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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.

Invariants to Symmetrical Convolution with Application to Dihedral Kernel Symmetry