This study proposes a novel blind watermarking algorithm based on radial harmonic Fourier moments (RHFMs) as well as discrete wavelet transform and discrete cosine transform (DWT-DCT) to achieve copyright protection. A non-adjacent coupled map lattice chaotic system was used to improve the safety in the watermark embedding process. First, a zero-watermark was obtained by performing DCT on the original image. Meanwhile, the direction information of the origin was calculated and embedded in the RHFM domain. During normal watermark embedding, the image-embedded direction information was transformed by a one-level DWT and the low-frequency sub-band was divided into $8\times 8$ non-overlapping blocks. Each block was transformed by DCT, and two low-frequency coefficients were selected to embed the encrypted watermark. Experimental results demonstrated that the proposed algorithm is robust against rotation and other attacks. The analysis also showed that the proposed algorithm satisfies the invisibility of watermarking algorithms and has good security performance.

这项研究提出了一种新颖的基于径向谐波傅立叶矩（RHFM）以及离散小波变换和离散余弦变换（DWT-DCT）的盲水印算法，以实现版权保护。为了提高水印嵌入过程的安全性，采用了非相邻的耦合图格混沌系统。首先，通过对原始图像执行DCT获得零水印。同时，计算出原点的方向信息并将其嵌入到RHFM域中。在普通水印嵌入期间，图像嵌入的方向信息通过一级DWT进行变换，并且将低频子带划分为$8\times 8$不重叠的块。每个块通过DCT变换，并选择两个低频系数来嵌入加密的水印。实验结果表明，该算法对旋转和其他攻击具有鲁棒性。分析还表明，该算法满足了水印算法的不可见性，并具有良好的安全性能。