Shape and mutual cross-ratios with applications to exterior, interior and relative orientation

  • Gunnar Sparr
  • Lars Nielsen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 427)


An affine concept of shape is introduced, which is independent of the coordinate description. By comparing the shapes of corresponding object and image configurations, it is possible to draw information about the projective mapping that associates them. This is done by means of mutual cross-ratios, which generalize the classical cross-ratio on the line. The geometric machinery is applied to the various orientation problems (exterior, interior and relative). It makes it possible to construct computational schemes, involving only the solutions of systems of linear equations and polynomial equations in one variable.


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  1. [1]
    Horn, B.K.P., Robot Vision, MIT Press, 1986.Google Scholar
  2. [2]
    Nielsen, L. and Sparr, G., Projective Area-Invariants as an Extension of the Cross-Ratio, in The 6th Scandinavian Conference on Image Analysis, Oulu, 969–986, 1989.Google Scholar
  3. [3]
    Sparr, G. and Nielsen, L., Shape and mutual cross-ratios with applications to orientation problems, Technical report, Dept. of Mathematics, Lund, 1990.Google Scholar
  4. [4]
    Veblen, O. and Young, J.W., Projective Geometry, Ginn and Company, Boston, 1910.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • Gunnar Sparr
    • 1
  • Lars Nielsen
    • 2
  1. 1.Dept. of MathematicsLund Institute of TechnologyLundSweden
  2. 2.Dept. of Automatic ControlLund Institute of TechnologyLundSweden

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