四元数傅立叶变换及数字水印算法研究
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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。
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.
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。
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.
引文
[1]蔡吉人.信息安全密码学[J].网络信息安全,2003,2:14-16.
[2]孙圣和,陆哲明,牛夏牧等数字水印技术及应用[M].北京:科学出版社,2004.
[3] Bruce Schneier著,吴世忠,马芳译.网络信息安全的真相[M].北京:机械工业出版社,2001.
[4]陈明奇,钮心忻,杨义先.数字水印的研究进展和应用[J].通信学报,2001,22(5):71-79.
[5]刘振华,尹萍.信息隐藏技术及应用[M].北京:科学出版社,2002.
[6] Chung-Ping Wu. Techniques For Audiovisial Data Confidentiality, Integrity andCopyright Protection.[D], A Dissertation Presented to the Faculty of the GraduateSchool University of Sothern California (PHD), Electrical Engineering of Universityof Sothern California. December,2001.
[7]宋玉杰,刘瑞祯,谭铁牛等.数字水印技术在印刷品防伪中的应用[J].中国图像图形学报,2001,6(5):450-454.
[8]陈明奇,钮心忻,杨义先.数字水印的研究进展和应用[J].通信学报,2001,22(5):71-79.
[9]李海峰.稳健性数字图像水印算法研究[D]长春:吉林大学通信学院.2006.
[10] I. J. Cox, J. Kilian, T. Leighton and T. Shamoon. Secure Spread SpectrumWatermarking for Multimedia[J]. IEEE Trans. on Image Processing,1997,6(12):1673-1687.
[11]梁华庆,钮心忻,杨义先.基于数字水印的证件防伪技术[J].信号处理,2000(2):143-145.
[12]汪小帆,戴跃伟,茅耀斌.信息隐藏技术方法与应用[M].北京:机械工业出版社,2001.
[13] Xia-mu Niu, Zhe-ming Lu and Sheng-he Sun (2000): Digital Watermarking of StillImages with Gray-level Digital Watermarks. IEEE Transactions on ConsumerElectronics.46(1):137-145.
[14] Z. M. Lu, C. H. Liu, D. G. Xu and S. H. Sun. Semi-fragile Image WatermarkingMethod Based on Index constrained Vector Quantization[J]. IEEElectronics Letters,2003,39(1):35-36.
[15] Damien delannay Digital Watermarking Algorithms Robust Against Loss ofSynchronization[D], Universite catholique de Louvain,2004.
[16] Ingemar J. Cox Digital Watermarking[M]. Publishing House of Electronics Industry2003.
[17] C. J. Vanden Branden Lambrecht and J.E. Farrell. Perceptual Quality metric forDigitally Coded Color Images[J]. Proceedings of EUSIPCO,1996:1175-1178.
[18] F. A. P. Petitcolas, R. J. Anderson and M. G. Kuhn. Information Hiding-A Survey[C].Proceedings of IEEE,1999,87(7):1062-1078.
[19]尤新刚，郭云彪，周琳娜峰值信噪比不宜用来评价信息隐藏技术[C].信息隐藏全国学术研讨会（CIHW2000/2001）论文集，西安电子科技大学出版社，2001,pp51-56.
[20] S Voloshynovskiy, A Herrigel, N Baumgarter, and T Pun. A Stochastic Approach toContent Adaptive Digital Watermarking[C]. Lecture Notes in Computer Science.2000,1768:212-236.
[21] S.Pereira, S. Voloshynovskiy, M. Maribel, S. M. Marchand and T. Pun. SecondGeneration Benchmarking and Application Oriented Evaluation [J]. In: LNCS2137,Berlin: Spinger Verlag,2001:340-353.
[22] http://watermarking.unige.ch/Checkmark/index.html.
[23]温泉.多媒体数字水印的鲁棒性和不可感知性研究[D]长春:吉林大学博士学位论文
[24] Methodology for the Subjective Assement of the Quality of Television Pictures:Recommendation ITU-R BT.500-10.ITU Radiocommunication Assembly,2000.
[25] F.A.P. Petitcolas. Watermarking Schemes Evaluation[J]. IEEE Transactions onSignal Processing,2000,17(5):58-64.
[26] F. A. P. Petitcolas, R. J. Anderson and M. G. Kuhn. Attacks on Copyright MarkingSystems. In David Aucsmith (Ed), Information Hiding, Second InformationalWorkshop,IH98, Portland, Oregon, U. S. A.,April15-17,1998, Proceedings, LNCS1525, Springer-Verlag,1998:219-239.
[27] C.H. Chou, T.L. Wu. Embedding Color Watermarks in Color Images[J]. IEEE FourWorkshop on Multimedia Signal Processing, Oct,2001:327-332.
[28]曾高荣,裘正定.数字水印的鲁棒性评测模型[J],物理学报,2010,59(8):5870-5879.
[29] R. Van Schyndel, A. Z. Tirkel, C. F. Osborne, A Digital Watermark[C].1st IEEEInternational Conference on Image Processing, Austin Texas USA,1994,2:86-90.
[30]李海峰,宋巍巍,王树勋.基于Contourlet变换的稳健性图像水印算法[J].通信学报,2006,27(4):87-94.
[31]高西奇,甘露,邹采荣.多小波变换的理论及其在图像处理中的应用[J].通信学报,1999,20(11):55-60.
[32]刘九芬,黄达人,胡军全.数字水印中的正交小波基[J].电子与信息学报，2003,25(4):453-459.
[33] Watson A. B. DCT Quantization Matrices Visually Optimized for IndividualImages[J]. In: Proc. of SPIE: Human Vision, Visual Processing and Digital DisplayIV, Washington: SPIE,1993,1913:202-216.
[34] Liu Kuo-cheng, Wavelet-based Watermarking for Color Images Through Visualmasking[J]. AEU International Journal of Electronics and Communications.2010,64(2):112-124.
[35]唐笑年,王树勋,王丹. Balanced opt-rec多小波域内信息分层隐藏的分析与实现[J],电子学报. June,2009,37(6):1226-1231.
[36] Gui-jun Nian, Zhi-yuan Xie and Shu-xun Wang. Audio Watermarking Based onReverberation[C]，2006International Conference on Intelligent Information Hidingand multimedia signal Processing(IIH-MSP2006), Pasadena, California, USA,18-20December2006.
[37]宋伟,侯建军,李赵红,黄亮.一种基于Logistic混沌系统和奇异值分解的零水印算法[J],物理学报,2009,58(7):4449-4456.
[38] Dan. Yu, F. Sattar, and K. K. Ma. Watermark Detection and Extraction UsingIndependent Component Analysis Methods[J]. EURASIP journal on Applied SignalProcessing,2002,(1):92-104.
[39] A. Hyv rinen and E. Oja. Independent Component Analysis: Algorithm andApplications [J]. Neural Networks,2000,13(4):411-430.
[40]温泉,王树勋,李靖,谐波水印信号的模式[J]，吉林大学学报(工学版)，2004(1):40-45.
[41]孙锬锋，温泉,王树勋,基于人类视觉的混沌阵列在图象上的水印算法[J]，电子学报,2003(1):149-153.
[42]李海峰,王树勋,温泉,宋巍巍;基于SVD和ICA的鲁棒水印算法[J]，中山大学学报（自然科学版），2004,43(2):53-57.
[43] Chun-hua Li Application Research on Support Vector Machine in ImageWatermarking[C]; Neural Networks and Brain,2005. ICNN&B '05. InternationalConference on,2005,2:1129-1134.
[44] Yong-Gang Fu, Rui-Min Shen. Color Image Watermarking Scheme Based on LinearDiscriminant Analysis[J] Computer Standards&Interfaces,2008,30:115-120.
[45]赵春晖,刘巍.基于分块压缩感知的图像半脆弱零水印算法[J].自动化学报,2012,38(4):609-617
[46]艾鸽,伍家松,段宇平,舒华忠.一种基于压缩感知的无损图像认证算法[J]东南大学学报（自然科学版）2013,(03):489-493.
[47] Brassil, J., et al. Electronic Marking and Identification Techniques to DiscourageDocument Copying[J], In Proceedings of INFOCOM94,1994,(3):1278-1287.
[48] Brassil, J.T, Low, S.H.; Maxemchuk, N.F. Copyright Protection for the ElectronicDistribution of Text Documents[C]. Proceedings of the IEEE1995,87(7):1181-1196.
[49] Brassil, J.T, Low, S.H., Maxemchuk, N.F. Electronic Marking and IdentificationTechniques to Discourage Document Copying[J]. Selected Areas inCommunications,2002,13(8):1495-1504.
[50] W. Bender, D. Gruhl, and N. Morimoto. Techniques for Data Hiding. TechnicalReport[J], MIT Media Lab,1994,35(3.4):313-336.
[51] W. Bender, MacNeil, R. Design of Electronic Information[J] IBM Systems Journal1996,35(3.4):497-498
[52] K. Tanaka, Y. Nakamura and K. Matsui. Embedding Secret Information into ADithered Multilevel Image[C] In Procedings of the1990IEEE MilitaryCommunications Conference,1990:216-220.
[53] Eleni E. Varsaki, Vassilis Fotopoulos; Data Hiding Based on Image TextureClassification[J]. Signal Image and Video Processing2013, March2013,7(2):247-253.
[54] Pereira, Shelby， O Ruanaidh, Joseph J.K.; Deguillaume, Frederic, Template BasedRecovery of Fourier-based Watermarks Using Log-polar and Log-log Maps[J]Proceedings of the19996th International Conference on Multimedia Computingand Systems-IEEE ICMCS'99,pp:870-874.
[55] Sun, Jinguang, Lan, Shishuang. Geometrical Attack Robust Spatial DigitalWatermarking based on Improved SIFT[C]2010International Conference onInnovative Computing and Communication and2010Asia-Pacific Conference onInformation Technologu and Ocean Engineering CICC-ITOC2010:98-101.
[56] Zhu, Xinshan. A New Spatial Perceptual Mask for Image Watermarking[C].19thInternational Conference on Pattern Recogniton:1794-1797.
[57] M. S. Fu, O. C. Au. Data Hiding Watermarking for Halftone Images. IEEETransactions on Image Processing, April2002,11(4):477-484.
[58] R. Liu and T. Tan. A SVD-based Watermarking Scheme for Protecting RightfulOwnership[J]. IEEE Trans. On Multimedia, March2002,4(1):121-128.
[59] F. Alturki, R. Mersereau. An Oblivious Robust Digital Watermarking Using ImageTransform Phase Modulation.International Conference on Image Processing,Sept.2000,2:84-87.
[60]许君一,熊昌镇,齐东旭,黄继武.量化水印算法分析[J]通信学报2006,27(3):15-27.
[61] Debnath Bhattacharyya, Pallabi Chakraborty. Quantum Watermarking: A ReviewInternational Journal of Security and Its Applications July,2010,4(3):46-54.
[62] Guo Q, Liu, ZJ,Liu ST. Image Watermarking Algorithm Based on FractionalFourier Transform and Random Phase Encoding[J], Optics Communications2011,284:3918-3923.
[63] Ante Poljicak, Lidija Mandic, Darko Agic. Discrete Fourier Transform-basedWatermarking Method with an Optimal Implementation Radius[J]. Electron.Imaging.2011,20(3):869-882.
[64] Gaurav Bhatnagar. Distributed Multiresolution Discrete Fourier Transformmand itsApplication to Watermarking[J]. Wavelets Multiresolut Inf. Process.2010,08(02):225-241.
[65] C. Y. Lin, M. Wu, J. A. Bloom. et al. Rotation,Scale and Translation ResilientWatermarking for Images[J]. IEEE Transactions on Image Processing,2001,10(5):767-782.
[66] Dong Zheng, Jiying Zhao, Abdulmotaleb El Saddik. RST-Invariant Digital ImageWatermarking Based on Log-Polar Mapping and Phase Correlation[J]. IEEETransactions on Circuits and Systems for Video Technology, August.2003,13(8):753-765.
[67] Xiangui Kang, Jiwu Huang, and Wenjun Zeng, Efficient General Print-ScanningResilient DataHiding Based on Uniform Log-Polar Mapping[J],IEEE Transactionson Information Forensics and Security,2010,5(1):1-11
[68] S. J. Sangwine, Fourier Transforms of Colour Images Using Quaternion orHypercomplex, Numbers[J]. Electron. Lett.1996,32(21):1979-1980.
[69]江淑红,郝明非,张建秋,胡波;快速超复数服饰变换和超复数互相关的新算法及应用[J].电子学报.2008,36(1):100-105,
[70]江淑红,张建秋,胡波.一种超复数频域的有意义数字水印算法[J].系统工程与电子技术.2009,31(9):2242-2245.
[71] Tsz Kin Tsui, Xiao-Ping Zhang, and Dimitrios Androutsos, Color ImageWatermarking Using Multi-dimensional Fourier Transforms[J]. IEEE Transactionson Information Forensics and Security, March,2008,3(1):16-28.
[72] Ce LI, Baosen LI Limei XIAO, A Watermarking Method Based on HypercomplexFourier Transform and Visual Attention[J]. Journal of Information&ComputationalScience9,2012,15:4485-4492.
[73]孙菁,杨静宇.四元数域彩色图像整体式水印算法[J].电子与信息学报2012,34(10):2389-2395.
[74]孙菁,杨静宇,傅德胜.彩色图像四元数频域幅值调制水印算法[J].计算机科学.201138(3):123-126.
[75] Wang Xiang-yang, Wang Chun-peng, Yang Hong-ying, Niu Pan-pan；A robust BlindColor Image Watermarking in Quaternion Fourier Transform Domain[J] The Journalof Systems and Software86.2013:255-277.
[76] C. E. Moxey, T. A. Ell, and S. J. Sangwine, Vector Correlation of Color Images[J] InProc.1st Eur. Conf. Color in Graphics, Imaging, and Vision, Apr.2002:343-347.
[77] C E Moxey, Sangwine S J, Ell T A. Color-grayscale Image Registration usingHypercomplex Phase Correlation[C]. IEEE International Conference on ImageProcessing,2002:385-388
[78]冯巍,胡波.基于超复数相位相关的彩色图像配准算法[J].系统工程与电子技术2010,32(1):183-187.
[79]陈北京,孙星明,王定成,赵晓平;基于彩色图像四元数表示的彩色人脸识别[J]自动化学报2012,38(6):1-9.
[80]郝明非,张建秋,胡波.一种超复数鲁棒相关图像配准算法[J].复旦学报；2007,46(1):91-95.
[81] W. R. Hamilton, Elements of Quaternions [M]. London, U.K.: Longman,1866.
[82] Hamilton Elements of Quaternions (1899) VolumeI,(1901) VolumeII. Edited byCharles Jasper Joly; published by Longmans.
[83] Hermann Grassmann. Die Lineale Ausdehnungslehre [J]. Hermann GüntherGra mann,1844.
[84] P. G. Tait. Elementary Treatise on Quaternions [M].1867.
[85]杰姆斯.克勒克.麦克斯韦著.戈革译.《电磁通论》（上、下卷）.武汉出版社.
[86] James Clerk Maxwell. A Dynamical Theory of the Electromagnetic Field,Philosophical Transactions of the Royal Society of London.1865,155:459-512
[87] E. B. Wilson, Vector Analysis, A Text-book for the Use of Students of Mathematicsand Physics, Founded upon the Lectures of J. Willard Gibbs [M]. New Haven: YaleUniversity Press,1929.
[88] Heaviside Oliver. Electromagnetic Theory [M].1893.
[89]丁光涛.偏振光学的四元数方法[J].光学学报.2013,33(7):
[90] Adler S L. Quaternionic Quantum Mechanics and Quantum Fields [M].OxfordUniversity, New York,1995.
[91] Ian Duck and E. C. G. Sudarshan, Toward an Understanding of the Spin-statisticsTheorem, Am. J. Phys. April1998.66(4),284-303.
[92] Nadler, A., Bar-Itzhack. On Algorithms for Attitude Estimation Using GPS[C]Decision and Control2000. Proceedings of the39th IEEE Conference on Vol.43321-3326.
[93]张荣辉,贾宏光,陈涛,张跃.基于四元数法的捷联式惯性导航系统的姿态解算[J].光学精密工程,2008,16(10):1963-1970.
[94] Fjellstad, O.-E, Fossen, T.I. Quaternion Feedback Regulation of Under-waterVehicles[J],1994., Proceedings of the Third IEEE Conference on ControlApplications.
[95]金良海,李德华.基于四元数旋转的开关型矢量中值滤波器[J].中国图形图象学报,2007,12(11):185-191.
[96] S. C. Pei and C. M. Cheng. A Novel Block Ttruncation Coding of Color ImagesUsing a Quaternion-moment-preserving Principle [J]. IEEE Trans. Commun., Apr.1997,45(4):583-595.
[97] S. C. Pei，Jian Jun Ding, Ja-Han Chang; Efficient Implementation of QuatertinionFourier Transform, Convolution, and Correlation by2-D Complex FFT [J]. IEEETransactions on Signal Processing,2001,49(11):2783-2797
[98] C. E. Moxey, S. J. Sangwine, T. A. Ell. Hypercomplex Correlation Techniques forVector Images [J]. IEEE Trans. Signal Process., Jul.2003,51(7):1941-1953.
[99] S. J. Sangwine and T. A. Ell, Hypercomplex Auto-and Cross-correlation of Colorimages [J]. In Proc. IEEE Int. Conf. Image Processing, Kobe, Japan, Oct.1999, pp.319-322.
[100] T. A. Ell, Hypercomplex Spectral Transforms[D]. Ph.D. Dissertation, Univ.Minnesota, Minneapolis,1992.
[101] Wang Dan, Nian GuiJun, Wang Ke; Eular s Formula in Computing Hyper-ComplexFourier Transform[C].20114th International Congress on Image and SignalProcessing2011,2:770-774.
[102] Wang Dan, Nian GuiJun, Wang Ke; Computing Quaternion Fourier TransformUsing Algebraic Method[C].2011International Conference of YouthCommunication.2011,2:5-8.
[103]王慧琴,李人厚.一种基于DWT的彩色图像数字水印算法[J].小型微型计算机系统.2003,24(2):299-302.
[104]李岩山；一种新的彩色图像盲水印算法[J].计算机应用研究.201128(1):349-351
[105]盖琦.基于四元数理论的彩色图像信息隐藏技术[D].天津:南开大学博士学位论文.2009
[106]江淑红.彩色图像的超复数整体处理理论及应用研究[D].上海:复旦大学2009.
[107]盖琦，孙云峰，王晓雷，王明伟，翟宏琛基于离散四元数余弦变换的彩色图像数字水印技术[J].光电子激光2009.20(9):1193-1197.
[108]邢燕.四元数及其在图形图像处理中的应用研究[D].安徽:合肥工业大学博士学位论文,2009
[109]曹汉强,朱光喜，朱耀庭等；一种基于超复数系的数字全息图像生成方法[J].光学学报2001Vol.21,No1.
[110]许姜严.基于小波的岩石节理裂隙图像处理[D].安徽:电子科技大学博士学位论文,2010.
[111]王宇庆,刘维亚,王勇.基于四元数的彩色图像质量评价方法[J]，中北大学学报（自然科学版）2010:31(1):59-64.
[112]苏本跃，盛敏；彩色图像缩放的四元数插值算法[J]，中国图形图像学报14(12):2607-2610
[113]高朝邦等基于四元数分数阶方向微分的图像增强[J]，自动化学报,201137(2)150-159
[114] J.J.K. O Ranaidh, T. Pun. Rotation, Scale and Translation Invariant Spread SpectrumDigital Image Watermarking[J]. Signal Processing, May1998,66(5):303-317.
[115] J.J.K. O Ranaidh; Dowling, W.J.; Boland, F.M. Watermaking Digital Images forCopyright Protection[J] IEEE Proceedings: Vision, Image and Signal Processing,Aug1996,143(4):250-256.
[116] Ping Dong, Jovan G. Brakov, Yongyi Yang, Digital Watermarking Robust toGeometric Distortions[J], IEEE Transaction on Image Processing, December2005,14(12):2140-2150.
[117] Patrick Bas，N. Le Bihan; J.-M. Chassery. Color Image Watermarking UsingQuaternion Fourier Transform[J] ICASSP, Sep2003, Hong Kong. Proc of ICASSP.
[118]江淑红,张建秋,胡波.彩色图像超复数空间的自适应水印算法[J].2009,37(8):1773-1776.
[119] Dyson F J，Falk H. Period of a Discrete Cat Mapping[J]. The Amer Math Monthly,1992,99:603-614.
[120]朱岩，杨永田扩频CDMA水印性能分析及其应用研究[J],哈尔滨工业大学学报. Dec,2006,38(12):2116-2120.
[121]冈萨雷斯,阮秋琦等译.数字图像处理(Matlab版).[M].北京:电子工业出版社.2005.9.
[122] M. Barni, F. Bartolini, V.Cappellini and A. Piva. A DCT-domain System for RobustImage Watermarking[J]. Signal Processing.1998,66:357-372.
[123] A. P. M. Barni, F. Bartolini and Cppellini.Threshhold Selection for Correlation-Based Watermark Detection[C]. Proc. COST254Workshop on Intelligent Com-munications,1998, L Aquila, Italy.
[124] R. C. Gonzalez and R. E. Woods. Digital Image Processing[M]. Seconded. UpperSaddle River, N. J.: Prentice Hall,2002.
[125] P. K. Saha, J. K Udupa., Odhner D. Scale-Based Fuzzy Connected ImageSegmentation: Theory, Algorithms, and Validation[J]. Computer Vision and ImageUnderstanding.2000,77:145-174.
[126] P K, Saha, J K, Udupa. Optimum Image Thresholding via Class Uncertainty andRegion Homogeneity[J]. IEEE Transactions on Pattern Analysis and MachineIntelligence,2001,23(7):689-706.
[127] Chen K. Adaptive Smoothing via Contextual and Local Discontinuities [J]. IEEETransactions on Pattern Analysis and Machine Intelligence2005,27(10):1552-1567.
[128] Kutter M. and Winkler S.. A vision Based Masking Model for Spread SpectrumImage Watermarking [J]. IEEE Trans. On Image Process,2002,11(1):16-25.
[129] Chun-Hsien Chou and Yun-Chin Li. A Perceptual Tuned Subband Image CoderBased on the Measure of Just-noticeable Distortion Profile [J]. IEEE Transactions onCircuits and Systems for Video Technology.1995,5(6):467-476.
[130] A B Watson, G Y Yang, JA Solomon, J Villasenor. Visual Thresholds for WaveletQuantization Error [J]. Proceedings of SPIE Human Vision and Electronic Imaging.1996,2657:381-392.
[131] Anderson G L, Netravali A N. Image Restoration Based on a Subjectibe Criterion [J].IEEE Transactions on Systems, Man, and Cybernetics,1976,6(12):845-853.
[132] Irene G. Karybali and Kostas Berberidis，Efficient Spatial Image Watermarking viaNew Perceptual Masking and Blind Detection Schemes [J], IEEE Transactions OnInformation Forensics And Security,2006,7(1):256-269.
[133]年桂君,刘鸿石,车晓镭,孙晓颖.预测滤波器在空域盲加性水印系统中的应用[J].吉林大学学报（工学版）,2011,41(1):249-253.
[134] Voloshynovskiy S, Herrigel A, Baumgaertner N, Pun T. A Stochastic Approach toContent Adaptive Digital Image Watermarking[C]3rd Int. Workshop InformationHiding, Dresden, Germany, Sep.1999:211-236.
[135] Delaigle J. F., Vleeschouwer C. D., and Macq B. Watermarking Algorithm Based ona Human Visual model[J]. Signal Process.1998,66(5):319-335
[136]王丹,李阳,年桂君,王珂;非均质度量掩蔽函数在空域水印中的应用[J].吉林大学学报(工学版).2013,43(3):771-775.
[137]谷利民.稳健数字水印中的通信方法[D].中山:中山大学博士学位论文2004.
[138]孟祥林,王正志.基于视觉掩蔽效应的图像扩散[J].自动化学报,2011,37(1):21-27.
[139]年桂君.抗同步攻击鲁棒性数字水印技术研究[D].吉林大学通信学院.2008
[140] Malay K Kundu, Arpan K Maiti. An Inexpensive Digital Piscataway：WatermarkingScheme for Printed Document[C]. IET IEEE Press, International Conference onVisual Information Engineering2006:378-383.
[141]张静,张春田.能抗打印－扫描过程的数字图像水印算法[A].全国第三届信息隐藏学术研讨会论文集[C],机械工业出版社,2001:151-157
[142]年桂君,刘鸿石,王丹,王乃丹.彩色照片中隐藏水印信息的分析与实现[J].吉林大学学报（工学版）2011. Vol.41. Sup.1339-343.
[143]葛云露,年桂君,王树勋.基于Walsh编码调制的抗打印扫描数字水印算法[J]东南大学学报（自然科学版）2007: Vol.37S1,197-200.
[144]牛少彰,伍宏涛,谢正程,刘歆,杨义先.抗打印扫描数字水印算法的鲁棒性[J].中山大学学报(自然科学版),2004,43:1-4.
[145] Soo-Chang Pei, Jing-Ming Guo, and Hua Lee. Novel Robust WatermarkingTechnique in Dithering Halftone Images[J]. IEEE Signal Processing Letter.2005,12(4):333-336.
[146]肖颖喆,王娟娟.抗打印扫描数字水印技术的研究进展[J].包装学报. July2012.4(3):49-53.
[147]梁华庆,钮心忻,杨义先.基于数字水印的证件防伪技术[J].信号处理,2000(2):143-145.
[148] D Simitopoulos, D E Kout sonanos, M Gerassimos Strintzis. Robust ImageWatermarking Based on Generalized Radon Transformations [J]. IEEE Trans onCircuits and Systems for Video Technology,2003,13(8):732-745.
[149] Lee Hae-Yeoun, Lee Choong-hoon, Lee Heung-Kyu.Geometrically invariantwatermarking: Synchronization Through Circular Hough Transform[J]. MultimedTools App.2007. Vol.34:337-353.
[150] D Simitopoulos, D Kout sonanos, M G Strintzis. Image Watermarking Resistant toGeometric Attacks Using Generalized Radon Transformations[C]. Proc of14th IntConf on Digital Signal Processing (DSP2002).2002.85-88.
[151] F Deguillaume, S Voloshynovskiy, T Pun. A Method for the Estimation andRecovering from General Affine Transforms in Digital Watermarking Applications[A]. Proc of SPIE-Security and Watermarking of Multimedia Contents IV.2002.p313-322.
[152] Dajun He; Sun, Q. A RST Resilient Object-based Video Watermarking Scheme [J]In Proc. IEEE Int. Conf. Image Processing,2004,2:737-740.
[153] Kaushal Solanki, Upamanyu Madhow, B.S.Manjunath etal. Print and Scan ResilientData Hiding[J]. IEEE Transactions on Information Forensics and Security,December2006,1(4):464-478.
[154] Ping Wah Wong, and Nasir Memon. Secret and Public Key Image WatermarkingSchemes for Image Authentication and Owership Verification [J]. IEEE Transcationson Image Processing,2001,10(10):1539-1601.
[155] H H Yu, X. Y. Kong, W. Wolf. Techniques for Content-based Graph Authentication[J]. Signal Processing: Image Communication,2001,16(5):461-475.
[156] Frank Hartung, Martin Kutter, Multimedia Watermarking Techniques [J]. Proceedings of the IEEE.1999,87(7):1079-1107.
[157]费曼著,关洪译.物理定律的本性[J].长沙:湖南科学技出版社,2005.
[158] S Pereira, T Pun. Robust Template Matching for Affine Resistant ImageWatermarks [J]. IEEE Trans on Image Processing,2000,9(6):1123-1129.
[159] S. J. Sangwine, Todd A. Ell, arXiv:1001.4379.
[2]孙圣和,陆哲明,牛夏牧等数字水印技术及应用[M].北京:科学出版社,2004.
[3] Bruce Schneier著,吴世忠,马芳译.网络信息安全的真相[M].北京:机械工业出版社,2001.
[4]陈明奇,钮心忻,杨义先.数字水印的研究进展和应用[J].通信学报,2001,22(5):71-79.
[5]刘振华,尹萍.信息隐藏技术及应用[M].北京:科学出版社,2002.
[6] Chung-Ping Wu. Techniques For Audiovisial Data Confidentiality, Integrity andCopyright Protection.[D], A Dissertation Presented to the Faculty of the GraduateSchool University of Sothern California (PHD), Electrical Engineering of Universityof Sothern California. December,2001.
[7]宋玉杰,刘瑞祯,谭铁牛等.数字水印技术在印刷品防伪中的应用[J].中国图像图形学报,2001,6(5):450-454.
[8]陈明奇,钮心忻,杨义先.数字水印的研究进展和应用[J].通信学报,2001,22(5):71-79.
[9]李海峰.稳健性数字图像水印算法研究[D]长春:吉林大学通信学院.2006.
[10] I. J. Cox, J. Kilian, T. Leighton and T. Shamoon. Secure Spread SpectrumWatermarking for Multimedia[J]. IEEE Trans. on Image Processing,1997,6(12):1673-1687.
[11]梁华庆,钮心忻,杨义先.基于数字水印的证件防伪技术[J].信号处理,2000(2):143-145.
[12]汪小帆,戴跃伟,茅耀斌.信息隐藏技术方法与应用[M].北京:机械工业出版社,2001.
[13] Xia-mu Niu, Zhe-ming Lu and Sheng-he Sun (2000): Digital Watermarking of StillImages with Gray-level Digital Watermarks. IEEE Transactions on ConsumerElectronics.46(1):137-145.
[14] Z. M. Lu, C. H. Liu, D. G. Xu and S. H. Sun. Semi-fragile Image WatermarkingMethod Based on Index constrained Vector Quantization[J]. IEEElectronics Letters,2003,39(1):35-36.
[15] Damien delannay Digital Watermarking Algorithms Robust Against Loss ofSynchronization[D], Universite catholique de Louvain,2004.
[16] Ingemar J. Cox Digital Watermarking[M]. Publishing House of Electronics Industry2003.
[17] C. J. Vanden Branden Lambrecht and J.E. Farrell. Perceptual Quality metric forDigitally Coded Color Images[J]. Proceedings of EUSIPCO,1996:1175-1178.
[18] F. A. P. Petitcolas, R. J. Anderson and M. G. Kuhn. Information Hiding-A Survey[C].Proceedings of IEEE,1999,87(7):1062-1078.
[19]尤新刚，郭云彪，周琳娜峰值信噪比不宜用来评价信息隐藏技术[C].信息隐藏全国学术研讨会（CIHW2000/2001）论文集，西安电子科技大学出版社，2001,pp51-56.
[20] S Voloshynovskiy, A Herrigel, N Baumgarter, and T Pun. A Stochastic Approach toContent Adaptive Digital Watermarking[C]. Lecture Notes in Computer Science.2000,1768:212-236.
[21] S.Pereira, S. Voloshynovskiy, M. Maribel, S. M. Marchand and T. Pun. SecondGeneration Benchmarking and Application Oriented Evaluation [J]. In: LNCS2137,Berlin: Spinger Verlag,2001:340-353.
[22] http://watermarking.unige.ch/Checkmark/index.html.
[23]温泉.多媒体数字水印的鲁棒性和不可感知性研究[D]长春:吉林大学博士学位论文
[24] Methodology for the Subjective Assement of the Quality of Television Pictures:Recommendation ITU-R BT.500-10.ITU Radiocommunication Assembly,2000.
[25] F.A.P. Petitcolas. Watermarking Schemes Evaluation[J]. IEEE Transactions onSignal Processing,2000,17(5):58-64.
[26] F. A. P. Petitcolas, R. J. Anderson and M. G. Kuhn. Attacks on Copyright MarkingSystems. In David Aucsmith (Ed), Information Hiding, Second InformationalWorkshop,IH98, Portland, Oregon, U. S. A.,April15-17,1998, Proceedings, LNCS1525, Springer-Verlag,1998:219-239.
[27] C.H. Chou, T.L. Wu. Embedding Color Watermarks in Color Images[J]. IEEE FourWorkshop on Multimedia Signal Processing, Oct,2001:327-332.
[28]曾高荣,裘正定.数字水印的鲁棒性评测模型[J],物理学报,2010,59(8):5870-5879.
[29] R. Van Schyndel, A. Z. Tirkel, C. F. Osborne, A Digital Watermark[C].1st IEEEInternational Conference on Image Processing, Austin Texas USA,1994,2:86-90.
[30]李海峰,宋巍巍,王树勋.基于Contourlet变换的稳健性图像水印算法[J].通信学报,2006,27(4):87-94.
[31]高西奇,甘露,邹采荣.多小波变换的理论及其在图像处理中的应用[J].通信学报,1999,20(11):55-60.
[32]刘九芬,黄达人,胡军全.数字水印中的正交小波基[J].电子与信息学报，2003,25(4):453-459.
[33] Watson A. B. DCT Quantization Matrices Visually Optimized for IndividualImages[J]. In: Proc. of SPIE: Human Vision, Visual Processing and Digital DisplayIV, Washington: SPIE,1993,1913:202-216.
[34] Liu Kuo-cheng, Wavelet-based Watermarking for Color Images Through Visualmasking[J]. AEU International Journal of Electronics and Communications.2010,64(2):112-124.
[35]唐笑年,王树勋,王丹. Balanced opt-rec多小波域内信息分层隐藏的分析与实现[J],电子学报. June,2009,37(6):1226-1231.
[36] Gui-jun Nian, Zhi-yuan Xie and Shu-xun Wang. Audio Watermarking Based onReverberation[C]，2006International Conference on Intelligent Information Hidingand multimedia signal Processing(IIH-MSP2006), Pasadena, California, USA,18-20December2006.
[37]宋伟,侯建军,李赵红,黄亮.一种基于Logistic混沌系统和奇异值分解的零水印算法[J],物理学报,2009,58(7):4449-4456.
[38] Dan. Yu, F. Sattar, and K. K. Ma. Watermark Detection and Extraction UsingIndependent Component Analysis Methods[J]. EURASIP journal on Applied SignalProcessing,2002,(1):92-104.
[39] A. Hyv rinen and E. Oja. Independent Component Analysis: Algorithm andApplications [J]. Neural Networks,2000,13(4):411-430.
[40]温泉,王树勋,李靖,谐波水印信号的模式[J]，吉林大学学报(工学版)，2004(1):40-45.
[41]孙锬锋，温泉,王树勋,基于人类视觉的混沌阵列在图象上的水印算法[J]，电子学报,2003(1):149-153.
[42]李海峰,王树勋,温泉,宋巍巍;基于SVD和ICA的鲁棒水印算法[J]，中山大学学报（自然科学版），2004,43(2):53-57.
[43] Chun-hua Li Application Research on Support Vector Machine in ImageWatermarking[C]; Neural Networks and Brain,2005. ICNN&B '05. InternationalConference on,2005,2:1129-1134.
[44] Yong-Gang Fu, Rui-Min Shen. Color Image Watermarking Scheme Based on LinearDiscriminant Analysis[J] Computer Standards&Interfaces,2008,30:115-120.
[45]赵春晖,刘巍.基于分块压缩感知的图像半脆弱零水印算法[J].自动化学报,2012,38(4):609-617
[46]艾鸽,伍家松,段宇平,舒华忠.一种基于压缩感知的无损图像认证算法[J]东南大学学报（自然科学版）2013,(03):489-493.
[47] Brassil, J., et al. Electronic Marking and Identification Techniques to DiscourageDocument Copying[J], In Proceedings of INFOCOM94,1994,(3):1278-1287.
[48] Brassil, J.T, Low, S.H.; Maxemchuk, N.F. Copyright Protection for the ElectronicDistribution of Text Documents[C]. Proceedings of the IEEE1995,87(7):1181-1196.
[49] Brassil, J.T, Low, S.H., Maxemchuk, N.F. Electronic Marking and IdentificationTechniques to Discourage Document Copying[J]. Selected Areas inCommunications,2002,13(8):1495-1504.
[50] W. Bender, D. Gruhl, and N. Morimoto. Techniques for Data Hiding. TechnicalReport[J], MIT Media Lab,1994,35(3.4):313-336.
[51] W. Bender, MacNeil, R. Design of Electronic Information[J] IBM Systems Journal1996,35(3.4):497-498
[52] K. Tanaka, Y. Nakamura and K. Matsui. Embedding Secret Information into ADithered Multilevel Image[C] In Procedings of the1990IEEE MilitaryCommunications Conference,1990:216-220.
[53] Eleni E. Varsaki, Vassilis Fotopoulos; Data Hiding Based on Image TextureClassification[J]. Signal Image and Video Processing2013, March2013,7(2):247-253.
[54] Pereira, Shelby， O Ruanaidh, Joseph J.K.; Deguillaume, Frederic, Template BasedRecovery of Fourier-based Watermarks Using Log-polar and Log-log Maps[J]Proceedings of the19996th International Conference on Multimedia Computingand Systems-IEEE ICMCS'99,pp:870-874.
[55] Sun, Jinguang, Lan, Shishuang. Geometrical Attack Robust Spatial DigitalWatermarking based on Improved SIFT[C]2010International Conference onInnovative Computing and Communication and2010Asia-Pacific Conference onInformation Technologu and Ocean Engineering CICC-ITOC2010:98-101.
[56] Zhu, Xinshan. A New Spatial Perceptual Mask for Image Watermarking[C].19thInternational Conference on Pattern Recogniton:1794-1797.
[57] M. S. Fu, O. C. Au. Data Hiding Watermarking for Halftone Images. IEEETransactions on Image Processing, April2002,11(4):477-484.
[58] R. Liu and T. Tan. A SVD-based Watermarking Scheme for Protecting RightfulOwnership[J]. IEEE Trans. On Multimedia, March2002,4(1):121-128.
[59] F. Alturki, R. Mersereau. An Oblivious Robust Digital Watermarking Using ImageTransform Phase Modulation.International Conference on Image Processing,Sept.2000,2:84-87.
[60]许君一,熊昌镇,齐东旭,黄继武.量化水印算法分析[J]通信学报2006,27(3):15-27.
[61] Debnath Bhattacharyya, Pallabi Chakraborty. Quantum Watermarking: A ReviewInternational Journal of Security and Its Applications July,2010,4(3):46-54.
[62] Guo Q, Liu, ZJ,Liu ST. Image Watermarking Algorithm Based on FractionalFourier Transform and Random Phase Encoding[J], Optics Communications2011,284:3918-3923.
[63] Ante Poljicak, Lidija Mandic, Darko Agic. Discrete Fourier Transform-basedWatermarking Method with an Optimal Implementation Radius[J]. Electron.Imaging.2011,20(3):869-882.
[64] Gaurav Bhatnagar. Distributed Multiresolution Discrete Fourier Transformmand itsApplication to Watermarking[J]. Wavelets Multiresolut Inf. Process.2010,08(02):225-241.
[65] C. Y. Lin, M. Wu, J. A. Bloom. et al. Rotation,Scale and Translation ResilientWatermarking for Images[J]. IEEE Transactions on Image Processing,2001,10(5):767-782.
[66] Dong Zheng, Jiying Zhao, Abdulmotaleb El Saddik. RST-Invariant Digital ImageWatermarking Based on Log-Polar Mapping and Phase Correlation[J]. IEEETransactions on Circuits and Systems for Video Technology, August.2003,13(8):753-765.
[67] Xiangui Kang, Jiwu Huang, and Wenjun Zeng, Efficient General Print-ScanningResilient DataHiding Based on Uniform Log-Polar Mapping[J],IEEE Transactionson Information Forensics and Security,2010,5(1):1-11
[68] S. J. Sangwine, Fourier Transforms of Colour Images Using Quaternion orHypercomplex, Numbers[J]. Electron. Lett.1996,32(21):1979-1980.
[69]江淑红,郝明非,张建秋,胡波;快速超复数服饰变换和超复数互相关的新算法及应用[J].电子学报.2008,36(1):100-105,
[70]江淑红,张建秋,胡波.一种超复数频域的有意义数字水印算法[J].系统工程与电子技术.2009,31(9):2242-2245.
[71] Tsz Kin Tsui, Xiao-Ping Zhang, and Dimitrios Androutsos, Color ImageWatermarking Using Multi-dimensional Fourier Transforms[J]. IEEE Transactionson Information Forensics and Security, March,2008,3(1):16-28.
[72] Ce LI, Baosen LI Limei XIAO, A Watermarking Method Based on HypercomplexFourier Transform and Visual Attention[J]. Journal of Information&ComputationalScience9,2012,15:4485-4492.
[73]孙菁,杨静宇.四元数域彩色图像整体式水印算法[J].电子与信息学报2012,34(10):2389-2395.
[74]孙菁,杨静宇,傅德胜.彩色图像四元数频域幅值调制水印算法[J].计算机科学.201138(3):123-126.
[75] Wang Xiang-yang, Wang Chun-peng, Yang Hong-ying, Niu Pan-pan；A robust BlindColor Image Watermarking in Quaternion Fourier Transform Domain[J] The Journalof Systems and Software86.2013:255-277.
[76] C. E. Moxey, T. A. Ell, and S. J. Sangwine, Vector Correlation of Color Images[J] InProc.1st Eur. Conf. Color in Graphics, Imaging, and Vision, Apr.2002:343-347.
[77] C E Moxey, Sangwine S J, Ell T A. Color-grayscale Image Registration usingHypercomplex Phase Correlation[C]. IEEE International Conference on ImageProcessing,2002:385-388
[78]冯巍,胡波.基于超复数相位相关的彩色图像配准算法[J].系统工程与电子技术2010,32(1):183-187.
[79]陈北京,孙星明,王定成,赵晓平;基于彩色图像四元数表示的彩色人脸识别[J]自动化学报2012,38(6):1-9.
[80]郝明非,张建秋,胡波.一种超复数鲁棒相关图像配准算法[J].复旦学报；2007,46(1):91-95.
[81] W. R. Hamilton, Elements of Quaternions [M]. London, U.K.: Longman,1866.
[82] Hamilton Elements of Quaternions (1899) VolumeI,(1901) VolumeII. Edited byCharles Jasper Joly; published by Longmans.
[83] Hermann Grassmann. Die Lineale Ausdehnungslehre [J]. Hermann GüntherGra mann,1844.
[84] P. G. Tait. Elementary Treatise on Quaternions [M].1867.
[85]杰姆斯.克勒克.麦克斯韦著.戈革译.《电磁通论》（上、下卷）.武汉出版社.
[86] James Clerk Maxwell. A Dynamical Theory of the Electromagnetic Field,Philosophical Transactions of the Royal Society of London.1865,155:459-512
[87] E. B. Wilson, Vector Analysis, A Text-book for the Use of Students of Mathematicsand Physics, Founded upon the Lectures of J. Willard Gibbs [M]. New Haven: YaleUniversity Press,1929.
[88] Heaviside Oliver. Electromagnetic Theory [M].1893.
[89]丁光涛.偏振光学的四元数方法[J].光学学报.2013,33(7):
[90] Adler S L. Quaternionic Quantum Mechanics and Quantum Fields [M].OxfordUniversity, New York,1995.
[91] Ian Duck and E. C. G. Sudarshan, Toward an Understanding of the Spin-statisticsTheorem, Am. J. Phys. April1998.66(4),284-303.
[92] Nadler, A., Bar-Itzhack. On Algorithms for Attitude Estimation Using GPS[C]Decision and Control2000. Proceedings of the39th IEEE Conference on Vol.43321-3326.
[93]张荣辉,贾宏光,陈涛,张跃.基于四元数法的捷联式惯性导航系统的姿态解算[J].光学精密工程,2008,16(10):1963-1970.
[94] Fjellstad, O.-E, Fossen, T.I. Quaternion Feedback Regulation of Under-waterVehicles[J],1994., Proceedings of the Third IEEE Conference on ControlApplications.
[95]金良海,李德华.基于四元数旋转的开关型矢量中值滤波器[J].中国图形图象学报,2007,12(11):185-191.
[96] S. C. Pei and C. M. Cheng. A Novel Block Ttruncation Coding of Color ImagesUsing a Quaternion-moment-preserving Principle [J]. IEEE Trans. Commun., Apr.1997,45(4):583-595.
[97] S. C. Pei，Jian Jun Ding, Ja-Han Chang; Efficient Implementation of QuatertinionFourier Transform, Convolution, and Correlation by2-D Complex FFT [J]. IEEETransactions on Signal Processing,2001,49(11):2783-2797
[98] C. E. Moxey, S. J. Sangwine, T. A. Ell. Hypercomplex Correlation Techniques forVector Images [J]. IEEE Trans. Signal Process., Jul.2003,51(7):1941-1953.
[99] S. J. Sangwine and T. A. Ell, Hypercomplex Auto-and Cross-correlation of Colorimages [J]. In Proc. IEEE Int. Conf. Image Processing, Kobe, Japan, Oct.1999, pp.319-322.
[100] T. A. Ell, Hypercomplex Spectral Transforms[D]. Ph.D. Dissertation, Univ.Minnesota, Minneapolis,1992.
[101] Wang Dan, Nian GuiJun, Wang Ke; Eular s Formula in Computing Hyper-ComplexFourier Transform[C].20114th International Congress on Image and SignalProcessing2011,2:770-774.
[102] Wang Dan, Nian GuiJun, Wang Ke; Computing Quaternion Fourier TransformUsing Algebraic Method[C].2011International Conference of YouthCommunication.2011,2:5-8.
[103]王慧琴,李人厚.一种基于DWT的彩色图像数字水印算法[J].小型微型计算机系统.2003,24(2):299-302.
[104]李岩山；一种新的彩色图像盲水印算法[J].计算机应用研究.201128(1):349-351
[105]盖琦.基于四元数理论的彩色图像信息隐藏技术[D].天津:南开大学博士学位论文.2009
[106]江淑红.彩色图像的超复数整体处理理论及应用研究[D].上海:复旦大学2009.
[107]盖琦，孙云峰，王晓雷，王明伟，翟宏琛基于离散四元数余弦变换的彩色图像数字水印技术[J].光电子激光2009.20(9):1193-1197.
[108]邢燕.四元数及其在图形图像处理中的应用研究[D].安徽:合肥工业大学博士学位论文,2009
[109]曹汉强,朱光喜，朱耀庭等；一种基于超复数系的数字全息图像生成方法[J].光学学报2001Vol.21,No1.
[110]许姜严.基于小波的岩石节理裂隙图像处理[D].安徽:电子科技大学博士学位论文,2010.
[111]王宇庆,刘维亚,王勇.基于四元数的彩色图像质量评价方法[J]，中北大学学报（自然科学版）2010:31(1):59-64.
[112]苏本跃，盛敏；彩色图像缩放的四元数插值算法[J]，中国图形图像学报14(12):2607-2610
[113]高朝邦等基于四元数分数阶方向微分的图像增强[J]，自动化学报,201137(2)150-159
[114] J.J.K. O Ranaidh, T. Pun. Rotation, Scale and Translation Invariant Spread SpectrumDigital Image Watermarking[J]. Signal Processing, May1998,66(5):303-317.
[115] J.J.K. O Ranaidh; Dowling, W.J.; Boland, F.M. Watermaking Digital Images forCopyright Protection[J] IEEE Proceedings: Vision, Image and Signal Processing,Aug1996,143(4):250-256.
[116] Ping Dong, Jovan G. Brakov, Yongyi Yang, Digital Watermarking Robust toGeometric Distortions[J], IEEE Transaction on Image Processing, December2005,14(12):2140-2150.
[117] Patrick Bas，N. Le Bihan; J.-M. Chassery. Color Image Watermarking UsingQuaternion Fourier Transform[J] ICASSP, Sep2003, Hong Kong. Proc of ICASSP.
[118]江淑红,张建秋,胡波.彩色图像超复数空间的自适应水印算法[J].2009,37(8):1773-1776.
[119] Dyson F J，Falk H. Period of a Discrete Cat Mapping[J]. The Amer Math Monthly,1992,99:603-614.
[120]朱岩，杨永田扩频CDMA水印性能分析及其应用研究[J],哈尔滨工业大学学报. Dec,2006,38(12):2116-2120.
[121]冈萨雷斯,阮秋琦等译.数字图像处理(Matlab版).[M].北京:电子工业出版社.2005.9.
[122] M. Barni, F. Bartolini, V.Cappellini and A. Piva. A DCT-domain System for RobustImage Watermarking[J]. Signal Processing.1998,66:357-372.
[123] A. P. M. Barni, F. Bartolini and Cppellini.Threshhold Selection for Correlation-Based Watermark Detection[C]. Proc. COST254Workshop on Intelligent Com-munications,1998, L Aquila, Italy.
[124] R. C. Gonzalez and R. E. Woods. Digital Image Processing[M]. Seconded. UpperSaddle River, N. J.: Prentice Hall,2002.
[125] P. K. Saha, J. K Udupa., Odhner D. Scale-Based Fuzzy Connected ImageSegmentation: Theory, Algorithms, and Validation[J]. Computer Vision and ImageUnderstanding.2000,77:145-174.
[126] P K, Saha, J K, Udupa. Optimum Image Thresholding via Class Uncertainty andRegion Homogeneity[J]. IEEE Transactions on Pattern Analysis and MachineIntelligence,2001,23(7):689-706.
[127] Chen K. Adaptive Smoothing via Contextual and Local Discontinuities [J]. IEEETransactions on Pattern Analysis and Machine Intelligence2005,27(10):1552-1567.
[128] Kutter M. and Winkler S.. A vision Based Masking Model for Spread SpectrumImage Watermarking [J]. IEEE Trans. On Image Process,2002,11(1):16-25.
[129] Chun-Hsien Chou and Yun-Chin Li. A Perceptual Tuned Subband Image CoderBased on the Measure of Just-noticeable Distortion Profile [J]. IEEE Transactions onCircuits and Systems for Video Technology.1995,5(6):467-476.
[130] A B Watson, G Y Yang, JA Solomon, J Villasenor. Visual Thresholds for WaveletQuantization Error [J]. Proceedings of SPIE Human Vision and Electronic Imaging.1996,2657:381-392.
[131] Anderson G L, Netravali A N. Image Restoration Based on a Subjectibe Criterion [J].IEEE Transactions on Systems, Man, and Cybernetics,1976,6(12):845-853.
[132] Irene G. Karybali and Kostas Berberidis，Efficient Spatial Image Watermarking viaNew Perceptual Masking and Blind Detection Schemes [J], IEEE Transactions OnInformation Forensics And Security,2006,7(1):256-269.
[133]年桂君,刘鸿石,车晓镭,孙晓颖.预测滤波器在空域盲加性水印系统中的应用[J].吉林大学学报（工学版）,2011,41(1):249-253.
[134] Voloshynovskiy S, Herrigel A, Baumgaertner N, Pun T. A Stochastic Approach toContent Adaptive Digital Image Watermarking[C]3rd Int. Workshop InformationHiding, Dresden, Germany, Sep.1999:211-236.
[135] Delaigle J. F., Vleeschouwer C. D., and Macq B. Watermarking Algorithm Based ona Human Visual model[J]. Signal Process.1998,66(5):319-335
[136]王丹,李阳,年桂君,王珂;非均质度量掩蔽函数在空域水印中的应用[J].吉林大学学报(工学版).2013,43(3):771-775.
[137]谷利民.稳健数字水印中的通信方法[D].中山:中山大学博士学位论文2004.
[138]孟祥林,王正志.基于视觉掩蔽效应的图像扩散[J].自动化学报,2011,37(1):21-27.
[139]年桂君.抗同步攻击鲁棒性数字水印技术研究[D].吉林大学通信学院.2008
[140] Malay K Kundu, Arpan K Maiti. An Inexpensive Digital Piscataway：WatermarkingScheme for Printed Document[C]. IET IEEE Press, International Conference onVisual Information Engineering2006:378-383.
[141]张静,张春田.能抗打印－扫描过程的数字图像水印算法[A].全国第三届信息隐藏学术研讨会论文集[C],机械工业出版社,2001:151-157
[142]年桂君,刘鸿石,王丹,王乃丹.彩色照片中隐藏水印信息的分析与实现[J].吉林大学学报（工学版）2011. Vol.41. Sup.1339-343.
[143]葛云露,年桂君,王树勋.基于Walsh编码调制的抗打印扫描数字水印算法[J]东南大学学报（自然科学版）2007: Vol.37S1,197-200.
[144]牛少彰,伍宏涛,谢正程,刘歆,杨义先.抗打印扫描数字水印算法的鲁棒性[J].中山大学学报(自然科学版),2004,43:1-4.
[145] Soo-Chang Pei, Jing-Ming Guo, and Hua Lee. Novel Robust WatermarkingTechnique in Dithering Halftone Images[J]. IEEE Signal Processing Letter.2005,12(4):333-336.
[146]肖颖喆,王娟娟.抗打印扫描数字水印技术的研究进展[J].包装学报. July2012.4(3):49-53.
[147]梁华庆,钮心忻,杨义先.基于数字水印的证件防伪技术[J].信号处理,2000(2):143-145.
[148] D Simitopoulos, D E Kout sonanos, M Gerassimos Strintzis. Robust ImageWatermarking Based on Generalized Radon Transformations [J]. IEEE Trans onCircuits and Systems for Video Technology,2003,13(8):732-745.
[149] Lee Hae-Yeoun, Lee Choong-hoon, Lee Heung-Kyu.Geometrically invariantwatermarking: Synchronization Through Circular Hough Transform[J]. MultimedTools App.2007. Vol.34:337-353.
[150] D Simitopoulos, D Kout sonanos, M G Strintzis. Image Watermarking Resistant toGeometric Attacks Using Generalized Radon Transformations[C]. Proc of14th IntConf on Digital Signal Processing (DSP2002).2002.85-88.
[151] F Deguillaume, S Voloshynovskiy, T Pun. A Method for the Estimation andRecovering from General Affine Transforms in Digital Watermarking Applications[A]. Proc of SPIE-Security and Watermarking of Multimedia Contents IV.2002.p313-322.
[152] Dajun He; Sun, Q. A RST Resilient Object-based Video Watermarking Scheme [J]In Proc. IEEE Int. Conf. Image Processing,2004,2:737-740.
[153] Kaushal Solanki, Upamanyu Madhow, B.S.Manjunath etal. Print and Scan ResilientData Hiding[J]. IEEE Transactions on Information Forensics and Security,December2006,1(4):464-478.
[154] Ping Wah Wong, and Nasir Memon. Secret and Public Key Image WatermarkingSchemes for Image Authentication and Owership Verification [J]. IEEE Transcationson Image Processing,2001,10(10):1539-1601.
[155] H H Yu, X. Y. Kong, W. Wolf. Techniques for Content-based Graph Authentication[J]. Signal Processing: Image Communication,2001,16(5):461-475.
[156] Frank Hartung, Martin Kutter, Multimedia Watermarking Techniques [J]. Proceedings of the IEEE.1999,87(7):1079-1107.
[157]费曼著,关洪译.物理定律的本性[J].长沙:湖南科学技出版社,2005.
[158] S Pereira, T Pun. Robust Template Matching for Affine Resistant ImageWatermarks [J]. IEEE Trans on Image Processing,2000,9(6):1123-1129.
[159] S. J. Sangwine, Todd A. Ell, arXiv:1001.4379.