近年來，由於網路應用的普及以及網路頻寬的增加，使得網路使用者可以輕易藉由網路獲得、交換與傳輸數位多媒體，如照片、影像、語音等。然而，部份多媒體的傳輸與複製並未獲得媒體所有人的認可，造成媒體所有人的損失。因此，數位多媒體財產權的保護與認證，便成為一項廣受重視的研究議題。
在數位多媒體的保護技術中，數位浮水印是其中一項廣受重視的技術。它的原理是將稱為浮水印(watermark)的秘密訊息或是公司的標誌嵌入於數位多媒體中。當多媒體的所有人需要宣告該媒體的所有權時，即可將浮水印從已嵌入浮水印的數位多媒體中擷取出來，以證明該數位多媒體的財產權。
然而，這些嵌入浮水印的數位多媒體，在網路流通的同時，極可能受到影像處理或是影像壓縮等相關技術的改變，甚或是受到惡意的攻擊，使得嵌入的浮水印無法被擷取出來。所以，浮水印的強固性(robustness)－也就是嵌入浮水印的多媒體，經過善意或惡意的相關技術處理後，浮水印能否仍有效的被擷取出來，以證明該數位多媒體的所有權，便成為評量浮水印技術優良與否的一項重要指標。
目前衡量浮水印的強固性有許多的測試基準。這些基準各自涵蓋了許多相關的壓縮及攻擊技術，然而，即便是浮水印的演算法通過了測試，仍無法保證該演算法能夠承受所有攻擊技術的攻擊。因為，更多更新的攻擊技術也正不斷的被發展出來。因此，研究人員不能僅研究嵌入浮水印的方法，應該同時涉獵相關浮水印的攻擊方法，藉由瞭解最新的浮水印攻擊策略，使得所提出的浮水印演算法能夠更加周延。
過去許多的浮水印移除法視浮水印為雜訊，並藉由移除雜訊的方法移除浮水印。然而，雜訊移除法在移除雜訊能量的同時，也一併將原始影像的能量一併移除。因此，當移除浮水印與原始影像能量時，必須權衡的問題是－如果移除浮水印的能量不足，浮水印將仍可能被偵測出來；反之，若移除太多的浮水印能量，移除浮水印後所得的影像品質勢必不佳。
為了解決這個問題，我們首先根據統計模型，建立浮水印能量、原始影像能量及嵌入浮水印影像能量間的關係。接著，利用影像視覺的特性，估量浮水印能量的大小。最後，根據特徵影像能量分布的特性，移除各個特徵影像中的浮水印能量。
實驗的結果顯示，我們提出的方法較適應性Ｗiener濾波器所得的移除浮水印影像，影像品質PSNR平均提升 2.2dB，所擷取的浮水印與原始浮水印的NC值，平均降低 0.27。另外，我們也隨機選取100張第二屆「破解我們的浮水印系統」比賽用的測試影像施以盲目攻擊，在平均影像品質PSNR為24.1dB時，其中的90張影像已成功的移除浮水印。這結果與比賽要求的影像品質20dB，以及比賽中盲目攻擊階段的最佳成績24.3dB相較，在在顯示所提出的方法，確為一個有效的浮水印移除法。
藉由浮水印的研究，相信能使得未來浮水印的設計更加強固。對於企業主的投資以及數位工作者的智慧結晶，也能得到更多的保障。當然也希望多媒體的產業，包含數位影像、數位音樂、數位動態影像與電子書等，它們的發展能因此更加蓬勃。

Most watermark-removal methods treat watermarks as noise and apply denoising approaches to remove them. However, denoising methods remove not only this watermark energy, but also some of the energy of the original image. A trade-off therefore exists: if not enough of the watermark energy is removed, then the watermark will still be detected, but if too much is removed, the image quality will be noticeably poor.
To solve this problem, the relationship among the energies of the original image, the watermark and the watermarked image is initially determined using stochastic models. Then, the energy of the watermark is estimated using just-noticeable-distortion (JND). Finally, the watermark energy is removed from the watermarked image based on the energy distribution of its Eigen-images.
The experimental results show that the proposed approach yields a mean peak signal-to-noise ratio (PSNR) of the predicted images that is 2.2dB higher than that obtained using the adaptive Wiener filter, and a mean normalized correlation (NC) value of the extracted watermarks that is 0.27 lower than that obtained using the adaptive Wiener filter. In removing watermark energy from 100 randomly selected watermarked images in which watermarks were embedded using the ‘Broken Arrows (BA)’ algorithm proposed for the second Breaking Our Watermarking System (BOWS-2) contest, the mean PSNR of 100 predicted images is 24.1dB and the proposed approach successfully removed watermarks from 90 of these images. This result exceeds the minimum requirement of PSNR 20dB for the BOWS-2 contest. Clearly, the proposed approach is a very effective watermark-removal approach for removing watermarks.

誌謝 I
摘要 II
ABSTRACT IV
CONTENTS VI
LIST OF FIGURES VIII
LIST OF TABLES X
CHAPTER 1 INTRODUCTION 1
1.1 Motivation 1
1.2 Background 3
1.3 Dissertation Organization 8
CHAPTER 2 RELATED WORKS 9
2.1 Broken arrows 9
2.1.1 Four nested spaces of Broken arrows 9
2.1.2 Watermark embedding and detection 11
2.1.3 New criterion based on the nearest border point attack 12
2.2 Regression-based scheme 14
2.2.1 Removal watermark in the wavelet domain 15
2.2.2 Postprocessing 16
2.3 Subspace estimation approach 17
2.3.1 OPAST applied on Broken Arrows 17
2.3.2 Cone estimation using ICA 17
CHAPTER 3 WATERMARK-REMOVAL METHOD BASED ON EIGEN-IMAGE ENERGY 19
3.1 Eigen-image energy 19
3.2 SVD-based filter 21
3.3 Adaptive Wiener filter 22
3.4 Watermark-removal method 22
CHAPTER 4 EXPERIMENTAL RESULTS 29
CHAPTER 5 CONCLUSIONS AND FUTURE WORKS 39
REFERENCES 41

[1] I. J. Cox, J. Kilian, F. T. Leighton, and T. Shamoon, “Secure Spread Spectrum Watermarking for Multimedia,” IEEE Transactions on Image Processing, vol. 6, no. 12, pp. 1673-1687, Dec. 1997.
[2] D. Kundur and D. Hatzinakos, “Toward Robust Logo Watermarking Using Multiresolution Image Fusion Principles,” IEEE Transactions on Multimedia, vol. 6, no. 1, pp. 185-198, Feb. 2004.
[3] R. Liu and T. Tan, “An SVD-Based Watermarking Scheme for Protecting Rightful Ownership,” IEEE Transactions on Multimedia, vol. 4, no. 1, pp. 121-128, March 2002.
[4] M. Ramkumar and A. N. Akansu, “A Robust Protocol for Proving Ownership of Multimedia Content,” IEEE Transactions on Multimedia, vol. 6, no. 3, pp. 469-478, June 2004.
[5] M. U. Celik, G. Sharma, E. Saber, and A. M. Tekalp, “Hierarchical Watermarking for Secure Image Authentication with Localization,” IEEE Transactions on Image Processing, vol. 11, no. 6, pp. 585-595, June 2002.
[6] R. Radhakrishman and N. Memon, “On the Security of The Digest Function in the SARI Image Authentication System,” IEEE Transactions on Circuits and Systems for Video Technology, vol. 12, no. 11, pp. 1030-1033, Nov. 2002.
[7] C. H. Lin and W. S. Hsieh, ”Applying Projection And B-spline to Image Authentication And Remedy,” IEEE Transactions on Consumer Electronics, vol. 49, no. 4, pp. 1234-1239, Nov. 2003.
[8] P. Bao and X. Ma, “Image Adaptive Watermarking Using Wavelet Domain Singular Value Decomposition,” IEEE Transactions on Circuits and Systems for Video Technology, vol. 15, no. 1, pp. 96-102, Jan. 2005.
[9] Z. M. Lu, D. G. Xu, and S. H. Sun, “Multipurpose Image Watermarking Algorithm Based on Multistage Vector Quantization,” IEEE Transactions on Image Processing, vol. 14, no. 6, pp. 822-831, June 2005.
[10] F. Peticolas and R. J. Anderson, “Attacks on Copyright Marking Systems,” Second International Information Hiding workshop, Portland, Oregon, USA, pp. 219-239, April 1998.
[11] S. Voloshynovskiy, S. Pereira, V. Iquise, and T. Pun, “Attack Modeling: Towards a Second Generation Watermarking Benchmark,” Signal Processing, vol. 81, pp. 1177-1214, June 2001.
[12] V. Solachidis, A. Tefas, N. Nikolaidis, S. Tsekeridou, A. Nikolaidis, and I. Pitas, “A Benchmarking Protocol for Watermarking Methods,” IEEE Int. Conf on Image Processing, vol. 3, pp. 1023-1026, Oct. 2001.
[13] “The Break Our Watermarking System (BOWS) Contest,” http://lci.det.unifi.it/BOWS/, accessed Dec. 2005.
[14] “The 2nd Break Our Watermarking System (BOWS2) Contest,” http://bows2.ec-lille.fr/, accessed July 2007.
[15] “The Break Our Steganographic System (BOSS) Contest,” http://www.agents.cz/boss/BOSSFinal/, accessed Sep. 2010.
[16] A. Westfeld, “Lessons from the BOWS Contest,“ International Multimedia Conference archive Proceedings of the 8th workshop on Multimedia and security, pp. 208-213, 2006.
[17] S. Voloshynovskiy, S. Pereira, T. Pun, J. J. Eggers, and J. K. Su, “Attacks on Digital Watermarks: Classification, Estimation-based Attacks, and Benchmarks,” IEEE Communications Magazine, vol. 39, issue 8, pp. 118-126, Aug. 2001.
[18] P. F. Luis, C. Pedro, T. P. Juan Ramon, and P. G. Fernando, “Watermarking Security: a Survey”, LNCS Transactions on Data Hiding and Multimedia Security, vol. 4300, pp. 41-72, 2006.
[19] V. M. Potdar, S. Han, and E. Chang, “A Survey of Digital Image Watermarking Techniques,” IEEE International Conference on INDIN, pp. 709-716, Aug. 2005.
[20] M. Kutter, S. Voloshynovskiy, and A. Herrigel, “The Watermark Copy Attack,” IS&T/SPIE’s 12th Annual Symposium, Electronic Imaging 2000: Security and Watermarking of Multimedia Content II, SPIE Proc., vol. 3971, San Jose, CA, USA, pp. 23-28, Jan. 2000.
[21] S. Voloshynovskiy, A. Herrigel, N. Baumgrtner, and T. Pun, “A Stochastic Approach to Content Adaptive Digital Image Watermarking,” In Proceeding of International Workshop on Information hiding, Dresden, Germany, Sep. 1999.
[22] S. Voloshynnovskiy, S. Pereira, A. Herrigel, N. Baumgartner, and T. Pun, “Generalized Watermarking Attack based on Watermark Estimation and Perceptual Remodulation,” In Proceedings of SPIE: Security and Watermarking of Multimedia Content II, San Jose, CA, USA, Jan. 2000.
[23] S. Craver, N. Memon, B. L. Yeo, and M. Yeung, “Resolving Rightful Ownerships with Invisible Watermarking Techniques: Limitations, Attacks, and Implications,” IEEE Journal on Selected Areas in communications, vol. 16, pp. 573-586, May 1998.
[24] J. Du, C. H. Lee, H. K. Lee, and Y. Suh, “A New Approach for Watermark Attack,” Multimedia Software Engineering, 2002. Proceedings. Fourth International Symposium on, pp. 182-187, 2002.
[25] M. Choubassi and P. Moulin, “Noniterative Algorithms for Sensitivity Analysis Attacks,” IEEE Transactions on Information Forensics and Security, vol. 2, issue 2, pp. 113-126, June 2007.
[26] Q. Zhao, Z. Wang, and B. Yin, “Analysis on the Sensitivity Attack to Watermarking Schemes with Patchwork Detection Boundaries,” International Conference on Computational Intelligence and Security, pp. 940-944, Dec. 2007.
[27] P. Comesana and F. Perez-Gonzalez, “Breaking the BOWS Watermarking System: Key Guessing and Sensitivity Attacks,” EURASIP Journal on Information Security, vol. 2007, Article ID 25308.
[28] L. Prez-Freire, F. Prez-Gonzlez, T. Furon, and P. Comesana, “Security of Lattice-Based Data Hiding Against the Known Message Attack,” IEEE Transactions on Information Forensics and Security, vol. 1, pp. 421-439, Dec. 2006.
[29] R. Anderson and M. Kuhn, “Low Cost Attacks on Tamper Resistant Devices,” International Workshop on Security Protocols, vol. 1361 of Lecture Notes in Computer Science., Paris, France, Springer Verlag, pp. 125-136, 1997.
[30] M. L. Miller, G. Doerr, and I. J. Cox, “Applying Informed Coding and Embedding to Design a Robust High-capacity Watermark,” IEEE Transactions on image processing, vol. 13, no 6, June 2004.
[31] T. Furon and P. Bas, “Broken Arrows,” EURASIP Journal on Information Security, vol. 2008, Article ID 597040, 2008.
[32] C. H. Chou and Y. C. Li, “A Perceptually Tuned Subband Image Coder based on the Measure of Just-noticeable-distortion Profile,” IEEE Transactions on Circuits System Video Technology, vol. 5, no. 6, pp. 467-476, Dec. 1995.
[33] J. Ni, C. Wang, J. Huang, R. Zhang and M. Huang, “A GA-based Joint Coding and Embedding Optimization for Robust and High-Capacity Image Watermarking,” Proceedings of 2007 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), vol. 2, pp. 181-184, April, 2007.
[34] J. Mayer and J.C.M. Bermudez, “Multi-bit Informed Embedding Watermarking with Constant Robustness,” IEEE International Conference on Image Processing, vol. 1, pp. 669-672 , Sep. 2005.
[35] A. Westfeld, “A Regression-based Restoration Technique for Automated Watermark Removal,” Proceedings of the 10th ACM workshop on Multimedia and security, pp. 215-220, 2008.
[36] C. Rey, G. Do‥err, G. Csurka, and J. L. Dugelay, “Toward Generic Image Dewatermarking,” In IEEE International Conference on Image Processing ICIP, vol. 2, pp. 633–636, Sep. 2002.
[37] J. Cox, J. Kilian, F. T. Leighton, and T. Shamoon, “Secure Spread Spectrum Watermarking for Multimedia,” IEEE Transactions on Image Processing, vol. 6, no. 12, pp. 1673-1687, Dec. 1997.
[38] J. Huang, Y. Q. Shi, and Y. Shi, “Embedding image watermarks in DC components,” IEEE Transactions on Circuits and Systems for Video Technology, vol. 10, no. 6, pp. 974-979, Sep. 2000.
[39] S. P. Maity, P. Nandy, T. S. Das, and M. K. Kundu, “Robust image watermarking using multi-resolution analysis,” India Annual Conference, 2004. Proc. of the IEEE INDICON 2004, first 20-22, pp. 174-179, Dec. 2004.
[40] C. H. Lee and Y. K. Lee, “An Adaptive Digital Image Watermarking Technique for Copyright Protection,” IEEE Transactions on Consumer Electronics, vol. 45, no. 4, pp. 1005-1015, Nov. 1999.
[41] D. Kirovski and F.A.P. Petitcolas, “Blind Pattern Matching Attack on Watermarking Systems,” IEEE Transactions on Signal Processing, vol. 51, issue 4, pp. 1045-1053, April 2003.
[42] C. Rey, G. Doerr, G. Csurka, and J. L. Dugelay, “Toward Generic Image Dewatermarking,” IEEE International Conference on Image Processing, pp. 633-636, Sep. 2002.
[43] G. J. Doerr, J. L. Dugelay, and D. Kirovski, “On the Need for Signal-coherent Watermarks,” IEEE Transactions on Multimedia, vol. 8, no. 5, Oct. 2006.
[44] M. L. Miller, G. Doerr, and I. J. Cox, “Applying Informed Coding and Embedding to Design a Robust High-capacity Watermark,” IEEE Transactions on image processing, vol. 13, no 6, June 2004.
[45] P. Bas and A. Westfeld, “Two Key Estimation Techniques for the Broken Arrows Watermarking Scheme,” MM&Sec’09, Princeton, New Jersey, USA, Sep. 2009.
[46] K. Konstantinides and K. Yao, “Statistical Analysis of Effective Singular Values in Matrix Rank Determination,” IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 36, pp. 757-763, May 1988.
[47] Y. Wongsawat, K. R. Rao, and S. Oraintara, “Multichannel SVD-Based Image De-Noising,” IEEE International Symposium on Circuits and Systems, ISCAS 2005, vol. 6, pp. 5900-5993, May 2005.
[48] W. Lu, “Adaptive Noise Attenuation of Seismic Image Using Singular Value Decomposition and Texture Direction Detection,” International Conference on Image Processing, vol. 2, pp. II-465-II-468, Sep. 2002.
[49] Z. L. Shi, Z. J. Zhang, and Y. T. Tang, “SVD-Based Image De-Noising With the Minimum Energy Model,” World Automation Congress, WAC ’06, pp. 1-7, July 2006.
[50] Q. Li, C. Yuan, and Y. Z. Zhong, “Adaptive DWT-SVD Domain Image Watermarking using Human Visual Model,” Advanced Communication Technology, The 9th International Conference, vol. 3, pp. 1947-1951, Feb. 2007.
[51] W. Liu, L. Dong, and W. Zeng, “Optimal Detection for Speed-Spectrum Watermarking That Employs Self-Masking,” IEEE Transactions on Information Forensics and Security, vol. 2, pp. 645-654, Dec. 2007.
[52] P. H. Wong and O. C. Au, “A Capacity Estimation for JPEG-to-JPEG Image Watermarking,” IEEE Transactions on Circuits and Systems for Video Technology, vol. 13, pp. 746-752, Aug. 2003.