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Mathematical Problems in Engineering
Volume 2013, Article ID 179489, 9 pages
Research Article

Estimation of Large Scalings in Images Based on Multilayer Pseudopolar Fractional Fourier Transform

1College of Math & Physics, Nanjing University of Information Science & Technology, Nanjing 210044, China
2School of Information Science and Technology, East China Normal University, No. 500 Dong-Chuan Road, Shanghai 200241, China
3Department of Computer and Information Science, University of Macau, Avenue Padre Tomás Pereira, Taipa, Macau

Received 20 January 2013; Accepted 28 April 2013

Academic Editor: Hai-lin Liu

Copyright © 2013 Zhenhong Li et al. 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.


Accurate estimation of the Fourier transform in log-polar coordinates is a major challenge for phase-correlation based motion estimation. To acquire better image registration accuracy, a method is proposed to estimate the log-polar coordinates coefficients using multilayer pseudopolar fractional Fourier transform (MPFFT). The MPFFT approach encompasses pseudopolar and multilayer techniques and provides a grid which is geometrically similar to the log-polar grid. At low coordinates coefficients the multilayer pseudopolar grid is dense, and at high coordinates coefficients the grid is sparse. As a result, large scalings in images can be estimated, and better image registration accuracy can be achieved. Experimental results demonstrate the effectiveness of the presented method.