Invariants to Symmetrical Convolution with Application to Dihedral Kernel Symmetry

  • Jiří Boldyš
  • Jan Flusser
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8157)


We derive invariants to convolution with a symmetrical kernel in an arbitrary dimension. They are expressed in the Fourier domain as a ratio of the Fourier transform and of the symmetrical projection of the Fourier transform. In 2D and for dihedral symmetries particularly, we newly express the invariants as moment forms suitable for practical calculations. We clearly demonstrate on real photographs, that all the derived invariants are irreplaceable in pattern recognition. We further demonstrate their invariance and discriminability. We expect there is potential to use these invariants also in other fields, including microscopy.


moment invariants dihedral symmetry symmetrical blur 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Jiří Boldyš
    • 1
  • Jan Flusser
    • 1
  1. 1.Institute of Information Theory and Automation of the ASCRPraha 8Czech Republic

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