International Journal of Computer Vision

, Volume 58, Issue 1, pp 73–86 | Cite as

Curve and Surface Duals and the Recognition of Curved 3D Objects from their Silhouettes

  • Amit Sethi
  • David Renaudie
  • David Kriegman
  • Jean Ponce


This article addresses the problem of recognizing a solid bounded by a smooth surface in a single image. The proposed approach is based on a new representation for two- and three-dimensional shapes, called their signature, that exploits the close relationship between the dual of a surface and the dual of its silhouette in weak-perspective images. Objects are modeled by rotating them in front of a camera without any knowledge of or constraints on their motion. The signatures of their silhouettes are concatenated into a single object signature. To recognize an object from novel viewpoint other than those used during modeling, the signature of the contours extracted from a test photograph is matched to the signatures of all modeled objects signatures. This approach has been implemented, and recognition examples are presented.

three-dimensional object recognition invariants duals pedal curves 


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  1. Arbogast, E. and Mohr, R. 1991. 3D structure inference from image sequences. Journal of Pattern Recognition and Artificial Intelligence, 5(5):749.Google Scholar
  2. Boyer, E. and Berger, M. 1997. 3D surface reconstruction using occluding contours. Int. J. Computer Vision, 22(3):219–233.Google Scholar
  3. Bruce, J. and Giblin, P. 1992. Curves and Singularities. Cambridge University Press.Google Scholar
  4. Cipolla, R., Aström, K., and Giblin, P. 1995. Motion from the frontier of curved surfaces. In Int. Conf. on Computer Vision, pp. 269–275.Google Scholar
  5. Cipolla, R. and Blake, A. 1992. Surface shape from the deformation of the apparent contour. Int. J. Computer Vision, 9(2):83–112.Google Scholar
  6. Cipolla, R. and Giblin, P. 2000.Visual Motion of Curves and Surfaces. Cambridge University Press: Cambridge.Google Scholar
  7. Forsyth, D. and Ponce, J. 2002. Computer Vision: A Modern Approach. Prentice Hall.Google Scholar
  8. Giblin, P. and Weiss, R. 1995. Epipolar curves on surfaces. Image and Vision Computing, 13(1):33–44.Google Scholar
  9. Glachet, R., Dhome, M., and Lapersté, J. 1991. Finding the perspective projection of an axis of revolution. Pattern Recognition Letters, 12:693–700.Google Scholar
  10. Huttenlocher, D. and Ullman, S. 1987. Object recognition using alignment. In Int. Conf. on Computer Vision. London, U.K., pp. 102–111.Google Scholar
  11. Joshi, T., Vijayakumar, B., and Kriegman, D. 1997. HOT curves for modeling and recognition of smooth curved 3D objects. Image and Vision Computing, 15(7):479–498.Google Scholar
  12. Kergosien, Y.L. 1981. La famille des projections orthogonales d'une surface et ses singularités. C.R. Acad. Sc. Paris, 292:929–932.Google Scholar
  13. Koenderink, J.J. 1984. What does the occluding contour tell us about solid shape?. Perception, 13:321–330.Google Scholar
  14. Koenderink, J.J. and Van Doorn, A.J. 1976. The singularities of the visual mapping. Biological Cybernetics, 24:51–59.Google Scholar
  15. Kriegman, D. and Ponce, J. 1990a. On recognizing and positioning curved 3D objects from image contours. IEEE Trans. Pattern Anal. Mach. Intelligence, 12(12):1127–1137.Google Scholar
  16. Kriegman, D.J. and Ponce, J. 1990b. Computing exact aspect graphs of curved objects: Solids of revolution. Int. J. Computer Vision, 5(2):119–135.Google Scholar
  17. Liu, J., Mundy, J., Forsyth, D., Zisserman, A., and Rothwell, C. 1993. Efficient recognition of rotationally symmetric surfaces and straight homogeneous generalized cylinders. In Proc. IEEE Conf. on Comp. Vision and Patt. Recog. New York City, NY, pp. 123–128.Google Scholar
  18. Lockwood, E.H. 1967. Pedal curves. In A Book of Curves. Cambridge University Press: Cambridge, England, pp. 152–155.Google Scholar
  19. Lowe, D.G. 1987. The viewpoint consistency constraint. Int. J. Computer Vision, 1(1):57–72.Google Scholar
  20. Maclaurin, C. 1718. Tractatus de Curvarum Constructione & Mensura. Philosophical Transactions, 30(356):803–812.Google Scholar
  21. Murase, H. and Nayar, S. 1995. Visual learning and recognition of 3-d objects from appearance. Int. J. Computer Vision, 14(1):5–24.Google Scholar
  22. Ponce, J. and Chelberg, D. 1987. Finding the limbs and cusps of generalized cylinders. Int. J. Computer Vision, 1(3):195–210.Google Scholar
  23. Ponce, J., Hoogs, A., and Kriegman, D. 1992. On using CAD models to compute the pose of curved 3D objects. CVGIP: Image Understanding, 55(2):184–197.Google Scholar
  24. Renaudie, D., Kriegman, D., and Ponce, J. 2000. Duals, invariants, and the recognition of smooth objects from their occluding contour. In Proc. European Conf. on Computer Vision, vol. 1, pp. 784–798.Google Scholar
  25. Richetin, M., Dhome, M., Lapresté, J., and Rives, G. 1991. Inverse perspective transform from zero-curvature curve points: Application to the localization of some generalized cylinders from a single view. IEEE Trans. Pattern Anal. Mach. Intelligence, 13(2):185–191.Google Scholar
  26. Sullivan, S. and Ponce, J. 1998. Automatic model construction, pose estimation, and object recognition from photographs using triangular splines. IEEE Trans. Pattern Anal. Mach. Intelligence, 20(10):1091–1096.Google Scholar
  27. Torr, P. and Zisserman, A. 2000. MLESAC: A new robust estimator with application to estimating image geometry. CVIU, 78(1):138–156.Google Scholar
  28. Vaillant, R. and Faugeras, O. 1992. Using extremal boundaries for 3D object modeling. IEEE Trans. Pattern Anal. Mach. Intelligence, 14(2):157–173.Google Scholar
  29. Vijayakumar, B., Kriegman, D., and Ponce, J. 1998. Invariantbased recognition of complex curved 3-D objects from image contours. Computer Vision and Image Understanding, pp. 287–303.Google Scholar
  30. Zeroug, M. and Medioni, G. 1995. The challenge of generic object recognition. In Object Representation for Computer Vision, M. Hebert, J. Ponce, T. Boult, and A. Gross (Eds.). Springer-Verlag, pp. 271–232.Google Scholar

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Amit Sethi
    • 1
  • David Renaudie
    • 1
  • David Kriegman
    • 1
  • Jean Ponce
    • 1
  1. 1.Department of Computer Science and Beckman InstituteUniversity of IllinoisUrbanaUSA

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