0397178 20240103203053.120131112235959.9 000329811200038 10.1007/978-3-642-41184-7_38 10 s. P cav_un_epca*0395916978-3-642-41183-0Image Processing, Computer Vision, Pattern Recognition, and Graphics369-378BerlinSpringer-Verlag2013PetrosinoA. moment invariants dihedral symmetry symmetrical blur cav_un_auth*0101071 Boldyš Jiří Zpracování obrazové informace Department of Image Processing ZOI ZOI UTIA-B Department of Image Processing Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0101087 Flusser Jan Zpracování obrazové informace Department of Image Processing ZOI ZOI UTIA-B Department of Image Processing Ústav teorie informace a automatizace AV ČR, v. v. i. http://library.utia.cas.cz/separaty/2013/ZOI/boldys-0397178.pdf GAP103/11/1552 GA ČR cav_un_auth*0273618 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. cav_un_auth*0294771 Image Analysis and Processing – ICIAP 2013 Neapol 11.09.2013-13.09.2013 IT 2014 BD 2 PR RVO:67985556 http://hdl.handle.net/11104/0225889 2013 000329811200038 WOS cav_un_epca*0395916 Image Analysis and Processing – ICIAP 2013 978-3-642-41183-0 369 378 Berlin Springer-Verlag 2013 Lecture Notes in Computer Science 8157 Image Processing, Computer Vision, Pattern Recognition, and Graphics Petrosino A. 340