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How to use the cross ratio to compute projective invariants from two images

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Applications of Invariance in Computer Vision (AICV 1993)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 825))

Abstract

We are interested in the applications of invariant theory to computer vision problems. A survey and clarification of the different invariant calculation methods are detailed in our extented technical report

This work has been sponsored by the “Ministère de Recherche et de la Technologie” and by the “Centre National de la Recherche Scientifique” through the Orasis project as part of the Prc Communication Homme-Machine and funded by CEC through Esprit-Bra 6448 (the Viva project).

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References

  1. P. Gros and L. Quan. Projective Invariants for Vision. Technical Report RT 90 IMAG — 15 LIFIA, Lifia-Irimag, Grenoble, France, December 1992.

    Google Scholar 

  2. M.K. Hu. Visual pattern recognition by moment invariants. Ieee Trans. on Information Theory, 8:179–187, 1962.

    Google Scholar 

  3. B. Bamieh and R.J.P. de Figueiredo. A general moment-invariants/attributed-graph method for three-dimensional object-recognition from a single image. Ieee Journal of Robotics and Automation, 2(1):31–41, 1986.

    Google Scholar 

  4. P. Gros and R. Mohr. Automatic object modelization in computer vision. In H. Bunke, editor, Proceedings of the workshop “Advances in Structural and Syntactic Pattern Recognition”, Bern, Switzerland, volume 5 of Series on Machine Perception and Artificial Intelligence, pages 385–400. World Scientific, August 1992.

    Google Scholar 

  5. Y. Lamdan, J. T. Schwartz, and H. J. Wolfson. Affine invariant model-based object recognition. Ieee Journal of Robotics and Automation, 6:578–589, 1990.

    Google Scholar 

  6. H.J. Wolfson. Model-based object recognition by geometric hashing. In O. Faugeras, editor, Proceedings of the 1st European Conference on Computer Vision, Antibes, France, pages 526–536. Springer-Verlag, April 1990.

    Google Scholar 

  7. C.A. Rothwell, A. Zisserman, D.A. Forsyth, and J.L. Mundy. Canonical frames for planar object recognition. In G. Sandini, editor, Proceedings of the 2nd European Conference on Computer Vision, Santa Margherita Ligure, Italy, pages 757–772. Springer-Verlag, May 1992.

    Google Scholar 

  8. I. Weiss. Projective invariants of shapes. In Proceedings of DARPA Image Understanding Workshop, Cambridge, Massachusetts, USA, pages 1125–1134, 1988.

    Google Scholar 

  9. I. Weiss. Noise-resistant invariant of curves. In Proceeding of the Darpa-Esprit tworkshop on Applications of Invariants in Computer Vision, Reykjavik, Iceland, pages 319–344, 1991.

    Google Scholar 

  10. L. Van Gool, P. Kempenaers, and A. Oosterlinck. Recognition and semi-differential invariants. In Proceedings of the Conference on Computer Vision and Pattern Recognition, Maui, Hawaii, USA, pages 454–460, June 1991.

    Google Scholar 

  11. L. Van Gool, L.T. Moons, E. Pauwels, and A. Oosterlinck. Semi-Differential Invariants. In J. Mundy and A. Zisserman, editors, Geometric Invariance in Computer Vision, pages 157–192. MIT Press, 1992.

    Google Scholar 

  12. R. Mohr, L. Morin, and E. Grosso. Relative positioning with poorly calibrated cameras. In Proceeding of the Darpa-Esprit workshop on Applications of Invariants in Computer Vision, Reykjavik, Iceland, pages 7–45, March 1991.

    Google Scholar 

  13. D. Forsyth, J. Mundy, and A. Zisserman. Transformationnal invariance — a primer. In Proceedings of the British Machine Vision Conference, Oxford, England, pages 1–6, September 1990.

    Google Scholar 

  14. D. Kapur and J. L. Mundy. Fitting affine invariant conics to curves. In Proceeding of the Darpa-Esprit workshop on Applications of Invariants in Computer Vision, Reykjavik, Iceland, pages 209–233, March 1991.

    Google Scholar 

  15. J.L. Mundy and A. Zisserman, editors. Geometric Invariance in Computer Vision. MIT Press, Cambridge, Massachusetts, USA, 1992.

    Google Scholar 

  16. R. Mohr, L. Morin, C. Inglebert, and L. Quan. Geometric solutions to some 3D vision problems. In J.L. Crowley, E. Granum, and R. Storer, editors, Integration and Control in Real Time Active Vision, Esprit Bra Series. Springer-Verlag, 1991.

    Google Scholar 

  17. R. Mohr and L. Morin. Relative positioning from geometric invariants. In Proceedings of the Conference on Computer Vision and Pattern Recognition, Maui, Hawaii, USA, pages 139–144, June 1991.

    Google Scholar 

  18. J.J. Koenderink and A. J. van Doorn. Affine structure from motion. Technical report, Utrecht University, Utrecht, The Netherlands, October 1989.

    Google Scholar 

  19. O. Faugeras. What can be seen in three dimensions with an uncalibrated stereo rig? In G. Sandini, editor, Proceedings of the 2nd European Conference on Computer Vision, Santa Margherita Ligure, Italy, pages 563–578. Springer-Verlag, May 1992.

    Google Scholar 

  20. D. Forsyth, J.L. Mundy, A. Zisserman, C. Coelho, A. Heller, and C. Rothwell. Invariant descriptors for 3D object recognition and pose. Ieee Transactions on PAMI, 13(10):971–991, October 1991.

    Google Scholar 

  21. R. Hartley. Invariants of lines in space. In DARPA Image Understanding Workshop, pages 737–744, 1993.

    Google Scholar 

  22. W.H. Press, B.P. Flannery, S.A. Teukolsky, and W.T. Vetterling W.T. Numerical Recipes in C. Cambridge University Press, 1988.

    Google Scholar 

  23. O.D. Faugeras, Q.T. Luong, and S.J. Maybank. Camera Self-Calibration: Theory and Experiments. In G. Sandini, editor, Proceedings of the 2nd European Conference on Computer Vision, Santa Margherita Ligure, Italy, pages 321–334. Springer-Verlag, May 1992.

    Google Scholar 

  24. R. Mohr, F. Veillon, and L. Quan. Relative 3D reconstruction using multiple uncalibrated images. In Proceedings of the Conference on Computer Vision and Pattern Recognition, New York, USA, pages 543–548, June 1993.

    Google Scholar 

  25. K. Åström and L. Morin. Random cross ratios. Technical Report RT 88 IMAG — 14 LIFIA, Lifia-Irimag, October 1992.

    Google Scholar 

  26. S.J. Maybank. Classification based on the Cross Ratio. In Proceeding of the Darpa-Esprit workshop on Applications of Invariants in Computer Vision, Azores, Portugal, pages 113–132, October 1993.

    Google Scholar 

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Authors and Affiliations

  1. Lifia - Inria Rhône-Alpes, 46, avenue Félix Viallet, 38031, Grenoble Cedex 1, France

    Patrick Gros

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  1. Patrick Gros
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Joseph L. Mundy Andrew Zisserman David Forsyth

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© 1994 Springer-Verlag Berlin Heidelberg

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Gros, P. (1994). How to use the cross ratio to compute projective invariants from two images. In: Mundy, J.L., Zisserman, A., Forsyth, D. (eds) Applications of Invariance in Computer Vision. AICV 1993. Lecture Notes in Computer Science, vol 825. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58240-1_6

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  • DOI: https://doi.org/10.1007/3-540-58240-1_6

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  • Print ISBN: 978-3-540-58240-3

  • Online ISBN: 978-3-540-48583-4

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