Fast image reconstruction method using radial harmonic Fourier moments and its application in digital watermarking

IF 3.7 3区计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS

Journal of The Franklin Institute-engineering and Applied Mathematics Pub Date : 2024-11-13 DOI:10.1016/j.jfranklin.2024.107391

Hao Zhang , Zhenyu Li , Yongle Chen , Chenchen Lu , Pengfei Yan

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引用次数: 0

Abstract

The Radial Harmonic Fourier Moments(RHFMs) is a kind of continuous orthogonal moments with good performance of image representation and reconstruction. Most of existing methods focused on improving the computation of RHFMs, and ignored the research about the reconstruction. Therefore, a fast reconstruction method based on RHFMs by using inverse fast Fourier transform(IFFT) is proposed in this paper. The time cost of reconstruction is greatly decreased. Then, the fast computation method is extend to the quaternion radial harmonic Fourier moments(QRHFMs) by using quaternion theory, which is suitable for the color image representation. Finally, a color image watermarking scheme based on the QRHFMs is conducted. During the embedding process, considering the association between QRHFMs and quaternion discrete Fourier transform(QDFT), the watermark is embedded in the magnitude of QRHFMs symmetrically. The center area of cover image is ignored in order to improve the quality of watermarked image. Experiments denote that proposed watermarking algorithm has low computation complexity and good robust against geometric attacks and common attacks.

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利用径向谐波傅里叶矩的快速图像重建方法及其在数字水印中的应用

径向谐波傅里叶矩（RHFMs）是一种连续正交矩，具有良好的图像表示和重建性能。现有方法大多侧重于改进 RHFMs 的计算，而忽略了重建方面的研究。因此，本文提出了一种基于 RHFMs 的反快速傅里叶变换（IFFT）快速重建方法。重建的时间成本大大降低。然后，利用四元数理论将快速计算方法扩展到四元数径向谐波傅里叶矩（QRHFMs），该方法适用于彩色图像的表示。最后，本文提出了一种基于 QRHFMs 的彩色图像水印方案。在嵌入过程中，考虑到 QRHFMs 与四元离散傅里叶变换（QDFT）之间的关联，水印被对称地嵌入到 QRHFMs 的幅值中。为了提高水印图像的质量，忽略了覆盖图像的中心区域。实验表明，所提出的水印算法计算复杂度低，对几何攻击和常见攻击具有良好的鲁棒性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of The Franklin Institute-engineering and Applied Mathematics 工程技术-工程：电子与电气

CiteScore

7.30

自引率

14.60%

发文量

586

审稿时长

6.9 months

期刊介绍： The Journal of The Franklin Institute has an established reputation for publishing high-quality papers in the field of engineering and applied mathematics. Its current focus is on control systems, complex networks and dynamic systems, signal processing and communications and their applications. All submitted papers are peer-reviewed. The Journal will publish original research papers and research review papers of substance. Papers and special focus issues are judged upon possible lasting value, which has been and continues to be the strength of the Journal of The Franklin Institute.