The projective invariants for polygons

  • Tomáš Suk
  • Jan Flusser
Part of the Lecture Notes in Computer Science book series (LNCS, volume 970)


The paper deals with features of a general polygon which are invariant with respect to projective transform. First, some properties of the area of a triangle under projective transform are discussed. New projective triangular invariants of polygons are derived as the quotient of two different products of the areas of the triangles formed by the vertices of the polygon. The features are proved to be invariant to numbering of the vertices of the polygon. The number of projective triangular invariants for polygons with the given number of vertices is discussed. Numerical experiments dealing with three octagons deformed by projective transforms are described.


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  1. [1]
    T. H. Reiss, Recognition Planar Objects Using Invariant Image Features, Lecture Notes in Computer Science 676, Springer (1993)Google Scholar
  2. [2]
    J. Flusser and T. Suk, Pattern recognition by affine moment invariants, Pattern Recognition 26 (1993) 167–174Google Scholar
  3. [3]
    C. C.Lin and R. Chellapa, Classification of partial 2-D shapes using Fourier descriptors, IEEE Trans. Pattern Anal. Mach. Intell. 9 (1987) 686–690Google Scholar
  4. [4]
    D. Forsyth, J. L. Mundy, A. Zisserman, C. Coelho, A. Heller and C. Rothwell, Invariant Descriptors for 3-D Object Recognition and Pose, IEEE Trans. Pattern Anal. Mach. Intell. 10 (1987) 971–991Google Scholar
  5. [5]
    T. Suk, J. Flusser, Vertex-based features for recognition of projectively deformed polygons (to appear in Pattern Recognition)Google Scholar
  6. [6]
    I. Shur, Vorlesungen über Invariantentheorie, Springer, (1968) (in German)Google Scholar
  7. [7]
    R. Lenz, P. Meer, Point configuration invariants under simultaneous projective and permutation transformations, Pattern Recognition, 11 (1994) 1523–1532Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

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

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