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- 1. A New Image Watermarking Algorithm Using CTand NormalizationDandan Zhu1,21School of Computer ScienceTonghua Normal universityTonghua 134002, Chinazhudan0526@163.comQiang Tong22College of Information Science & EngineeringNortheastern UniversityShenyang 110819, Chinatongq@swc.neu.edu.cnAbstract—Contourlet transform is a very efficient anisotropyanalysis tool in high dimensions, which can not only possessthe main features of directionality and anisotropy, but alsoeffectively capture the intrinsic geometrical structures such assmooth contours (at different scales and directions) in naturalimages. In this paper, an image normalization based robustdigital watermarking scheme in contourlet domain isproposed. Firstly, the geometrically invariant space isconstructed by using image normalization and the significantregion is obtained from the normalized image by utilizing theinvariant centroid theory. Then, the contourlet transform isperformed on the significant region. Finally, the digitalwatermark is adaptively embedded into the significant regionby quantizing the low-frequency contourlet coefficientsaccording to the Human Visual System (HVS). Especially, thepredistortion compensation technique is applied to reduceimage distortion generated by image normalization.Experimental results show that the proposed scheme is notonly invisible and robust against common signals processingsuch as noise adding, and JPEG2000 compression, but alsorobust against the geometric distortion such as rotation,translation, scaling, row or column removal, cropping.Keywords-image watermarking; contourlet transform;geometric attacks; normalizationI. INTRODUCTIONDigital watermarking has been widely used forprotection of multimedia in the Internet [1, 2]. In recentyears, there has been an unprecedented development in theimage watermarking field, especially in the transformdomain images. For example, discrete cosine transform(DCT) [3, 4] and discrete wavelet transform (DWT) [5, 6]are widely used for designing watermarking algorithms.However, because of its limitation for processing anisotropy,ones try to find out other methods to represent theanisotropy of signals. After ridgelet [7] and curvelet [8],being an improvement on the curvelet transform, contourlettransform (CT) is proposed by Minh in [9] using pyramidaldirectional filter bank (PDFB). The main advantage ofcontourlet transform over other directional representations isthat it allows different number of directions at each scalewhile achieving nearly critical sampling. Besides, itemploys iterated filter banks, which makes itcomputationally efficient. By utilizing the performance ofthe contourlet transform in capturing directional informationof image edges, some watermarking algorithms have beenproposed [10, 11]. In [12-14], the additive watermarkingmethods and the multiplicative watermarking are proposed.Most of the previous watermarking schemes are robust tocommon signal processing, in order to against geometricalattacks such as rotation, scaling and translation, randombending attack and shearing, etc. In this paper, an imagenormalization based robust digital watermarking scheme incontourlet domain is proposed. Firstly, the geometricallyinvariant space is constructed by using image normalizationand the significant region is obtained from the normalizedimage by utilizing the invariant centroid theory. Then, thecontourlet transform is performed on the significant region.Finally, the digital watermark is adaptively embedded intothe significant region by quantizing the low-frequencycontourlet coefficients according to the human visualsystem (HVS). Our algorithm has advantages oftransparency and robustness.II. CONTOURLET TRANSFORMA. The Characteristics of ContourletContourlet is a geometrical transform based on image. Itcan effectively represent an image with rich contours andtextures through separately processing the multiresolutionanalysis and multidirection analysis. Its basic functions haveelongated support with aspect ratio varying with scale thatcan efficiently capture the linear discontinuities and facediscontinuities. Compared to wavelet, the contourlet hasricher basic functions. It uses fewer coefficients to representsmooth edges and combines the discontinuity points in thesame direction into a discontinuity line or a discontinuityface. The contourlet has some characteristics as shown inFig.1,.(a) (b)Figure 1. The compare diagram of basis function(a) DWT and (b) Contourlet2012 IEEE International Conference on Systems, Man, and CyberneticsOctober 14-17, 2012, COEX, Seoul, Korea978-1-4673-1714-6/12/$31.00 ©2012 IEEE 3239
- 2. 2More flexible multiscale is represented in the image.As shown in Fig.2, first, the multiscale decomposition useslaplacian pyramid (LP) filters. The LP decomposition ateach level generates a downsampled lowpass version of theoriginal, resulting in a bandpass image. The directionaldecomposition stage is constructed based on the idea ofusing an appropriate combination of shearing operatorstogether with two direction partition of quincunx filter banksat each node in a binary tree structured filter bank.(2,2)ImageLFDCoarse scaleFine scaleDFBLPDDFB......Directional subbands(a) Diagram of contourlet transforms( , )(- , - )(b) Frequency decompositionw2w1Figure 2. Contourlet decomposition frameworkThe directional subbands of contourlet transform capturethe distribution of contours and edges in the correspondingdirection more accurately than wavelet. Compared towavelet, after contourlet transform, the correlation betweenimage coefficients is approximately decorrelated. From Fig.2, it can be seen that the energy is mainly concentrated onthe textures and edges in each directional subband atdifferent scales, and the variation of coefficientsconditionally correlates to that of significant coefficients.Therefore, the distribution of contourlet coefficients isnonlinear dependent.(a)(b)Figure 3. Decomposition of zoneplate image(a) DWT and (b) ContourletB. Pyramidal Directional Filter BankThe contourlet transform, also called pyramidaldirectional filter bank (PDFB), is a nonseparable multiscalerepresentation for signals. The PDFB first decomposes animage via laplacian pyramid (LP) transform to capture thesingularity points and then combines the singularity pointsalong the same direction into one coefficient using adirectional filter bank (DBF). This transform structuremakes contourlet achieve near optimal nonlinearapproximation performance. Repeating the procedure abovein the coarsest subband, we can obtain the multiscale andmultidirectional subbands of images. Let I be the originalimage with size of M × N, Il and Bl be the lowpass imageand bandpass image after l-level LP transform, respectively.The LP transform of the lth level decomposes the lowpassimage Il-1 into a lowpass Il and a bandpass image Bl, Thenthe DFB of the th level is employed to decompose Bl into2λdirectional subbands Cl,d (d = 0, 1, …, 2λ-1).III. IMAGE NORMALIZATIONThe image normalization used in this paper is based onthe approach proposed in [15]. Generally, an affinetransformed image of image f (x, y) is defined as f (xa, ya).dyxAddyxaaaayxaa+=+=2122211211 (1)The procedure of normalizing an image includes foursteps:1) Re-center the image. Find x and y , the re-centeredimage has supporting coordinate as follow:xxx ac −= , yyy ac −= (2)After the re-centering, the translation is eliminated. Theaffine transform matrix used to normalize the image can beseparated as:−==ccccaayxyxaaaayx10100cossinsincos22211211 βδαφφφφ (3)Here α, β, δ ∈ (0, 2π) and 0221211 ≠+ aa is required foruniqueness of the separation and the normalized image. If3240
- 3. 3the order of the normalizations is neglected, thenormalizations destroy each other.2) X_shearing normalization. The transform parameter βis calculated by normalizing the equation below to zero:0021111 =+= ccshβμμμ (4)Thuscc0211μμβ −= . Then the x_shearing invariant supportingcoordinate set ),( shsh yx is:=ccshshyxyx101 β(5)3) Scaling normalization. From the transform moment:shsc20320 δμαμ = , shsc02302 αμδμ = (6)we get two scaling parameters α and δ :( )832002shshμμα = ,( )830202shshμμδ = (7)We have four possible solution pairs. Unique solutioncan be obtained by choosing 050 >scμ and 005 >scμ . Thescaling invariant coordinate set is as follows.=shshscscyxyxδα00 (8)4) Rotation normalization. The rotation parameterφ canbe computed by normalizing the equation below to zero:( ) ( ) φμμφμμμμ sin2cos2 210312301230scscscscrr+++=+ (9)Thus++−= scscscsc210312301 arctanμμμμφ or πφφ += 12 .Choose one of the two solutions by requiring 02103 <+ rrμμ .Finally, the normalized coordinate set (xn , yn) is:−=− scscnnyxyxφφφφcossinsincos (10)Thus the standard position of the image is obtained. Theinverse normalization procedure can be performed bymultiplying of (xn, yn) with A-1step by step.Important area of normalized image determinationmethod can be described as:Step 1: Using the gaussian filter to normalized imagesmoothing, in order to eliminate noise interference.Step 2: According to the image region invariant centroiddefinition, calculating the normalized image centroid C0 (x1,y1), as the normalization image invariant centroid initialvalue.Step 3: According to the image region invariant centroiddefinition, calculating the normalized image center C1 (xc,yc), (x1, y1) as center, r as radius.If C1 (xc, yc) = C0 (x1, y1), turning the third step.C0 (x1, y1) is the normalized image center of mass.With the whole normalization image invariantcentroid as center, selecting size S1×S2 rectangularregion. In Fig.4, test results show that normalizedimportant areas has good robustness, here, (a) isrepresenting original image, (b) is representingnormalized image, (c) is representing significantregion.(a) (b) (c)original image (lena) significant region(a) (b) (c)adding noise image (lena) significant region(a) (b) (c)geometric distortion image (lena) significant regionFigure 4. Normalized image and significant regionIV. WATERMARK EMBEDDING ALGORITHMWe test original image on the popular image 512×512,where F = {f (i, j), 1 ≤ i ≤ M, 1 ≤ j ≤ N}, digitalwatermarking is two values image WS = {ws (i, j), 1 ≤ i ≤ P,1 ≤ j ≤ Q}. Among them, f (i, j) and ws (i, j) representoriginal image and binary image watermark, respectively.Let us decompose the embedding scheme into thefollowing different steps:Step 1: Watermarked encryption processing. We usetwo-dimension arnold [16] transform. In the transform, theimage of a pixel coordinate is x, y ∈ (0, 1, …, N-1), N is the3241
- 4. 4exponent number of image matrix, and N =16. Then thetransform formula is as follows:)(mod2111Nyxyx= (11)With the iterative operation, the transformation matrix isA. In the formula above, the right (x, y) is input, the left (x’,y’) is output, and we get the following formulas.)(mod,,1NyxnAPyxnp =+ (12)2,1,0),,(,== nyxyxnp (13)Here n represents the times of iteration. Fig. 5 represents theresults when an image whose size is 16×16 is scrambled byarnold transformation. Here we set n = 5.(a) (b)Figure 5. (a) original watermark (b) encryption watermarkStep 2: Normalizing the original image. Based on thenormalization technology, the original image F isnormalized to get the corresponding the normalized image I.Step 3: Obtaining the important area of the normalizedimage. With the regional unchanged centroid theory, theimportant area O is extracted from the normalized image I.Step 4: For the important area O, we make a two-levelcontourlet transform. We select contourlet transform for lowfrequency sub-band as a watermark embedding area.Step 5: Watermark Embedding. We use the odd-evenquantitative method to change the low frequency sub-bandcoefficient with the rules as follows.[ ][ ]≠==Δ∗−==Δ∗+=),(2),,(mod(),,(0),(2),,(mod(,1),(1),(2),,(mod(,1),(),(jiWsjirifjiyjiWsjirifjirjiWsjirifjirjiy(14)Here, r (i, j) = round (y (i, j)/ ). And y (i, j) is the coefficientbefore watermark is embedded, y’(i, j) is the coefficientafter watermark is embedded, and deta is a quantitative steplength.Step 6: Obtaining the watermarked image. Inversingcontourlet transform and gaining watermarked image I’. Weuse the predistortion compensation strategy to gainwatermarked image as follows:The first is to calculate the original normalizedimage I and the watermarked normalized image I’.Then D-value image D = I - I’.The second is to makes an inverse normalizationoperation on the D-value image D, obtaining theinverse D-value image D’.The third is to add the image D’ into the originalimage F, gaining the watermarked image F’.V. WATERMARK DETECTION ALGORITHMIn general, the watermark detection is an inverseprocedure of embedding. The image being detected is F’.The proposed detection scheme is detailed as follows.Step 1: Normalizing the watermarked image F’, gaining theimage I’’.Step 2: Obtaining the important area of the normalizedimage. With the regional unchanged centroid theory, theimportant area O’ is extracted from the normalized imageI”.Step 3: The important area O’make two levels contourlettransform, the paper select contourlet transform lowpassarea as detecting region, rules are as follows:===0)2),,(mod(,01)2),,(mod(,1),(jirifjirifjisW (15)Here, r(i, j) = round (y’’(i, j)/ ). And y’’(i, j) is thecoefficient of the extracted low frequency sub-band, and W’sis the extracted encrypted watermark. Then based on the keyK to the two dimension arnold scrambling decryption, thewatermark Ws is recovered.VI. SIMULATION RESULTSTo prove the capability of our method in the paper, wegive the experimental results of our system. We test theproposed watermarking scheme on the popular test images512×512 Lena, Baboon, and Peppers. A size 16×16 is usedas the watermark pattern. The size of normalized significantregion is 128×128, the watermark strength is 65. As shownin Fig. 6, the watermark images have a good transparency,lena (psnr = 42.05), mandrill (psnr = 42.31) and barb (psnr= 41.77).We embed the watermark in the perceptually texturedregion, so the embedded watermark is less visible. Table 1and Table 2 summarize the detection results. Differentattacks are listed as follows.(a) lena (b) barb (c) mandrillFigure 6. Watermarked image (psnr)3242
- 5. 5Removed rows and columns: (a) (1, 1), (b) (1, 5), (c)(5, 1), (d) (1, 8), (e) (8, 1), removing the rownumber and the column number.Scaling: (a) 0.5, (b) 0.8, (c) 2.0, (d) 3.0, (e) 4.0, thedecimal represent scaling.Rotation: (a) 10, (b) 30, (c) 45, (d) 60, (e) 90, thefigures show the rotation angle.Shearing: (a) (0, 1%), (b) (0, 5%), (c) (1%, 0), (d)(5%, 0), (e) (1%, 1%), -x-shearing and -y-shearingpercent.JPEG: (a) 80, (b) 60, (c) 30, (d) 20, (e) 10, thefigures show Quality factor.JPEG2000: (a) 20, (b) 30, (c) 60, (d) 80, (e) 90, thefigures show Quality factor.Translation-x and –y:(a) (10, 10), (b) (15, 15), (c)(20, 20) , (d) (30, 30).Common signal processing: (a) 3×3 Median filter,(b) 3×3 Gaussian filter, (c) 3×3 wiener filter, (d)5×5 wiener filter.TABLE 1. THE WATERMARK DETECTION GEOMETRIC ATTACKS AND COMMON ATTACKS (NC)Attacks (a) (b) (c) (d) (e)Removed rows and columns 0.9388 0.8796 0.8519 0.8013 0.7918Scaling 0.7855 0.9125 0.9775 0.9648 0.9700Rotation 0.9364 0.7505 0.7208 0.8198 0.9622Shearing 0.9901 0.9786 0.9926 0.9875 0.9825JPEG 0.9775 0.9775 0.9876 0.9649JPEG2000 0.9596 0.9775 0.9775 0.9876 0.9975Translation 0.9926 0.9892 0.9806 0.9799Common signal processing 0.9920 0.9986 0.9929 0.9895TABLE 2. THE WATERMARK DETECTION UNDER MIXED ATTACKS (NC)Attacks NC Dete. imageJPEG 30 and 3×3 Gaussian filter 0.9571Salt&Pepper noise(0, 0.01)and Gaussian noise(0, 0.005) 0.9290Centered cropping (0,5%)and Rotation 10 0.9800Translation-x-10 and –y-10 and 3×3 Median filter 0.9257Removed 1rows and 5columns and Rotation 20 0.9040-x-shearing5%,-y-shearing 5% and JPEG2000 60 0.9075JPEG2000 90 and Scaling 0.8 0.9025Scaling 2.0 and Gaussian noise(0, 0.005) 0.9368VII. CONCLUSIONA robust image watermarking scheme is designed in thepaper against both common signal-processing andde-synchronization attacks. There are several key elementsin our scheme, which are as follows.The CT can effectively represent an image with richcontours and textures through separately processingthe multiresolution analysis and multidirection analysis.Hence it is helpful for against noise attacks andtranslation attacks.By applying normalization technique and predistortioncompensation theory, the invisibility and robustness ofwatermarking scheme are increased.3243
- 6. 6Besides, we also extend the proposed method to a blindtechnique which does not need additional information,which makes it applicable in a wider range of situations.REFERENCES[1] R. S. Run, S. J. Horng, J. L. Lai and T. W. Kao, “An improvedSVD-based watermarking technique for copyright protection”,2012 Expert Systems with Applications: An International Journal,2012, pp. 673-689.[2] X. Y. Wang, L. M. Hou and J. Wu, “A feature-based digital imagewatermarking against geometric attacks”, Image Vis. Comput, 2008,pp. 980-989.[3] F. Duan, D. Abbott and F. C. Blondeau, “The application ofsaturating detectors to a DCT-domain watermarking scheme”, Fluct.Noise Lett, 2008, pp. 65-79.[4] X. C. Bo, L. C. Shen, W. S. Chang and Y. F. Niu, “Adaptivedetection for blind image watermarking in DCT domain”, J. Comput.Res. Develop, 2002, pp. 502-510.[5] Q. Li, C. Yuan, Y. Z. Zhong, “Adaptive DWT-SVD Domain imagewatermarking using human visual model”, ICACT2007, 2007, pp.1947-1951.[6] M. Jayalakshmi, S. N. Merchant and U. B. Desai, “Significant pixelwatermarking using human visual system model in wavelet domain”,ICVGIP 2006, pp. 206-215.[7] L. C. Jiao, S. Tan and F. Liu, “Ridgelet theory: From ridgelettransform to curvelet”, Chinese J. Engrg, 2005, pp.761-773.[8] J. L. Starck, E. Candes, D. Donoho, “The Curvelet Transform forImage Denoising”, IEEE Trans, Image Processing, 2002, pp.670-684[9] N. D. Minh, M. Vetterli, “The Contourlet transform: an efficientdirectional multiresolution image representation”, IEEE Transactionson Image Processing to appear, 2005, pp. 2091-2106.[10] A. Bouzidi and N. Baaziz, “Contourlet domain feature extraction forimage content authentication”, IEEE 8th Workshop on MultimediaSignal Processing, 2006, pp. 202-206.[11] M. Jayalakshmi, S. N. Merchant and U. B. Desai, “Digitalwatermarking in contourlet domain”, IEEE Computer Society, 2006,pp. 861 864.[12] X. Lian, X. Ding and D. Guo, “Digital watermarking based onnon-sampled contourlet transform,” IEEE Int. WorkshopAnti-counterfeiting, 2007, pp. 138-141.[13] H. Li, W. Song and S. Wang, “A novel blind watermarkingalgorithm in contourlet domain,” in Proc. 18th Int. Conf. PatternRecognition, 2006, pp. 639-642.[14] S. Xiao, H. Ling, F. Zou and Z. Lu, “Adaptive image watermarkingalgorithm in contourlet domain,” Japan-China Joint Workshop onFrontier of Computer Science and Technology, 2007, pp. 125-130.[15] P. Dong and N. P. Galatsanos, “Affine transformation resistantwatermarking based on image normalization”, Image Processing.2002, pp. 24-28.[16] C. Zhang, J. Wang, X. Wang, “Digital Image WatermarkingAlgorithm with Double Encryption by Arnold Transform”, TheFourth International Conference on Networked Computing andAdvanced Information Management, 2008, pp. 329-334.3244

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