Journal of Mathematical Imaging and Vision

, Volume 6, Issue 4, pp 393–412 | Cite as

On the consistency of line-drawings, obtained by projections of piecewise planar objects

  • Anders Heyden


This paper deals with line-drawings, obtained from images of piecewise planar objects after edge detection. Such images are used, e.g., for navigation and recognition. In order to be a possible image of a three dimensional piecewise planar object, it has to obey some projective conditions. Criteria for a line-drawing to be correct is given in this paper, along with methods to find possible interpretations. In real life situations, due to digitization errors and noise, a line-drawing in general does not obey the geometric conditions imposed by the projective imaging process. Under various optimality conditions, algorithms are presented for the correction of such distorted line-drawings.


line-drawings shape depth consistency correction 


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  1. 1.
    W.E.L. Grimson, D.P. Huttenlocher, and D.W. Jacobs, “A study of affine matching with bounded sensor error,” ECCV'92, Lecture Notes in Computer Science, G. Sandini (Ed.), Springer-Verlag, Vol. 588, pp. 291–306, 1992.Google Scholar
  2. 2.
    A. Guzman, “Decomposition of a visual scene into three-dimensional bodies,” FJCC, Vol. 33, Part 1, pp. 291–304.Google Scholar
  3. 3.
    A. Heyden, “Methods for correction of images of origami/polyhedral objects,” Proceedings of the 8th Scandinavian Conference on Image Analysis, Tromsø, Norway, 1993, pp. 777–784.Google Scholar
  4. 4.
    H. Imai, “On combinatorial structures of line drawings of polyhedra,” Discrete Applied Mathematics, North Holland, Vol. 10, pp. 79–92, 1985.Google Scholar
  5. 5.
    R. Penrose, “On the cohomology of impossible figures,” Structural Topology, No. 17, pp. 11–16, 1991.Google Scholar
  6. 6.
    A. Persson, “A method for correction of images of origami/polyhedral objects,” Proc. Symposium on Image Analysis, SSAB, Uppsala, Sweden, 1992, pp. 93–96.Google Scholar
  7. 7.
    A. Schrijver, Theory for Linear and Integer Programming, John Wiley & Sons: Chichester, New York, Brisbane, Toronto, Singapore, 1986.Google Scholar
  8. 8.
    G. Sparr, “Projective invariants for affine shapes of point configurations,” ESPRIT/DARPA Invariants Workshop, Reykjavik, Iceland, 1991.Google Scholar
  9. 9.
    G. Sparr, “Depth-computations from polyhedral images,” ECCV'92, Lecture Notes in Computer Science, G. Sandini (Ed.), Springer-Verlag, Vol. 588, pp. 378–386, 1992. Also in Image and Vision Computing, Vol. 10, pp. 683–688, 1992.Google Scholar
  10. 10.
    K. Sugihara, Machine Interpretation of Line Drawings, MIT Press: Cambridge, Massachusets, London, England, 1986.Google Scholar
  11. 11.
    D.J.A. Welsh, Matroid Theory, Academic Press: London, New York, San Francisco, 1976.Google Scholar
  12. 12.
    W. Whiteley, “Some matroids on hypergraphs, with applications in scene analysis and geometry,” Discrete and Computational Geometry, Part 4, pp. 75–95, 1989.Google Scholar

Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • Anders Heyden
    • 1
  1. 1.Dept. of MathematicsLund Institute of TechnologyLundSweden

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