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Rotation Invariance in 2D-FRFT with Application to Digital Image Watermarking

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Abstract

The extraction of rotation invariant representation is important for many signal processing tasks such as image analysis, computer vision, pattern recognition and so forth. In this paper, we show that, under certain conditions, the Two-Dimensional Fractional Fourier Transform (2D-FRFT) possesses this attractive property through mathematical analysis and extensive computer simulations. Based on this property, we propose a novel digital image watermarking method which combines 2D chirp signal with the addition and rotation invariant properties of 2D-FRFT in order to improve robustness and security of digital image watermark in 2D-FRFT domain. Experimental results show that the proposed method is robust against numerous watermarking attacks including rotation geometrical transform, JPEG compression, crop, median filtering, histogram equalization, salt & pepper noise, Gaussian lowpass filter, shift, dithering and Gaussian noise, and secures against unauthorized information copying and redistribution.

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Acknowledgments

This work is supported by the National Natural Science Foundation of China, No.61071211, No.60472044, and the Canada Research Chair Program. Authors are very thankful to Dr. Feng Zhang for giving very useful and suggestive discussion.

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Authors and Affiliations

  1. Zhengzhou University, Zhengzhou, 450001, China

    Lei Gao, Lin Qi, Enqing Chen, Shouyi Yang & Ling Guan

  2. Ryerson University, Toronto, M5B 2K3, Canada

    Yongjin Wang & Ling Guan

Authors
  1. Lei Gao
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  2. Lin Qi
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  3. Yongjin Wang
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  4. Enqing Chen
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  5. Shouyi Yang
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  6. Ling Guan
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Correspondence to Lei Gao.

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Gao, L., Qi, L., Wang, Y. et al. Rotation Invariance in 2D-FRFT with Application to Digital Image Watermarking. J Sign Process Syst 72, 133–148 (2013). https://doi.org/10.1007/s11265-012-0722-2

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  • DOI: https://doi.org/10.1007/s11265-012-0722-2

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