Fast and robust numerical solutions to minimal problems for cameras with radial distortion

26th IEEE Conference on Computer Vision and Pattern Recognition, CVPR

Volumn , Issue , 2008, Pages

  Byröd, Martin ^a   Kukelova, Zuzana ^b   Josephson, Klas ^a   Pajdla, Tomas ^b   Åström, Kalle ^a  

^a LUND UNIVERSITY   (Sweden)

^b CZECH TECHNICAL UNIVERSITY IN PRAGUE   (Czech Republic)

Author keywords

[No Author keywords available]

Indexed keywords

ARTIFICIAL INTELLIGENCE; CAMERAS; COMPUTER VISION; DIGITAL ARITHMETIC; ESTIMATION; FEATURE EXTRACTION; IMAGE PROCESSING; MATRIX ALGEBRA; NUMERICAL METHODS; PATTERN RECOGNITION;

ESSENTIAL MATRICES; FLOATING POINT ARITHMETICS; FLOATING POINT IMPLEMENTATION; FUNDAMENTAL MATRICES; IMAGE POINTS; NUMERICAL SOLUTIONS; RADIAL DISTORTIONS; REAL EXPERIMENTS; SIMULTANEOUS ESTIMATION; STABLE ALGORITHMS; STRUCTURE-FROM-MOTION;

PARAMETER ESTIMATION;

EID: 52249090469     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/CVPR.2008.4587674     Document Type: Conference Paper

References (19)

1. A. Almadi, A. Dhingra, and D. Kohli. A gröbner-sylvester hybrid method for closed-form displacement analysis of mechanisms. Journal of Mechanical Design, 122(4):431-438, 12 2000.
2. J. Barreto and K. Daniilidis. Fundamental matrix for cameras with radial distortion. In IEEE International Conference on Computer Vision, Beijing, China, 2005.
3. M. Byröd, K. Josephson, and K. Åström. Improving numerical accuracy of gröbner basis polynomial equation solver. In International Conference on Computer Vision, 2007.
4. D. Cox, J. Little, and D. O'Shea. Ideals, Varieties, and Algorithms. Springer Verlag, 2007.
5. J.-C. Faugère. A new efficient algorithm for computing grobner bases (f4). Journal of pure and applied algebra, 139:61-88, 6 1999.
6. J.-C. Faugère. A new efficient algorithm for computing gröbner bases without reduction to zero (f5). In ISSAC '02: Proceedings of the 2002 international symposium on Symbolic and algebraic computation, pages 75-83, New York, NY, USA, 2002. ACM Press.
7. J.-C. Faugère and A. Joux. Algebraic cryptanalysis of hidden field equation (hfe) cryptosystems using gröbner bases. In CRYPTO 2003, pages 44-60, 2003.
8. 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.
9. A. W. Fitzgibbon. Simultaneous linear estimation of multiple view geometry and lens distortion. In Proceedings of Computer Vision and Pattern Recognition Conference (CPVR), pages 125-132, 2001.
10. D. Grayson and M. Stillman. Macaulay 2. Available at http://www.math. uiuc.edu/Macaulay2/, 1993-2002. An open source computer algebra software.
11. R. I. Hartley and A. Zisserman. Multiple View Geometry in Computer Vision. Cambridge University Press, ISBN: 0521540518, second edition, 2004.
12. Z. Kukelova and T. Pajdla. A minimal solution to the autocalibration of radial distortion. In Proceedings of Computer Vision and Pattern Recognition Conference (CPVR). IEEE Press, 2007.
13. Z. Kukelova and T. Pajdla. Two minimal problems for cameras with radial distortion. In Proceedings of The Seventh Workshop on Omnidirectional Vision, Camera Networks and Non-classical Cameras (OMNIVIS), 2007.
14. H. Li and R. Hartley. A non-iterative method for lens distortion correction from point matches. In Workshop on Omnidirectional Vision, Beijing China, Oct. 2005.
15. J. Matas, O. Chum, M. Urban, and T. Pajdla. Robust widebaseline stereo from maximally stable extremal regions. Image Vision Computing, 22(10):761-767, 2004.
16. H. Stewénius. Gröbner Basis Methods for Minimal Problems in Computer Vision. PhD thesis, Lund University, Apr. 2005.
17. H. Stewénius, C. Engels, and D. Nistér. Recent developments on direct relative orientation. ISPRS Journal of Photogrammetry and Remote Sensing, 60:284-294, June 2006.
18. 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.
19. H. Stewénius, F. Schaffalitzky, and D. Nistér. How hard is three-view triangulation really? In Proc. 10th Int. Conf. on Computer Vision, pages 686-693, Beijing, China, 2005.