Advertisement

Recognising rotationally symmetric surfaces from their outlines

  • David A. Forsyth
  • Joseph L. Mundy
  • Andrew Zisserman
  • Charles A. Rothwell
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 588)

Abstract

Recognising a curved surface from its outline in a single view is a major open problem in computer vision. This paper shows techniques for recognising a significant class of surfaces from a single perspective view. The approach uses geometrical facts about bitangencies, creases, and inflections to compute descriptions of the surface's shape from its image outline. These descriptions are unaffected by the viewpoint or the camera parameters. We show, using images of real scenes, that these representations identify surfaces from their outline alone. This leads to fast and effective recognition of curved surfaces.

The techniques we describe work for surfaces that have a rotational symmetry, or are projectively equivalent to a surface with a rotational symmetry, and can be extended to an even larger class of surfaces. All the results in this paper are for the case of full perspective. The results additionally yield techniques for identifying the line in the image plane corresponding to the axis of a rotationally symmetric surface, and for telling whether a surface is rotationally symmetric or not from its outline alone.

Keywords

Plane Tangent Indexing Function Camera Parameter Cross Ratio Birational Mapping 
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.

References

  1. 1.
    Brady, J.M. and Asada, H., “Smoothed Local Symmetries and their implementation,” IJRR-3, 3, 1984.Google Scholar
  2. 2.
    Brooks, R. A., “Model-Based Three-Dimensional Interpretations of Two Dimensional Images,” IEEE PAMI, Vol. 5, No. 2, p. 140, 1983.Google Scholar
  3. 3.
    Canny J.F. “Finding Edges and Lines in Images,” TR 720, MIT AI Lab, 1983.Google Scholar
  4. 4.
    Dhome, M., LaPreste, J.T, Rives, G., and Richetin, M. “Spatial localisation of modelled objects in monocular perspective vision,” Proc. First European Conference on Computer Vision, 1990.Google Scholar
  5. 5.
    D.A. Forsyth, J.L. Mundy, A.P. Zisserman, A. Heller, C. Coehlo and C.A. Rothwell (1991), “Invariant Descriptors for 3D Recognition and Pose,” IEEE Trans. Patt. Anal. and Mach. Intelligence, 13, 10.Google Scholar
  6. 6.
    Forsyth, D.A., “Recognising an algebraic surface by its outline,” Technical report, University of Iowa Department of Computer Science, 1992.Google Scholar
  7. 7.
    H. Freeman and R. Shapira, “Computer Recognition of Bodies Bounded by Quadric Surfaces from a set of Imperfect Projections,” IEEE Trans. Computers, C27, 9, 819–854, 1978.Google Scholar
  8. 8.
    Koenderink, J.J. Solid Shape, MIT Press, 1990.Google Scholar
  9. 9.
    Malik, J., “Interpreting line drawings of curved objects,” IJCV, 1, 1987.Google Scholar
  10. 10.
    J.L. Mundy and A.P. Zisserman, “Introduction,” in J.L. Mundy and A.P. Zisserman (ed.s) Geometric Invariance in Computer Vision, MIT Press, 1992.Google Scholar
  11. 11.
    J.L. Mundy and A.P. Zisserman, “Appendix” in J.L. Mundy and A.P. Zisserman (ed.s) Geometric Invariance in Computer Vision, MIT Press, 1992.Google Scholar
  12. 12.
    Ponce, J. “Invariant properties of straight homogenous generalised cylinders,” IEEE Trans. Patt. Anal. Mach. Intelligence, 11, 9, 951–965, 1989.Google Scholar
  13. 13.
    J. Ponce and D.J. Kriegman (1989), “On recognising and positioning curved 3 dimensional objects from image contours,” Proc. DARPA IU workshop, pp. 461–470.Google Scholar
  14. 14.
    Rothwell, C.A., Zisserman, A.P., Forsyth, D.A. and Mundy, J.L., “Using Projective Invariants for constant time library indexing in model based vision,” Proc. British Machine Vision Conference, 1991.Google Scholar
  15. 15.
    Rothwell, C.A., Zisserman, A.P., Forsyth, D.A. and Mundy, J.L., “Canonical frames for planar object recognition,” Proc. 2nd European Conference on Computer Vision, Springer Lecture Notes in Computer Science, 1992.Google Scholar
  16. 16.
    Rothwell, C.A., Zisserman, A.P., Forsyth, D.A. and Mundy, J.L., “Fast Recognition using Algebraic Invariants,” in J.L. Mundy and A.P. Zisserman (ed.s) Geometric Invariance in Computer Vision, MIT Press, 1992.Google Scholar
  17. 17.
    Terzopolous, D., Witkin, A. and Kass, M. “Constraints on Deformable Models: Recovering 3D Shape and Nonrigid Motion,” Artificial Intelligence, 36, 91–123, 1988.Google Scholar
  18. 18.
    Wayner, P.C. “Efficiently Using Invariant Theory for Model-based Matching,” Proceedings CVPR, p.473–478, 1991.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • David A. Forsyth
    • 1
  • Joseph L. Mundy
    • 2
  • Andrew Zisserman
    • 3
  • Charles A. Rothwell
    • 3
  1. 1.Department of Computer ScienceUniversity of IowaIowa CityUSA
  2. 2.The General Electric Corporate Research and Development LaboratorySchenectadyUSA
  3. 3.Robotics Research Group, Department of Engineering ScienceOxford UniversityEngland

Personalised recommendations