A Robust Image Zero-Watermarking Algorithm Based on DWT and PCA

A Robust Image Zero-Watermarking Algorithm Based on DWT and PCA Xiaoxu Leng, Jun Xiao, and Ying Wang Graduate University of Chinese Academy of Sciences, 100049 Beijing, China lengxiaoxu@163.com, {xiaojun,ywang}@gucas.ac.cn Abstract. Zero-watermarking which doesn t modify the original image but constructs zero watermarks from it, is a useful technique for resolving the contradiction between robustness and invisibility. In this paper, a robust image zero-watermarking algorithm that based on Discrete Wavelet Transformation (DWT) and Principal Component Analysis (PCA) is proposed. In the proposed algorithm, the original image is first transformed with DWT, and its LL band is divided into nonoverlapping image blocks with each image block transformed into a vector, and then it performs a PCA on the set of vectors. Finally, it constructs the zero-watermark sequence by judging the positive and negative polarity of the coefficient which has the maximal absolute value in each analyzed vector. The robustness of the proposed algorithm to given image processes is analyzed, and the results show that the proposed algorithm is very robust to conventional signal processing, such as noise, filtering, JPEG compression, and cropping etc. Keywords: Robustness, Arnold, Principal component analysis (PCA), Discrete wavelet transformation (DWT). 1 Introduction With the rapid development of digital multimedia and the Internet, the pirating phenomenon aiming at the digital product is becoming more and more serious. In order to protect the copyright of digital images, the conventional watermarking has to modify them so as to embed watermarks. But this leads to a contradiction between robustness and imperceptibility [1]. To solve this problem, Wen, Sun and Wang proposed the zero-watermarking schema which doesn t embed watermark but constructs zero watermark from the original image [1]; and the zero watermark must be kept in a third party agency, for example, the Intellectual Property Rights (IPR) information database. The most important part of a zero-watermarking algorithm is the image feature detection method. The detected image feature should have properties of stability and otherness, the stability means that the image feature can still be detected after the image is attacked; and the otherness means that different images have different features. Generally, the image feature detected from the original image can be used M. Zhao and J. Sha (Eds.): ICCP 2012, Part II, CCIS 289, pp. 484 492, 2012. Springer-Verlag Berlin Heidelberg 2012

A Robust Image Zero-Watermarking Algorithm Based on DWT and PCA 485 straightforwardly as a zero watermark in copyright protection application, but it cannot reflect information of stakeholders due to its unmeaning bit stream. Some zero-watermarking algorithms use encryption method to embed meaningful information into image features. In recent years, zero-watermarking has gained great development, and many zerowatermarking algorithms have been proposed. For example, Wen constructs zero watermarks on the basis of the high order cumulat [2]; Gao, Luo and Liu construct zero watermarks on the basis of the Most Significant Bit (MSB) of the original image [3]; Wen, Sun and Wang construct zero watermarks on the basis of the low frequency coefficients in DCT domain [1]; Ma and He construct zero watermarks on the basis of the LL band in Discrete Wavelet Transformation (DWT) domain [4]; Hu and Zhu construct zero watermarks on the basis of Principal Component Analysis (PCA) [5]; Ye, Ma and Niu etc. construct zero watermarks on the basis of singular values of the image matrix [6]; Wu and Sun construct zero watermarks on the basis of the image moments [7]. These algorithms have very good performances resisting conventional signal processing, but existing zero-watermarking algorithms use somewhat single methods to detect image features, and the robustness is still can be improved by combination of several methods. In this paper, a new zero-watermarking algorithm is proposed based on the theory of DWT and PCA. The rest of this paper is organized as follows. Section 2 describes the detailed design of the proposed algorithm. Section 3 presents the experimental results. The paper is concluded in section 4. 2 Proposed Algorithm The image zero-watermarking algorithm proposed by Hu and Zhu [5] is one of the most typical algorithms. In the algorithm proposed by [5], the original image is first subdivided block by block and PCA is used to decorrelate the image pixel to obtain the principal components of an image. Then a chaotic sequence is generated based on Renyi mapping and the principal components are thrown into confusion. Finally, the zero watermark sequence is generated by comparing the confused principal components. The robustness of this algorithm depends largely on the magnitude relationship of the confused principal components. Based on the above algorithm, this paper proposes an improved algorithm by introducing DWT and constructing zero watermark sequence in accordance with the positive and negative polarity of the principal components. For the first improvement strategy, PCA is performed on the transform domain instead of the spacial domain, which could improve the performance of the algorithm resisting conventional signal processing. For the second improvement strategy, the positive and negative polarity is more stable than the magnitude relationship of the principal components when the image is attacked. Furthermore, a binary meaningful watermark image is embedded into the image feature with XOR operation and the Arnold scrambling method is used to encrypt the watermark image in the proposed algorithm.

486 X. Leng, J. Xiao, and Y. Wang Fig.1 shows the zero watermark construction diagram of this algorithm, while Fig.2 shows the zero watermark detection diagram of this algorithm. Because the construction procedure and the detection procedure use identical method to extract image features, they both have the same central process. The main difference is that the detection method adds the similarity calculation between the extracted watermark image and the original watermark image. 2.1 Zero Watermark Constructing Method Suppose the original image I is a gray image with size of W H, and choose db1 as the wavelet. Then the zero watermark constructing process can be described as the following six steps. Step 1: pre-process the watermark image W. Scramble the watermark image W with Arnold transformation taking K as the number of scrambling times. The chaotic watermark image is indicated by W. Step 2: extraction of the low frequency components in DWT domain. The original image I is transformed with DWT at level c, and its LL band of level c is indicated by LL. Step 3: block LL. Divide LL into nonoverlapping blocks with size of s s. Convert each block into column vectors X count = ( W /4 s) ( H /4 s). The matrix m n vectors, where m= s sand n count =, as shown in (1). X = x1, x2,, xn x, where i 1,..., count i = and is constituted by the set of these (1) 2 Step 4: construct the covariance matrix C x. Calculate the covariance pq between row vectors X p and X q of matrix X according to (2), then construct Cx according to (3). 2 1 T σ pq X p Xq = (2) n 1 σ C x 2 2 2 σ11 σ12 σ 1n 2 2 2 σ21 σ22 σ2n = 2 2 2 σm1 σm2 σmn (3)

A Robust Image Zero-Watermarking Algorithm Based on DWT and PCA 487 Step 5: diagonalize the covariance matrix C x, and then get the eigenvectorv and the eigenvalue D. According to the magnitude of diagonal elements, sort D in descending order, and at the same time transform synchronously the corresponding eigenvectorv into P. Step 6: construct the zero watermark sequence EW. Generate the matrix Y according to (4). Then the image feature C is produced by (5). Finally, utilize XOR operation to embedw in C, and get the zero watermark EW which is kept in the IPR information database. Y = ( PX) T (4) 1, Y = > 0, = i1 ci i 1,2,..., n 0, Yi 1 0 (5) K Fig. 1. The zero watermark constructing diagram 2.2 Zero Watermark Detecting Method The zero watermark detecting method is similar with the constructing method. For the convenience of description, P is used to represent the image to be authenticated with the same size as I. The detecting process can be described as the following four steps. Step 1: image feature extraction. According to the 2-6 steps in the constructing P process, extract the image feature C from P.

488 X. Leng, J. Xiao, and Y. Wang Step 2: extract the watermark sequence DW. Generate the chaotic watermark P image DW by performing XOR operation on C and EW fetched from the IPR database. And then extract DW from DW with Arnold transformation according to K. Step 3: calculate the similarity degree between DW and W. Since the original watermark and the extracted watermark are both binary sequences, calculating the bit error rate is a simple and effective way to measure robustness. Define BER = A / B, where A indicates the number of different elements between them, and B indicates the total number of elements. Step 4: given a watermark detection threshold T, if BER < T, then there is watermark in the detected image, otherwise there isn t. According to the above detection procedure, the proposed algorithm does not require the inverse transformation of DWT and PCA, thus avoids the numerical errors while converting. K N Y Fig. 2. The zero watermark detecting diagram

A Robust Image Zero-Watermarking Algorithm Based on DWT and PCA 489 3 Experimental Results Since the robustness to given processes and attacks is a crucial issue in the design of zero-watermarking algorithms, the validity of the proposed algorithm is studied in this section. In the experiments, BER is used to measure the robustness, and the thresholdt is set to be 0.4. The 8-bit gray scale image Lena is used as the original image, the size of which is 256 256. The level of DWT is set to be 2, and the size of blocks is set to be 2 2. According to the above parameters, the original image can generate a binary sequence of 1024 bits. A binary image with size of 32 32 is used as the meaningful watermark image. Fig. 3 (a) shows the original image; Fig.3 (b) shows the binary watermark image; Fig.3 (c) shows the zero watermark constructed by the proposed algorithm; Fig.3 (d) shows the watermark detected without being attacked, and its BER is 0. (a) The original image (b) The binary watermark image (c) The zero watermark (d) The detected watermark Fig. 3. Results of the availability test Comparative experiments of robustness resisting typical kinds of conventional signal processing between the proposed algorithm and the Hu algorithm [5] are tested. Results are described below.

490 X. Leng, J. Xiao, and Y. Wang (1) Noise Add salt and pepper noise to the original image, with mean 0 and variance from 0.01 to 0.10, 10 testing images in total, from which extract watermarks to test this algorithm s robustness resisting such noise. Fig. 4 shows the comparison of experimental results between the two algorithms. According to the experimental results, the highest BER of the proposed algorithm is lower than 0.04, while the BER of Hu is lower than 0.05, both are lower than the threshold 0.4, and can easily detect the watermarks, but the proposed algorithm has lower bit error rate. Add gaussian noise to the original image, with mean 0 and variance from 0.01 to 0.10, 10 testing images in total, from which extract watermarks to test this algorithm s robustness resisting such noise. Fig. 5 shows the comparison of experimental results between the two algorithms. From the experimental results, the highest BER of this algorithm is lower than 0.07, while the BER of Hu is lower than 0.09, both are lower than the threshold 0.4, and can easily detect the watermarks, but the proposed algorithm has lower bit error rate. Fig. 4. Comparison of two algorithms resisting salt & pepper noise Fig. 5. Comparison of two algorithms resisting gaussian noise (2) Filtering Tab.1 shows the comparison of experimental results between the two algorithms resisting filtering attacks. Under the same attack parameters, the BER of the proposed algorithm is lower than that of Hu, except the first attack.

A Robust Image Zero-Watermarking Algorithm Based on DWT and PCA 491 Table 1. Comparison of two algorithms resisting filtering Filtering types Size of template Proposed algorithm Hu algorithm Mean filtering 3*3 0.0176 0.0176 Mean filtering 5*5 0.0215 0.0293 Median filtering 3*3 0.0049 0.0117 Median filtering 5*5 0.0127 0.0156 (3) Shearing Tab.2 shows the comparison of experimental results between the two algorithms resisting shearing attacks. The BER of the proposed algorithm is a bit higher than that of Hu when the shearing degree is small (cut 1/8), and is smaller when the shearing degree is large (cut 1/4 and 1/2). Table 2. Comparison of two algorithms resisting cropping Shearing degree Proposed algorithm Hu algorithm cut 1/8 of the upper left 0.0762 0.0625 cut 1/4 of the upper left 0.1963 0.2227 cut half of the left 0.2549 0.2871 (4) JPEG Compression Tab.3 shows the comparison of experimental results between the two algorithms resisting JPEG compression, in which the greater the quality factor is, the better the compressed image quality has or vice versa. Both algorithms can extract intact watermarks when the compression quality factor is 75 or 90. When the compression quality factor is reduced to 50, the BER of the proposed algorithm is lower than that of Hu. The proposed algorithm can extract the intact watermark when the compression quality factor drops to 5 while the Hu algorithm cannot. Thus the performance of the proposed algorithm is superior to the Hu algorithm. Table 3. Comparison of two algorithms resisting JPEG compression the quality factor Proposed algorithm Hu algorithm 90 0.0000 0.0000 75 0.0000 0.0000 50 0.0001 0.0020 5 0.0000 0.0605 (5) Translation Tab. 4 shows the comparison of experimental results between the two algorithms resisting translation attacks. This algorithm has robustness of a certain degree

492 X. Leng, J. Xiao, and Y. Wang resisting translation, and its performance is superior to the comparison algorithm under the same attack parameters. Table 4. Comparison of two algorithms resisting translation translation parameters Proposed algorithm Hu algorithm [5 0] 0.1416 0.1660 [0 5] 0.0850 0.1270 [5 5] 0.1797 0.2324 4 Conclusions In this paper, an optimized zero-watermarking algorithm based on DWT and PCA has been presented. The proposed algorithm makes full use of properties of DWT and PCA. Experimental results show that the proposed algorithm can resist typical conventional image attacks, such as noise, filtering, cropping and JPEG compression attacks etc., and has lower BER compared with Hu algorithm in most cases. Namely, the proposed algorithm has very good robustness to conventional image attacks. Acknowledgments. This work is supported by National Natural Science Foundation of China (No. 61003275) and President Fund of GUCAS. References 1. Wen, Q., Sun, T.F., Wang, S.X.: Concept and Application of Zero-Watermark. Acta Electronica Sinica 31(2), 214 216 (2003) 2. Wen, Q.: Research on Robustness and Imperceptibility of Multimedia Digital Watermarking. Jilin University, Jilin (2005) 3. Gao, S.Q., Luo, X.Y., Liu, B., et al.: A Robust Zero-Watermarking Algorithm Based on Chaotic Array. Computer Science 32(9), 76 81 (2005) 4. Ma, J.H., He, J.X.: A Wavelet-Based Method of Zero-Watermark. Journal of Image and Graphics 12(4), 581 585 (2007) 5. Hu, Y.F., Zhu, S.A.: Zero-watermark algorithm based on PCA and chaotic scrambling. Journal of Zhejiang University(Engineering Science) 42(4), 593 597 (2008) 6. Ye, T.Y., Ma, Z.F., Niu, X.X., et al.: A Zero-Watermark Technology with Strong Robustness. Journal of Beijing University of Posts and Telecommunications 33(3), 126 129 (2010) 7. Wang, Z., Sun, Y.: Zero watermarking algorithm based on Zernikemoments. Computer Applications 28(9), 2233 2235 (2008)