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Point projective and permutation invariants

  • Tomáš Suk
  • Jan Flusser
Invariants
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1296)

Abstract

The paper deals with features of a point set which are invariant with respect to projective transform. First, projective invariants for five-point sets, which are simultaneously invariant to the permutation of the points, are derived. They are expressed as functions of five-point cross-ratios. Possibilities of the choice of their roots are referred and their normalization is discussed.

Then, the invariants for more than five points are derived. Stability and discriminability of the features is demonstrated by numerical experiments.

Keywords

Convex Hull Projective Invariant Point Projective Imaginary Root Configuration 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.

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References

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    N. S. V. Rao, W. Wu, C. W. Glover, “Algorithms for Recognizing Planar Polygonal Configurations Using Perspective Images”, IEEE Trans. on Robotics and Automation, Vol. 8, No. 4, pp. 480–486, 1992.CrossRefGoogle Scholar
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    T. H. Reiss, “Recognition Planar Objects Using Invariant Image Features”, Lecture Notes in Computer Science 676, Springer, 1993.Google Scholar
  3. 3.
    R. Lenz, P. Meer, “Point configuration invariants under simultaneous projective and permutation transformations”, Pattern Recognition, Vol. 27, No. 11, pp. 1523–1532, 1994.CrossRefGoogle Scholar
  4. 4.
    T. Suk, J. Flusser, “The Features for Recognition of Projectively Deformed Images”, Proc. ICIP'95, Washington, Vol. III, pp. 348–351, 1995.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Tomáš Suk
    • 1
  • Jan Flusser
    • 1
  1. 1.Institute of Information Theory and AutomationAcademy of Sciences of the Czech RepublicPraha 8The Czech Republic

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