A Robust Color Image Watermarking Using Maximum Wavelet-Tree Difference Scheme

A Robust Color Image Watermarking Using Maximum Wavelet-Tree ifference Scheme Chung-Yen Su 1 and Yen-Lin Chen 1 1 epartment of Applied Electronics Technology, National Taiwan Normal University, Taipei, Taiwan, R.O.C Abstract - igital watermarking is a technique for copyright protection. In literature, many watermarking methods for gray images have been presented. Some of them are directly applied to the luminance component of a color image. A previous method applies to the difference between RGB components instead, and shows that the image quality can be improved. In this paper, we present a robust color image watermarking method to further improve the image quality. The proposed method is based on the maximum wavelet-tree difference scheme. Experimental results show the feasibility of the proposed method. Keywords: watermarking, wavelet-tree, robustness, discrete wavelet transform, copyright protection 1 Introduction Nowadays, along with the multimedia technology to flourish, piracy also increases day by day. Therefore, copyright protection is getting more attention. igital watermarking is such a technique, which embeds some information into a given media. In literature, many watermarking methods for gray images have been presented [1]-[6]. Especially, wavelet-tree based watermarking methods have been made great progress. Previous works show that the problem of gray image watermarking is how to quantize the wavelet trees to resist common image attacks, such as filtering, compression, cropping and noise. In [5], Run et al. proposed a more effective watermarking scheme than [1]-[4]. They embedded each watermark bit into the maximum and second maximum coefficients of a wavelet tree. In [6], Al- Otum and Samara presented a scheme to embed a binary watermark into wavelet-tree mutual differences between grouped coefficients of the wavelet-trees. In [7], the gray scale watermark is embedded into all the frequency-subbands of the image in each color component of YCbCr space. In [8][9], a binary watermark is embedded into the Y component while in [10] it is embedded three times separately in the YCbCr components of the image. Since the Y component of a color image is directly modified in these methods [7]-[10], the image quality will be degraded. To solve this problem, Al- Otum and Samara presented a method based on the selection of difference between the RGB components of a color image. In this study, we will present a method to further improve the image quality. The proposed method is mainly based on the maximum wavelet-tree difference scheme. The organization of this study is as follows. Section 2 briefly introduces the previous watermark scheme in. Section 3 describes the proposed method. For completeness, the extraction algorithm is given in Section 4. Section 5 shows the experimental results to demonstrate the effectiveness of the proposed method. Finally, conclusions are given in Section 6. 2 Previous Watermark ding Scheme We briefly introduce the algorithm in as follows. We extract the R, G, and B components from a color RGB image. Then, we decompose each color component into the 4-layer subbands by using the 5/3 discrete wavelet transform (WT). In each layer, the WT produces four subbands. One is the low-pass band (LL) and the other three are the horizontal band (HL), the vertical band (LH), and the diagonal band (HH), respectively. The LL band is further decomposed into the next layer. We combine one coefficient in the LH4 (or HL4, HH4) band and four corresponding coefficients in the LH3 (or HL3, HH3) band and sixteen corresponding coefficients in the LH2 (or HL2, HH2) band to be a wavelettree, as shown in Fig. 1. LL4 HL4 LH4 HH4 LH3 HL3 HH3 HL2 HL1 LH2 HH2 LH1 HH1 LH4 C 4, 1 LH3 LH2 C2, 1 C 2, 2 C 2, 16 Tree C 3,1 C 3,2 C3,3 C 3, 4 C4,1 C 3, 1 C3,4 C 2, 1 C 2, 16 Fig. 1. The wavelet-tree scheme by 4-layer wavelet transform. Next, we shuffle the order of the N-bit watermark with a seed by a pseudorandom number generator. After that, the N trees are formed respectively from R, G and B domains as T R, T G and T B. Let d RG, d GB and d BR denote the differences between corresponding trees in the same layers as

where i and j denote the ith wavelet-tree and the jth coefficient in the ith wavelet-tree, respectively. Here,,. The sum of differences in the corresponding trees in the same layers is calculated by (1) Case 1: if the watermark bit is 1, define the (i) as the maximum value of the ith (i, p). Adjust the (i) if (i) is less than or equal to the positive THR(p) by ( ) ( ) ( ) ( ) (2) ( ) ( ) (6) where RG, GB and BR can be used to construct robust watermark selection scheme. Since there are three sum-of-differences, it is possible to embed a watermark bit into one of them. The choice is depending on the least modification of the wavelet-tree coefficients to represent the watermark bit. We group all the differences into an array by the following order ( ) (3) Otherwise, the corresponding trees are kept intact. That is, Case 2: if watermark bit is 0, define the (i) as the minimum value of the ith (i, p). Adjust the (i) if (i) is greater than or equal the negative THR(p) by ( ( )) ( ( )) (7) where p is a number of 1 to 3, which denotes the choice of RG, GB, and BR, respectively. The mean difference M(p) is computed by ( ( )) ( ( )) To improve the robustness of the watermark, a thresh THR(p) is defined as (4) (5) where α is an embedding factor; is the absolute value function. Next, the embedding algorithm for each watermark bit is as follows. ( ( )) ( ( )) Otherwise, the corresponding trees are kept intact as that in equation (7). After all the watermark bits are embedded, a 4-layer inverse WT is used to generate the watermarked image. Fig. 2 shows the flow chart of the aforementioned watermark embedding scheme. (8)

(i, p) Is "1" embedded? No Min((i, p)) (i) THR(p)? Yes Equation(7) Yes No Max((i, p)) Equation(8) "0" Equation(7) Yes (i) THR(p)? No Equation(6) "0" "1" "1" Fig. 2. The flow chart of the watermark embedding scheme. 3 Proposed Watermark ding Scheme As the algorithm stated in Section 2, the value of (i) may be over adjusted, which leads to degraded image quality. If watermark is 1 (a) (b) If watermark is 0 0 THR p 0 THR ' p For example, the negative (i) in Fig. 3(a) will be adjusted to the positive THR(p) when the watermark bit is 1. Another example is the positive (i) as shown in Fig. 3(c) will be adjusted to the negative THR(p) when the watermark bit is 0. To solve this problem, we modify the equation (3), (5), (6) and (8) and define a positive thresh T. Specifically, we separately use the following four equations (9), (10), (11) and (12) to replace (3), (5), (6) and (8). ( ) where, and p can be the number of 4, 5, and 6 to represent the choice of GR, BG, and RB, respectively. ( ) ( ) where is the maximum value function; is the minimum value function. ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) (9) (10) (11) (c) THR p 0 ( ) ( ) (d) THR ' p Fig. 3. ifferent watermark embedding schemes in ((a) and (c)) and in the proposed scheme ((b) and (d)). 0 ( ) ( ) (12)

The new embedding algorithm for each watermark bit is as follows. Case 1: if the watermark bit is 1, define the (i) as the maximum value of the ith. Adjust the (i) if (i) is less than or equal to the in (10) (see Fig. 3(b)). Case 2: if watermark bit is 0, define the (i) as the minimum value of the ith. Adjust the (i) if (i) is greater than or equal to the in (10) (see Fig. 3(d)). With the proposed method, we not only can reduce the distortion of an image but also can increase the robustness of the embedded watermark. This improvement partly comes from the six sum-of-differences and partly comes from the positive thresh T. It is worth mentioning that the predefined positive thresh T can provide a tradeoff between the strength of the watermark and the quality of the watermarked image. 4 Watermark Extraction We use the same algorithm as that in to extract the watermark. For completeness, we briefly introduce the watermark extraction scheme herein. A watermarked image is decomposed into the 4-layer subbands by using the same WT. Then, we generate, and from the watermarked image and form new (i, p) by using (9). To extract a watermark bit, we use the following equation (16) where and respectively represent the height and width of watermark, and respectively represent the bit value of the original watermark and the extracted watermark. We use 4 color images (see Fig. 4) for the experiment. Each image has the size 512 512 and 24 bits per pixel. In addition, we use two types of watermarks. Both of them have the size 64 48. One is named as, which consists of 2347 white points (watermark bit 1) and 725 black points (watermark bit 0). The other is named as, which consists of 725 white points and 2347 black points... 3. (13) where i is the ith wavelet tree; p is the position selection of the watermark bit from the embedding process. Finally, we reshuffle the order of the N-bit watermark by a pseudorandom number generator with the same seed as that in the watermark embedding process to obtain the binary watermark image. 5 Experimental Results We use the peak-signal to noise ratio (PSNR) and the normalized correlation coefficient (NC) to evaluate the image quality and the robustness of watermark. The PSNR of the color image is defined as below. [ ] where MSE is the mean square error of the watermarked image and is defined as below. [ ] (15) where H and W respectively represent the height and width of the image, and respectively represent the pixel value of the original image and the watermarked image. We define the NC as follows. 4. 5.Watermark N 6. Watermark N Fig. 4. The 4 color images and the two watermarks used in the experiment. Table. 1 PSNR comparison with the thresh. Proposed Image Watermark α PSNR T PSNR 1165 40.0065 160 40.0275 1159 40.0041 160 40.0275 545 40.0097 199 40.0558 558 40.0066 199 40.0558 30 40.2827 156 40.0427 30 40.0294 156 40.0427 26 40.1419 173 40.0220 26 40.3469 173 40.0220 For a fair comparison, we adjust the thresh T of the proposed method and the parameter α of the method in to result in the PSNR values near 40 db. Table 1 tabulates the corresponding values of α and T. Table 2 lists the NC comparison after attacks by Gaussian filters (3 3, 5 5, 7 7), average filters (3 3, 5 5, 7 7), and median filters (3 3, 5 5, 7 7). Table 3 lists the NC comparison after attacks by JPEG compression with the quality factor 10 to 90. Table 4 lists the NC comparison after attacks by the Gaussian noise with the variance 0.005, 0.01, 0.02, and 0.03, and the salt/pepper noise with the density 0.05, 0.1, 0.2 and 0.3.

Through the experiment, we found that the NC values of the proposed method are higher than those of the method in at most of the cases of attacks except that case where the image is attacked by JPEG compression with the quality factor 10. Therefore, the proposed method is more robust than the method in as expected. Note that the NC values of the proposed method for both watermarks are the same. This is because we use the maximum difference of the corresponding trees in the same layers to embed, which results in the chosen position will be the same for both types of watermarks. Table 2. NC comparison for watermarked images by attacks of common signal filters. Image Method W. Null Gauss. 3 3 Gauss. 5 5 Gauss. 7 7 Avg. 3 3 Avg. 5 5 Avg. 7 7 Med. 3 3 Med. 5 5 Med. 7 7 0.9843 0.9866 0.9541 0.9583 0.9944 0.9944 0.9147 0.9215 0.9746 0.9746 0.9651 0.9716 0.9964 0.9964 0.8323 0.8492 0.8958 0.8958 0.7750 0.7832 0.8134 0.8134 0.9498 0.9495 0.9941 0.9941 0.8522 0.8626 0.9111 0.9111 0.7893 0.7945 0.8336 0.8336 0.9967 0.9661 0.9667 0.9742 0.9742 0.9130 0.9140 0.9280 0.9280 0.9778 0.9820 0.9860 0.9860 0.7441 0.7418 0.7500 0.7500 0.6679 0.6595 0.6699 0.6699 0.9541 0.9466 0.9648 0.9648 0.7307 0.7246 0.7382 0.7382 0.6412 0.6455 0.6569 0.6569 0.9990 0.9993 0.9667 0.9736 0.9371 0.9414 0.9986 0.9986 0.9111 0.9130 0.9899 0.9899 0.9446 0.9527 0.8502 0.8430 0.9222 0.9222 0.7805 0.7796 0.8398 0.8398 0.9401 0.9417 0.9977 0.9977 0.8697 0.8746 0.9544 0.9544 0.8138 0.8235 0.8736 0.8736 0.9986 0.9892 0.9895 0.9661 0.9641 0.9804 0.9804 0.9947 0.9928 0.9993 0.9993 0.8841 0.8883 0.9121 0.9121 0.8154 0.8108 0.8313 0.8313 0.9873 0.9905 0.9960 0.9960 0.9088 0.9108 0.9267 0.9267 0.8417 0.8388 0.8554 0.8554 Table 3. NC comparison for watermarked images by attacks of JPEG compression. Image Method W. QF10 QF20 QF30 QF40 QF50 QF60 QF70 QF80 QF90 0.6367 0.6308 0.6738 0.6650 0.7024 0.7109 0.7337 0.7333 0.7314 0.7483 0.7737 0.7737 0.7594 0.7633 0.8001 0.8001 0.7698 0.7799 0.8147 0.8147 0.7799 0.7958 0.8349 0.8349 0.7929 0.8079 0.8466 0.8466 0.8245 0.8268 0.8717 0.8717 0.8362 0.8463 0.8854 0.8854 0.6132 0.6090 0.6129 0.6087 0.6783 0.6699 0.6884 0.6884 0.7125 0.7106 0.7340 0.7340 0.7278 0.7275 0.7587 0.7587 0.7496 0.7522 0.7672 0.7672 0.7701 0.7669 0.7825 0.7825 0.7936 0.7897 0.8056 0.8147 0.8186 0.8186 0.8626 0.8590 0.8847 0.8847 0.6347 0.5732 0.6692 0.5960 0.6940 0.6888 0.7272 0.7265 0.7200 0.7216 0.7721 0.7721 0.7457 0.7535 0.7962 0.7958 0.7760 0.7682 0.8219 0.8219 0.7884 0.7874 0.8522 0.8522 0.7985 0.8144 0.8597 0.8597 0.8092 0.8782 0.8782 0.8359 0.8499 0.9143 0.9143 0.6682 0.6695 0.6930 0.6904 0.7447 0.7460 0.7698 0.7701 0.7711 0.7734 0.8004 0.8004 0.8017 0.7978 0.8209 0.8209 0.8151 0.8229 0.8401 0.8401 0.8206 0.8411 0.8557 0.8557 0.8496 0.8473 0.8707 0.8707 0.8554 0.8652 0.8886 0.8886 0.8916 0.8919 0.9114 0.9114

Table 4. NC comparison for watermarked images by attacks of Gaussian noise and salt/pepper noise. Image Method W. 0.005 0.8365 0.8457 0.9147 0.9241 0.9257 0.9280 0.9433 0.9514 0.8232 0.8173 0.9140 0.9121 0.8964 0.8889 0.9241 0.9306 Gaussian Noise 0.01 0.7972 0.7942 0.8632 0.8583 0.8753 0.8697 0.8994 0.9140 0.7802 0.7877 0.8619 0.8505 0.8395 0.8437 0.8798 0.8671 0.02 0.7347 0.7343 0.7939 0.7952 0.8186 0.7978 0.8444 0.8395 0.7213 0.7197 0.7796 0.7783 0.7675 0.7731 0.8050 0.03 0.7021 0.7041 0.7320 0.7298 0.7597 0.7646 0.8020 0.7968 0.6871 0.7067 0.7428 0.7320 0.7376 0.7408 0.7506 0.7688 ensity 0.05 0.7548 0.7581 0.8154 0.8105 0.8356 0.8238 0.8619 0.8629 0.7317 0.7483 0.8020 0.8089 0.7942 0.7945 0.8261 0.8365 Salt / Noise ensity 0.1 0.6907 0.6783 0.7324 0.7366 0.7558 0.7617 0.7900 0.7848 0.6725 0.6940 0.7252 0.7207 0.7197 0.7086 0.7438 0.7366 ensity 0.2 0.6383 0.6331 0.6591 0.6500 0.6735 0.6604 0.6878 0.6940 0.6191 0.6207 0.6448 0.6481 0.6292 0.6542 0.6650 0.6634 ensity 0.3 0.5833 0.5852 0.6051 0.6113 0.6243 0.6422 0.6292 0.6542 0.5888 0.5878 0.6188 0.5934 0.6116 0.6123 0.6292 0.6282 6 Conclusion In this paper, we proposed a robust watermarking algorithm for color images. The proposed algorithm includes a maximum difference selection of the wavelet-trees and an improved wavelet-tree embedding scheme. In addition, a positive thresh T is also proposed to make a balance between the image quality and the robustness of the watermark. Experimental results show that the proposed algorithm is feasible and it not only can produce higher image quality but also can produce more robust watermark than the previous methods. 7 References [1] S.H. Wang and Y.P. Lin, Wavelet tree quantization for copyright protection watermarking, IEEE Transactions on Image Processing, vol.13, pp. 154-165, 2004. [2] B.K. Lien and W.H. Lin, A watermarking method based on maximum distance wavelet tree quantization, in the Proc. the 19th conference computer vision, graphics and image processing, 2006. [3] W.H. Lin, S.J. Horng, T.W. Kao, P.Z. Fan, C.L. Lee, and Y. Pan, An efficient watermarking method based on significant difference of wavelet coefficient quantization, IEEE Transactions on Multimedia, vol.10, pp. 746-757, 2008. [4] W.H. Lin, Y.R. Wang, and S.J. Horng, A wavelet-treebased watermarking method using distance vector of binary cluster, Expert Systems with Applications, vol.36, pp. 9869-9878, 2009. [5] R.S. Run, S.J. Horng, W.H. Lin, T.W. Kao, and P. Fan, An efficient wavelet-tree-based watermarking method, Expert Systems with Applications, vol.38, pp. 14357-14366, 2011. [6] H. Al-Otum and N. Samara, Adaptive blind waveletbased watermarking technique using tree mutual differences, Journal of Electronic Imaging, vol.15, 043011, 2006. [7] S. Rawat and B. Raman, A new robust watermarking scheme for color images, in the Proc. IEEE 2nd International Advance Computing Conference, pp. 206-209, 2010. [8] Q. Su, X. Liu, and W. Yang, A watermarking algorithm for color image based on YIQ color space and integer wavelet transform, in the Proc. International Conference on Image Analysis and Signal Processing, pp. 70-73, 2009. [9] S. Hongqin and L. Fangliamg, A blind digital watermark technique for color image based on integer wavelet transform, in the Proc. International Conference on Biomedical Engineering and Computer Science, pp. 1-4, 2010. [10] Y. Li, Y. Hao, and C. Wang, A research on the robust digital watermark of color radar images, in the Proc. IEEE International Conference on Information and Automation, pp. 1091-1096, 2010. H. Al-Otum and N. Samara, A robust blinds color image watermarking based on wavelet-tree bit host difference selection, Signal Processing, vol.90, pp. 2498-2512, 2010.