A frequency domain algorithm for detection and classification of cyclic and dihedral symmetries in two-dimensional patterns

This paper presents a very effective algorithm for detecting and classifying cyclic and dihedral symmetries from images of finite patterns. Some results concerning reflectional and rotational symmetries of Fourier transforms are presented and exploited to define a convenient frequency domain function whose zero-crossings contain distinctive pairs of orthogonal lines related to the order of the symmetry. The discrimination between cyclic and dihedral symmetries is accomplished by comparing these zero-crossings with those of a second frequency domain function. Several examples of symmetric patterns correctly classified by our algorithm are reported and discussed in the paper.