ROBUSTNESS TESTING OF SOME WATERMARKING METHODS USING IDCT-II G. Petrosyan 1, H. Sarukhanyan 1, S.Agaian 2, J. Astola 3

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1 ROBUSTNESS TESTING OF SOME WATERMARKING METHODS USING I G. Petrosyan 1, H. Sarukhanyan 1, S.Agaian 2, J. Astola 3 Institute for Informatics and Automation Problems of NAS Armenia, 1 P.Sevak 1, Yerevan, Armenia, spl,hakop@ipia.sci.am 2 University of Texas at San Antonio, Tufts University, Medford, MA, sagaian@utsa.edu 3 Tampere International Center for Signal Processing, Tampere University of Technology, P.O.Box 553, FIN Tampere, FINLAND, jta@cs.tut.fi ABSTRACT The article presents the application of an integer discrete cosine transform of type two (I) in invisible watermarking area and the approach of factorization with sparse and integer lifting matrices, that allow to cut down the number of operations and avoid using numbers with a floating point. The experiments show that IDCT using integer arithmetic, almost does not lack quality to classic and by the time of processing, exceed it. The paper also presents three methods of insertion watermark into image with I. So the main goal of this paper is to test the I in watermarking area taking into consideration that is faster transform than classic. 1. INTRODUCTION Digital watermarking is defined as a process of embedding data (watermark) into a multimedia object to help to protect the owner's right to that object. The embedded data may be either visible or invisible. In visible watermarking of images, a secondary image (the watermark) is embedded in a primary (host) image such that watermark is intentionally perceptible to a human observer whereas in the case of invisible watermarking the embedded data is not perceptible, but may be extracted/detected by a computer program. Information can be hidden by different ways in images. To hide information, straight message insertion may encode every bit of information in the image or selectively embed the message in noisy areas that draw less attention those areas where there is a great deal of natural color variation. The message may also be scattered randomly throughout the image. A number of ways exist to hide information in digital images. Common approaches include Least significant bit insertion, Masking and filtering, Algorithms and transformations. Each of these techniques can be applied, with varying degrees of success, to different image files. A large number of watermarking algorithms work with some form of unitary transformation of the image of interest, as for example the Discrete Wavelet, or Discrete Fourier, or Discrete Cosine Transform (DWT, DFT, and DCT). This is because transform domain techniques offer various advantages. For example, by modifying only the spatial frequency bands human beings are not very sensitive to, a watermark embedded in an image can be less visible. Some of the desired characteristics of visible watermarks are listed below [1, 2]. - The watermark should be visible yet must not significantly obscure the image details beneath it. - The watermark must be difficult to remove; removing a watermark should be more costly and labor intensive than purchasing the image from the owner. - The information carried by the watermark is robust to content manipulations, compression, and soon. - The watermark should be applied automatically with little human intervention and labor. In this paper we consider three methods for embedding watermark image into an original image by using IDCT. Test for robustness also has been done with IDCT related to JPEG compression and as well as to white noise. 2. and I The DCT- II matrix of order N is defined as follows [3] C where II N = 2 N k m 1, if m 0, k m =, = 0. 1 if 2 m. cos m( 2n + 1) π 2N N 1 m,n= 0 For N = 8 matrix represents as c3 c5 c5 c 2 1 c3 c5 c5 =, C8 II c5 c3 c5 c 6 c5 c3 c5 kπ where c k = 2Cos. 16,

2 Note that, all the rows of matrix, except the first row, are mirror reflections of the right part of the row with negative or positive sign. The matrix can be factorized into multipliers so, that it combines the rows with positive mirror reflection into one group and the rows with negative mirror reflection of their right parts, into another group. As a result, matrix can be factorized into sparse matrices, and matrices that contain rotations cosσ sinσ R 0 =. sinσ cosσ These formulas are well known in computer graphics area, as they are applied for computation of rotation point for a given angle [6]. This formula can be factorized with lifting matrices [4], that needs only 3 additions and 3 multiplications: R 0 1 = tg σ sinσ 1 1 tg σ 2 After that we can replace lifting matrices with their approximated versions. So we got factorization using sparse matrices and lifting matrices. Lifting matrices, in their turn, were replaced by integer lifting matrices. Using the approximations of lifting matrices, we avoided floating operations, and according to experiments presented in Table 1, integer almost does not lack quality and exceeds in time of processing the classical [5]. Experiments are done for Lena.bmp image for each 8x8 block. In the following table there are presented experimental results for Y component of YCrCb color system and processor ticks for one 8x8 ordered image block. Table 1. Experimental results for and I TRANS. MSE PSNR Comp. Ratio Processor Ticks , (double precision) with MMX , (single precision) I using MMX in frequency domain. Before discuss these methods there is need to say about images used in experiments. Original image that contains watermark is a true color Lena.bmp with size 256x256. In first and second methods watermark image is a true color image which for every color component is shifted right with controlled SH number. In third method watermark is a binary 32x32 ordered image.those three images are presented in Fig. 1. (a) (b) (c) Fig. 1. Test images used in experiments. (a) Lena256x256, (b) Denise256x256, (c) Logo32x32. In the first algorithm it is suggested to lower information of watermark in the source image and those watermark frequency components are saved into the main frequency component of the source image. It is obvious that with 99% compression watermark image is recognizable and doesn t lose appreciably it s quality. Schematic representation of the first method is shown in Fig. 2. Divide original and watermark image into 8x8 ordered blocks. Perform a forward IDCT for each block. Add watermark image frequency component to an original image block principal component. Perform an inverse IDCT for each block. Experiments have been done on the AMD Athlon XP processor. 3. EMBEDDING WATERMARK Digital watermarking is a technique, where an identifier signal is embedded into information carrying signal. The watermark is embedded so, that it does not disturb the information in normal conditions, but can be easily extracted from the signal for source identification.[7] Watermarking techniques are developed in two domains: the spatial domain and the frequency domain [8]. The spatial domain watermarking techniques are usually faster, less memory and computation consuming. The frequency domain watermarks have better perceptual invisibility because human eyes are more sensitive to changes in spatial domain. In this paper we have tested three approaches of watermark insertion. All of them are Fig. 2. First approach of watermark insertion Experimental results of this method are presented in table 2, table 3 and Fig. 3, Fig. 4. Table 2. First method for Jpeg compression Compression Coefficient A (PSNR) B (PSNR) C (PSNR) 50% % % where A is the difference between the original and watermarked images, B is the difference between origi-

3 nal and recovered images and C is the difference between watermarked and transformed images. Transformed image Perform a forward IDCT for each block. Zigzag scan of each block to 64 ordered vector. We can suppose that middle frequency elements are nearly put in the middle of the vector. In the second method we control the inserting of watermark in to the source image by WS (watermarked seek) element that shows the place of watermark in the source image vector as shown in Fig. 5 Fig. 3. Experimental results for 95% Jpeg Compression First method is also tested for white noise and results are shown in table 3 and Fig. 4. Noise is used as follow: I i I i + rand( 0, ϑ), where ϑ -is the random function interval, i = 1,2, K, n, and I i is the i-th pixel of watermarked image. Table3.Experimental results of I method for white noise ϑ A B C ,21 40, , , where A is the difference between the source and watermarked images, B is the difference between the original and recovered watermark and C is the difference between the watermarked and noised image. Noised image Fig. 5. Inserting with controlled shifts Add original and watermark images vectors with controlled shift. Inverse zigzag scan of each vector. Inverse IDCT for each block. Fig. 6. Second approach of watermark insertion Actually, if we want to get more efficient algorithm of recovering watermark image we need to connect watermark components with low frequency components of original image. But in this case, changing low frequency components of original image we can damage image. Experimental results of second method are presented in table 4 and Fig. 7. Transformed image Fig4. Experimental results for ϑ = 10 white noise Since high frequency features do not survive low pass filtering and JPEG compression, and changes in low-frequency are more perceptual for human vision, then it is pricipal to use a middle range coefficients to embed watermark bits. The second method is shown in Fig. 6. It is implemented by the following steps: Divide original and watermark image into 8x8 ordered blocks. Fig. 7. Exp. results for II method. 75% compression

4 Table4. Experimental results of second method for Jpeg compression A B C WS = 15, SH = 3, ZC = WS = 15, SH = 3, ZC = WS = 15, SH = 3, ZC = WS = 32, SH = 3, ZC = First and second methods are called non-blind algorithms Watermarking algorithm is said non-blind if it needs the original data to extract the information contained in the watermark. Conversely, a watermarking algorithm is said blind if it does not resort to the comparison between the original non-marked asset and the marked one to recover the watermark. Early works in digital watermarking insisted that blind algorithms are intrinsically less robust than non-blind ones, since the true data in which the watermark is hidden is not known and must be treated as disturbing noise. However, this is not completely true, since the host asset is known by the encoder and thus it should not be treated as ordinary noise, which is not known either by the encoder or by the decoder [9]. The next algorithm is a blind and it doesn t need source image. In this method we take binary watermark image and the embedding 0 or 1 is done using Even(.) or Odd(.) function, respectively, depending on quantization coefficient. In this case we don t do the simple addition, but we insignificantly change the principal component of the spectral block of initial image according to the watermark image bit. Let the W i be the i -th component of watermark image, and I i be the i -th blocks principal component of original image I i qi Even, if Wi = 1, i = 1,2, K,n, qi I i I i q Odd = = i, if Wi 0, i 1,2, K,n, qi where n is the number of blocks, q i is the i-th component of quantization table, and Even and Odd functions approximate I i to the nearest odd or even integer, respectively. The extraction process is straightforward: I If i is even, then W i = 1, else W i = 0. qi When one knows principles of those algorithms one can easily extract or damage watermark that is why we need to additionally protect the image. Thereby, we connect watermark picture with some key, without which we can t extract the watermark image. Let s assume the watermark be a size image. Depending on the K key we generate a size pseudorandom matrix. We perform the exclusive or (XOR) to watermark image matrix with pseudorandom matrix. During the restoration, we can create the same pseudorandom matrix with the help of K key, and we can obtain the watermark. This algorithm is presented in Fig. 8. Fig. 8: Key depended watermarking Experimental results of the third method are presented in table 5 and Fig. 9. Table 5. Experimental results of the third method for 99% Jpeg compression. A B C ZC = 99% Transformed image Fig. 9. Experimental result for the third method with 99% jpeg compression We use simple watermark embedding methods considering hence fastness and simplicity requirements. To get higher quality of watermark recovery you can perform an analysis of image block and at first define the deepness of embedding and then control it by coefficients as shown in [10]. 4. CONCLUSION All transforms are done for each 8x8 block of images. The original image (Lena.bmp) is true color image, and watermarks (logo32.bmp and Denise.bmp) are grayscale images. In the third method the watermark is a binary image. Experimental results of the first method presented in table 2 and table 3 show that the watermark image influences on source image are a perceptible, but even by 95% compressing we can recognize watermark image. Test for robustness also has been done for white noise.

5 Comparative results with classical are presented in Fig. 10. Experimental results of the second method, which save watermark frequency components in the middle frequency domain, are shown in table 4 and Fig. 7. This algorithm decreases influence on source image, but it is less robust conserning to compression and noise. Comparative results of this method with classical are presented in Fig. 11. The third method has the high robustness concerning to compression, but is non-robust to noise. Experimental results of the third method are presented in table 5, fig. 9 and fig REFERENCES [1] Yeung M.M., et al., "Digital Watermarking for High-Quality Imaging", Proc. of IEEE First Workshop on Multimedia Signal Processing, Princeton, NJ, pp , June [2] Mintzer F., et al., "Effective and Ineffective Digital Watermarks", Proc. of IEEE International Conference on Image Processing ICIP-97, Vol.3, pp. 9-12, [3] Ahmed,Rao. Orthogonal Transforms for Digital Signal Processing. New York [4] Lizhi Cheng, Yonghong Zeng. Fast Multiplierless Approximations of DCT. IEEE Trans. Circuits and Systems-II [5] G.A. Petrosyan, H.G. Sarukhanyan, I And Realization Using MMX Technology, Information Technologies and Management. Number 3, pages [6] David F.Rogers «Procedural Elements for Computer Graphics» MIR (in Russian) [7] Ingemar J. Cox, Matthew L. Miller, Jeffrey A. Bloom Digital Watermarking. Academic Press, 2002 [8] Fabien A. P. Peitcolas, Ross J. Anderson, and Markus G. Kuhn, Information Hiding A Survey, in Proc. Of the IEEE, vol. 87, no.7, Jul.1999, pp [9] Mauro Barni, Franco Bartolini, Watermarking Systems Engineering, Marcel Dekker, Inc., New York Basel, ISBN: [10] Kankanhalli M.S., et al., "Content Based Watermarking for Images", Proc. of 6th ACM International Multimedia Conference, ACM-MM 98, Bristol, UK, pp.61-70, Sep PSNR 4,8 4,7 4,6 4,5 4,4 4,3 4,2 4,1 4 4,68 4,31 First Method 4,68 4,31 50% 75% 95% Compression Coefficient 4,74 4,39 I Fig. 10. Difference between the original and recovered watermark using and I. The first method. Second Method PSNR ,38 9,17 10,3 I ,35 50% 75% 95% Compression Coefficient Fig. 11. Difference between the original and recovered watermark using and I. The second method.

6 PSNR Third Method 48,13 48,13 48,13 50% 75% 95% Comrpession Coefficient I Fig. 12. Difference between the original and recovered watermark using and I.The third method.