极谐波分数傅里叶矩及其零水印算法应用  

Polar Harmonic Fractional Fourier Moment and Its Application in Zero-watermarking Algorithm

作　　者：徐丽云 张敏 XU Liyun;ZHANG Min(Institute of Big Data Science and Industry,Shanxi University,Taiyuan 030006,China;School of Computer and Information Technology,Shanxi University,Taiyuan 030006,China)

机构地区：[1]山西大学大数据科学与产业研究院,太原030006 [2]山西大学计算机与信息技术学院,太原030006

出　　处：《小型微型计算机系统》2025年第1期151-157,共7页Journal of Chinese Computer Systems

基　　金：国家自然科学基金项目(61901248)资助;山西省基础研究计划面上项目(202303021211023)资助。

摘　　要：图像矩作为一种图像的全局特征描述符,已经成为模式识别和图像分析的一种有力工具.为了能够有效抵抗常见的图像处理攻击和几何攻击,本文提出了可用于描述图像特征的极谐波分数傅里叶矩和四元数极谐波分数傅里叶矩.首先,将极谐波多项式作为径向函数,分数傅里叶变换的核函数作为角向函数,得到了极谐波分数傅里叶矩,并分析了其相关性质.其次,将图像的极谐波分数傅里叶矩应用到零水印算法,计算和提取图像中极谐波分数傅里叶矩,随机选择合适的特征图像,并构造二值特征图像,将得到的二值特征图像与水印图像进行异或运算,构造作为零水印的特征图像.最后,针对提出的零水印算法,通过噪声、滤波、旋转、缩放进行鲁棒性和对比分析实验.实验结果表明,本文所提出的极谐波分数傅里叶矩,综合了极谐波多项式和分数傅里叶变换的优点,在零水印算法中能够有效抵抗图像处理攻击和几何攻击,与同类算法相比鲁棒性更优.As a global feature descriptor,image moment has become a powerful tool for pattern recognition and image analysis.In order to resist common image processing attacks and geometric attacks effectively,Polar harmonic fractional Fourier moment and quaternion polar harmonic fractional Fourier moment are proposed to describe image features.Firstly,taking the polar harmonic polynomial as the radial function and the kernel function of the fractional Fourier transform as the angular function,the polar harmonic fractional Fourier moment is obtained,and its related properties are analyzed.Secondly,the polar harmonic fractional Fourier moment of the image are applied to the zero-watermarking algorithm,to calculate and extract the polar harmonic fractional Fourier moment of the image,randomly select the appropriate feature image,and construct the binary feature image.The obtained binary feature image is performed by XOR operation with the watermark image to construct the feature image as a zero-watermark.Finally,the proposed zero-watermarking algorithm is tested by noise,filtering,rotation and scaling.The experimental results show that the polar harmonic fractional Fourier moment proposed in this paper combines the advantages of polar harmonic polynomial and fractional Fourier transform,and can effectively resist image processing attacks and geometric attacks in zero-watermarking algorithm,and is more robust than other algorithms.

关 键 词：正交矩 分数傅里叶变换 极谐波多项式 四元数 零水印 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]