基于小波变换极大模算法的数字水印技术  

Hiding digital watermarks using wavelet transform modulus maxima

作　　者：冉启文[1] 郎俊[1] 张海莹[1] 

机构地区：[1]哈尔滨工业大学数学系,哈尔滨150001

出　　处：《黑龙江大学自然科学学报》2007年第5期586-591,共6页Journal of Natural Science of Heilongjiang University

摘　　要：提出一种新颖的在小波变换极大模域中嵌入的基于多尺度边缘的数字水印方法。利用小波变换极大模表示的几乎完全重构和奇异性刻画等优点来得到图像的一种稀疏表示,其中系数较大点表示了图像之中的感知重要的结构性边缘。因此,给定一幅图像,首先计算其二进小波变换,它的两个部分分别和该点处梯度向量成比例,则可以得到该点处的模和幅角信息,通过沿幅角给定的方向寻找模值的局部极大值来得到图像的多尺度边缘。通过取阀值和选择正Lipschitz指数的点来选取嵌入位置,将视觉可识别的图形冗余地嵌入到多尺度边缘中而保留幅角信息不变,经过逆小波极大模变换就可得到嵌入了水印信息的图像。实验结果表明该方法具有较高的保真度和极强的抗有损压缩的能力。A novel multiscale - edge - based digital watermarking technique in the wavelet modulus maxima domain is proposed. The nearly perfect reconstruction and singularity characterization properties of the wavelet transform modulus maxima representation （WTMM） are employed to obtain a sparse image representation, where the significant coefficients represent the perceptually important structural edges of the image. Therefore, given an image, compute the dyadic wavelet transform which is proportional to the gradient vector, then obtain the modulus and angle information. The associated multiscale - edge images are obtained by means of finding local modulus maxima along the angle directions at each scale, modulus maxima larger than a given threshold are selected, and eventually watermark with visually recognizable patterns is embedded into different levels of the modulus maxima to achieve the robustness of the watermarking. Robustness and transparency are proved by the experimental results.

关 键 词：数字水印 小波变换极大模 二进小波变换 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]