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<p><b>Abstract</b>—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 <it>first three</it> nonzero generalized complex (GC) moments. This method is theoretically guaranteed to detect all the axes of symmetries of <it>every</it> 2D image, if more nonzero GC moments are used in the feature set. Furthermore, we establish the relationship between reflectional symmetry and rotational symmetry in an image, which can be used to check the correctness of symmetry detection. This method has been demonstrated experimentally using more than 200 images.</p>
Symmetry detection, reflectional and rotational symmetry, symmetric axis, generalized complex (GC) moments, fold number, fold axes, rotationally symmetric image, reflection-symmetric image.

D. Shen, K. K. Cheung, E. K. Teoh and H. H. Ip, "Symmetry Detection by Generalized Complex (GC) Moments: A Close-Form Solution," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 21, no. , pp. 466-476, 1999.
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