浮水印技術已被廣泛的運用在保護多媒體被拷貝上，且有顯著的進展。不論在音頻或是二維與三維影像方面的浮水印架構都有非常多研究報告提出。但是，每一種浮水印架構對於各種不同的攻擊結果都是有利與不利各有的現象。至今，沒有出現對所有攻擊都有最佳抵抗能力的浮水印架構。一般而言，灰關聯分析是用來分析不確定因素的方法，而且有很好的結果。在此篇論文中，我們將提出採用灰關聯分析方法找出最佳的浮水印架構。實驗證明用灰關聯分析方法，可以依不同需求的浮水印找出相對較好的浮水印架構。在相對而言最佳的浮水印架構中，決定加浮水印的強度係數大小會影響加浮水印的影像品質與耐攻擊的能力。這種介於加浮水印的影像品質與耐攻擊能力的決擇也是一種不確定因素，因此，吾人也可透過灰關聯分析方法找出最佳的加浮水印強度係數。另外，也可用灰關聯分析方法找出最佳的取出浮水印門檻值係數。在浮水印架構中決定加浮水印的區域，往往也會影響加浮水印的影像品質與耐攻擊的能力，因此，吾人也透過灰關聯分析方法找出最佳的加浮水印區域。本文經過實驗證明用灰關聯分析方法，可以找出最佳的取出浮水印門檻值係數與最佳的加浮水印區域。

Watermarking technology has been widely used in multimedia copyright protection with good progress in development. Watermarking in sound files and 2D or 3D images with good features has been reported in many studies. However, each watermarking scheme has its advantages and disadvantages against various attacks, and the optimal resistance against all attacks has yet to be achieved. Usually, the grey-relational analysis method is used to analyze uncertain factors, as it can obtain good results. In this dissertation, we first find the optimal watermarking scheme using grey-relational analysis. The experimental results show that a relatively better watermarking scheme can be selected based on the various requirements of watermarking. The aim of this study is to use the grey-relational analysis method to assess watermarking schemes that have been published in recent years. Watermarking methods proposed in recent studies have needed to determine the strength of the factor-added watermark or the threshold value factor strength in the watermark inspection method. The parameter is a tradeoff between the strength of the watermark and the quality of the watermarked image. In the proposed method, the optimal threshold value factor strength and the optimal embedding region allow the watermarking methods to achieve a combined effect for the optimal resistance to various attacks. The experimental results show that the optimal threshold value factor strength and the optimal embedding region can be selected using grey-relational analysis.

[1] Jinh-Long Deng, “The Control Problems of Grey System,” Journal of Systems & Control Leetters, No. 5, pp. 288-294, 1982.
[2] Antonis K. Mairgiotis, Nikolaos P. Galatsanos, and Yongyi Yang, “New Additive Watermark Detectors Based on a Hierarchical Spatially Adaptive Image Model,” IEEE Transactions on Information Forensics and Security , March 2008, Vol. 3, No. 1, pp. 29-37.
[3] Wei Liu, Lina Dong, and Wenjun Zeng, “Optimum Detection for Spread-Spectrum Watermarking That Employs Self-Masking,” IEEE Transactions on Information Forensics and Security, Vol. 2, No. 4, pp. 645-654 , Dec. 2007.
[4] Srdjan Stankovic’, Irena Orovic’, and Nikola ˇ Zaric’, “An Application of Multidimensional Time-Frequency Analysis as a Base for the Unified Watermarking Approach,” IEEE Transactions on IMAGE PROCESSING, VOL. 19, NO. 3, pp. 736-745 , MARCH 2010.
[5] Shijun Xiang and Jiwu Huang, “Histogram-Based Audio Watermarking Against Time-Scale Modification and Cropping Attacks ,” IEEE Transactions on Multimedia, Vol. 9, No. 7, pp. 1357-1372, Nov. 2007.
[6] R. Tachibana, S. Shimizu, T. Nakamura, and S. Kobayashi, “An Audio Watermarking Method Robust Against Time and Frequency Fluctuation,” Proc. SPIE Security and Watermarking of Multimedia Contents III, Vol. 4314, pp. 104–115, 2001.
[7] M. Mansour and A. Tewfik, “Data Embedding in Audio Using Time-Scale Modification,” IEEE Trans. Speech Audio Process., Vol. 13, No. 3, pp. 432–440, 2005.
[8] W. Li and X. Xue, “Audio Watermarking Based on Music Content Analysis: Robust Against Time Scale Modification,” Proc. the 2nd Int. Workshop of Digital Watermarking (IWDW 2003), Vol. 2939, LNCS, pp. 289–300, 2004.
[9] W. Li and X. Xue, “Localized Audio Watermarking Technique Robust Against Time-Scale Modification,” IEEE Trans. Multimedia, Vol. 8, No. 1, pp. 60–69, Feb. 2006.
[10] R. Tachibana, “Improving Audio Watermarking Robustness Using Stretched Patterns Against Geometric Distortion,” Proc. IEEE Int. Conf. on Multimedia, pp. 647–654, 2002.
[11] Dong Zheng, Sha Wang, and Jiying Zhao, “RST Invariant Image Watermarking Algorithm with
Mathematical Modeling and Analysis of the Watermarking Processes,” IEEE Transactions on Image Processing, Vol. 18, No. 5, pp. 1055–1068, May 2009.
[12] Mohammad Ali Akhaee, S. Mohammad Ebrahim Sahraeian, Bulent Sankur, and Farokh Marvasti, “Robust Scaling-Based Image Watermarking Using Maximum-Likelihood Decoder With Optimum Strength Factor,” IEEE Transactions on Multimedia, Vol. 11, No. 5, pp.822–833, Aug. 2009.
[13] Xiangyang Wang, Jun Wu, and Panpan Niu, “A New Digital Image Watermarking Algorithm Resilient to Desynchronization Attacks,” IEEE Transactions on Information Forensics and Security, Vol. 2, No. 4, pp. 655–663, Dec. 2007.
[14] Giulia Boato, Valentina Conotter, Francesco G. B. De Natale, and Claudio Fontanari, “Watermarking Robustness Evaluation Based on Perceptual Quality via Genetic Algorithms,” IEEE Transactions on Information Forensics and Security, Vol. 4, No. 2, pp. 207–216, June 2009.
[15] Wei-Hung Lin, Shi-Jinn Horng, Tzong-Wann Kao, Pingzhi Fan, Cheng-Ling Lee, and Yi Pan, “An Efficient Watermarking Method Based on Significant Difference of Wavelet Coefficient Quantization,” IEEE Transactions on Multimedia, Vol. 10, No. 5, pp. 746–757, Aug. 2008.
[16] Ning Bi, Qiyu Sun, Daren Huang, Zhihua Yang, and Jiwu Huang, “Robust Image Watermarking Based on Multiband Wavelets and Empirical Mode Decomposition,” IEEE Transactions on Image Processing, Vol. 16, No.
8, pp. 1956–1966, Aug. 2007.
[17] Parag Agarwal and Balakrishnan Prabhakaran, “Robust Blind Watermarking of Point-Sampled Geometry,” IEEE Transactions on Information Forensics and Security, Vol. 4, No. 1, pp. 36–48, March 2009.
[18] F. Cayre and B. Macq, “Data Hiding on 3-D Triangle Meshes,” IEEE Trans. Signal Process., Vol. 51, No. 4, pp. 939–949, Apr. 200.
[19] J.-W. Cho, R. Prost, and H.-Y. Jung, “An Oblivious Watermarking for 3-D Polygonal Meshes Using Distribution of Vertex Norms,” IEEE Trans. Signal Process., Vol. 55, No. 1, pp. 142–155, Jan. 2007.
[20] P. Maheshwari, P. Agarwal, and B. Prabhakaran, “Progressive Compression Invariant Semi-Fragile Watermarks for 3-D Meshes,” Proc. 9th ACM Multimedia and Security Workshop, pp. 245–250, 2007.
[21] F. Uccheddu, M. Corsini, and M. Barni, “Wavelet-Based Blind Watermarking of 3D Models,” Proc. Workshop on Multimedia and Security, Magdeburg, Germany, pp. 143–154, Sep. 20–21, 2004.
[22] S. Zafeiriou, A. Tefas, and I. Pitas, “Blind Robust Watermarking Schemes for Copyright Protection of 3-D Mesh Objects,” IEEE Trans. Vis. Comput. Graph., Vol. 11, Issue 5, pp. 596–607, Sep. 2005.
[23] Wei-Hung Lin, Shi-Jinn Horng, Tzong-Wann Kao, Rong-Jian Chen, Yuan-Hsin Chen, Cheng-Ling Lee, and Takao Terano, Image copyright protection with forward error correction, Expert Systems with Applications (SCI 1/64, 2.596), Vol. 36, Issue 9, Nov. 2009, pp. 11888-11894.
[24] Wei-Hung. Lin, Yuh-Rau Wang, Shi-Jinn Horng, and Yi Pan, A blind watermarking method using maximum wavelet coefficient quantization, Expert Systems with Applications (SCI 1/64, 2.596), Vol. 36, Issue 9, Nov. 2009, pp. 11509-11516.
[25] Wei-Hung. Lin, Yuh-Rau Wang and Shi-Jinn Horng, A wavelet-tree-based watermarking method using distance vector of binary cluster, Expert Systems with Applications (SCI 1/64, 2.596), Vol. 36, Issue 6, Aug. 2009, pp. 9869-9878.
[26] Chih-Cheng Lo, Jeng-Shyang Pan and Bin-Yih Liao, A HOS-based Watermark Detector, International Journal of Innovative Computing, Information and Control, vol.5, no.2, pp.293-300, 2009.
[27] Chih-Chin Lai, Hsiang-Cheh Huang and Cheng-Chih Tsai, A Digital Watermarking Scheme Based on Singular Value Decomposition and Micro-genetic Algorithm, International Journal of Innovative Computing, Information and Control, vol.5, no.7, pp.1867-1874, 2009.
[28] Daxing Zhang, Zhigeng Pan, Jianping Han and Hongjuan Zhang, A Watermarking Protocol to Protect Data in Cloud Computing System, ICIC Express Letters, vol.4, no.4, pp.1121-1126, 2010.
[29] Qiaolun Gu and Tiegang Gao, A Novel Reversible Watermarking Algorithm Based on Wavelet Lifting Scheme, ICIC Express Letters, vol.3, no.3 (A), pp.397-402, 2009.
[30] K. Ramanjaneyulu, K. Rajarajeswari, Wavelet-based oblivious image watermarking scheme using genetic algorithm
,IET Image Process, Vol. 6, Iss. 4, pp. 364–373, 2012
[31] Tsz Kin Tsui, Student Member, IEEE, Xiao-Ping Zhang, Senior Member, IEEE, and Dimitrios Androutsos, Senior Member, IEEE, “Color Image Watermarking Using Multidimensional Fourier Transforms,” in IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY, VOL. 3, NO. 1, MARCH 2008, pp. 16–28.
[32] Henrique S. Malvar,Fellow,IEEE, and Dinei A. F. Florencio, Member,IEEE, “Improved Spread Spectrum : A New Modulation Technique for Robust Watermarking ,” IEEE Trans. Signal Process., vol. 51, no. 4, Apr. 2003, pp. 898–905.
[33] Karen Su, Student Member, IEEE, Deepa Kundur, Senior Member, IEEE, and Dimitrios Hatzinakos, Senior Member, IEEE, “Spatially Localized Image-Dependent Watermarking for Statistical Invisibility and Collusion Resistance ,” IEEE Transactions on Multimedia, Vol. 7, No. 1, pp. 52–66, FEBRUARY 2005.
[34] Alper Koz, Cevahir Cigla, and A. Aydin Alatan, Member, IEEE, “ Watermarking of Free-view Video,” in IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 19, NO. 7, JULY 2010, pp. 1785–1797.
[35] Siyue Chen,Student Member, IEEE, and Henry Leung, Member, IEEE, “ Ergodic Chaotic Parameter Modulation With Application to Digital Image Watermarking ,” in IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 14, NO. 10, OCTOBER 2005, pp. 1590–1602.
[36] Alessandro Piva, Member, IEEE, Tiziano Bianchi, Member, IEEE, and Alessia De Rosa, “Secure Client-Side ST-DM Watermarking Embedding,” in IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY, VOL. 5, NO. 1, MARCH 2010, pp. 13–26.
[37] Jen-Sheng Tsai, Win-Bin Huang, and Yau-Hwang Kuo, “ On the Selection of Optimal Feature Region Set for Robust Digital Image Watermarking , ” IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 20, NO. 3, MARCH 2011, pp. 735–743.
[38] Xinge You, Liang Du,Yiu-ming Cheung, and Qiuhui Chen, “ A Blind of Watermarking Scheme Using New Nontensor Product Wavelete Filter Banks , ” IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 19, NO. 12, DECEMBER 2010, pp. 3271–3284.
[39] Xiangui Kang, Rui Yang, and Jiwu Huang, “Geometric Invariant Audio Watermarking Based on an LCM sking , ” IEEE TRANSACTIONS ON MULTIMEDIA, VOL. 13, NO. 2, APRIL 2011, pp. 181–190.
[40] Fabrizio Guerrini, Masahiro Okuda, Nicola Adami, and Riccardo Leonardi, “High Dynamic Range Image Watermarking RobustAgainst Tone-Mapping Operators, ” IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY, VOL. 6, NO. 2, JUNE 2011, pp. 283–295.
[41] Ashok Patel, Member, IEEE, and Bart Kosko, Fellow, IEEE, “Noise Benefits in Quantizer-Array Correlation Detection and Watermark Decoding , ” IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 59, NO. 2, FEBRUARY 2011, pp. 488–505.
[42] Hui Zhang, Member, IEEE, Huazhong Shu, Senior Member, IEEE, Gouenou Coatrieux, Member, IEEE, Jie Zhu, “Affine Legendre Moment Invariants for Image Watermarking Robust to Geometric Distortions , ” IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 20, NO. 8, AUGUST 2011, pp. 2189–2199.
[43] Mohammad Ali Akhaee, Member, IEEE, Sayed Mohammad Ebrahim Sahraeian, Student Member, IEEE, and
Craig Jin, Member, IEEE, “Blind Image Watermarking Using a Sample Projection Approach , ” IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY, VOL. 6, NO. 3, SEPTEMBER 2011, pp. 883–893.
[44] Dinu Coltuc, Member, IEEE, “Improved Embedding for Prediction-Based Reversible Watermarking, ” IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY, VOL. 6, NO. 3, SEPTEMBER 2011, pp. 873–882.
[45] Ming Luo and Adrian G. Bors, Senior Member, IEEE, “Surface-Preserving Robust Watermarking of 3-D Shapes , ” IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 20, NO. 10, OCTOBER 2011, pp. 2813–2826.
[46] Dinu Coltuc, Member, IEEE, “Low Distortion Transform for ReversibleWatermarking , ” IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 21, NO. 1, JANUARY 2012, pp. 412–417.
[47] Hongjie He, Fan Chen, Heng-Ming Tai, Senior Member, IEEE, Ton Kalker, and Jiashu Zhang
, “Performance Analysis of a Block-Neighborhood- Based Self-Recovery Fragile Watermarking Scheme , ” IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY, VOL. 7, NO. 1, FEBRUARY 2012, pp. 185–196.
[48] Chuntao Wang, Member, IEEE, Jiangqun Ni, Member, IEEE, and Jiwu Huang, Senior Member, IEEE
, “An Informed Watermarking Scheme Using Hidden Markov Model in the Wavelet Domain , ” IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY, VOL. 7, NO. 3, JUNE 2012, pp. 853–867.
[49] A. V. Subramanyam, Sabu Emmanuel, Member, IEEE, and Mohan S. Kankanhalli, Senior Member, IEEE
, “Robust Watermarking of Compressed and Encrypted JPEG2000 Images, ” IEEE TRANSACTIONS ON MULTIMEDIA, VOL. 14, NO. 3, JUNE 2012, pp. 703–716.
[50] Shun-Te Lin1, Shi-Jinn Horng2;_, Bih-Hwang Lee1, Pingzhi Fan3, Yi Pan4 Jui-Lin Lai5, Rong-Jian Chen5 and Muhammad Khurram Khan6 , “APPLICATION OF GREY-RELATIONAL ANALYSIS TO FIND THE
MOST SUITABLE WATERMARKING SCHEME, ” International Journal of Innovative Computing, Information and Control ICIC International Volume 7, Number 9, September 2011, pp. 5389–5401.
[51] Yong Xiang, Iynkaran Natgunanathan, Dezhong Peng, Member, IEEE, Wanlei Zhou, Senior Member, IEEE, and Shui Yu, Member, IEEE , “A Dual-Channel Time-Spread Echo Method for Audio Watermarking, ” IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY, VOL. 7, NO. 2, APRIL 2012, pp. 383–392.
[52] Jiantao Zhou, Member, IEEE, and Oscar C. Au, Fellow, IEEE , “Determining the Capacity Parameters in PEE-Based Reversible Image Watermarking, ” IEEE SIGNAL PROCESSING LETTERS, VOL. 19, NO. 5, MAY 2012, pp. 287–290.