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Green Image
Issue No. 09 - September (2010 vol. 32)
ISSN: 0162-8828
pp: 1659-1672
Seungkyu Lee , The Pennsylvania State University, State College
Yanxi Liu , The Pennsylvania State University, State College
We present a novel and effective algorithm for affinely skewed rotation symmetry group detection from real-world images. We define a complete skewed rotation symmetry detection problem as discovering five independent properties of a skewed rotation symmetry group: 1) the center of rotation, 2) the affine deformation, 3) the type of the symmetry group, 4) the cardinality of the symmetry group, and 5) the supporting region of the symmetry group in the image. We propose a frieze-expansion (FE) method that transforms rotation symmetry group detection into a simple, 1D translation symmetry detection problem. We define and construct a pair of rotational symmetry saliency maps, complemented by a local feature method. Frequency analysis, using Discrete Fourier Transform (DFT), is applied to the frieze-expansion patterns (FEPs) to uncover the types (cyclic, dihedral, and O(2)), the cardinalities, and the corresponding supporting regions, concentric or otherwise, of multiple rotation symmetry groups in an image. The phase information of the FEP is used to rectify affinely skewed rotation symmetry groups. Our result advances the state of the art in symmetry detection by offering a unique combination of region-based, feature-based, and frequency-based approaches. Experimental results on 170 synthetic and natural images demonstrate superior performance of our rotation symmetry detection algorithm over existing methods.
Skewed rotation symmetry, symmetry group, frieze group, discrete Fourier transform, saliency map, cyclic group, dihedral group.

S. Lee and Y. Liu, "Skewed Rotation Symmetry Group Detection," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 32, no. , pp. 1659-1672, 2009.
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