中文摘要：

单个的数字水印算法或方案难以应付多种攻击方法的攻击，为此，文章对应用多水印方法提高水印抗攻击鲁棒性问题进行探讨，根据水印抵抗攻击的能力，给出了水印抗攻击鲁棒性的分类定义，同时根据这种能力提高的程度对多水印进行了分类，并由此引申出相关的命题．深入探讨了多水印带来的主要问题，并提出了解决多水印问题的多目标优化数学模型．以视频水印为例，对抗几何变换攻击和帧同步攻山的视频水印联合进行了实验，实验结果表明多目标优化模型能够有效解决多水印带来的问题，且多水印方法能够提高水印抵抗攻击的能力．

英文摘要：

Individual watermarking is difficult to resist the multiple combined attacks. There. fore, problems of the multi-watermark method applied to increase the anti-attack robustness of the watermarking are discussed in this paper. According to the ability of watermark resisting the combined attacks, the classification definition of robustness of the watermarking is given and the multiple comhined watermarks are classified in term of the enhancement degree of this kind of ability. Then the corresponding propositions are derived. Main problems brought by multi watermark are investigated profoundly and the mathematical model of multi-objective optimization is proposed to solve the problems discussed. As an example, the experiment of multiple video watermarks combined by the temporal-synchronous watermarking and the watermarking resistant to geometric attacks is performed. The experimental results show that the model proposed is consid erably beneficial and the multi watermark method can increase the ability resisting attacks.