Symmetry detection by generalized complex (GC) moments: A close-form solution

This paper presents a unified method for detecting both reflection-symmetry and rotation-symmetry of 2D images based on an identical set of features, i.e., the first three nonzero generalized complex (GC) moments. This method is theoretically guaranteed to detect all the axes of symmetries of every 2D image, if more nonzero GC moments are used in the feature set. Furthermo re, we establish the relationship between reflectional symmetry and rotatio nal symmetry in an image, which can be used to check the correctness of sym metry detection. This method has been demonstrated experimentally using mor e than 200 images.