抵抗几何攻击是鲁棒水印研究的关键问题之一。为实现水印同步，提出了一种结合Zernike矩和小波域模板实现由粗到精几何同步的算法，即首先利用平移归一化图像的Zernike矩估计旋转和缩放参数，并用校正旋转和缩放后的图像和原图像之间的质心增量估计平移参数；然后基于粗略估计的参数，通过匹配小波域模板实现旋转、缩放和平移（RST）参数的精确识别和校正，该同步方法可以较大程度地降低搜索空间。水印嵌入和检测采用了小波域向量隐马尔可夫模型（DWT HMM）。仿真结果表明，利用由粗到精的几何同步方法和基于HMM的水印算法能有效抵抗StirMark平台的多种单项攻击和联合攻击，算法具有较好的鲁棒性能。

One of the key issues for robust watermarking is to resist geometrical attacks. A matching strategy from coarse to fine scale to achieve the geometrical synchronization incorporating Zernike moments and the template in wavelet domain is proposed. At the coarse stage, the rotation and scaling parameters are estimated with the Zernike moments of the translation normalized image, while the translation parameters are estimated with the centroid’s increments between the original image and the image that are corrected for rotation and scaling. At the fine stage, the accurate values of rotation, scaling, and translation (RST) are obtained by matching the template around the roughly estimated RST values, which hence reduces the searching spaces to some extent. Finally, the attacked image is corrected with the accurate RST values. A watermarking scheme based on the vector Hidden Markov Model in wavelet domain (DWT HMM) is also adopted. Good robustness is observed against StirMark attacks and their joint attacks.