Cayley transformation and numerical stability of calibration equation

International Journal of Computer Vision

Volumn 82, Issue 2, 2009, Pages 156-184

  Wu, F C ^a   Wang, Z H ^a   Hu, Z Y ^a  

^a INSTITUTE OF AUTOMATION   (China)

Author keywords

Calibration equation; Camera calibration; Cayley transformation; Numerical stability; The absolute conic

Indexed keywords

CAMERAS; CONVERGENCE OF NUMERICAL METHODS; FOURIER TRANSFORMS; MATHEMATICAL TRANSFORMATIONS; NUMBER THEORY; ONTOLOGY; ROTATION; STABILITY; STANDARDS;

CALIBRATION EQUATION; CAMERA CALIBRATION; CAYLEY TRANSFORMATION; NUMERICAL STABILITY; THE ABSOLUTE CONIC;

CALIBRATION;

EID: 60349110253     PISSN: 09205691     EISSN: 15731405     Source Type: Journal    
DOI: 10.1007/s11263-008-0193-x     Document Type: Article

References (27)

1. D. C. Brown 1971 Close-range camera calibration Photogrammetric Engineering 37 8 855 866
2. Bell, S. (1992). The Cayley transform, potential theory and conformal mapping. Boca Raton: CRC Press.
3. W. Faig 1975 Calibration of close-range photogrammetry systems: Mathematical formulaton Photogrammetric Engineering and Remote Sensing 41 21 1479 1486
4. Faugeras, O. (1993). Three-dimensional computer vision: A geometric viewpoint. Cambridge: MIT Press.
5. Faugeras, O., Luong, Q.-T., & Manybank, S. J. (1992). Camera self-calibration: Theroy and experiments. In Proc. of European conference on computer vision (pp. 321-334).
6. R. Hartley 1997 Kruppa's equations derived from the fundamental matrix IEEE Transactions on Pattern Analysis and Machine Intelligence 19 2 133 135
7. R. Hartley 1997 Self-calibration of stationary cameras International Journal of Computer Vision 22 1 5 -23
8. R. Hartley 1997 In defense of the eight-point algorithm IEEE Transactions on Pattern Analysis and Machine Intelligence 19 6 580 593
9. Hartley, R., & Zisserman, A. (2000). Multiple view geometry in computer vision. Cambridge: Cambridge University Press.
10. Harris, C., & Stephens, M. J. (1988). A combined corner and edge detector. In Proceeding 4th alvey vision conference.
11. Q. T. Luong O. Faugeras 1997 Self-calibration of a moving camera from point correspondence and fundamental matrices International Journal of Computer Vision 22 3 261 289
12. D. G. Lowe 2004 Distinctive image feature from scale invariant keypoint International Journal of Computer Vision 60 2 91 110
13. S. J. Maybank O. Faugeras 1992 A theory of self-calibration of a moving camera International Journal of Computer Vision 8 2 123 152
14. J. Oliensis R. Hartley 2007 Iterative extensions of the Sturm/Trigs algorithm: Convergence and nonconvergence IEEE Transactions on Pattern Analysis and Machine Intelligence 29 12 2217 2233
15. M. Pollefeys L. Gool 1999 Stratified self-calibration with the modulus constraint IEEE Transactions on Pattern Analysis and Machine Intelligence 21 8 707 724
16. Pollefeys, M., Gool, L., & Osterlinck, A. (1996). The modulus constraint: A new constraint for self-calibration. In: Proc. of international conference of pattern recognition (pp. 31-42).
17. Ponce, J., McHenry, K., Papadopoulo, T., Teillaud, M., & Teiggs, B. (2000). On the absolute quadratic complex and its application to autocalibration. In Proc. of computer vision and pattern recognition (pp. 780-787).
18. Press, W. H., Flannery, B. P., Teukolsky, S. A., & Vetterling, W. T. (1988). Numerical recipes in C: The art of scientific computing. Cambridge: Cambridge University Press.
19. Sturm, P., & Maybank, S. J. (1999). On plane-based camera calibration: A general algorithm, singularities, applications. In Proc. of computer vision and pattern recognition (pp. 432-437).
20. Sturm, P., & Triggs, B. (1996). A factorization based algorithm for mulit-image projective structure and motion. In Proc. of European conference on computer vision (pp. 709-720).
21. Tsai, R. (1986). An efficient and accurate camera calibration technique for 3D machine vision. In Proc. of computer vision and pattern recognition (pp. 364-374). Miami Beach, USA.
22. Triggs, B. (1997). Auto-calibration and the absolute quadric. In Proc. of computer vision and pattern recognition (pp. 609-614).
23. Wang, L., Wu, F. C., & Hu, Z. Y. (2007). Multi-camera calibration with one-dimensional object under general motions. In Proc. of international conference on computer vision (pp. 1-7).
24. F. C. Wu Z. Y. Hu H. J. Zhu 2005 Camera calibration with moving one-dimensional objects Pattern Recognition 38 5 755 765
25. Zhang, Z. (1999). Flexible camera calibration by viewing a plane from unknown orientations. In Proc. of international conference on computer vision (pp. 666-673).
26. Z. Zhang 2000 A flexible new technique for camera calibration IEEE Transactions on Pattern Analysis and Machine Intelligence 22 11 1330 1334
27. Z. Zhang 2004 Camera calibration with one-dimensional objects IEEE Transactions on Pattern Analysis and Machine Intelligence 26 7 892 899