Understanding the shape properties of trihedral polyhedra

  • Charlie Rothwell
  • Julien Stern
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1064)


This paper presents a general framework for the computation of projective invariants of arbitrary degree of freedom (dof) trihedral polyhedra. We show that high dof. figures can be broken down into sets of connected four dof. polyhedra, for which known invariants exist. Although the more general shapes do not possess projective properties as a whole (when viewed by a single camera), each subpart does yield a projective description which is based on the butterfly invariant. Furthermore, planar projective invariants can be measured which link together the subparts, and so we can develop a local-global description for general trihedral polyhedra. We demonstrate the recovery of polyhedral shape descriptions from images by exploiting the local-global nature of the invariants.


Projective Invariant Cross Ratio Closed Region Pinhole Camera Planar Invariant 
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.


  1. [1]
    S. Carlsson. Multiple image invariance using the double algebra. In Applications of Invariance in Computer Vision, volume 825 of LNCS, p. 145–164. Springer-Verlag, 1994.Google Scholar
  2. [2]
    R. Duda and P. Hart. Pattern Classification and Scene Analysis. Wiley, 1973.Google Scholar
  3. [3]
    G. Ettinger. Large hierarchical object recognition using libraries of parameterized model sub-parts. Proc. CVPR, p.32–41, 1988.Google Scholar
  4. [4]
    M. Kass, A. Witkin, and D. Terzopoulos. Snakes: Active contour models. Proc. ICCV, p.259–268, 1987.Google Scholar
  5. [5]
    C. Rothwell, J. Mundy, and W. Hoffman. Representing objects using topology. In preparation, 1996.Google Scholar
  6. [6]
    C. Rothwell, J. Mundy, W. Hoffman, and V.-D. Nguyen. Driving vision by topology. Proc. IEEE International Symposium on Computer Vision, p.395–400, 1995.Google Scholar
  7. [7]
    C. Rothwell, D. Forsyth, A. Zisserman, and J. Mundy. Extracting projective information from single views of 3D point sets. TR 1927/92, Oxford Univ. Dept Eng. Sci., 1992.Google Scholar
  8. [8]
    C. Rothwell, D. Forsyth, A. Zisserman, and J. Mundy. Extracting projective structure from single perspective views of 3D point sets. Proc. ICCV, p.573–582 1993.Google Scholar
  9. [9]
    C. Rothwell and J. Stern. Understanding the shape properties of trihedral polyhedra. TR 2661, INRIA, 1995.Google Scholar
  10. [10]
    C. Rothwell. Object recognition through invariant indexing. Oxford University Press, 1995.Google Scholar
  11. [11]
    K. Sugihara. Machine Interpretation of Line Drawings. MIT Press, 1986.Google Scholar
  12. [12]
    A. Sugimoto. Geometric invariant of noncoplanar lines in a single view. Proc. ICPR, p. 190–195, 1994.Google Scholar
  13. [13]
    A. Zisserman, D. Forsyth, J. Mundy, C. Rothwell, J. Liu, and N. Pillow. 3D object recognition using invariance. TR 2027/94, Oxford Univ. Dept Eng. Sci., 1994, to appear the AI Journal.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Charlie Rothwell
    • 1
  • Julien Stern
    • 1
  1. 1.INRIASophia Antipolis, 06902 CedexFrance

Personalised recommendations