Although zero-watermarking can provide an effective and distortion-free scheme for image copyright protection, its robustness and discriminability do not meet expectations in existing methods. Some cannot resist effectively geometric attacks, others do not consider the discriminability and equalization. For that reason, this paper proposes a robust and distinguishable color image zero-watermarking algorithm based on polar harmonic transforms (PHTs) and compound chaotic map. In the proposed algorithm, firstly three PHTs moments of an image are computed simultaneously and accurate moments are selected for the robustness. Then, content-based binary feature sequence is acquired by judging the relation between magnitudes of adjacent moments for the discriminability. Finally, compound chaotic map is employed to encrypt copyright logo for ensuring security and scramble binary feature sequence for improving the equalization. Experimental results show that the proposed zero-watermarking algorithm has good equalization and discriminability, and an advantage in robustness compared with other zero-watermarking and traditional watermarking.

尽管零水印可以提供一种有效且无失真的图像版权保护方案，但其鲁棒性和可辨别性未达到现有方法的期望。有些不能有效抵抗几何攻击，而另一些则不考虑可分辨性和均衡性。因此，本文提出了一种基于极性谐波变换（PHT）和复合混沌映射的鲁棒且可区分的彩色图像零水印算法。在提出的算法中，首先同时计算图像的三个PHT矩，并为鲁棒性选择准确的矩。然后，通过判断相邻矩的大小之间的关系来判别基于内容的二进制特征序列。最后，采用复合混沌图对版权标志进行加密，以确保安全；对二进制特征序列进行加扰，以提高均衡性。实验结果表明，与其他零水印和传统水印相比，本文提出的零水印算法具有良好的均衡性和可分辨性，在鲁棒性方面具有优势。