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Double Medical Images Zero-Watermarking Algorithm Based on the Chaotic System and Ternary Accurate Polar Complex Exponential Transform

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Abstract

Different from the traditional watermarking schemes, zero-watermarking schemes are lossless embedding methods, which are applicable to be used in medical, military, remote sensing and other fields requiring high-integrity image copyright protection. However, most of the existing zero-watermarking schemes only provide copyright protection for one image at a time, which has certain limitations. This paper proposes a novel zero-watermarking scheme for protecting the copyright of two similar medical images simultaneously. Firstly, an accurate polar complex exponential transform (APCET) is designed using Gaussian numerical integration (GNI) method, which effectively improves the computation accuracy of polar complex exponential transform (PCET). Then, ternary accurate polar complex exponential transform (TAPCET) is constructed based on ternary number theory and APCET, which describes two similar medical images simultaneously. Finally, a robust zero-watermarking algorithm for two similar medical images is proposed based on TAPCET and chaotic mapping. The experimental results show that the proposed scheme can resist common image processing attacks and geometric attacks, and is superior to other zero-watermarking algorithms, being applicable for the copyright protection of two similar medical images simultaneously.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (61802212 and 61872203), the Shandong Provincial Natural Science Foundation (ZR2019BF017 and ZR2020MF054), the China Postdoctoral Science Foundation (2020M670728), Major Scientific and Technological Innovation Projects of Shandong Province (2019JZZY010127, 2019JZZY010132 and 2019JZZY010201), Plan of Youth Innovation Team Development of Colleges and Universities in Shandong Province (SD2019-161), Jinan City “20 universities” Funding Projects (2020GXRC056 and 2019GXRC031), and the Project of Shandong Province Higher Educational Science and Technology Program (J18KA331).

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Authors and Affiliations

  1. School of Cyber Security, Qilu University of Technology (Shandong Academy of Sciences), Jinan, 250353, China

    Bin Ma, Lili Chang, Chunpeng Wang, Jian Li, Zhiqiu Xia & Xingyuan Wang

  2. Shandong Computer Science Center (National Supercomputer Center in Jinan), Shandong Provincial Key Laboratory of Computer Networks, Qilu University of Technology (Shandong Academy of Sciences), Jinan, 250014, China

    Bin Ma, Lili Chang, Chunpeng Wang, Jian Li, Gang Li, Zhiqiu Xia & Xingyuan Wang

  3. School of Information Science and Technology, Dalian Maritime University, Dalian, 116026, China

    Zhiqiu Xia & Xingyuan Wang

Authors
  1. Bin Ma
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  2. Lili Chang
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  3. Chunpeng Wang
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  4. Jian Li
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  5. Gang Li
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  6. Zhiqiu Xia
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  7. Xingyuan Wang
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Correspondence to Chunpeng Wang.

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Ma, B., Chang, L., Wang, C. et al. Double Medical Images Zero-Watermarking Algorithm Based on the Chaotic System and Ternary Accurate Polar Complex Exponential Transform. J Math Imaging Vis 63, 1160–1178 (2021). https://doi.org/10.1007/s10851-021-01048-w

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