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Mathematical Problems in Engineering
Volume 2012, Article ID 353406, 17 pages
Research Article

An Algorithm for Fast Computation of 3D Zernike Moments for Volumetric Images

1Department of Computer Science, Community College, Najran University, P.O. BOX 1988, Najran, Saudi Arabia
2Department of Information Technology, Faculty of Computers and Informatics, Zagazig University, Zagazig 44519, Egypt
3Department of Mathematics, College of Science and Arts, Najran University, P.O. BOX 1988, Najran, Saudi Arabia

Received 9 May 2012; Revised 6 August 2012; Accepted 29 August 2012

Academic Editor: Wanquan Liu

Copyright © 2012 Khalid M. Hosny and Mohamed A. Hafez. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


An algorithm was proposed for very fast and low-complexity computation of three-dimensional Zernike moments. The 3D Zernike moments were expressed in terms of exact 3D geometric moments where the later are computed exactly through the mathematical integration of the monomial terms over the digital image/object voxels. A new symmetry-based method was proposed to compute 3D Zernike moments with 87% reduction in the computational complexity. A fast 1D cascade algorithm was also employed to add more complexity reduction. The comparison with existing methods was performed, where the numerical experiments and the complexity analysis ensured the efficiency of the proposed method especially with image and objects of large sizes.