A Novel Blind Watermarking Algorithm in Contourlet Domain

收稿日期：2009-05-08基金项目：中国民航大学科研基金资助项目（y ）；中国民航大学科研基金资助项目（_）作者简介：韩绍程（），男，天津人，实验师，硕士，主要研究方向为数字水印。

2010年工程图学学报2010第2期J OURNAL OF ENG INEERING GRAPHICSNo.2基于多小波变换和分块SVD 的彩色图像水印算法韩绍程1，罗长杰1，张兆宁2，王玉松1（1.中国民航大学基础实验中心，天津300300；2.中国民航大学空中交通管理学院，天津300300）摘要：提出了一种基于多小波变换和分块SVD 的非盲水印算法。

选择彩色图像的饱和度分量作为水印的嵌入域，水印为有意义的灰度图像，水印经Arnold 置乱后被嵌入到饱和度分量多小波变换的不同中频区域中。

实验证明，该算法不仅对噪声、JPEG 压缩、剪切及Photoshop 处理具有很好的鲁棒性，而且能抵抗旋转、放缩和平移等几何攻击。

关键词：计算机应用；图像水印；多小波变换；分块奇异值分解中图分类号：TP 391文献标识码：A文章编号：1003-0158(2010)02-0128-06A C olor Image Water mar king Algorithm Based onM ulti-Wavelet Transfor m and Block-SVDHAN Shao-cheng 1,LUO Chang-jie 1,ZHANG Zhao-ning 2,WANG Yu-song 1(1.Basic Experiment al Center,Civil Avi ation University of China,Tianj in 300300,Chi na;2.Air Traffic Management College,Civil Avi ation Universit y of China,Tianji n 300300,China )Abstr act:A non-blind watermarking algorithm is proposed based on multi-wavelet transform and block singular value decomposition.Choosing the saturation component of a color image as the watermark embedding domain,the watermark is a meaningful grayscale image.After Arnold scrambling,watermark is embedded into the different mid-frequency regions of the saturation component which through multi-wavelet transform.The examples demonstrate that the algorithm not only has good robustness to the noise,JPEG compression,shear and Photoshop processing ,but also can resist to some geometric attacks such as rotation,scale and translation.K ey wor ds:computer application;image watermarking;multi-wavelet transform;block singular value decomposition07k m1209cauc e101981-随着计算机技术和网络技术的飞速发展和广泛应用，数字多媒体信息的存储、复制与传播变得非常方便，数字化产品的产权保护成为急需解决的问题。

一种鲁棒的数字水印算法龚成清【摘要】数字水印是信息隐藏和版权保护的有效手段。

针对一般数字水印算法的视觉性和鲁棒性无法兼顾的问题，对JPEG 2000的图像格式提出了一种自适应的盲水印算法。

算法使用m+n位的线性反馈移位寄存器对水印图像进行移位置乱，然后利用JPEG 2000图像的特点，对原始图像进行小波变换处理后选择低频子带进行水印的嵌入，在量化处理的同时完成了水印的嵌入，提高了水印嵌入的速度。

根据LSFR的性质，算法对水印进行有效地检测和移位复原，实现了水印的盲提取。

实验表明，该算法具有良好的视觉性和抵抗攻击的鲁棒性。

%Digital watermarking is an effective means of information hiding and copyright protection. For general digital watermarking algorithm can not balance the visuality and robustness,this paper proposes a robust blind watermarking algorithm of JPEG2000 images.It designes a Linear Shift Feedback Register of m+n bits to scramble the watermark image,then choses the low frequency which is processed after the wavelet transform to embed the watermark bit.It completes the watermark embedding with the quantification processing.It improves the watermark embedding speed. According to the nature of LSFR, the watermark is detected and to be shifted to restore the watermark image.So it achieves blind watermark extraction.Experiments show that, the algorithm has a good visuality and robustness.【期刊名称】《齐齐哈尔大学学报（自然科学版）》【年(卷),期】2014(000)005【总页数】6页(P10-15)【关键词】水印;量化;移位;鲁棒性【作者】龚成清【作者单位】广东女子职业技术学院应用设计系，广州 511450【正文语种】中文【中图分类】TP391.9数字水印技术广泛用于图像、视频和音频作品中的信息隐藏和版权保护。

基于映射机制的遥感影像盲水印算法任娜;朱长青;王志伟【摘要】A blind watermarking algorithm resistance against the geometric attacks for remote sensing data is presented based on mapping mechanism. First, the pseudo-random binary sequence, which is generated by the random number generator, is used as the watermarking information. Then, the mapping function of the image data and watermark information is established, and the mapping variable is expanded, which can determine the watermark embedding position. Finally, the modified pixelvaluebit-plane, which is based on mapping mechanism, is used as the watermark embedded rules. Watermark detecting is the inverse process of watermark embedding, and the watermark information is determined by majority rule. The presented method overcomes the limitation that the image size and the pixel relative coordinate remain the same after the traditional attacking. The watermark capacity has been effectively expanded, and the presented method has good robustness, invisibility and maintains the accuracy of features and statistical properties of image.%针对遥感影像数据，提出一种基于映射机制的抵抗几何攻击的强抗差性盲水印算法。

A Blind Image Watermarking Algorithm Based on Dual TreeComplex Wavelet TransformS. Mabtoul , E. Ibn-Elhaj, D. AboutajdineAbstract —This paper presents a watermarking procedure for digital image in the Complex Wavelet Domain. First, a watermark image as copyright sign is preprocessed with a random location matrix. The original image is transformed in the complex wavelet domain by using DT-CWT, then, according to the characteristics of the image data, the preprocessed watermark image is adaptively spread spectrum and added into the host image DT-CWT coefficients. The superior results for image processing applications compared to the DWT [5, 6].In the proposed scheme, we applied the Dual Tree Complex Wavelet Transform; the watermark image is preprocessed with a random matrix, adaptively spread spectrum [7] and added into the host image DT-CWT coefficients.proposed watermark algorithm needs two keys: a random location matrix ensures the security of watermarking procedure and spread spectrum watermark sequence guarantees its robustness. Simulation results demonstrate the robustness of our image watermarking procedure, especially under the typical attacks of geometric operations.MI. INTRODUCTIONultimedia watermarking technology has evolved very quickly during the last few years. A digital watermark is information that is imperceptibly and robustly embedded in the host data such that it cannot be removed [1, 2].There are several watermarking algorithms transform the original image into critically sampled domain (The Discrete Real Wavelet Transform (DWT, the DiscreteCosine Transform (DCT or the Discrete Fourier Transform (DFT, and add a random sequence to the transformed image coefficients [3, 4].In general, the DWT produces watermark images with the best visual quality due to the absence of blocking artifacts. However, it has two drawbacks:--Lack of shift invariance, which means that small shifts in the input signal can cause major variations in the distribution of energy between DWT coefficients at different scales.--Poor directional selectivity for diagonal features, because the wavelet filters are separable and real.An important recent development in wavelet-related research is the design and implementation of 2-D multiscale transforms that represent edges more efficiently than does the DWT. Kingsbury’s complex dual-tree wavelet transform (DT-CWT is an outstanding example [5]. The DT-CWT is an overcomplete transform with limited redundancy (2m: 1 for m-dimensional signals. This transform has good directional selectivity and its subband responses are approximately shift-invariant. The 2-D DT-CWT has given S. Mabtoul is with the GSCM, University Mohamed V, Rabat, Morocco (e-mail: mabtoul_samira@yahoo.fr.E. Ibn-Elhaj is with the National Institute of Telecommunication (INPT, Rabat, Morocco ( phone: (+212 37 77 30 79 ; fax : (+212 37 77 30 44 e-mail:ibnelhaj@inpt.ac.ma.D. Aboutajdine is with the GSCM, University Mohamed V, Rabat, Morocco (e-mail: aboutaj@fsr.ac.ma.II. T HE P ROPOSED M ETHODA. Watermark image disorder preprocessingThe first step consists to change the watermark image W , which is a binary image {-1, 1}, into a pseudo random matrix W d by using the following equation:K: W Î Wd , Wd (K(i, j = W(i, j; i, j∈N (1Where K present the first key in our watermark procedure, which is an exclusive key to recreate the watermark image. Figure 1 visualizes an example of watermark image disorder.Original watermark image Disorder watermark imageFig. 1. The original and disorder watermark image.B. Watermark embeddingThe original image is transformed in the complex wavelet domain by using DT-CWT [5]. The watermark image is changed into a pseudo random matrix W d , then its adaptively spread spectrum W k and add into low pass subband from final level. Figure 2 shows a block diagram of the proposed watermark embedding.Fig. 3. Image detection schemeImage detection algorithm Fig. 2. Image embedding schemeImage embedding algorithm 1 DT-CWT: perform a 2-level Dual Tree Complex Wavelet on original image I orig . The DT-CWT coefficients are denoted by~. 2 Generated the spread spectrum watermark Wk : foreach pixel (i, j of the low pass image from final level in ~, the value is compared with those of its eight neighbors, t denotes the total number which the value is larger than its neighbors, as described by the following formula:≥ 4 and Wd d (i, j = 1W k (i, j = -1The spread spectrum watermark W k present the second key of our image watermarking scheme.3 Embedded watermark: the spread spectrum watermark sequence W k is embedded by the following rule:ˆI (i , j =~I (i , j +α. W ~k (i , j . I (i , j (3Where: ˆI : are the watermarked DT-CWT coefficients. ~I : are the original DT-CWT coefficients.W α: is an intensity parameter of image watermark.k : is the spread spectrum watermark image sequence. 4 IDT-CWT: by the inverse DT-CWT, we obtain the watermarked image.C. Watermark detectionWatermark detection is accomplished without referring to the original image and the original watermark image. Figure 3 shows a watermark detection scheme.1 The DT-CWT is performed on watermarked image. ˆIdenote the DT-CWT coefficients. 2 Constructed Watermark image disorderWˆd : for each embed watermark pixel inˆI, its value is compared with those of its eight n eighbors; t’ denotes the total number which the value is larger than its neighbors. Disorder watermark image can be formed as:1 if (t’ ≥ 4 and Wk (i, j = 1W ˆd (i, j’ < 4 and Wk (i, j = -13 Reconstructed watermark imageW ˆ: the reconstructed watermark i mageWˆ is obtained by using the inverse transform of the preprocessing with the first key. III. R ESULTS AND ANALYSIS Our proposed scheme has been tested under variousattacks. We chose to test this scheme under PSNR, median filter, JPEG compression, remove lines and scaling attacks introduced by Stirmark [8] and also rotation attack. We have performed the algorithm under Matlab 6.5 environment. In the experiments, we have tested tree test images ("Lena", "Barbara" and "Cameraman", and there have the similarresults. Here, we use "Lena" as an example and the watermark is a binary image with the size of 128x128 pixels.Figure 4 presents the original image, the watermarked image and the reconstructed watermark image, in which the watermark intensity factor α equal 0.004. We see that the watermarked image is not distinguishable from the originalimage. Original image Watermarked image Reconstructed watermark(256x256 pixels (256x256 pixels image (128x128pixelsFig. 4. Original and watermarked image and the reconstructedwatermark image.The robustness of watermarking is measured by thesimilarity of the detected watermark Wˆ and the originalwatermark W , which is defined as:IV. C ONCLUSIONIn this paper, we have proposed a novel scheme of imageˆ, W =ˆ(i,j.W(i,j Sim ( W (W (W(i,j (5 watermarking. This scheme applies the Dual Tree Complexi j i j Wavelet Transform; the watermark image is preprocessedwith a random matrix, adaptively spread spectrum and addedWe tested this watermark approach with DWT transform; into the DT-CWT coefficients. The experimental results the results are gathered in figure 6. have confirmed that this new scheme has high fidelity and In the first simulation, we tested the scheme’s robustness it’s robust against JPEG compression, geometr ic attacks under different PSNR situation. Figure 5.a show a typical (scaling, remove line and rotation with small angle and result. Results show that we can still correctly detect the signal processing (PSNR, median filter introduced in ∑∑∑∑2watermark under these types of PSNR attacks (figure 6.a. The results obtained with DT-CWT transform are better than the results obtained with DWT transform.We tested the robustness against median filter. Figure 5.bhas shown a typical result. The similarities of original watermark and reconstructed watermark are shown in figure 6.b. We noticed that we can still correctly detect the watermark with the algorithm used the DT-CWT transform. With the algorithm used the DWT transform, we can’t detectthe watermark if the filter factor is bigger than 7.We tested this scheme when the image undergone a scaling (see figure 5.c. The results are shown in figure 6.c. from the results obtained we notices that we can detect thewatermark image if we used the DT-CWT or the DWT. The lines dropping, which are some lines are removedfrom the watermarked image. We tested this scheme against this type of attack (see figure 5.d. The experiment result is plotted in figure 6.d. The results show that we canreconstruct the watermark image correctly if we used the DT-CWT or the DWT.We have also tested the robustness against JPEG compression (see example in figure 5.e. The corresponding results are presented in figure 6.e. this scheme is robustnessagainst this type of attack.We evaluated the robustness of this scheme against rotation attacks. Image rotation makes the coordinate axes changed. Without synchronization of orthogonal axes, we cannot reconstruct the image mark correctly Figure 5.f illustrates the effect of thistransformation. The results are shown in figure 5.f. according to the results we notices that we can reconstruct correctly the watermark image if we used the DT-CWT.StirMark. A CKNOWLEDGMENTThe authors would like to thank Dr. Nick Kingsbury forallowing use to use his DT-CWT algorithm, and for hisvaluable discussions. R EFERENCES [1] F. P. Gonzalez & Juan R. Hernandez, " A tutorial on digitalwatermarking", In IEEE Annual Carnahan Conference on SecurityTechnology, 1999. [2] Ingemar J. Cox, Matt L. Miller, " The first 50 years of electronic watermarking", Journal of Applied Signal Processing, 2, 126-132,2002.[3] A. Piva, M. Barni, F. Bartolini, and V. Cappellini, "DCT-basedwatermark recovering without restoring to the uncorrupted original image," in Inter-national Conference on Image Processing, vol. III, pp.520-523, 1997. [4] D. Kundur and D. Hatzinakos, ―A robust digital image watermarkingmethod using wavelet-based fusion,‖ in Proc. IEEE Int. Conf. Image Processing 1997 (ICIP 97, vol. 1, Santa Barbara, CA, Oct. 1997, pp. 544–547.[5] N.G. Kingsbury, ―Complex wavelets for shift invariant analysis and filtering of signals‖, Applied Computational Harmonic Anal, vol. 10,no. 3, pp. 234-253, May 2001. [6] T H Reeves and N G Kingsbury, ―Overcomplete image coding usingiterative projection-based noise shaping‖, ICIP 02, Rochester, NY, Sept 2002.[7] Z. Huai-yu, L. Ying and C. Wu: A blind spatial-temporal algorithm based on 3D wavelet for video watermarking. ICME 2004: 1727-1730.[8] F. A. P. Petitcolas, R. J. Anderson, and M. G. Kuhn, ―Attacks oncopyright marking systems,‖ in Lecture Notes in Computer Science: Information Hiding. Berlin, Germany: Springer, 1998, pp. 218–238.Watermarked image detected watermark imagewith 40 % of PSNR qualitya. Test image under PSNR attackMedian filtered Watermarked detected watermark imageimage under factor 9b. Test image under median filter attackScaled Watermarked image detected watermark image(ratio 50%c. Test image under scaling attackRemoved 100 lines of the detected watermark imagewatermarked imaged. Test image under remove lines attackJPEG compressed Watermarked image detected watermark imageof quality 35%e. Test image under JPEG compression attackRotated Watermarked Recovered image detected watermarkimage angle (10° imagef. Test image under rotation attackFig. 5. The effect of attacksPSNR (db filter factora. the effect of PSNR attackb. the effect of median filter attack factor scaling (% the number of line droppingc. the effect of scaling attackd. the effect of remove lines attackthe quality of image (%e. the effect of JPEG compression attackangle ( °f. the effect of rotation attackFig. 6. The experiment results of many attacks to the watermarking algorithm。

江雪梅（1979-），博士，副教授。

积极参与国家863计划，国家自然科学基金重点项目、国际合作交流项目和教育部重点科技攻关等多项国家省部级项目。

在国内外重要学术期刊和学术会议上发表学术论文14篇，其中被美国《工程索引（EI）》、《科学引文索引（SCI）》、《科技会议论文索引（ISTP）》收录收录10篇。

已获授权国家发明专利4项。

2007年获湖北省科学技术发明二等奖。

发表学术论文：[1]Liu Quan, Jiang Xuemei, Zude Zhou. A unified digital watermark algorithm based onsingular value decomposition and spread spectrum technology. Chinese Journal of Electronics, v 14, n 4, October, 2005, p 621-624（SCI收录：IDS number: 037FU）[2]Jiang Xuemei; Liu Quan; Wu Qiaoyan. A Real-time Watermarking Scheme of H.264/AVCCompressed Video，Multimedia Tools and Applications，2013.2 （SCI收录IDS 号: 086VF）。

[3]Tu, Xiaoli ; Jiang, Xuemei; Zhang, Xiaomei. An improved reversible watermarkingalgorithm in wavelet domain for two-dimensional CAD engineering graphics, 2012 3rd International Conference on Advances in Materials and Manufacturing Processes, ICAMMP 2012, 2013（EI收录Accession number: 20130916061882）[4]Jiang, Xue Mei; Li, Bo; Zhang, Xiao Mei. A blind watermarking algorithm for 2D CADdrawings based on SVD, 2013 International Conference on Advances in Materials Science and Manufacturing Technology, AMSMT 2013, 2013（EI收录Accession number: 20134116843545）[5]Jiang, Xue Mei; Tu, Xiao Li ; Li, Bo ; Zhang, Xiao Mei. Reversible watermarking algorithmin DFT domain for 2D CAD engineering graphics, 2013 International Conference on Advances in Materials Science and Manufacturing Technology, AMSMT 2013, 2013（EI收录Accession number: 20134116843546）[6]Quan Liu, Xuemei Jiang. Applications of mobile agent and digital watermarkingtechnologies in mobile communication network. Proceedings 2005 International Conference on Wireless Communications, Networking and Mobile Computing, WCNM 2005, v 2, p 1168-1170（EI收录：Accession number: 06229914833）[7]Liu Quan, Jiang Xuemei. Sensor fault diagnosis based on discrete wavelet transform and BPneural network. Proceedings of SPIE - The International Society for Optical Engineering, v 5998, Sensors for Harsh Environments II, 2005, p 59980J（EI收录：Accession number: 06109746197）[8]Jiang Xuemei. Design and study on optic fiber sensor detection system. Proceedings of SPIE- The International Society for Optical Engineering, v 5998, Sensors for Harsh Environments II, 2005, p 59980U（EI收录：Accession number: 06109746208）[9]Liu Quan, Jiang Xuemei. Design and realization of a meaningful digital watermarkingalgorithm based on RBF neural network. Proceedings of 2005 International Conference on Neural Networks and Brain Proceedings, ICNNB'05, v 1, p 214-218（EI收录：Accession number: 070910446960）[10]Liu Quan, Jiang Xuemei, Namin Yu. Research on adaptive digital watermarking based onspread spectrum. the Third International Symposium on Multi-spectral Image Processing and Pattern Recognition 2003, p 359-362（EI收录：Accession number: 0410*******）[11]Quan Liu, Xuemei Jiang, Ai Qingsong. A new digital watermarking scheme for images.International Symposium on Computational Intelligence and Industrial Applications, 2005, 23-27[12]Quan Liu, Xuemei Jiang.Research on channel capacity estimation of digital watermarkalgorithm based on DCT. International Symposium on Computational Intelligence and Industrial Applications, 2005, 302-306[13]Quan Liu, Xuemei Jiang. Researches on JPEG2000 image compress based on wavelettransform, Proceedings of the 8th Joint International Computer Conference, 2002,11.[14]刘泉，江雪梅. 基于小波神经网络复合材料损伤检测的研究，武汉理工大学学报，2002,12.已授权国家发明专利：[1]已授权国家发明专利：基于病毒检测和水印嵌入的数字版权保护方法，专利号：201010215081.9，授权公告号:101945093B（排序第三）[2]已授权国家发明专利：基于双重身份认证的动态数字版权保护方法，专利号：201010214589.7，授权公告号:1018723399B（排序第三）[3]已授权国家发明专利：基于奇异值分解和扩频技术的统一数字水印的方法及装置. 专利号：ZL031253369（排序第五）[4]已授权国家发明专利：基于三维模型深度投影的三维数字水印方法及装置(申请号：200710169095.X ）（排序第六）获奖：[1]获湖北省科学技术发明二等奖：支持网络制造的信息安全基本理论与关键技术，2007年（排序第五）。

ROI和轮廓波结合的医学图像盲水印算法李文娜;高立群;孔祥勇;崔兆华【摘要】A blind watermarking algorithm which combined region of interest (ROI) with Contourlet transform has been proposed in view of the existing watermark algorithms which can not realize simultaneously the information hid⁃ing and authentication for digital imaging and communications in medicine (DICOM) images. The watermark w1 consisted of patient's private information and the subblocks means of ROI was embedded into background (BG) of DICOM image using a reversible technique based on modified difference expansion. After that authentication water⁃mark w2 was embedded into the high⁃order greater energy directional subbands of the first watermarked image's cont⁃ourlet domain using the method of comparing the contourlet coefficient and its 8⁃neighborhood mean. The scheme is a blind watermarking algorithm, and is able to locate and recover tampered regions with a very good visual quality to ensure image authenticity and integrity for diagnosis. Theoretical analysis and numerical experiments show that the scheme has a high capacity of data hiding as well as anti⁃attack ability.% 针对现有水印方法不能很好地实现信息隐藏和认证同时进行的不足，提出一种基于ROI和轮廓波变换域的DI⁃COM图像水印技术．该技术应用改进的可逆差分扩展方法在DICOM图像的背景区域嵌入水印w1，即患者的隐私信息和感兴趣区域的子块均值．水印w1嵌入后，在图像的轮廓波域中能量较大的高阶方向子带的位置上，采用轮廓波系数与8邻域均值比较的方法嵌入认证水印w 2．算法实现了水印图像的盲提取，同时具有对感兴趣区域的篡改进行定位并修复的能力，保障诊断时图像的真实性和完整性．仿真实验表明，该技术具有较强的数据信息隐藏能力和较好的抗攻击能力．【期刊名称】《哈尔滨工程大学学报》【年(卷),期】2013(000)007【总页数】6页(P918-923)【关键词】盲水印算法;医学图像;数字水印;图像认证;轮廓波变换;活动轮廓模型【作者】李文娜;高立群;孔祥勇;崔兆华【作者单位】东北大学信息科学与工程学院，辽宁沈阳110819; 辽宁石油化工大学信息与控制工程学院，辽宁抚顺113001;东北大学信息科学与工程学院，辽宁沈阳110819;东北大学信息科学与工程学院，辽宁沈阳110819;东北大学信息科学与工程学院，辽宁沈阳110819【正文语种】中文【中图分类】TP391.58数字水印是一种数字标记，将它秘密地内嵌到数字产品中可以帮助识别产品的所有者、内容、使用权、完整性等［1-2］.20世纪早期提出的基于离散余弦变换(discrete cosine transformation，DCT)的频域水印算法是目前研究最多的算法，它具有鲁棒性强、隐蔽性好等特点［3］，可以与JPEG、MPEG等压缩标准的核心算法相结合，能较好地抵抗有损压缩.小波变换(wavelet transform，WT)算法是在小波域中隐藏数字水印信息的算法，并取得了较好的效果［4］.由一维小波张成的可分离小波只具有有限的方向性，不能“最优”地表示具有线奇异性和面奇异性的高维函数，如图像的边缘、轮廓等［5］.随着曲线波和轮廓波变换的提出，出现了一些新的数字水印算法［6-7］.随着现代医学的发展，医学影像(如X线、CT、MR、超声、内窥镜以及血管造影等)在诊疗中起着越来越重要的作用.在数字医学成像及通信(digital imaging and communications in medicine，DICOM，DICOM)和标准的图像存档及通信系统(picture archiving and communication system，PACS)的实际应用中提出了如何防止医学图像被篡改的问题.医学图像数据的标识信息往往比数据本身更具有保密价值，如拍摄日期、诊断病理等患者隐私信息.直接将信息标记在原始文件上可能会导致患者隐私的外泄，没有标识信息的数据通常无法诊疗中使用.最好是将患者的隐私信息隐藏到对应的医学图像中，数字水印则是实现信息隐藏技术中的一种方法，可以实现隐藏标识的功能.考虑到医学图像对于图像的完整性和可信性有较高的要求，提出了一种基于内容的数字水印算法，能够实现患者隐私信息的隐藏、感兴趣区域内信息篡改的定位和恢复以及版权的认证等功能.1 本文算法涉及的相关理论1.1 主动轮廓模型基于偏微分方程的图像分割的基本思想是将图像分割问题转化为求取能量函数最小值问题［8］，经典模型主要有参数活动轮廓模型和几何活动模型，主要是基于曲线演化理论和水平集方法.测地线活动轮廓(geodesic active contour，GAC)模型是基于梯度信息和曲线的几何信息构建的能量函数，其能量函数为式中:C是给定的封闭曲线，s表示Euclidean弧长，g为边缘停止函数:式中:∇Gσ*I是标准差为σ的高斯核卷积图像.求取LR的最小值，得到曲线C的曲线演化方程:式中:k是曲线的曲率;N是曲线单位内法向量，指向曲线的内部;∇g指向g增大的方向，即离开边缘的方向.为加快轮廓曲线在平坦区域的运动速度，同时促使轮廓曲线能够进入目标的凹陷区域，在曲线演化方程中增加αg|∇φ|，得到新的曲线演化方程:将曲线演化方程修改为关于水平集的梯度下降流:为了进一步解决GAC模型的弱边界问题和凹陷问题，文献［8］融合了测地线活动轮廓模型和测地线或区域模型的优点，采用测地线活动区域模型的均值信息构建新的边缘停止函数，代替GAC模型的边缘停止函数.新的边缘停止函数定义如下:式中:c1、c2是采用测地线活动区域模型计算得到的区域均值，即区域内的灰度均值和区域外的灰度均值:其中:将新的边缘停止函数f(I(x))代入GAC模型的梯度下降流中，得到新的梯度下降流:1.2 轮廓波变换和交互块跳频技术轮廓波变换是Minh N.Do等在2002年提出的一种“真正”的二维图像表示方法，将多尺度分析和方向分析分开进行.轮廓波变换由LP和DFB2个部分结合而成［5］，具有双重迭代滤波器组结构，可以将图像在多个尺度上分解为许多方向子带.从滤波器的角度来看，图像由LP分解为低频子带和高频子带.低频子带是由原始图像经过二维低通滤波和隔行隔列下采样产生的，经过上采样和低通滤波后形成与原始图像尺寸相同的低频分量，原始图像减去这个低频分量后即形成高频子带.高频子带经过DFB分解成为2l个方向子带，每个子带都呈楔形.如图1所示，对低频子带重复上述过程就可实现图像的多分辨多方向分解.轮廓波变换直接作用使变换域系数之间的依赖性减弱.它针对图像小波变换的弱点设计的，两者有相同的应用领域，其效能优于小波变换［9］.图1 轮廓波分解示意Fig.1 The contourlet decomposition2 基于图像内容的数字水印生成为提高水印系统的安全性和实用性，结合图像分割理论，提出一种全新的数字水印构造方法，即从载体图像中提取特征信息作为水印的一部分.首先利用改进的活动轮廓模型方法将图像分割为初始ROI和BG.然后对分割后的图像进行修正，将图像进行5×5分块，边界围线处子块并入图像的感兴趣区域，这样做的目的是减少边缘信息嵌入量，提高算法的不可见性.保存修正的分割图像，分别对ROI和BG赋值1和0，生成图像模板.根据图像模板和原始医学图像计算感兴趣区域内每一子块的均值，按位保存均值信息.患者的隐私信息可看成二值图像，考虑到其重要性，采用希尔伯特扫描对其进行加密，将此二维信息转化为一维信号，即希尔伯特扫描码流(Hilbert scan stream，Hss).扫描重排后的Hss与第一步获得的均值信息mean合并生成水印w1，水印w2为认证水印，即由医疗单位的信息构成的二值图像经希尔伯特扫描生成的一维码流.3 DICOM图像水印算法提出的水印算法包括载体预处理、水印预处理、水印位置选择、水印嵌入和提取等部分.分别对水印的嵌入过程和提取及检测过程进行阐述.3.1 水印嵌入基于内容的医学图像数字水印嵌入方案的主要步骤如下:1)获取图像模板和水印.按照第2节获得图像模板，生成基于图像内容的自适应水印w1，并确定认证水印w2.2)生成密钥.记录图像模板ROI和BG分界处左上角的点的坐标，以此作为顶点坐标.在生成模板的过程中对图像进行了5×5分块，因此ROI边缘上每隔5个像素的点即为重要点，用差分的方法记录重要点的坐标形成坐标差序列.顶点坐标和坐标差序列是若干行两列的数组，行列转换生成的一维数据，作为密钥1.3)选择水印w1的嵌入位置.由于大多数医学图像的BG为低灰度区域，选择图像的BG作为嵌入水印w1的位置.对BG进行5×5分块，按照环形的扫描从图像最外部依次向内部推进形成5×5子块串，目的是考虑算法的特殊性，使接收端在逆轮廓波变换时减少频谱扩展现象对ROI的影响，得到较高质量的ROI.因此在BG嵌入水印w1时尽可能选择距离ROI的边缘处较远的位置.4)嵌入数字水印w1.Chun等在文献［10］采用2×2分块的差分嵌入技术，即以2×2子块中左上的像素作为参照像素点，其他3个像素点与其进行比较，差分嵌入信息码流，这样每个图像子块内可以嵌入3 bit的水印信息.考虑到医学图像特殊的用途，需要嵌入的信息数据量很大，为增加嵌入能力，改进了文献［10］中的算法，选择5×5子块的中心像素作为参照像素点(用r表示)，将通常的4邻域和8邻域扩展到可以不相邻的24邻域.24邻域中的任意一个像素值与参照像素点比较，按照一定的规则可以在每个图像子块内嵌入24 bit的水印信息.设a为24邻域中任意一像素的值，aw为嵌入水印后的值.如果满足|r-a|＜2，像素能够按照下面的规则嵌入1 bitHss信息:在w1(i)=1时，用aw代替a，aw=a+2;在w1(i)=0 时，用aw代替a，aw=a-2.如果不满足|r-a|＜2，那么a=a+2，继续重复上面的操作.其它邻域像素都按上述规则进行处理.理论上，该算法嵌入数据的能力为每像素0.96 bit，大于文献［10］中2×2分块的每像素0.75 bit.5)选择水印w2的嵌入位置.将认证水印进行希尔伯特扫描得到一维信息，形成水印w2，对含水印w1信息的医学图像进行合适的轮廓波变换.轮廓波系数的低中频方向子带含有的能量大，嵌入数据的容量有限，只要稍微变动，就会产生很大影响.高频方向子带的纹理、边缘信息丰富，数据比较重要.选择高频方向子带作为嵌入水印w2的位置，能很好协调鲁棒性与透明性，作为密钥2.6)嵌入数据w2.本文算法利用含有水印信息w1的医学图像的轮廓波系数与其邻域系数均值之间的关系来嵌入水印w2.在选择轮廓波系数“网格”时，要保证选取的系数位置尽量相互远离，至少隔1个系数，以确保每个位置的嵌入过程互不干扰，按照对每个嵌入位置的系数做相应的修改.式中:d(i，j)c为嵌入位置的系数，dw(i，j)c为嵌入水印后的系数，mean(i，j)c为嵌入位置系数的8邻域均值，α为嵌入强度. 图2中对号的位置为嵌入水印的位置.对于远程医疗系统，直接将含有水印信息的轮廓波系数进行压缩编码传输，这充分考虑到了接收端是要从轮廓波系数中提取水印w2.轮廓波变换时LP分解滤波器组和重构滤波器组为二维可分离正交滤波器组，带宽均大于π/2.根据多采样率理论，滤波后的图像在进行隔行隔列采样时会产生频谱混叠.减少一次逆轮廓波变换可以削弱混频以及计算机处理的数据截断对医学图像的影响，同时节省计算时间.图2 水印w2嵌入位置示意Fig.2 Watermark w2 em bedding location diagram7)获得含水印的医学图像.如果无需远程传输，只需加密保存医学图像，对修正的轮廓波系数进行逆轮廓波变换，即可得到含有水印信息的医学图像.3.2 水印提取及检测过程在接收端水印提取及检测算法具体步骤为:1)生成图像模板.通过密钥1获得顶点坐标和重要点坐标差序列，在与载体医学图像相同尺寸的全零图像模板上找到顶点位置，根据坐标差就能找到下一个重要边缘点，以此为参照点，根据坐标差再找出下一个重要边缘点，直到找到所有重要点为止.找到的边缘点连线构成了一个封闭曲线，将整个平面分为ROI和BG，分别对其赋值1和0，生成图像模板.2)获得含水印的医学图像并提取水印w2.对解码端接收到的轮廓波系数数据流进行截断，形成多分辨率多方向的轮廓波子带系数，做逆的轮廓波变换，生成含有双重水印信息的医学图像，在某些场合该图像可以直接作为诊断图像.根据密钥2即水印嵌入的位置信息，利用提取的数据流生成二维图像水印w2.式中:dw(i，j)c为接收端的嵌入水印位置的轮廓波系数，mean(i，j)c为嵌入位置的8邻域均值.3)生成图像的ROI和BG.根据解码端生成的图像模板，在含有双重水印信息的医学图像上分别标定出ROI和BG区域.在ROI内对其进行5×5分块，计算每一子块的均值.4)提取水印w1.对含水印信息的图像中的背景区域进行5×5分块，按照环形的扫描从图像最外部依次向内部推进形成5×5子块串.选择5×5子块的中心像素作为参照像素点r，24邻域的像素值与其比较，每个图像子块内可提取24 bit的水印信息，如下式中:aw为嵌入水印后24邻域中任意一像素的值.对提取w1的码流进行截断后为含有患者隐私信息的一维信号和原始医学图像ROI 的均值，患者隐私信息的一维信号按照希尔伯特曲线的形式重新分布，生成患者隐私信息的二值图像.5)判断ROI是否篡改.如果接收端得到很高质量的水印w2表明轮廓波系数在传输过程中未受到攻击.在此情况下，将步骤4)接收端获得的原始医学图像ROI均值信息与步骤3)计算的ROI均值信息进行比较，如果差异很大，则说明原始图像的ROI受到了攻击，其子块的坐标点亦可用来定位被恶意篡改的区域.医生根据步骤4)获得的原始医学图像ROI均值信息代替对应的解码端ROI的被篡改区域或重新传输.4 实验结果与分析选取医学图像进行仿真实验，验证本文算法的可行性.医学图片源于天津某医科大学，实验在P4 2.80 GHz CPU，2 GB内存的 PC机上采用Matlab R2010a.0语言编程实现.4.1 水印性能比较图3为水印嵌入及提取实验结果.通过人眼直接观察，不能察觉出图像的失真和畸变，即可以看出提取的水印质量较好，接收端得到的含水印信息图像的视觉效果好.实验中水印w1和w2的比特数及嵌入前后医学图像的峰值信噪比和相似度统计在表1中.看出嵌入的水印w1和w2的数据量是很大的，获得的峰值信噪比和相似度很高.图3 水印嵌入及提取实验结果Fig.3 Watermark embedding and extracting results for medical images4.2 图像安全性检测当接收端提取的认证水印与嵌入的认证水印有一定程度的变化时，可判断图像在传输过程中受到了攻击.实验如图4.水印w1和w2的比特数及嵌入前后医学图像的峰值信噪比和相似度统计在表1中.篡改部分位于医学图像的感兴趣部分，恢复时对5×5子块进行操作，在BG上的篡改或医生认为不影响提取患者隐私信息的ROI篡改，可不重新传输被篡改部分.对医学图像进行了JPEG压缩、叠加噪声和滤波等常规操作，表2给出了测试结果.未受攻击时提取的水印的相似度为1，说明能够完整的提取嵌入的水印数据.当质量因子为90时，峰值信噪比和相似度分别达到42.57和0.93，表明对JPEG压缩有较强的稳健性。

一种基于SVR的数字图像水印算法赵杰;杨滨峰;李亚雯;毕秀丽【摘要】A new digital color image watermarking algorithm based on support vector regression (SVR) is proposed. The feature vector can be selected in the wavelet domain and the train model can be obtained by applying the support vector regression theory. The watermark signal can be embedded or extracted by utilizing the above train model. The proposed scheme can extract the digital watermark without the help of the original digital image. Experimemal results show that the proposed scheme is invisible and robust against common signal processing such as noise adding, JPEG compression, sharpening, smoothing, filtering, contrast enhancement, shearing and so on. Especially, it performs better than other image watermarking schemes based on support vector machine.%以回归型支持向量机为基础,提出一种彩色数字图像水印算法.在小波域内选取特征向量并获得支持向量机训练模型,进而利用该训练模型嵌入和提取水印信息.该算法以保证不可感知性和鲁棒性的良好平衡为前提,实现了水印的盲检测.实验仿真表明,该算法不仅具有较好的不可感知性,而且对叠加噪声、JPEG压缩、锐化、平滑滤波、对比度增强、剪切等常规处理具有较好的鲁棒性,其整体性能优于一般基于支持向量机的图像水印方案.【期刊名称】《现代电子技术》【年(卷),期】2011(034)006【总页数】4页(P18-21)【关键词】数字水印;回归型支持向量机;小波域;盲检测【作者】赵杰;杨滨峰;李亚雯;毕秀丽【作者单位】商洛学院,物理与电子信息工程系,陕西,商洛,726000;商洛学院,物理与电子信息工程系,陕西,商洛,726000;商洛学院,物理与电子信息工程系,陕西,商洛,726000;北京理工大学,珠海学院,计算机科学与技术学院,广东,珠海,510985【正文语种】中文【中图分类】TN919-34;TP3910 引言数字水印作为数字媒体版权保护和数据安全维护的有效办法，近年来在国际上引起了人们极大的兴趣与注意。

blindwatermark使用Blindwatermark是一种常用的数字图像水印技术，它可以在图像中嵌入不可见的信息，以确认图像的版权和完整性。

与传统的数字图像水印技术相比，Blindwatermark有更高的容忍度和更强的鲁棒性。

以下是一些与Blindwatermark相关的参考内容。

1. "Digital Image Watermarking Techniques: A Comprehensive Review" - 这篇论文对数字图像水印技术进行了全面的综述，包括Blindwatermark在内。

它讨论了不同的数字图像水印算法，并对它们的优缺点进行了比较和分析。

2. "BlindWaterMarking Algorithm for Image Authentication" - 这篇研究论文提出了一种基于Blindwatermark的图像认证算法。

它介绍了该算法的原理和实现细节，并对算法的性能进行了评估。

3. "A Robust Blind Watermarking Scheme Based on Discrete Wavelet Transform and Singular Value Decomposition" - 这篇论文提出了一种基于离散小波变换和奇异值分解的鲁棒性Blindwatermark方案。

它讨论了该方案的安全性和抗攻击能力，并进行了实验验证。

4. "Blind Watermarking for Image Tampering Detection and Recovery" - 这篇论文介绍了一种基于Blindwatermark的图像篡改检测和恢复方法。

它详细说明了该方法的步骤和流程，并通过实验结果验证了算法的有效性。

5. "A Survey on Digital Watermarking Techniques and its Applications" - 这篇综述性文章对数字水印技术及其应用进行了调研和总结。

NOVEL TECHNIQUES FOR WATERMARK EXTRACTION IN THE DCT DOMAINJ.R.Hern´a ndez,M.Amado and F.P´e rez-Gonz´a lezDept.Tecnolog´ıas de las Comunicaciones,ETSI Telecom.,Universidad de Vigo,36200Vigo,Spain email:jhernan@tsc.uvigo.es,fperez@tsc.uvigo.esABSTRACTA novel DCT-domain watermark extraction procedure for still im-ages that does not require the original image is presented.This method is based on the generalized Gaussian model,which in-cludes as a special case the cross-correlation-based watermark de-tector structures,used so far in the literature.Optimal maximum likelihood(ML)structures are given,which allow to analytically assess the performance of watermarking methods in the DCT do-main within a statistical framework.These original theoretical re-sults are validated with experiments that show a considerable im-provement over the existing watermark extraction techniques.The perceptual model used in the tests is also described.1.INTRODUCTIONIn recent years we have witnessed a striking proliferation of tech-niques for representation,storage and distribution of digital mul-timedia information.Unfortunately,these developments have also opened the gate to unathorized copying,distribution and manip-ulation of data,mostly images.Specialized and costly hardware may alleviate the problem of images duplication,at the price of a dramatic reduction in marketing possibilities–this is the crypto-graphic approach taken by pay TV channels,not foreseeable for scenarios such as Internet–.Watermarking techniques can at least ensure that ownership information is invisibly embedded into the image,thus preventing or deterring users from illegal uses.Although many watermarking methods have sprouted over the few past years,even with commercial products available,the re-sults up to date are quite discouraging,since there are freely avail-able programs(e.g.,unZign,Stirmark)that have succeeded in wip-ing the watermark away with little impact on the quality of the re-sulting image.Parallel to this,the lack of theoretical analyses in most of the available literature makes it difficult to know the actual limits in the performance of the various methods and to provide well-founded solutions which are the only way to eventually turn digital copyright protection into a mature discipline.In this paper we make a contribution in this direction by showing how water-marking in the DCT domain(the most commonly used)can be dramatically improved by carefully modeling the problem and de-signing the proper watermark detector.We will assume throughout the paper that the original image is not known.While knowledge of the original image greatly simplifies the extraction procedure [1]it also narrows the range of possible applications.Let be a two-dimensional sequence representing the lu-minance of the original image,where.For the sake of readability,we will use in the sequel this vector notation to rep-resent two-dimensional discrete indexes.Let be the result Work partially funded by CICYT under contract TIC-96-0500-C10-10of applying a DCT transform to in a pixels block ba-sis.For copyright protection purposes,a watermark car-rying some hidden information(owner and image identification number,transaction date,etc.)is added to the original image in the DCT domain,obtaining as a result the watermarked version.In the watermarking technique we analyze in this paper,the watermark is generated in the DCT domain employing a2-dimensional multipulse amplitude modulation scheme[2,3].In other words,can be expressed as the sum of orthogonal pulses(1)where the coefficients are used to encode the hidden message.The modulation pulses are gener-ated as a function of a secret key,only known by the copyright owner.They are expressed asotherwise(2) where is a key-dependent pseudorandom sequence such that,and the sets of indexes are also key-dependent and determine the spatial shape of the pulses.The sequence is called the perceptual mask and indicates the max-imum allowable magnitude of the alteration that the coefficient may suffer without achieving noticeable distortions.The sets are assumed to be non-overlapping,i.e.,and sparsely spread over the whole image in a pseudorandom fashion to provide security and robustness against cropping[2,3].Given a watermarked image and the secret key,first the presence of a watermark for that key is tried to be detected in the so-called watermark detection test.If the result is positive, then the watermark decoding procedure obtains an estimate of the message.We will assume in this paper that no attacks aimed at desynchronizing the watermark are performed.However,both the synchronization and watermark detection problems can be tackled within the statistical framework presented in sections2to4.The perceptual model used in our particular watermarking scheme is given in Section5.Section6is devoted to experimental results, while Section7presents our conclusions and future lines of re-search.2.STATISTICAL MODELDetector structures usually proposed for hidden information de-coding in DCT-domain spread spectrum data hiding techniques are based on the crosscorrelation between the watermarked imageand the pseudorandom sequence.This scheme would be appropriate if noise–in watermarking,the original image–fol-lowed a Gaussian distribution.However,the Gaussian assumption is inaccurate for DCT coefficients of common images.Some au-thors have proposed the generalized Gaussian probability density function(pdf)(3) as an alternative leading to improved statistical models[4].Note that the Gaussian and the Laplacian pdf’s are just special cases of this expression,given by and,respectively.Pre-vious works in thisfield show that DCT coefficients at low fre-quencies are reasonably well-modeled by a generalized Gaussian distribution with.Coefficients at high frequencies are better approximated by a Gaussian distribution and sometimes by a Laplacian distribution.The parameters and in Eq.(3)can be expressed as(4)where is the standard deviation.Hence,the pdf is completely specified by and.Let us define the sequencewhich results if we take the-th DCT coefficient of every block.We will model each of these64sequences as the output of a two-dimensional i.i.d.random process whose marginal distri-bution follows Eq.(3),with parameters and.Let us also define the sequences asand in a similar fashion.Thus,these two sequences indicate the parameters and associated with each sample.3.WATERMARK DECODERLet us assume that possible different messages can be encoded with the vector and letdenote the codeword associated to one of those messages.Also, let be the watermark obtained fromusing Eq.(1).Then,assuming the i.i.d.general-ized Gaussian model for,it can be easily shown that the op-timum decoder in the ML sense is the one that chooses the indexverifyingAssuming that, this optimization problem is equivalent tofinding the codeword which maximizes the expression where the coeffi-cients are sufficient statistics for the detection problem and are defined as When a binary antipodal constellation is used to encode possible messages,the ML detector structure is equivalent to a bit-by-bit hard decisor,so the outputs of the decoder areNow let us analyze the performance of the watermark decod-ing process in terms of the probability of bit error.Obviously, performance results strongly depend on image characteristics,so we will obtain conditioned to a given original image or,in other words,the probability of getting a bit error when a secret key is taken at random and is applied in both the watermarking and de-coding processes.In this context,will be regarded as a deter-ministic signal while the sequence and the setswill be modeled statistically.If the pseudorandom sequence is modeled as an i.i.d.two-dimensional random process with marginal pdf,then,each sufficient statistic is the sum of statistically independent contributions(is the cardinality of the set). Hence,by central limit theorem arguments,can be accurately approximated as the output of a vector Gaussian channel.Therefore,the probability of error conditioned tocan be expressed as a function of thefirst and second order mo-ments of.Let us define the two-dimensional sequenceextracted from Eq.(3).If the tiling generation process is such that each index belongs to with probability for all and assignments of indices to sets are performed independently,i.e.,then after some algebraic manipulations it can be proven[10]that(5)(6)Assume that.Then,, and,as a consequence,If follows a discrete uniform two-level distribution, ,it can be easily shown that the mean and variance ofareThese expressions can be applied in equations(5)and(6)to com-pute the moments of.When,it can be verified thatis given by Eq.(6)and is negative and its absolute value is given by Eq.(5).When a binary antipodal constelation with is used to encode the hidden message,the probabil-ity of bit error of the ML decoder(a bit-by-bit hard decisor)is,where and the signal to noise ratio is defined as(7)4.WATERMARK DETECTORNow let us analyze the watermark detection test,in which we have to decide whether a given image contains a watermark generated with a certain key.The watermark detection problem can be math-ematically formulated as the binary hypothesis test(8)where is the original image,not available during the test, and is a watermark generated from the secret key that is tested.If the watermark carries hidden information,it is not the goal of the watermark detection test to estimate the hidden mes-sage;this task is left to the decoding process.Therefore,we must take into account the uncertainty about the value of the codeword vector when designing the detector.The optimum ML(Maxi-mum Likelihood)decision rule for the test formulated above is(9)where is the decision threshold and is the likelihood func-tion(10)If we assume that the coefficients of the original image follow the generalized Gaussian model studied in Sect.2,and that the watermark does not carry hidden information,in other words, that there is only one pulse()and it is modulated by a known value,then the log-likelihood functionhas the form(11) where is the parameter in the generalized Gaussian pdf for the coefficient(it can be obtained from and using Eq.(4)).Let us now analyze the performance of the watermark detec-tion test conditioned to a certain original image.For this purpose, we will characterize statistically for each of the two hypoth-esis when we assume that is the only random element in the watermarking system.When is true,we have that.Therefore,which is a sum of statistically independent terms.Hence,applying the central limit theorem we can infer that is approximately Gaussian.Assuming that is an i.i.d.two-dimensional random sequence with a discrete marginal distribution with two equiprob-able levels,,then we can easily prove that the mean and variance of conditioned to are[10](12)(13)Similarly,we can prove that conditioned to is approxi-mately Gaussian with mean and variance(14)(15) Let us define and. If is decided in the detection test when,then the probabilities of false alarm()and detection()are(16)Let us define the following“signal to noise ratio”(17)If we denote by the value such that, then it can be easily proved,by examining the expressions in(16), that(18)Hence,the ROC(Receiver Operating Characteristic)of the water-mark detector depends exclusively on the value of.Obvi-ously,the larger the value of,the larger the associated with a certain and the better,as a consequence,the perfor-mance of the detector.5.PERCEPTUAL MODELIn Eqs.(1,2)the watermark depends on a perceptual mask that multiplies the pseudorandom sequence.This per-ceptual mask determines the maximum amplitude distortion that each coefficient of the original image may suffer while satisfying the invisibility constraint.A good psychovisual model in the DCT-domain(with8x8blocks)is capital to render the sequence. For our work we have followed the model proposed in[5,6]that has been also applied to derive adaptive quantization matrices forthe JPEG algorithm[7].This model has been here simplified by disregarding the so-called contrast-masking effect for which the perceptual mask at a certain coefficient depends on the amplitude of the coefficient itself.Consideration of this effect constitutes a future line of research.On the other hand,the background inten-sity effect,for which the mask depends on the magnitude of the DC coefficient(i.e.,the background),has been taken into account.The so-called visibility threshold,,,determines the maximum allowable magnitude of an invisible alteration of the-th DCT coefficient and can be approximated in logarithmic units by the following quadratic function with parameterwhere and are respectively the vertical and horizontal spatial frequencies(in cycles/degree)of the DCT-basis functions, is the minimum value of,associated to the spatial frequency,and is taken as0.7following[5].The threshold can be corrected for each block by considering the DC co-efficient and the average luminance of the screen(1024 for an8-bit image)in the following wayNote that the actual dependence of on the block indices has been dropped in the notation for conciseness.Following[5],the parameters used in our scheme have been set to, cycles/degree,and. Once the corrected threshold value has been obtained,the per-ceptual mask is calculated as(19)where,and is a scaling factor that allows to introduce a certain degree of conservativeness in the watermark due to those effects that have been overlooked (e.g.,spatial masking in the frequency domain[8]).The remaining factors in(19)allow to express the corrected threshold in terms of DCT coefficients instead of luminances.6.EXPERIMENTAL RESULTSIn order to validate the theoretical analysis presented in previous sections,we have watermarked the well-known image Lena(256x 256pixels)following the method described in Sect.1,modifying only22coefficients in the mid-frequency range(low frequency co-efficients have very low capacity,i.e.,slight modifications become quite visible;high frequency coefficients can be easily erased by compression algorithms).To analyze the performance of the watermark decoding pro-cess,we watermarked the image Lena with100different keys for different bit rates,measured in terms of the number of coefficients altered by each information bit,and computed the resulting bit er-ror rate(BER).Figure1shows one of the watermarks used in the experiment.In Figure2both empirical and theoretical resultsforFigure1:One of the watermarks used in the tests.Laplace GaussianEmpirical29.3829.0721.39Theoretical29.3428.7120.78Table1:Empirical and theoretical signal to noise ratio(in dB)in the watermark detection test.different values of the generalized Gaussian parameter are plot-ted.Note that the parameter in Eq.(19)has been set to1/5–so the watermark is well below the visibility level–in order to produce statistically significant results.The actual performance is substantially better,but the qualitative conclusions remain the same.As can be inferred from Figure2and also from Figure 3,where the SNR in Eq.(7)is plotted for different values of, good results are obtained in the range.Interestingly enough,the performance for,corresponding to the cross-correlation-based detector used so far in the literature[9],suffers a severe deterioration,corresponding to a drop of more than6dB in the SNR(cf.Fig.3).Although not directly discussed here,our analysis can be some-what straightforwardly extended to the case of JPEG compression. Figure4shows the theoretical BER obtained when image‘Lena’is watermarked(with a100bits hidden message)and later com-pressed with JPEG to a percentage of its original quality.As it can be seen,in this case,the Laplacian detector()per-forms slightly better than the one with.The Gaussian (cross-correlation)detector,not shown in thefigure,leads to a much higher BER.The curves labeled as‘Optimum’correspond to a detector specifically designed for the JPEG compression at-tack.To measure the performance of the watermark detection test, we have watermarked the image Lena with1000different keys us-ing“pure”watermarks carrying no additional information.In Ta-ble1we show both empirical and theoretical values of the“signal to noise ratio”for the image Lena and detector structures based on three values of.As we have already discussed, completely determines the shape of the ROC.We can see that the theoretical approximations accuratelyfit the empirical data.Em-pirical measures of and,not shown here,clearly validate the accurateness of approximations in Eq.(16)[10].Besides this, it is clear that substantial gains in performance are obtained by abandonning the Gaussian statistical assumption.Figure2:BER as a function of the pulse size for Lena().Figure3:SNR as a function of for Lena().7.CONCLUSIONS AND FURTHER WORKNovel structures based on the use of generalized Gaussian models have been proposed for the ML detection of DCT-domain water-marks embedded in still images.By considering these models, we have been able to dramatically improve the performance of the cross-correlation-based detectors that have been used up to date. In any case,we also have presented a theoretical analysis that al-lows to assess the performance of DCT-based methods,measured in terms of the bit error rate and the probabilities of false alarm and detection,for a given image.The Gaussian detector is simply a particular case of the generalized model,so the analytical results given here are directly applicable.One immediate extension of our analysis is the consideration of channel codes which have been already shown to considerably improve on spatial-domain water-marking methods[11].Another future line of research consists infitting a generalized Gaussian model(from a discrete set of pa-rameters and)to the DCT coefficients histogram so as to decide upon and apply the optimal detector structure.8.REFERENCES[1]I.J.Cox,J.Kilian,F.T.Leighton,and T.Shamoon,“Se-cure spread spectrum watermarking for multimedia,”IEEE Transactions on Image Processing,vol.6,pp.1673–1687, December1997.Figure4:BER as a function of JPEGfinal quality for Lena.[2]J.R.Hern´a ndez,F.P´e rez-Gonz´a lez,J.M.Rodr´ıguez,andG.Nieto,“Performance analysis of a2d-multipulse ampli-tude modulation scheme for data hiding and watermarking of still images,”IEEE J.Select.Areas Commun.,vol.16, pp.510–524,May1998.[3]J.R.Hern´a ndez,F.P´e rez-Gonz´a lez,and J.M.Rodr´ıguez,“The impact of channel coding on the performance of spatial watermarking for copyright protection,”in Proc.ICASSP’98, vol.5,(Seattle,Washington(USA)),pp.2973–2976,May 1998.[4]R.J.Clarke,Transform Coding of Images.Academic Press,1985.[5] A.J.Ahumada and H.A.Peterson,“Luminance-model-based DCT quantization for color image compression,”in Human Vision,Visual Processing,and Digital Display III (Proc.of the SPIE)(B.E.Rogowitz,ed.),1992.[6]J.A.Solomon,A.B.Watson,and A.J.Ahumada,“Visi-bility of DCT basis functions:Effects of contrast masking,”in Proc.Data Compression Conference,(Snowbird,Utah (USA)),pp.361–370,IEEE Computer Society Press,1994.[7] A.B.Watson,“Visual optimization of DCT quantization ma-trices for individual images,”in Proc.,AIAA Computing in Aerospace9,(San Diego,California(USA)),pp.286–291, American Institute of Aeronautics and Astronautics,1993.[8] ravali and B.G.Haskell,Digital Pictures.Repre-sentation,Compression and Standards.New York:Plenum Press,1995.[9]M.Barni,F.Bartolini,V.Cappellini,and A.Piva,“A DCT-domain system for robust image watermarking,”Signal Pro-cesing,vol.66,pp.357–372,May1998.[10]J.R.Hern´a ndez,T´e cnicas de Sellado Invisible para la Pro-tecci´o n de los Derechos de Autor en Im´a genes Digitales.PhD thesis,Universidade de Vigo,1998.[11]J.R.Hern´a ndez,J.M.Rodr´ıguez,and F.P´e rez-Gonz´a lez,“Improving the performance of spatial watermarking of im-ages using channel coding.”Accepted for publication in Sig-nal Procesing,Elsevier.。