【作者】 王丹；

【导师】 王树勋； 王珂；

【作者基本信息】 吉林大学 ， 通信与信息系统， 2013， 博士

【摘要】 数字水印可实现对数字产品的版权保护、验证产品的真伪以及跟踪产品的流通等目的。目前，空域数字水印和彩色图像傅立叶频域水印仍存在许多待解决的问题。本文在推导了四元数的傅立叶变换的计算过程后，以彩色图像为载体，提出了抗几何攻击的频域数字水印算法。在对空域数字水印掩蔽函数问题进行了深入的研究后，提出了以非均质度量为掩蔽函数的数字水印算法，并将其应用于彩色图像的抗打印扫描技术中。论文的主要工作有如下几方面：1.为解决四元数傅立叶变换（Quaternion Fourier Transform, QFT）中双侧变换使用范围的局限性，提出了基于Pauli算符和欧拉公式的四元数极坐标表达式。应用该表达式结合指数算符公式详细推导了双侧四元数傅立叶变换的求解过程，给出了双侧傅立叶逆变换（Inverse Quaternion Fourier Transform，IQFT）的求解思路，将该算法推广至单侧QFT的求解过程，证明了该算法求得的离散QFT结果与现有算法的一致性。2.提出了基于极坐标映射关系的笛卡尔坐标系彩色图像数字水印算法。为使彩色图像的各颜色通道之间的强相关性不被破坏，采用基于四元数的理论研究彩色图像数字水印。根据前述推出的QFT算法，选择QFT中频区域直角坐标系为嵌入区域，根据实部矩阵的对称特性嵌入；为提高算法的抗几何攻击能力，给出了直角坐标系与极坐标系对应点的位置关系；为避免极坐标逆变换插值造成的嵌入点不为整数的问题，在已有灰度图像算法的基础上，给出了具体的解决方案并予以实施。与其他四元数水印技术比较，本算法提高了水印系统的抗几何攻击能力。3.提出了基于非均质度量理论的空域数字水印算法。比较了不同的掩蔽函数对于数字水印图像的影响，考察了非均质度量在去噪和平滑技术中的应用，提出可用非均质度量（Inhomogeneity）作为掩蔽函数并用于灰度图像空域数字水印的研究。结合人类视觉感知系统，将水印信息以扩频方式嵌入，保证了水印的鲁棒性。提取水印时将非均质度量与误差扩散理论结合以去除攻击，估计出原始图像，实现了水印信息的盲提取。和其他空域算法相比较，应用非均质度量作为掩蔽函数，对图像的纹理信息判断准确，符合视觉感知的要求，水印算法的稳健性更强。4.提出了基于非均质度量的彩色图像抗打印扫描的数字水印算法。图像经历打印和扫描过程后会产生像素失真问题和几何失真。由于非均质度量掩蔽函数（Inhomogeneity Mask, IHM）应用了模糊数学的理论，决定了其可对像素失真图像的纹理信息准确判断、并且对小角度旋转攻击具有鲁棒性。由此可知，应用IHM的水印系统可实现彩色印刷图片真伪验证。为保证彩色图像各颜色之间的强关联性，将水印信息扩频调制后，构造成四元数的形式，再整体嵌入于载体中。通过实验分析可知，应用此水印算法，可抵抗彩色图像在印刷及扫描过程产生的像素失真和几何失真等攻击，亦适用于多次打印扫描以及复印等实际操作后的水印提取。更多还原

【Abstract】 Digital watermarking can be used to realize the protection of digital products, verifythe authenticity of products, tracking the circulation of products and so on. But, there arestill many problems to be solved in the digital watermarking of spatial domain and FourierTransform frequency domain. In the paper, we give the calculating process of QuaternionFourier Transform (QFT). Then, we use the QFT algorithm in color digital watermarkingto resist the geometric attack. We also propose a perceptual mask named inhomogeneity inspatial domain watermarking and use it in the color image print-scan watermarking.Our main innovate pursuits can be summarized as the following four aspects.Firstly, to solve the Quaternion Fourier Transform (QFT) calculating of bilateraltransform, we introduce the Pauli operator and give the new express of Quaternion. Then,with the combination of the Euler’s Equation, we deduce the bilateral QFT in detail. Wealso calculate the inverse transform of Quaternion to prove its reversibility. The methodcan be extended to compute the unilateral QFT and launched in the form of inversetransformation.Secondly, a kind of color image digital watermarking method is proposed. It isknown that there are strong correlations in the three channels of a color digital image. Andthe quaternion can exactly express the correlation among them. To contain the colorrelationships, we use the bilateral QFT computed last chapter to solve the problem ofdigital watermarking. According to the symmetrical characteristic of the real matrix; wechoose the real part of bilateral QFT frequency in Cartesian coordinate system as theembedded area. We should find the location of the Cartesian system correspond to thelog-polar system according to the given relationship between them. Then thewatermarking information is embedded in Cartesian system directly to avoid the deviationfrom the inverse log-polar transformation. On the basis of the existing algorithm forcalculating grayscale image, we give the specific solutions for color image. Comparedwith other quaternion watermark technology, It is proved that the algorithm we chose canresist the geometric attacks.Thirdly, an algorithm of spatial watermarking based on inhomogeneity is proposed.Inhomogeneity underlying an image is employed as a multi-scale measure to detectcontextual discontinuities for feature preservation. Compared the features with other maskfunctions, we use inhomogeneity as a mask function in gray image spatial research of digital watermarking. Combined with human visual perception system, we embed thewatermark information in spread spectrum way which guarantees the robustness of thewatermark. During the extracting process, we choose error diffusion theory to removeattack and estimate the original image that will realize the blind watermark extraction. theapplication of inhomogeneity as a mask function can give the image texture informationaccurately, more in line with the requirements of visual perception. Thanks to the use ofinhomogeneity, compared with previous spatial algorithms our watermarking scheme hasbetter visual perception and stronger robustness extraction.Finally, a digital watermarking scheme of color image for print-scan is proposed. Theinhomogeneity, which is the application of the theory of fuzzy mathematics, can determinethe distortion of the pixels of the image texture information and give the accuratejudgment. It can also improve the robustness of small angle rotation attacks. Therefore,apply the inhomogeneity mask function of watermarking system can realize color printingimage authenticity verification. In order to guarantee the strong correlation among thecolor channels of color image, we construct the spread spectrum modulated watermarkinformation into the form of quaternion, and embedded the information as a whole.Experiments show that applying this watermarking algorithm can resist color image pixeldistortion in printing and scanning process and attacks, such as geometric distortion. Thisscheme is also suitable for the verification of multiple print-scan and copy after the actualoperation of watermark extraction.更多还原