Geometric Invariant Semi-fragile Image Watermarking Using Real Symmetric Matrix

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1 Proceedings of the 5th WSEAS Internationa Conference on Signa Processing, Istanbu, Turkey, May 27-29, 2006 (pp70-75) Geometric Invariant Semi-fragie Image Watermarking Using Rea Symmetric Matrix Ching-Tang Hsieh, and Yeh-Kuang Wu Dep. of Eectrica Engineering, Tamkang University, Taipei, Taiwan, 25137, R.O.C. Abstract: - In order to improve the detection of maicious tampering images, it necessary to decrease the fragiity of hidden watermarks, even for digita images which have been incidentay dtorted. In th paper, we propose a new invariant semi-fragie digita watermarking technique based on eigenvaues and eigenvectors of rea symmetric matrix generated by the four pixe pairs. A signature bit for detecting the maicious tampering of an image generated using the dominant eigenvector. And the muti-rings Zernike transform (MRZT) proposed to achieve geometric invariance. The MRZT method to the geometric dtortions even when the image under maicious attacks. Experimenta resuts show that th agorithm can rest high quaity JPEG compression, and improve the detection performance of various maicious tampering. Key-Words: fragie watermarking, Eigenvaue, Geometric invariance, Zernike moment 1 Introduction Due to advances in digita technoogies, most data are digitized and can be easiy copied or edited. Such situation hinders popuarization of digita technoogies. Image watermarking provides a soution for protecting the copyright of digita contents. Many watermarks for sti images and video content are sensitive to geometric dtortions. It cear that even very sma geometric dtortions can prevent the detection of watermarks. However, the geometric dtortion of the digita image, such as rotation and scaing, can be inverted with ossess of the image intensity. The desired geometric invariance can be achieved by using the FMT (fourier meien transform) to convert rotation and scae to spatia shifts. A og-poar transform converts rotation and scaing to spatia shifts, and permits recovery from rotation and scaing. O Ruanaidh et a. first have outined the theory of integra transform invariants and showed that are restant to rotation, scaing, and transation. However, the og-poar mapping used in th technique causes a oss of image quaity and the quaity definitey unacceptabe. Of various types of moments defined in the iteratures, Zernike moments have been shown to be superior to the others in terms of their insensitivity to image noe, information content, and abiity to provide faithfu image representation, used as the invariant watermarking [16]-[20]. Some invariant watermark schemes proposed with embedding methods based on the Zernike transform coefficients to achieve the geometric invariance, but the geometric invariance methods restricted to the proposed watermarking, not suitabe for a watermark embedding schemes [16]-[19]. Chen [20] proposed a geometric invariance watermarking based on waveet and Zernike transform where the embedding system independent to geometric invariance method. But the geometric invariance method not robust to more than two maicious attacks, such as rotation and cropping combining as a severey maicious attack. Fragie digita watermarking essentia for addressing the probem of data integrity, but most fragie digita watermarks are very fragie even for sight atering. It cannot rest any processing even some vaid processing such as high quaity JPEG compression (ossy compression) and not suitabe for factua appication. Some of semi-fragie digita watermarking [1][3][4][5] has been brought forward and researched. Typica approaches of semi-fragie digita watermarking can be categorized as signaturebased or watermark-based or a combination of both. Kundur and Hatzinakos [1] embedded a watermark vaue by moduating a seected waveet coefficient into the quantized interva determined by the corresponding watermark vaue. However, they didnot provide a mechanm to detect the combination of maicious tampering and incident dtortion. Lin

2 Proceedings of the 5th WSEAS Internationa Conference on Signa Processing, Istanbu, Turkey, May 27-29, 2006 (pp70-75) and Chang [3] stores the reation of DCT coefficients at a pairs of two random 8x8 bocks as digita signature. Their method can detect maicious tampering under JPEG compression, but the digita signature based method cannot point out tampering regions ceary or some specia tampers, such as those with background changed to pure white, and cannot be used for muti-watermarks system [6]. Fridrich[8] proposed a muti-watermarking system by embedding fragie watermarks on top of robust watermarks. The fragie watermarks detect a the tampers, and the robust watermarks can dtinguh maicious and innocuous changes in the images. The method makes a vauabe too for authentication of images and detection of a types of tamperings. In th paper, we propose a new semi-fragie digita watermarking technoogy based on the dominant eigenvaue and its corresponding eigenvector of rea symmetric matrix, the proposed method abbreviated as EVRSM. Because of the orthogona property of rea symmetric matrix, we combine both superiority of watermark-based and signature-based semi-fragie watermarking technoogy for image authentication in our method to improve the performance of maicious tampering and aso rest high quaity JPEG compression processing. The proposed watermarking system a geometric invariance system based on the proposed muti-rings Zernike transform that robust to geometric attacks even when the image under maicious or innocuous attacks. The MRZT reduce the accumuation of the attacked coefficients in the Zernike transform and avoid maiciousy attacked components. In section 2, we wi describe the proposed muti-rings Zernike transform. And the new semi-fragie watermarking shown in section 3. Section 4 describes how to embed and extract the digita watermark and anayze the deta of semi-fragie digita watermarking technique. The experimenta resuts and the evauation of the proposed agorithm are presented in section 5. Finay, in section 6, we wi make a concusion. 2 Muti-rings Zernike transform Zernike transform the mapping of an image onto a set of compex poynomias that have the rotation invariant charactertics. The rotation invariance of the feature vectors aows the feature set, the magnitude of the Zernike moments extracted from the image, to be the same at any orientation. Let the set of these poynomias be denoted by V(x,y) : V ( x, y) = V ( ρ, θ) = R ( ρ) exp( jmθ ) where R( ) the radia poynomia defined as : R ( ρ ) ( n m ) ( 1 ) / 2 ( n s ) s = s = 0 n + m s! 2 n m s! 2! s! (1) (2) n 0, n- m even, and m n. the ength of vector from origin to pixe at (x,y). the ange between vector and X ax in countercockwe direction. Unfortunatey, the moment based methods require too much computation for practica purposes and are sensitive to noe, such as cropping and compression. In th paper, we proposed a nove fast rotation and scae variance method, muti-rings Zernike transform, consting of two stages. In the first stage the image divided into 11 co-centric rings and the moments are computed based on these co-centric rings. Secondy, the candidates of the non-attacked bocks are seected by K-means method according to the density dtribution. The muti-rings method can avoid the regions with maicious attacks, ighten the dtortion from stattics of the attacked pixes and be suitabe for any watermark scheme. The image I divided into m sub-rings. I = { I1 I2 I3... Im } (3) After the partition, the moment of ring computed according to (3). For each sub-image, the origina of host image instead of the center. n + 1 * A = f, π x y ( x, y ) V ( x y ) Assume that the th sub-bock image denoted by f ( ρ,θ ), α the ange of the rotation. The rotated image denoted by f ( ρ,θ ) r. The magnitudes of Zernike moments are invariant to rotation, and scae and transation normaizations are required to achieve simiarity. The reationship between the origina image and the rotated in poar coordination : f r A ( ρ θ ) = f ( ρ, θ α ) r = A exp( jmα ), (4) (5) The geometric dtortions of image, such as rotation and scaing, can be inverted that the intensity of the images unchanged. According to above section, 11 estimated rotation anges candidates with different radius are computed consted of coefficients interfered with and without maicious tampers. The custering widey performed by an iterative agorithm that known as the crp c-means agorithm. The crp c-means agorithm assigns each feature vector to a singe custer and was adopted to separate two custers, concentrated and dtributed ones. The

3 P and and and Proceedings of the 5th WSEAS Internationa Conference on Signa Processing, Istanbu, Turkey, May 27-29, 2006 (pp70-75) agorithm performs a partition for each eement in the feature space to c custer and c centers of the custers are generated. In the iterature, c equa to 2. The iterative processes continuous ti the custer center become stabe and there insignificant difference between custer centers in two consecutive iterations. One of the c custers wi be seected that the variance in th custer smaer than other ones. 3 Eigenvector and eigenvaue of rea symmetric matrix 4 Proposed watermarking method 4.1 Embedding agorithm Given an image, we divide it into severa bocks of 8x8 pixes. Each bock transformed with Dcrete Cosine Transform (DCT). We divide frequency domain into DC part and AC part, that, the DCTBDC_VaueB of DCT coefficients beongs to DC part and the DCTBAC_VaueB of DCT coefficients beong to AC part. In Eq.(7), the quantized DCTBDCB coefficient was integer rounding operation by dividing into the eigenvaue Each DCTBACB coefficient divided into the fixed quantization tabe BiB. The quantization functions BλB beow: λ DCT DC = λ = DCT _ Vaue AC _ Vaue BvB are defined V The rea symmetric matrix R defined by i (8) R = A T A λ dominant eigenvaue and BiB (8) fixed A = [ a xy ] x, y = 1,2... k 1, quantization tabe. the foor function. if f p ( i, f q ( i, + B ij 0 a xy = i, j = 0,1,.., n 1 In order to avoid the noe and artifact in JPEG m if f p ( i, f q ( i, + B ij < 0 (6) compression, Kunder et a. [1] proposed the k n T watermarking to reduce the noe competey, but where AP the transpose of matrix A, f Bp B(i, and significant information may be ignored by the f Bq B(i, are the DCT coefficients of the bock p and q, constant quantization. According to the above respectivey, and B B Bi random bias. f B Bp f Bq Bare reasoning, an adaptive quantization mode seected at the same frequency in different incorporating the eigenvaue of the rea symmetric non-overap bock. The vaues of seected bock p matrix as the quantization tabe. The adaptive and q are cose and wi be served as a secret key. k quantization tabe determined according to the the dimension of the matrix. The experimenta significance of the host image. If the watermarked resuts wi not ocate off the origina point since the image atered with maicious tampering, The random bias B B Bi added to the f B Bp f B Bq [4]. watermarking method robust, since the The argest eigenvaues are caed dominant quantization tabe wi change according to the eigenvaues and their corresponding eigenvectors maicious tampered image. are caed dominant eigenvectors. The dominant The watermark-based embedding function eigenvector with the main direction ocated in the DCTBDC_VaueB and the signature based embedding first quadrant and the rest eigenvectors are ocated in function DCTBAC_VaueB are given in Eq.(9) and the four quadrant. λ and its corresponding dominant Eq.(10), respectivey. W a binary sequence. The r eigenvector of the rea symmetric matrix R wi be checked to embed one bit at the pair of bocks. If r, evauated. Then we cacuate. For eigenvector [c, defined in Eq.(11), equa to the watermark T d]p P, the direction θ of the dominant eigenvector sequence W, the DCT coefficient remain defined by unchanged. On the other hand, the DCT coefficient wi be represented by Eq.(9) and Eq.(10) θ = tan 1 ( c d ) o where 0 θ 90. o DCT DCT ' DC. Vaue ' AC, Vaue 0 r = 1 ( λ 1) λ, if r W and λ 0 = ( λ + 1) λ, if r W and λ < 0 ( v 1) i, if r 0, r 1 and v 0 = ( v + 1) i, if r 0,r 1 and v < 0, if, if even odd (7) (9) (10) (11) The watermark 0 or 1 dependent on the decion of parameter r for the signature-based embedding function. The vaue of parameter r defined as foows. The vaue of signature bit compared with the watermarks at the procedure of the signature-based

4 Proceedings of the 5th WSEAS Internationa Conference on Signa Processing, Istanbu, Turkey, May 27-29, 2006 (pp70-75) embedding system. If they are different, the embedding system described by (9) and (10). The embedding agorithm approached as foows. a. The origina image transformed by the 8x8 bock DCT. b. We use Eq.(9) to embed watermark (W). c. We determine the corresponding signature bits of θ and embed the signature bits of θ by Eq.(10). d. Through the IDCT, we can obtain the watermarked image. The procedures of watermarks and signature bits extractions are simiar as the embedding method. The vaue of r, defined in Eq.(10), shoud be equa to the vaue of the watermark sequence W and signature bit θ from the watermarked image without any attacks. We embed the watermark to DC part and embed the signature bits, generating by the direction θ of eigenvector to the AC part. Even that θ changed, the embedding signature bits wi not be changed. If we change eigenvaue λ, the extracted watermarked image wi be changed. Thus we can detect maicious tampering of image even the image have aso been incidentay dtorted. 5. Experimenta resuts We use the Lenna, Baboon, Pepper and a natura image as the test images in our experiments with 256 * 256 pixes. And the size of digita watermark 32x32 pixes and the watermark a binary sequence in 0 s and 1 s. We embed the watermark with the mask of 8*8 pixes. The MRZT method proposed to achieve the rotation and scaing invariance and the robustness for maicious or innocuous attack simutaneousy. The framework suitabe for a kinds of watermark system. Tabe.1 shows the estimating anges when the watermarked image under quite genera kinds of manipuation with 30 degree rotating. The estimation process in Zernike transform quite sensitive to image manipuation and the error of the estimating rotation degree huge. And the estimating rotation degree by the proposed muti-ring Zernike moment method more accurate than the norma Zernike transform. During data transmsion, more than one maicious attack usua occurs. However, recenty proposed watermarking systems with geometrica invariance can not resove th probem. The MRZT method with simpe and ess computation can rest doube attacks and have the property of geometric invariance. The conception of muti-ring framework and candidate seection process reduce the accumuation of the attacked coefficients in the Zernike transform and avoid maiciousy attacked components. Fig. 1 shows the resut of digita watermarking on Lenna image by the proposed watermark embedding system. The PSNR vaue of watermarked image given in Tabe 2. Tabe.3 tabuates the bit error rate of the watermarked image compression with JPEG. We can extract the whoe watermarks when JPEG quaity 70. Some bit errors wi occur under the JPEG quaity beow 60. In Tabe.5, the vaue of PSNR given by Lin s method simiar to ours, and it s difficut to dtinguh between the two methods with subjective human eyes. But in Tabe.5, it obivious that the bit error rate of the watermark detecting using our method ess than the Lin s one. In the simuations of image authentication, we take two experiments in our simuations. One simuation gives the image authentication of the artificia manipuations. And the other one the image processing manipuations. We present the efficiency of authentication with some quite genera kinds of image processing manipuations as foows. (A). Deete (B). Deete Background textures (C). Add a ine drawing (D). Deete (E). Paste another contents (F). Desaturate (G). Change Hue (H). Deete (I). Move (J). Repace by computer generated texts (K). Deete ight coored contents (L). Add Foot (M). Skew (N). Copy The authenticated resuts for image processing manipuations are shown in Fig.2. Fig.2(a) the natura image with the fragie watermarks, and the modified image by the manipuations shown in Fig.2(b). The abes in the modified image, Fig.2(b), mark the manipuations mentioned at the above section. Fig2(c) the simuated image of image authentication with the proposed image, and Fig.2(d) the simuated image of image authentication using Lin s method. (a) Fig.1 (a) Origina Lenna image. (b) Watermarked Lenna image. (b)

5 Proceedings of the 5th WSEAS Internationa Conference on Signa Processing, Istanbu, Turkey, May 27-29, 2006 (pp70-75) Tabe.1 The estimating ange by Zernike transform and proposed muti-ring Zernike transform. Zernike Transform Muti-Ring Zernike Transform Estimating ange ( degree ) Noe JPEG Pinch Burring Sharpening Mosaic Twir Tabe.2 PSNR vaue with different dimension of the rea symmetric matrix. PSNR Lenna Baboon Peppers 2x x Fig2 (a) Watermarked natura image. (b) Modified natura image. (c) Modified areas are detected by proposed method. (d) Modified areas are detected by Lin [3] method. Tabe. 3 Bit error rate of the watermarked image under different quaity of JPEG compression. JPEG uaity Lenna Baboon Peppers Tabe.4 PSNR vaue of watermarked image. PSNR Lenna Baboon Peppers Proposed method Lin [3] method Concusion In th paper, we successfuy put forward a semi-fragie digita watermark based on the eigvenvectors and eigenvaues of rea symmetric matrix. The muti-ring Zernike moment proposed to be robust to the geometric dtortions with maicious attacks. The experimenta resuts show that th agorithm can rest high quaity JPEG compression, avoid the maicious attacks and detect the maicious tampering correcty. In the proposed method, we can choose a good resut for bit error rate after the JPEG compression robustness and maicious tampering detection. References: [1] Deepa Kundur and Dimitrios Hatzinakos, Digita Watermarking for Tetae Tamper Proofing and Authentication, Proceedings of IEEE, Vo. 87, No.7, 1999, pp [2] Eugene T.Lin and Edward J.Dep, A Review of Fragie Image Watermarks, Proceedings of the Mutimedia and Security Workshop, 1999, pp [3] C.-Y. Lin and S.-F. Chang, Semi-fragie watermarking for authenticating JPEG vua content, Proceeding of the SPIE, Security and Watermarking of Mutimedia Contents, 2000, pp [4] K. Maeno,. Sun, S-F Chang, M. Suto, New Semi-fragie Image Authentication Watermarking Techniques Using Random Bias and Non-Uniform uantization, Proceeding of the SPIE, Security and Watermarking of Mutimedia Contents, 2002, pp [5]Yuichi Nakai, Mutivaued Semi Fragie Watermarking Proceeding of the SPIE, Security and Watermarking of Mutimedia Contents, 2002, pp [6] C.S. Lu, L.Y. Liao, Mutipurpose watermarking for image authentication and protection IEEE Trans. on image Processing, Vo. 10, 2001, pp [7]. Sun, S.-F. Chang, K. Maeno and M. Suto, A new semi-fragie imageauthentication framework combining ECC and PKI infrastructures,

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