TAILIEUCHUNG - The total error limited by modifying the parameters of zernike moments computation in duplicated images

In the paper, an effective method for reducing Geometrical Error () and Numerical Error () of Zernike moments is proposed. By running MATLAB for the proposed Zernike’s algorithm, the results of our proposed methods have shown a remarkable improvement to the total error of the analysis. | Journal of Automation and Control Engineering Vol. 4, No. 1, February 2016 The Total Error Limited by Modifying the Parameters of Zernike Moments Computation in Duplicated Images Thuong Le-Tien and Tan Huynh-Ngoc Department of Electrical Electronics Engineering, HCM City University of Technology, HCMUT, Ho Chi Minh City, Vietnam Email: thuongle@ Tu Huynh-Kha School of Electrical Electronics Engineering, HCM City International University, HCMIU, Ho Chi Minh City, Vietnam Email: hktu@ area are not changed when they located in another area. Abstract—In the paper, an effective method for reducing Geometrical Error () and Numerical Error () of Zernike moments is proposed. By running MATLAB for the proposed Zernike’s algorithm, the results of our proposed methods have shown a remarkable improvement to the total error of the analysis. The new proposed technique in reducing significantly Geometrical Error is performed better than that in the traditional technique. Considering two sides of , minimization and the reconstructed images having their size are almost with unchanged forms compared to the original images, then the proposed method has proven its potential capability in significantly reducing the two main errors of Zernike moments computation. Finally, the copy-move-rotate detection program has written by C++ under supporting OpenCV and Boost libraries that helps to verify the authentication of images. Index Terms—tampered image detection, polynomial, geometric moments, region of interest I. Figure 1. Forgery model (O1 original area; O2 copied area of O1 area) Therefore, using Zernike moments, it is able to detect easily the copied areas of a tampered image (Fig. 1). To compute the Zernike moments for tampered image, a discrete-space image f ( x, y ) , which is combined by its ( NxN ) sub-images or Region of Interest (ROI), is mapped to the unit disc in polar form. Pixels fall outside the disc are not computed. Then, .

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• Journal of Automation and Control Engineering
• The total error limited by modifying the parameters
• Zernike moments computation in duplicated images
• Reducing Geometrical Error
• Tampered image detection
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