建立了同一信号在不同内积空间非空子空间变换系数之间的关系及性质,分析了在一个变换域系数中嵌入水印对另一个变换域系数的影响,得到了同一信号傅立叶变换与小波变换之间的联系及小波域中嵌入加性水印引起的傅立叶变换系数的变化量.进行了小波域含加性水印彩色图像的特征分析,即在小波域中嵌入加性水印,在自然对数幅频域的中频区产生特征点,借助该特征点能够有效地解决小波域大容量加性水印对几何变形敏感的问题,分析了插值运算对特征点分布的影响.通过实验验证了特征点的稳健性,即这些特征点的位置不具有严格的小波基依赖性,能够抗压缩、高斯噪声、椒盐噪声、常见的滤波操作及抗打印扫描攻击,并对扫描仪分辨率不敏感.通过特征点的有无进行数字水印检测.在此基础上提出了水印盲提取算法.实验结果表明,无需水印和原始图像即可实现连续色调彩色图像加性水印的鲁棒盲检测和盲提取.%The relationship between the transforms of the signal in different non-void subspaces of inner product space is established,the property of which is analyzed,based on which the connection between the Fourier transform and wavelet transform of the same signal is obtained.Embedding additive watermark in one transform domain can change the coefficients' value in another one,such as an additive watermark in the wavelet coefficients of images can change the frequencies' amplitude of the Fourier transform domain.The changed value is the convolution of watermark and the Fourier transform coefficients of the wavelet function.Accordingly,the characteristics of color images with multi-bits additive watermark in the wavelet domain are analyzed.There are stable and robust feature points in the logarithm domain of spectra's amplitude,positions of which are independent of wavelet basis,resistant to compression,Gaussian noise,pepper and salt noise,filtering and print-scanning attack,insensitive of scanning resolution as well.The feature points are used to detect watermark in color images,depending on which the watermark's sensitivity of geometric distortion can be solved.The change of the feature points' distribution caused by interpolation operation is also analyzed.Furthermore,the blind extraction algorithm is proposed.Watermark embedded in Haar wavelet diagonal coefficients of the color image undergone print-scan attack is extracted by Bior3.7 wavelet decomposition,the coefficients of which are processed as an image.The experimental results show that the blind and robust detection and extraction can be achieved without watermark and original images.
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