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The geometry and matching of curves in multiple views

  • Cordelia Schmid
  • Andrew Zisserman
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1406)

Abstract

In this paper there are two innovations. First, the geometry of imaged curves is developed in two and three views. A set of results are given for both conics and non-algebraic curves. It is shown that the homography between the images induced by the plane of the curve can be computed from two views given only the epipolar geometry, and that the trifocal tensor can be used to transfer a conic or the curvature from two views to a third.

The second innovation is an algorithm for automatically matching individual curves between images. The algorithm uses both photometric information and the multiple view geometric results. For image pairs the homography facilitates the computation of a neighbourhood cross-correlation based matching score for putative curve correspondences. For image triplets cross-correlation matching scores are used in conjunction with curve transfer based on the trifocal geometry to disambiguate matches. Algorithms are developed for both short and wide baselines. The algorithms are robust to deficiencies in the curve segment extraction and partial occlusion.

Experimental results are given for image pairs and triplets, for varying motions between views, and for different scene types. The method is applicable to curve matching in stereo and trinocular rigs, and as a starting point for curve matching through monocular image sequences.

Keywords

Epipolar Line Epipolar Geometry Curve Match Contour Extraction Trifocal Tensor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    P. Beardsley, P. Torr, and A. Zisserman. 3D model acquisition from extended image sequences. In Proc. ECCV, pages 683–695, 1996.Google Scholar
  2. 2.
    A. Blake and R. Cipolla. Robust estimation of surface curvature from deformation of apparent contours. In Proc. ECCV, pages 465–474, 1990.Google Scholar
  3. 3.
    F.L. Bookstein. Fitting conic sections to scattered data. In Computer Graphics and Image Processing, 9:56–71, 1979.Google Scholar
  4. 4.
    A.T. Brint and M. Brady. Stereo matching of curves by least deformation. In International Workshop on Intelligent Robots and Systems, pages 163–170, 1989.Google Scholar
  5. 5.
    R. C. K. Chung and R. Nevatia. Use of monocular groupings and occlusion analysis in a hierarchical stereo system. In Proc. CVPR, pages 50–56, 1991.Google Scholar
  6. 6.
    G. Cross and A. Zisserman. Quadric surface reconstruction from dual-space geometry. In Proc. ICCV, pages 25–31, 1998.Google Scholar
  7. 7.
    O. Faugeras and L. Robert. What can two images tell us about a third one? International Journal of Computer Vision, 18:5–19, 1996.CrossRefGoogle Scholar
  8. 8.
    R.I. Hartley. A linear method for reconstruction from lines and points. Proc. ICCV, pages 882–887, 1995.Google Scholar
  9. 9.
    R.I. Hartley. Lines and points in three views and the trifocal tensor. International Journal of Computer Vision, 22(2):125–140, 1997.CrossRefGoogle Scholar
  10. 10.
    P. Havaldar and G. Medioni. Segmented shape-descriptions from 3-view stereo. Proc. ICCV, pages 102–108, 1995.Google Scholar
  11. 11.
    Q. Luong and T. Vieville. Canonic representations for the geometries of multiple projective views. Technical report, University of California, Berkeley, 1993.Google Scholar
  12. 12.
    S. Ma. Conics-based stereo, motion estimation, and pose determination. International Journal of Computer Vision, 10(1):7–25, 1993.CrossRefGoogle Scholar
  13. 13.
    Maybank S. and Faugeras O. A theory of self-calibration of a moving camera. International Journal of Computer Vision, 8(2):123–151, 1992.CrossRefGoogle Scholar
  14. 14.
    J.L. Mundy and A. Zisserman, editors. Geometric Invariance in Computer Vision. The MIT Press, Cambridge, MA, USA, 1992.Google Scholar
  15. 15.
    S.K. Nayar and R.M. Bolle, Reflectance Based Object Recognition. International Journal of Computer Vision, 17(3):219–240, 1996.CrossRefGoogle Scholar
  16. 16.
    S.B. Pollard, J.E.W. Mayhew, and J.P. Frisby. PMF: A stereo correspondence algorithm using a disparity gradient constraint. Perception, 14:449–470, 1985.Google Scholar
  17. 17.
    L. Quan. Conic reconstruction and correspondence from two views, Ieee Transactions on Pattern Analysis and Machine Intelligence, 18(2):151–160, 1996.CrossRefGoogle Scholar
  18. 18.
    L. Robert and O.D. Faugeras. Curve-based stereo: Figural continuity and curvature. In Proc. CVPR, pages 57–62, 1991.Google Scholar
  19. 19.
    R. Safaee-Rad, I. Tchoukanov, B. Benhabib, and K.C. Smith. 3D pose estimation from a quadratic curved feature in two perspective views. In Proc. ICPR, pages 341–344, 1992.Google Scholar
  20. 20.
    C. Schmid and A. Zisserman. Automatic line matching across views. In Proc. CVPR, pages 666–671, 1997.Google Scholar
  21. 21.
    C. Schmid and A. Zisserman. The geometry and matching of lines and curves over multiple views. Research Report, 1998.Google Scholar
  22. 22.
    A. Shashua. Trilinearity in visual recognition by alignment. In Proc. ECCV, pages 479–484, 1994.Google Scholar
  23. 23.
    M. Spetsakis and J. Aloimonos. Structure from motion using line correspondences. International Journal of Computer Vision, pages 171–183, 1990.Google Scholar
  24. 24.
    P. Torr and A. Zisserman. Robust parameterization and computation of the trifocal tensor. Image and Vision Computing, 15:591–605, 1997.CrossRefGoogle Scholar
  25. 25.
    R. Vaillant. Using occluding contours for 3D object modeling. In Proc. ECCV, pages 454–464, 1990.Google Scholar
  26. 26.
    Z. Zhang, R. Deriche, O. Faugeras, and Q. Luong. A robust technique for matching two uncalibrated images through the recovery of the unknown epipolar geometry. Artificial Intelligence, 78:87–119, 1995.CrossRefGoogle Scholar
  27. 27.
    Y. Zhang and J.J. Gerbrands. Method for matching general stereo planar curves. Image and Vision Computing, 13(8):645–655, 1995.CrossRefGoogle Scholar
  28. 28.
    Zisserman A. and Maybank S. A case against epipolar geometry. In Applications of Invariance in Computer Vision LNCS 825. Springer-Verlag, 1994.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Cordelia Schmid
    • 1
  • Andrew Zisserman
    • 2
  1. 1.INRIA RhÔne-AlpesMontbonnotFrance
  2. 2.Dept of Engineering ScienceOxfordUK

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