Using representations of the dihedral groups in the design of early vision filters

An approach to filter design which uses only the geometrical properties of the grid on which the filters are defined is proposed. This leads naturally to the study of the dihedral groups (i.e., the groups that leave the regular polygons invariant). It is shown how the representations of these groups can be used to develop algorithms that simplify a whole class of operators. The transforms developed are noncommutative generalizations of the discrete Fourier transform. The results are illustrated with some examples from the design of early vision filters.<>