A Statistical Color Image Watermarking Scheme Using Local QPCET and Cauchy–Rayleigh Distribution


Based on local quaternion polar complex exponential transform (QPCET) and Cauchy–Rayleigh distribution, we propose a statistical color image watermarking scheme in this paper, which can achieve the trade-off among imperceptibility, robustness and data payload. Our color image watermarking scheme consists of two parts, namely embedding and detecting. In the embedding process, we divide the color host image into non-overlapping blocks and compute the local QPCET of color image blocks and then insert the watermark signal into the robust local QPCET magnitudes through multiplicative approach. In the detecting phase, robust local QPCET magnitudes are firstly modeled by employing the Cauchy–Rayleigh distribution, where the statistical properties of local QPCET magnitudes are captured accurately. Then, genetic algorithm-based maximum likelihood approach is introduced to estimate the statistical parameters of Cauchy–Rayleigh distribution model. And finally a color image watermark detector for multiplicative watermarking is developed using Cauchy–Rayleigh distribution and locally most powerful test. Also, we utilize the Cauchy–Rayleigh statistical model to derive the closed-form expressions for the watermark detector. Experimental results on some standard test images and comparison with well-known existing methods demonstrate the efficacy and superiority of the proposed scheme.

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Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.


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This work was supported partially by the National Natural Science Foundation of China (Nos. 61472171 and 61701212), China Postdoctoral Science Foundation (Nos. 2017M621135 and 2018T110220), Key Scientific Research Project of Liaoning Provincial Education Department (LZ2019001), Natural Science Foundation of Liaoning Province (2019-ZD-0468).

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Correspondence to Xiangyang Wang.

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Niu, P., Wang, L., Tian, J. et al. A Statistical Color Image Watermarking Scheme Using Local QPCET and Cauchy–Rayleigh Distribution. Circuits Syst Signal Process (2021). https://doi.org/10.1007/s00034-021-01678-w

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  • Color image watermarking
  • Local QPCET
  • Cauchy–Rayleigh distribution
  • GA-ML algorithm
  • LMP test