Research On Quaternion Fourier Transform And Digital Watermarking

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.