. F. Kahl and D. Henrion. Globally optimal estimates for geometric reconstruction problems. In Proc. 10th Int. Conf. on Computer Vision, Bejing, China, pages 978-985, 2005.
12. E. Kruppa. Zur Ermittlung eines Objektes Zwei Perspektiven mit innerer Orientierung. Sitz-Ber. Akad. Wiss., Wien, math. naturw. Kl. Abt, IIa(122):1939-1948, 1913.
13. J. Philip. A non-iterative algorithm for determining all essential matrices corresponding to five point pairs. Photogrammetric Record, 15(88):589-599, Oct. 1996.
14. R. Pless. Using many cameras as one. In Proc. Conf. Computer Vision and Pattern Recognition, Madison, USA, 2003.
15. H. Stewénius, D. Nistér, M. Oskarsson, and K. Åström. Solutions to minimal generalized relative pose problems. In Workshop on Omnidirectional Vision, Beijing China, Oct. 2005.
16. H. Stewénius, F. Schaffalitzky, and D. Nistér. How hard is three-view triangulation really? In Proc. Int. Conf. on Computer Vision, pages 686-693, Beijing, China, 2005.
17. H. Stewńius, F. Kahl, D. Nistér, and F. Schaffalitzky. A minimal solution for relative pose with unknown focal length. In Proc. Conf. Computer Vision and Pattern Recognition, San Diego, USA, 2005.
18. E. H. Thompson. A rational algebraic formulation of the problem of relative orientation. Photogrammetric Record, 14(3):152-159, 1959.
19. P. Torr and A. Zisserman. Robust parameterization and computation of the trifocal tensor. Image and Vision Computing, 15(8):591-605, 1997.
20. P. Torr and A. Zisserman. Robust computation and parametrization of multiple view relations. In Proc. 6th Int. Conf. on Computer Vision, Mumbai, India, pages 727-732, 1998.