中文摘要：

针对灰度值攻击如亮度值的绝对修改、对比度改变、参数直方图均衡化，以及组合攻击破坏数字图像水印，利用第一主成分向量方向的稳定性，提出了一种适应性很强的零水印方法，解决了水印的不可见性与鲁棒性的矛盾。首先分析了第一主成分方向的稳定性，接着通过实验测试它在空域与变换域的表现。在此基础上对输入图像执行多级DT—CWT分解，选择它的两个低频子带并分别进行分块，计算各子块的第一主成分向量；然后分别计算它们与一个秘密参考向量的夹角；最后比较两个低频子带对应子块的夹角关系抽取图像特征。此外对所提出的方案进行了安全性与鲁棒性分析。通过对6幅图像的20种单项攻击以及50种组合攻击进行实验，结果表明所提出的方案在鲁棒性、经受攻击的广泛性、实用性3方面综合性能优越。

英文摘要：

Image gray or intensity value attacks, including the absolute modification of gray values, contrast adjustment, parameter histogram equalization, and combined attacks can make many kinds of watermark detection approaches unsuccessful. Addressing these problems in this paper, a robust zero-watermark algorithm using the direction stability of the first principal component vector is proposed, which can effectively solve the conflict between invisibility and robustness. The direction stability of the first principal component vector is mathematically analyzed, and experiments are performed to observe the difference of the stability in the spatial domain and the frequency domain. On this basis, the input image is decomposed by the dual-tree complex wavelet transform （DT-CWT） and the output of the two low frequency bands is segmented into non-overlapping sub-blocks, respectively. After computing the first principal component vector for each sub-block, some vector angles between that of each sub-block and a secret reference vector can be obtained. By comparing the angles from two sub-blocks with the same position in the left and fight low frequency bands, zero-watermark feature extraction is accom- plished. In addition, we analyze the security and robustness for the proposed scheme. Sufficient experiments with six tested images, twenty kinds of common attacks and fifty kinds of combination attacks are carried out. Simulation results show the proposed scheme is superior in the comprehensive performance composed of robustness, withstanding diversity attack and practical application.