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

Dinggang Shen; Horace H.S. Ip; Kent K.T. Cheung; Earn Khwang Teoh

doi:10.1109/34.765657

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

Dinggang Shen, Horace H.S. Ip, Kent K.T. Cheung, Earn Khwang Teoh

Research output: Contribution to journal › Article › peer-review

97 Citations (Scopus)

Abstract

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. 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.

Original language	English
Pages (from-to)	466-476
Number of pages	11
Journal	IEEE Transactions on Pattern Analysis and Machine Intelligence
Volume	21
Issue number	5
DOIs	https://doi.org/10.1109/34.765657
Publication status	Published - 1999
Externally published	Yes

ASJC Scopus subject areas

Software
Computer Vision and Pattern Recognition
Computational Theory and Mathematics
Artificial Intelligence
Applied Mathematics

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abstract = "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. 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.",

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AU - Ip, Horace H.S.

AU - Cheung, Kent K.T.

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AB - 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. 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.

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

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