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Practical fast computation of Zernike moments

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Abstract

The fast computation of Zernike moments from normalized geometric moments has been developed in this paper. The computation is multiplication free and only additions are needed to generate Zernike moments. Geometric moments are generated using Hatamian’s filter up to high orders by a very simple and straightforward computation scheme. Other kinds of moments (e.g., Legendre, pseudo Zernike) can be computed using the same algorithm after giving the proper transformations that state their relations to geometric moments. Proper normalizations of geometric moments are necessary so that the method can be used in the efficient computation of Zernike moments. To ensure fair comparisons, recursive algorithms are used to generate Zernike polynomials and other coefficients. The computational complexity model and test programs show that the speed-up factor of the proposed algorithm is superior with respect to other fast and/or direct computations. It perhaps is the first time that Zernike moments can be computed in real time rates, which encourages the use of Zernike moment features in different image retrieval systems that support huge databases such as the XM experimental model stated for the MPEG-7 experimental core. It is concluded that choosing direct computation would be impractical.

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Authors and Affiliations

  1. Image Processing and Pattern Recognition Institute, Shanghai Jiaotong University, 200030, Shanghai, P.R. China

    Al-Rawi Mohammed & Yang Jie

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  1. Al-Rawi Mohammed
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  2. Yang Jie
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Correspondence to Al-Rawi Mohammed.

Additional information

Supported by the National Natural Science Foundation of China (No.30170274) and the National “863” High-Tech Programme of China (No. 863-306-ZB13-05-6).

Al-Rawi Mohammed was born in 1966, in Iraq, and received his M.S. degree from the College of Sciences, Baghdad University, in 1993. Currently, he is a Ph.D. candidate of the Institute of Image Processing & Pattern Recognition, SJTU. His major research interests are invariant pattern recognition, recognition of color texture, image processing.

YANG Jie was born in 1964, and received his Ph.D. degree from the Department of Computer Science, Hamburg University, Germany. Currently, he is vice director of the Institute of Image Processing & Pattern Recognition, SJTU. He has taken charge of many research projects (e.g. National Natural Science Foundation, National “863” High-Tech, Programme) and published a book in Germany and more than 70 journal papers. His major research interests are object detection and recognition, data fusion and data mining, intelligent systems and applications, medical image processing.

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Mohammed, AR., Yang, J. Practical fast computation of Zernike moments. J. Comput. Sci. & Technol. 17, 181–188 (2002). https://doi.org/10.1007/BF02962210

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  • DOI: https://doi.org/10.1007/BF02962210

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