Frequency domain classification of cyclic and dihedral symmetries of finite 2-D patterns

摘要

This paper presents a very simple and effective algorithm for classifying cyclic and dihedral symmetries from images of finite two-dimensional patterns. It consists in an extension of a frequency domain algorithm proposed by the author for estimating two-dimensional rotation of rigid objects. Within this framework, the estimation of rotation is conveniently turned into the problem of detecting two orthogonal lines within the locus of the zero crossings of a certain function represented in orthogonal Cartesian coordinates. The main contribution of this paper is the use and interpretation of the ambiguities that arise in such a locus in the form of additional pairs of orthogonal lines when applied to symmetric patterns and the development of other algorithmic steps which allow a simple and fast discrimination between cyclic and dihedral symmetries. Unlike any other available method, this algorithm does not require any conversion from Cartesian to polar image representations. Besides classification reliability and consistency, observed through several dozen testing experiments, the nice features of this new method also include robustness to noise and ease of implementation with fast Fourier transform algorithms, which makes it amenable to almost real-time pattern classifications applications. Several examples, representative of the performance of the algorithm through extensive testing, are reported and discussed in the paper.