Abstract: In order to improve the robustness of digital watermarking images, this paper proposes an algorithm of image digital watermarking based on Dual Tree Complex Wavelet Transform（DT-CWT） domain and Hard C-Means cluster（HCM）. The original image is decomposed by one level DT-CWT. The watermark embedding location is identified adaptively by applying HCM in the two low frequency sub-band which is produced by DT-CWT. The binary watermark is disposed after Hilbert curve scrambling transformation and dimension reduction. A one-dimensional signal sequence is formed. Using image itself local relevance, this paper adjusts the embedding strength and modifies wavelet coefficient value, to realize the one-dimensional signal sequence embed in the watermark embedding location. The finding is that this method is invisible and robust against various geometric attacks such as compression, cropping, noise adding, filters, and so on.

Key words: digital watermarking, Dual Tree Complex Wavelet Transform（DT-CWT）, hard C-means cluster, Hilbert curve scrambling

摘要： 为了提高数字水印图像的鲁棒性，提出一种基于硬C均值聚类和双树复小波变换域的图像水印算法。该算法对载体图像进行一层双树复小波变换分解，利用人类视觉特性对其2个低频子带进行硬C均值聚类划分，确定可嵌入信息区域。将二值水印图像信号经过Hilbert曲线置乱和降维，形成一维信号序列。利用图像自身局部相关性，调节水印嵌入强度并修改小波系数值，实现将水印嵌入到可嵌入信息区域。实验表明，该算法具有良好的透明性且对压缩、剪切、噪声和滤波等几何攻击具有高鲁棒性。

关键词: 数字水印, 双树复小波变换, C均值聚类, Hilbert曲线置乱