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QFPJFMs: Quaternion Fractional-Order Pseudo-Jacobi–Fourier Moments

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Abstract

As one promising solution, zero-watermarking approaches have been proposed to enhance the image visual quality and applied to protect the intellectual property rights of the medical images, remote sensing images and military images. The moments and their invariants have good image descriptive capability and geometrical invariance, which are common tools for image zero-watermarking. However, there are still some problems. Firstly, most of the existing algorithms ignore the problem of balancing robustness and discriminability. Secondly, the direct computation of image moments is time-consuming, numerically inaccurate, and unstable, thus affecting the effectiveness of these moment-based methods. Third, there is less research on zero-watermarking algorithms targeted at color images. To address these problems, this paper presents a zero-watermarking algorithm which is based on accurate quaternion fractional-order pseudo-Jacobi–Fourier moments with time–frequency analysis capability for color images. Firstly, we define a new set of orthogonal moments, named fractional-order pseudo-Jacobi–Fourier moments (FPJFMs), which is characterized by the generic nature and time–frequency analysis capability. And, we propose a scheme for the accurate computation of FPJFMs. Also, we extend accurate FPJFMs to the accurate quaternion FPJFMs (QFPJFMs), which is an efficient color image representation. Next, a new framework is proposed, namely hybrid low-order moment feature (HLMF) based on accurate QFPJFMs, which can simultaneously improve the legibility and robustness of the image representation. Finally, the accurate QFPJFMs-based HLMF is adapted to the zero-watermarking algorithm. Numerous experiment results indicate that this paper's presented zero-watermarking approach provides a good balance between robustness and discriminability, which is an effective and superior scheme.

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Acknowledgements

This work was supported partially by the National Natural Science Foundation of China (Nos. 61472171 & 61701212), Key Scientific Research Project of Liaoning Provincial Education Department (No. LJKZZ20220115) and Scientific Research Project of Liaoning Provincial Education Department (No. LJKMZ20221420).

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Authors and Affiliations

  1. School of Computer Science and Artificial Intelligence, Liaoning Normal University, Dalian, 116029, People’s Republic of China

    Xiangyang Wang, Maoying Deng, Panpan Niu & Hongying Yang

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  1. Xiangyang Wang
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  2. Maoying Deng
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  3. Panpan Niu
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  4. Hongying Yang
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Contributions

XW: Methodology, Supervision, Writing-review & editing. MD: Writing-review & editing, Software. PN: Supervision, Writing-review & editing. HY: Supervision, Writing-review & editing.

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Correspondence to Xiangyang Wang or Panpan Niu.

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Wang, X., Deng, M., Niu, P. et al. QFPJFMs: Quaternion Fractional-Order Pseudo-Jacobi–Fourier Moments. J Math Imaging Vis 66, 93–114 (2024). https://doi.org/10.1007/s10851-023-01165-8

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  • DOI: https://doi.org/10.1007/s10851-023-01165-8

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