Characterizing the Uncertainty of the Fundamental Matrix

Computer Vision and Image Understanding

Volumn 68, Issue 1, 1997, Pages 18-36

  Csurka, Gabriella ^a   Zeller, Cyril ^a   Zhang, Zhengyou ^a   Faugeras, Olivier D ^a  

^a INRIA   (France)

Author keywords

[No Author keywords available]

Indexed keywords

CAMERAS; COMPUTATIONAL GEOMETRY; COMPUTATIONAL METHODS; IMAGE RECONSTRUCTION; MATHEMATICAL MODELS; MATRIX ALGEBRA; STATISTICAL METHODS;

FUNDAMENTAL MATRIX; UNCERTAINTY ANALYSIS;

COMPUTER VISION;

EID: 0031258448     PISSN: 10773142     EISSN: None     Source Type: Journal    
DOI: 10.1006/cviu.1997.0531     Document Type: Article

References (38)

1. Y. Bard, Nonlinear Parameter Estimation, Academic, Press, New York, 1974.
2. P. Beardsley, D. Murray, and A. Zisserman, Camera calibration using multiple images, in Proceedings, 2nd European Conference on Computer Vision, 1992 (G. Sandini, Ed.), Lecture Notes in Computer Science, Vol. 588, pp. 312-320, Springer-Verlag, New York/Berlin, 1992.
3. P. Beardsley, A. Zisserman, and D. Murray, Sequential Update of Projective and Affine Structure from Motion, Tech. Report OUEL 2012/94, Department of Engineering Science, Oxford University, 1994.
4. B. Boufama and R. Mohr, Epipole and fundamental matrix estimation using the virtual parallax property, in Proceedings ICCV95, pp. 1030-1036.
5. S. Carlsson, Multiple image invariants using the double algebra, in Applications of Invariance in Computer Vision (J. Mundy and A. Zisserman, Eds.), Lecture Notes in Computer Science, Vol. 825, pp. 145-164, Springer-Verlag, New York/Berlin, 1993.
6. G. Csurka, Modélisation projective des objets tridimensionnels en vision par ordinateur, University of Nice, Sophia-Antipolis, France, 1996.
7. G. Csurka and O. D. Faugeras, Invariants projectifs en vision stéréoscopique :étude directe du cas de quatre droites et caractérisation de l'incertitude, in Proceedings, 9th RFIA Conference, AFCET, Paris, January 1994, pp. 187-196.
8. G. Csurka and O. D. Faugeras, Computing three-dimensional projective invariants from a pair of images using the Grassmann-Cayley algebra, in Proceedings, Europe-China Workshop of Geometric Modeling and Invariants for Computer Vision, Xian, China, April 1995, pp. 150-157.
9. O. D. Faugeras, What can be seen in three dimensions with an uncalibrated stereo rig?, in Proceedings, 2nd European Conference on Computer Vision 1992 (G. Sandini, Ed.), Lecture Notes in Computer Science, Vol. 588, pp. 563-578, Springer-Verlag, New York/Berlin, 1992.
10. O. D. Faugeras, Three-Dimensional Computer Vision: A Geometric Viewpoint, MIT Press, Cambridge, MA/London, 1993.
11. O. D. Faugeras and S. Laveau, Representing three-dimensional data as a collection of images and fundamental matrices for image synthesis, in Proceedings, ICPR, Jerusalem, Israel, 1994, pp. 689-691.
12. O. D. Faugeras, S. Laveau, L. Robert, C. Zeller, and G. Csurka, 3-D Reconstruction of urban scenes from sequences of images, in Proceedings, International Workshop on Automatic Extraction of Man-Made Objects from Aerial and Space Images, Ascona, Switzerland, 1995.
13. O. D. Faugeras, Q.-T. Luong, and S. Maybank, Camera self-calibration: theory and experiments, in Proceedings, 2nd European Conference on Computer Vision 1992 (G. Sandini, Ed.), Lecture Notes in Computer Science, Vol. 588, pp. 321-334, Springer-Verlag, New York/Berlin 1992.
14. R. I. Hartley, Invariants of lines in space, and cheirality invariants, in Proceedings ARPA IUW, 1993, pp. 737-753.
15. R. I. Hartley, Projective reconstruction and invariants from multiple images, PAMI 16, No. 10, 1994, 1036-1040.
16. R. I. Hartley, In defence of the 8-point algorithm, in Proceedings, ICCV 1995, pp. 1064-1070.
17. R. I. Hartley and R. Gupta, Computing matched-epipolar projections, in Proceedings, CVPR 1993, pp. 549-555.
18. R. I. Hartley, R. Gupta, and T. Chang, Stereo from uncalibrated cameras, in Proceedings, CVPR 1992, pp. 761-764.
19. R. I. Hartley and P. Sturm, Triangulation, in Proceedings ARPA IUW, 1994, pp. 957-866.
20. H. C. Longuet-Higgins, A computer algorithm for reconstructing a scene from two projections, Nature 293, 1981, 133-135.
21. Q.-T. Luong, Matrice fondamentale et calibration visuelle sur l'environnement: Vers une plus grande autonomie des systémes robotiques. Ph.D. thesis, University of Paris XI, Orsay, Paris, 1992.
22. Q.-T. Luong and O. D. Faugeras, A stability analysis of the fundamental matrix, in Proceedings, 3rd European Conference on Computer Vision 1994 (J.-O. Eklundh, Ed.). Lecture Notes in Computer Science, Vol. 800, pp. 577-588, Springer-Verlag, New York/Berlin, 1994.
23. Q.-T. Luong and O. D. Faugeras, Camera calibration, scene motion and structure recovery from point correspondences and fundamental matrices, Int. J. Comput. Vision. [to appear]
24. S. J. Maybank and O. D. Faugeras, A theory of self-calibration of a moving camera, International Journal of Computer Vision, 8(2):123-152, 1992.
25. R. Mohr, B. Boufama, and P. Brand, Accurate projective reconstruction, in Applications of Invariance in Computer Vision (J. Mundy and A. Zisserman, Eds.), Lecture Notes in Computer Science, Vol. 825, pp. 257-276, Springer-Verlag, New York/Berlin, 1993.
26. R. Mohr, F. Veillon, and L. Quan, Relative 3d reconstruction using multiple uncalibrated images in Proceedings, CVPR 1993, pp. 543-548.
27. S. Olsen, Epipolar line estimation, in Proceedings, 2nd European Conference on Computer Vision, 1992 (G. Sandini, Ed.), Lecture Notes in Computer Science, Vol. 588, pp. 307-311, Springer-Verlag, New York/Berlin, 1992.
28. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipies in C, Cambridge University Press, 1988.
29. L. Quan, Invariant of a pair of non-coplanar conies in space, in Proceedings, Europe-China Workshop of Geometric Modeling and Invariants for Computer Vision, Xian, China, April 1995, pp. 190-197.
30. C. Rothwell, G. Csurka, O. D. Faugeras, A comparison of projective reconstruction methods for pairs of views, in Proceedings, ICCV 1995, pp. 932-937. [a longer version in INRIA Tech Report RR2538]
31. M. Spivak, A Comprehensive Introduction to Differential Geometry, Publish or Perish, Berkeley, CA, 1979.
32. P. H. S. Torr and D. W. Murray, Stochastic motion clustering, in Proc. Third European Conference on Computer Vision, pages 328-337, Vol. II, 1994.
33. C. Zeller and O. Faugeras, Applications of non-metric vision to some visual guided tasks, in Proceedings, ICPR 1994, pp. 132-136. [a longer version in INRIA Tech Report RR2308]
34. C. Zeller and O. Faugeras, Projective, affine and metric measurements from video sequences, in Proceedings, International Symposium on Optical Science, Engineering and Instrumentation, San Diego, California, July 1995.
35. Z. Zhang, R. Deriche, Q.-T. Luong, and O. D. Faugeras, A robust technique for matching two uncalibrated images through the recovery of the unknown epipolar geometry, Artifi. Intell. J. 78, 1995, 87-119.
36. Z. Zhang, O. D. Faugeras, and R. Deriche, Calibrating a binocular stereo through projective reconstruction using both a calibation object and the environment, in Proceeding of Europe-China Workshop of Geometric Modeling and Invariants for Computer Vision, Xian, China, April 1995, pp. 253-260.
37. Z. Zhang and O. D. Faugeras, 3D Dynamic Scene Analysis: A Stereo Based Approach. Springer, Berlin, Heidelberg, 1992.
38. Z. Zhang, Q.-T. Luong, and O. Faugeras, Motion of an uncalibrated stereo rig: Selfcalibration and metric reconstruction, in Proceedings, 12th International Conference on Pattern Recognition Jerusalem, Israel, October 1994, pp. 695-697. [a longer version in INRIA Tech Report RR2079 to appear in IEEE Trans. Rob. Automat.]