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

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Abstract

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.

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References

  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.

  2. A. Guzman, “Decomposition of a visual scene into three-dimensional bodies,” FJCC, Vol. 33, Part 1, pp. 291–304.

  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.

  4. H. Imai, “On combinatorial structures of line drawings of polyhedra,” Discrete Applied Mathematics, North Holland, Vol. 10, pp. 79–92, 1985.

  5. R. Penrose, “On the cohomology of impossible figures,” Structural Topology, No. 17, pp. 11–16, 1991.

  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.

  7. A. Schrijver, Theory for Linear and Integer Programming, John Wiley & Sons: Chichester, New York, Brisbane, Toronto, Singapore, 1986.

    Google Scholar 

  8. G. Sparr, “Projective invariants for affine shapes of point configurations,” ESPRIT/DARPA Invariants Workshop, Reykjavik, Iceland, 1991.

  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.

  10. K. Sugihara, Machine Interpretation of Line Drawings, MIT Press: Cambridge, Massachusets, London, England, 1986.

    Google Scholar 

  11. D.J.A. Welsh, Matroid Theory, Academic Press: London, New York, San Francisco, 1976.

    Google Scholar 

  12. W. Whiteley, “Some matroids on hypergraphs, with applications in scene analysis and geometry,” Discrete and Computational Geometry, Part 4, pp. 75–95, 1989.

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Authors and Affiliations

  1. Dept. of Mathematics, Lund Institute of Technology, Box 118, S-221 00, Lund, Sweden

    Anders Heyden

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  1. Anders Heyden
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This work has been done within the ESPRIT-BRA project VIVA.

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Heyden, A. On the consistency of line-drawings, obtained by projections of piecewise planar objects. J Math Imaging Vis 6, 393–412 (1996). https://doi.org/10.1007/BF00123354

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