Abstract: The analysis of energy helps to balance the imperceptibility and robustness of digital watermarking. Currently, the digital watermarking embedding energy is often determined by repeat testing. Firstly, this paper introduces the watermarking model which is based on the similarity of vectors, and then it quantificationally analyzes the impact of embedding strength and the secret key on the Peak Signal to Noise Ratio（PSNR） and watermarking correct extraction rate. Finally, simulation experiments show that with the embedding strength increasing, the impact of the secret key on the PSNR and watermarking correct extraction rate is reduced; for a particular embedding strength, there are optimal subsets of the secret key which make watermarking correct extraction rate maximum. It is significant for the design of digital watermarking which is based on the similarity of vectors, and it can calculate the energy which is required to embed in watermarking in theory.

Key words: digital watermarking, energy analysis, similarity of vectors, Peak Signal to Noise Ratio（PSNR）, watermarking extraction accuracy

摘要： 数字水印能量分析有助于平衡水印的不可视性和鲁棒性。当前数字水印嵌入能量往往通过反复实验确定。为此首先介绍了基于向量相似度的水印模型。接着定量分析了嵌入强度和密钥对峰值信噪比以及水印提取正确率的影响。最后通过仿真实验验证了理论结果：随着嵌入强度的增大，密钥对峰值信噪比和水印提取正确率影响减弱；针对特定嵌入强度存在最佳密钥子集使得水印提取正确率最大。这对于基于向量相似度的数字水印设计具有指导意义，可以从理论上计算需要嵌入水印的能量。

关键词: 数字水印, 能量分析, 向量相似度, 峰值信噪比, 水印提取正确率