A New Spatial q-log Domain for Image Watermarking

Transcription

1 1 Ta Minh Thanh, 2 Pham Thanh Hiep, 3 Ta Minh Tam 1 Department of Network Security, Le Quy Don Technical University, 100 Hoang Quoc Viet, Cau Giay, Hanoi, Vietnam. taminhjp@gmail.com 2 Le Quy Don Technical University, 100 Hoang Quoc Viet, Cau Giay, Hanoi, Vietnam. phamthanhhiep@gmail.com 3 Satellite digital television Co. Ltd., Viet Nam. tam.ta@vstv.vn Abstract In this paper, we propose a novel watermarking based on the spatial q-log domain. After decomposing the RGB information of the cover image, we apply the q-log transform to obtain the q-log domain frequency. We embed the watermark into the low-frequency of q-svd domain in order to achieve the robustness of watermark. We choose in our method the Quantization Index Modulation (QIM) based watermarking scheme due to its good robustness and blind. In our proposed method, the tradeoff of robustness and quality can be controlled by a predefined quantization coefficient Q of QIM and q parameters of logarithm transform. 1. Introduction 1.1. Overview Keywords: Singular Value (SVs) of Singular Value Decomposition (SVD), q-logarithm SVD (q-svd), Quantization Index Modulation (QIM), Image Watermarking, q and Q parameters, RGB color space. With the advance of computer and network techniques, the internet has become an excellent distribution system for the multimedia products because of its inexpensiveness and efficiency. However, the multimedia products can be easily copied and altered, processed and transmitted which causes serious problems such as unauthorized use and manipulation of digital content. Therefore, the protection of digital content via network has become a great deal of an important research topic in recent years. Digital watermarking is the promising technique, which embeds additional information called digital signature or watermark into the digital content in order to secure it. This watermark information can be extracted later for authentication, copyright protection, traitor detection, etc [1]. In general, digital watermarking methods can be classified into two categories: spatial domain watermarking and transform domain watermarking. In the spatial domain watermarking, watermark information is embedded directly into the components of original content such as RGB information by modifying its value [2]. It has the advantages of low complexity and easy to implement. However, the spatial domain watermarking methods are not robust against the image processing attacks and the geometrical attacks. On the other hand, the transform domain watermarking methods embed the watermark information by adjusting the magnitude of coefficients in a transform domain such as discrete furrier transform (DFT), discrete cosine transform (DCT), discrete wavelet transform (DWT), singular value decomposition (SVD) and so on [3, 4, 5]. These techniques on transform domain seem more robust but rather complicated to compute because of a large quantity of computation and unmeet the requirement on data high accuracy. On the other hand, in the literature, SVD technique provides an efficient way for extracting algebraic features from an image and the stable SVD matrixes feature of image can be easily obtained. Therefore, when image is degraded under several image processing attacks, its singular values (SVs) do not change significantly [6, 7]. This feature of it normally used to embed the users' information into the image without the degradation of image quality. As shown in papers [6, 7], SVD-based image blind watermarking algorithms are proposed. Liu et al. [6] used a single watermark to embed into image, therefore, the watermark may be lost due to some attacks. In paper [7], Zhou et al. also proposed the watermarking method based on SVD domain, however, he needed the singular values or the orthogonal matrices for extracting the watermark. International Journal of Intelligent Information Processing(IJIIP) Volume5, Number1, March

2 1.2. Our contributions In this paper, we first propose the novel spatial q-log domain for RGB component, and then apply the SVD transform on it to obtain the q-logarithm SVD domain (q-svd) for image watermarking. We embed the watermark in the low-frequency of q-svd domain in order to achieve the robustness of watermark. We also choose the Quantization Index Modulation (QIM) based watermarking scheme due to its good robustness and blind. In our proposed method, the tradeoff of robustness and quality can be controlled by parameters Q of QIM and q parameters of logarithm transform. Therefore, by using our method, we can not only improve more the quality of embedded image, but also achieve the robustness of watermark Roadmap The rest of this paper is organized as follows. The proposed novel q-svd domain is described in Section 2 and we will explain why q-svd domain is suitable for our watermarking method. Section 3 describes our proposed watermarking method using QIM on q-svd domain and our simulation results are shown in Section 4. Section 5 concludes our paper. 2. Proposal of q-log domain and q-svd domain Figure 1. q-logarithm value of real variable x for different q parameters Spatial q-logarithm domain (q-log domain) In literature, q-logarithm is the concept of non-extensive statistics which is introduced by Tsallis [8]. This theory generalizes Boltzmann-Gibbs statistics by utilizing the q-exponential function and its inverse, the q-logarithm function. The q-exponential function is defined as the following: and the q-logarithm is defined as: It is easy to understand that these functions asymptotically approach exponential and natural logarithmic functions as q approaches 1. And then it can be seen that log q (x) varies with parameter q approaches log(x) when q is close to 1. Figure 1 shows the values of q-logarithm for real number x according to different q parameters. It can be observed that when x and q parameters are bigger, values 13

3 of q-logarithm function are more stable. Then, we can estimate that the bigger values of x have almost same values on q-logarithm domain. Figure 2. The efficiency of q-svd in image processing. Non-extensive statistics is mainly used for speech recognition [9, 10] and it seems to be very useful on this research area. In our knowledge, q-exponential and its inverse, q-logarithm, are not applied on image processing and watermarking research Proposal of q-svd In general, SVD is used to analyze matrices A that are separated from image. The real matrix A can be decomposed into three matrices A=USV T, where U and V are the orthogonal matrices, UU T =I, VV T = I and S = diag(λ 1, λ 2,...). Here, the singular values λ 1, λ 2,... of matrices A are sorted decreasingly. Note that, the columns of U are called the left singular vectors of A and the columns of V are called the right singular vectors of A. Therefore, the SVD can be formulated as: where r is the rank of matrix A. There are the following advantages when using SVD in digital image processing: (1) the size of the matrices A is not defined beforehand and it can be a square or a rectangle; (2) SVs in a digital image are less affected if general image processing is performed. Based on those properties, SVD can be used for watermarking against geometrical distortions. Inspired by the theory of non-extensive statistics, we propose q-svd to provide a new domain, which is very flexible by randomly choosing q parameter to control the quality of image. We employ the feature of q-exponential and q-logarithm in Eq. (1) and Eq. (1) to construct q-svd for image processing. Suppose an image I of size N N pixels is given. First, I is transformed to q-logarithm as below, where I(i,j) and I q (i, j) represent the pixel and the coefficient at coordinate (i, j) of spatial domain and q-logarithm domain. The matrices A k from I q can be transformed using q-svd as follows, 14

4 where k=1,2,..., M, and M is number of blocks. After performing q-svd, we can adjust the values of {U k, λ 1, V k T } q to control the quality of image. In order to reconstruct the image I', we should apply q-svd again based on the adjusted {U k, λ 1, V k T } q to obtain I' q and perform the q-exponential function, Since q-logarithm domain of image pixels are very stable with almost the same values, the lowfrequency of q-svd domain is considered to be more robust and to be very suitable for image watermarking method based on low-frequency. Therefore, the watermarking based on q-svd can be expected to improve not only the quality of embedded image, but also to remain the robustness of watermark information. Figure 3. The embedding method using q-svd and QIM. In order to show the efficiency of q-svd domain in image processing, we used Lena image to implement SVD, q-svd and compared those results. The comparison results were shown in Figure 2. We extracted 50 coefficients at position (0,0) of each non-overlap size 8 8 block from the original image, the SVD performed image and the q-svd performed images, respectively. We found that we can control the quality of image by controlling the q parameter of q-svd domain and it is clear that even the pixel value changes in RGB domain, the quality of images can be remained very good. According to the Figure 2, when q is larger, the distortion of image is conspicuous. Conversely, when q is smaller, the quality of image is similar to the quality of original image. 3. Watermarking method using q-svd We explain about the proposed watermarking method based on q-svd domain in this section. The detailed steps of those processes are given as follows Watermark embedding algorithm Before embedding, we prepare a logomark W as watermark information and extract a binary sequence bits denoted by w i is in {0,1}, i th bit of watermark. Figure 3 describes the detailed steps in our proposed embedding method. The embedding process is described in following. Step 1. Decompose the component R, G, and B from image I. We adopt the blue information B to implement our proposed method. The reason to choose B component is that human visual system is not sensitive to blue compare to other two chrominance (R and G) components. Transform B component using the q-logarithm to obtain B q. Divide the B q into non-overlapping blocks. Step 2. Perform q-svd, which is described in Sect. 2, on each block (A k matrix) to obtain the SVs ({S k } matrix) of each block. Step 3. Embed the binary sequence {w i } into {S k } by QIM method [11]: where S k (u,v) and S wk (u,v) are coefficients of S k block in q-svd domain at coordinate (u,v) of the original image and the watermarked image, respectively. sgn(.) function is equal to + if S k (u,v)>0, - 15

5 if S k (u,v)<0.. denotes the floor function, and Q denotes the embedding strength chosen to maintain the quality of embedded image. Note that, Q is a predefined quantization coefficient. Step 4. Perform q-svd again to make the watermarked A wk matrices and obtain B' q. Step 5. Apply the q-exponential function for B' q to obtain B'. Include R, G component with B' to reconstruct the watermarked image I'. According to above process, we embed the watermark W into q-svd domain of B component and we can control the quality of embedded image based on two parameters: q parameters for q-svd domain, and Q parameter of QIM for watermark strength. Therefore, our proposed method is more flexible than conventional methods using SVD domain Watermark extraction algorithm The extraction algorithm is very similar to that of watermark embedding algorithm, except for the step of watermark information extraction. Basic steps involved in the watermarking extraction, shown in Figure 4, are given as follows: Figure 4. The extraction method using q-svd and QIM. Step 1. Separate the component R *, G *, and B * from image I *. We extract the blue information B * as the embedding method. Transform B * component using the q-logarithm to obtain B q *. Divide the B q * into non-overlapping blocks having the same size used in the embedding process. Step 2. Perform q-svd on each block (A k * matrix) to obtain the SVs (S wk * matrix) of each block. Step 3. Extract the binary sequence of watermark from S * wk matrices based on the following rule. Step 4. Reconstruct w * i, we can obtain the logomark W *. w * i is reconstructed by using voting method, therefore, W * is the best extracted result and it is expected that it should be robust against some attacks. 4. Simulation results For assessing the performance of the proposed algorithm, we conducted four colors images of SIDBA (Standard Image Data-BAse) database [12]. All these test images are with size pixels. One binary image with bits, were used as watermark in the simulation and it is shown in Figure 5. Figure 5. Watermark image of bits. In order to evaluate the quality of watermarked images, we employ PSNR (Peak Signal to Noise Ratio) criterion. The PSNR of N N pixels of image I(i, j) and I * (i, j) is calculated with, 16

6 where MSE is mean square error. To provide objective judgment of the extracting fidelity, we used the Normalized Correlation (NC) value between the original watermark W and the extracted watermark W *, and NC is calculated as follows, To retain the image quality and provide a stronger robustness of a watermarking method, the coefficient modification based on q and Q parameters is further considered. First, we surveyed the efficiency of q and Q parameters for the visual quality of watermarked image and the robustness of watermark information. We tried with various values of q and Q to find out the appropriate value for those parameters. The experimental results of the color image, Lena, are given in Table I. According to the results shown in Table I, it can be observed that we can control the visual quality of watermarked image and the robustness of watermark information based on q parameter of q-svd domain and the embedding strength Q parameter. When q is with the larger value, PSNR value is more smaller. It means that the visual quality of the embedded image is worse. And when Q is with the larger value, NC value is close to 1. It means that the robustness of watermark is better. Therefore, according to the purpose of watermarking method, we can choose the appropriate q and Q parameters for it. After surveying the results of q and Q parameters, we chose {q=0.4, Q=5.5} and {q=0.5, Q=5.0} to simulate on the experimental images. The simulation results of the color images, Baboon, F16, Lena, and Scene, are given in Figure 6 and Figure 7. According to QIM, it is very clear that when Q is bigger, the robustness of the embedding method can be achieved but the distortion of image is conspicuous. However, with the smaller q value, the quality of the embedded image is improved. Therefore, by controlling the value of q parameter, our method can effectively control the quality of the embedded image. The comparison result of the watermarked image is described in Figure 8. Obviously, our method can be used to improve more the quality of the embedded image comparing with Chang et. al. [13] method. In order to show the robustness of our proposed method against common image processing attacks, we used ImageMagick [14] tool to attack the embedded image with several attacks such as Brightness, 17

7 Rotation with 5 degree, Gamma, Flip and Hue. Figure 9 shows the extracted watermarks that are obtained from the attacked images. From those results, we could confirm the logomark without the original logomark. Therefore, our proposed method is expected to be useful for authentication, copyright protection, traitor detection. Based on the experiments of our proposed method, we found that the idea which employs q-svd domain for image watermarking is useful in order to remain the quality of embedded images and to archive the robust against some common image processing attacks. Figure 6. The watermarked color images (q=0.4, Q=5.5). (a) Baboon, PSNR=46.00, (b) F16, PSNR=52.31, (c) Lena, PSNR=45.60, (d) Scene, PSNR=43.62, (e)~(h) is the different between the original image and the embedded image, respectively. Figure 7. The watermarked color images (q=0.5, Q=5.0). (a) Baboon, PSNR=43.42, (b) F16, PSNR=50.41, (c) Lena, PSNR=41.85, (d) Scene, PSNR=42.18, (e)~(h) is the different between the original image and the embedded image, respectively. 18

8 5. Conclusion Figure 8. The comparison of quality of the embedded image. In this paper, we proposed a novel image watermarking based on q-svd domain, which is not yet proposed for watermarking field before. The watermark is embedded into q-svd domain in order to achieve the robustness of watermark and to remain the quality of embedded image. According to our experimental results, the embedded watermark can successfully survive undergo several image processing attacks. Moreover, because we employed QIM method to watermarking method, the watermark embedding and extracting processes are very simple and the watermark can be extracted without the original image. Beside, the tradeoff of robustness and quality can be controlled by Q parameters of QIM and q parameters of logarithm transform. Simulation results show that the proposed scheme outperforms the earlier works. Therefore, we conclude that our new proposed method is suitable for authentication, copyright protection, traitor detection. In the future work, we will focus on improving more for the robustness of our proposed method under the geometrical attacks including rotation, scaling, translation (RST), cropping, tampering and so on. 6. References [1] F. Y. Shih (eds.), Digital Watermarking and Steganography: Fundamentals and Techniques, Taylor & Francis Group, CRC Press., Inc., Boca Raton, FL, USA, [2] M. M. Yeung, Digital watermarking, Commun. ACM, vol. 41, no. 7, [3] A. Nikolaidis and I. Pitas, Asymptotically optimal detection for additive watermarking in the DCT and DWT domains, IEEE Trans. Image Process., vol. 12, no. 5, pp , May [4] P. Bao and X. Ma, Image adaptive watermarking using wavelet domain singular value decomposition, IEEE Trans. Circuits and Systems for Video Technology, vol. 15, no. 1, pp , [5] R. Liu and T. Tan, An SVD-based watermarking scheme for protecting rightful ownership, IEEE Trans. Multimedia, vol. 4, no. 1, pp , Mar [6] J. Huang, Y.Q. Shi, Y. Shi, Embedding image watermarks in DC components, IEEE Trans. on Circuits and Systems for Video Technology, vol. 10, no. 6, pp , [7] B. Zhou and J. Chen, A Geometric Distortion Resilient Image Watermarking algorithm Based on SVD, Chinese Journal of Image and Graphics, Vol. 9, pp , [8] C. Tsallis, Possible generalization of Boltzmann ÄìGibbs statistics, J.Stat. Phys. vol. 52, pp , [9] H.F. Pardede, K. Shinoda, Generalized-log spectral mean normalization for speech recognition. In: Proc. Interspeech, pp , [10] H. F. Pardede, K. Iwano, K. Shinoda, Feature normalization based on non-extensive statistics for speech recognition, Speech Communication, vol. 55, no. 5, pp ,

9 Figure 9. The robustness of proposed method under some attacks (q=0.4, Q=5.5). [11] B. Chen and G. W. Wornell, Quantization index modulation methods for digital watermarking and information embedding of multimedia, J. VLSI Signal Process. Syst., vol. 27, pp. 7-33, [12] SIDBA images, [13] Chang, C.C, Lin, C.C., Hu, Y.S, An SVD Oriented Watermark Embedding Scheme with High Qualities for the Restored Images, Int. J. Innov. Comput. Inf. Control. vol. 3, no. 2, pp , [14] ImageMagick tool: 20