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IEEE Trans Image Process. 2011 Feb;20(2):345-60. doi: 10.1109/TIP.2010.2062195. Epub 2010 Jul 29.

Combined invariants to similarity transformation and to blur using orthogonal Zernike moments.

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Laboratory of Image Science and Technology, School of Computer Science and Engineering, Southeast University, Nanjing, China.


The derivation of moment invariants has been extensively investigated in the past decades. In this paper, we construct a set of invariants derived from Zernike moments which is simultaneously invariant to similarity transformation and to convolution with circularly symmetric point spread function (PSF). Two main contributions are provided: the theoretical framework for deriving the Zernike moments of a blurred image and the way to construct the combined geometric-blur invariants. The performance of the proposed descriptors is evaluated with various PSFs and similarity transformations. The comparison of the proposed method with the existing ones is also provided in terms of pattern recognition accuracy, template matching and robustness to noise. Experimental results show that the proposed descriptors perform on the overall better.

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