Chaos Based Spread Spectrum Watermarking algorithm Kais Feltekh Laboratoire SysCom, Ecole Nationale d Ingenieurs de Tunis Email: kais.feltekh@gmail.com Zouhair Ben Jemaa Laboratoire SysCom, Ecole Nationale d Ingenieurs de Tunis Email: zouhair.benjemaa@enit.rnu.tn Abstract This paper presents a blind spread spectrum watermarking algorithm in discret cosine transform (DCT) domain based on chaotic sequence features for still image. We used logistic map with two secret keys; one to generate a spread spectrum sequence and other to determinate the secret insertion positions of the mark; the insertion of the mark was done in the middle frequency of DCT of the image to be watermarked. This allowed to have a compromise between invisibility and robustness against scaling, rotation and cropping attacks. Index Terms Watermark, spread spectrum, Chaos, Attacks. I. INTRODUCTION Digital watermarking operation aims to embed many kinds of digital information into multimedia data (such as image, sound and video.); this allows multimedia identification and information copyright protection. As a technology of information hiding, digital watermarking targets to allow three main properties: invisibility, robustness and capacity. In recent years, to achieve these targets several watermarking algorithms have been proposed [3], [4], [5]. The results enabled by these algorithms have shown that the invisibility and robustness are often contradictory and improvement of one causes the degradation of the other. A compromise between the two became the target of proposed algorithms. As a result, many watermarking algorithms based on DCT was proposed in the few last years [2], [7], [8], [10]. Especially, Cox and al [9] and F. Hartung and al [1] proposed many works on digital watermarking based on spread spectrum schema which aims to spread the mark in almost all the spectrum band of the image. R.Munir and al [2] proposed a new spread spectrum watermarking algorithm based on the properties of chaotic sequences generated by non linear maps. The algorithm proposed in this work is based on the algorithm of R. Munir in which we made two modifications, the first is to put the watermark in the middle band of the spectrum in the aim to improve the invisibility of the watermark; the second is to do the DCT on blocks of 8 8 pixels instead of the entire image. We used a chaotic map to produce two pseudo-random sequences one to spread the spectrum of the watermark and the other to determinate the positions of the watermark in the set of DCT components. This paper is organized as follows. In section II, we will give a little idea on chaos and the motivation of using it in various applications. In section III, we will describe the algorithm proposed by Rinaldi Munir. In section IV, we will present the proposed method. After that, we will present the experimental results; and we will finish by a conclusion. II. CHAOS AND RANDOMNESS Chaos has many features that make it attractive for searchers in various fields, indeed all these features can be summarized by saying that chaos is a deterministic phenomena having almost all the features of a noise. Another feature of chaos is sensitivity to initial conditions; i.e two infinitesimal close initial conditions of a chaotic system give two solutions completely uncorrelated. Motivated by these features, chaotic systems have been used as a pseudo-random generator, this means a finite number of noise-like, deterministic and reproducible sequences can be generated [5]. One of the simplest chaotic systems is defined by the logistic map, described by x k+1 = λ.x k (1 x k ) (1) where 0 λ 4. For λ = 4, the map is in the chaotic state and for almost all initial condition x 0, the sequence generated by (1) is a pseudo-random sequence, in fig.1 we plotted the histogram of one of the sequences of length N = 10000. The generated real number sequence is quantized, a binary sequence s(n) {0, 1} is produced with approximately equal number of 1 s and 0 s. In our scheme, we use logistic map twice, one to spread the spectrum of the mark to be embedded and other to determine the positions among the DCT coefficients where the mark will be embedded. III. SPREAD SPECTRUM WATERMARKING WITH CHAOTIC MAP In this section we will describe the algorithm proposed in [2] and in which we introduced two modifications to improve its performance. The basic idea of this algorithm is to add a pseudo-random signal to the image as a watermark that is below the threshold of perception and that cannot be identified and thus removed without knowledge of the parameters of the watermarking algorithm [2]. The embedding and extracting algorithms are described bellow.
(generally K 1 K 2 ). Then the real value elements of this sequence is converted into integers by multiplying each element by NM then rounding it to the nearest integer, N M is the dimension of the image to be embedded. 5) The spread spectrum watermark is embedded into V, except DC component, on secret positions specified at step 4. The spread bit b i is modulated by the binary pseudo-noise sequence S 1 and the results are amplified with a watermarking strength factor α, to form the spread spectrum watermark w i = α.b i.p i (3) The watermark w i is added to image V = v i yielding a watermarked image Fig. 1. Histogram of a sequence generated by the logistic map. A. Embedding Scheme The embedding schema is described in fig.iii-a. ˆv i = v i + w i (4) 6) Finally, the inverse DCT is applied to reconstruct the watermarked image. B. Watermark Extracting Algorithm The extracting schema is described in fig.3. Fig. 2. Watermark embedding. 1) The DCT of the original image is computed; the coefficients of this transform is saved into a vector V. 2) The watermark A is spread by a factor cr to obtain a sequence B using equation (2) ; L is the length of B. B = {b i /b i = a j, j.cr i < (j + 1).cr} (2) 3) The first chaotic sequence S 1 is generate by using the logistic map and an initial condition x 0 = K 1 ; the length of this sequence is equal to L. 4) Next, secret positions for embedding watermark are defined; a second chaotic sequence S 2 is generated by using the logistic map and another initial condition K 2 Fig. 3. Extraction of Watermark. 1) The DCT transform of the test image is computed and saved in a vector ˆv i. 2) The same sequence P 1 used in embedding process is generated by using logistic map and the secret key K 1. 3) The same sequence P 2 corresponding to secret positions are generated by using logistic map and the secret key K 2. 4) Recover bits of the watermark A by using equation (5). P (i) = { 1 if (j+1).cr 1 i=j.cr p i.ˆv i > 0 1 if (j+1).cr 1 i=j.cr p i.ˆv i < 0 (5)
IV. PROPOSED SCHEME The watermarking algorithm proposed in this work is the result of two modifications introduced on the algorithm described in the previous section; The image is divided into blocs of dimension 8 8 and the DCT is computed for each bloc. the watermark is introduced in the middle band of the spectrum of the blocs. In the Following we describe the embedding and extracting algorithms resulting from these modifications A. Watermark Embedding Algorithm The embedding algorithm is shown in fig.iii-a; it is the same described above with the following differences To insert between the coefficients AC 6 and AC 27, we must have: 6 Y (i) 63 27 (8) Since P 2 takes values in the interval [0, 1] the inequality (8) is verified if { b 63 = 6 (9) (a + b) 63 = 27 From Equation (8) and (9) we find the following system: { b = 6/63 (10) a = 21/63 So Y (i) = 21 63.P 2(i) + 6 (11) 63 Since Y must contain the vector of integers giving the order of location of the mark, then we multiply each element by 63 and then round it to the nearest integer. We must ensure that there are L different positions of embedding. 5) Now we apply the function I.zigzag (Inverse Zigzag) to return to the 8x8 matrix form. Fig. 4. Proposed insertion algorithm. 1) The DCT is computed using 8x8 DCT block transformation. 2) The zigzag transformation is applied to arrange the spectral components in low, medium and high frequency. This will allow to put the watermark in the medium frequency. 3) We set a threshold K to convert elements of sequence (in real value) into binary element (+1/-1), according to the following formula: Fig. 5. Inverse zigzag transform of a vector to 64 coefficients. After the realization of I.Zigzag for each bloc, we must rearrange the blocs to get a single MxN matrix (Fig.6). { 1 P1 (i) > K P (i) = 1 P 1 (i) < K in the following we use the threshold (k=0.5). 4) To insert the watermark in the medium frequency band, we must find a linear transformation of Y values in the desired range. This equation is: (6) Y (i) = a.p 2 (i) + b (7) Fig. 6. Rearrangement of the 8x8 blocs.
We use both equations (3) and (4) to insert the watermark in the spread secret position B specified in the matrix MxN. B. Watermark Extracting Algorithm The extracting algorithm is illustrated in fig.7; it is done following the steps bellow. Where M and M are the matrices corresponding to the original A and the extracted A watermark images. { 1 if A(i, j) = 0 M(i, j) = 1 if A(i, j) = 1 and M (i, j) = { 1 if A (i, j) = 0 1 if A (i, j) = 1 The normalized correlation coefficient (NC) takes values between 0 (random relationship) to 1(perfect relationship). VI. EXPERIMENT RESULTS We used Lena 512 x 512 GIF images with 256 gray levels for our experiments. The watermark is 16 x 32 BMP image. We program the watermarking algorithm above by using MATLAB 7, and then the watermarked image is tested with some typical attacks. We considered intentional geometric attacks e.g.rotation, scaling and cropping. We have chosen K 1 = 0.2 and K 2 = 0.35 to obtain two logistic sequences. We use α = 16 for watermarking strength factor and spreading factor cr = 16. A. Robustness against geometric attacks The experimental results are shown as follows: Fig. 7. Proposed extracting algorithm. 1) We transform the original image in the frequency domain by using 8x8 DCT block transformation, then we apply the zigzag function on all 8x8 DCT blocks. 2) Generate the same chaotic sequence P 1 using the logistic map with the same initial condition K 1. 3) Generate the same secret positions; that we used when inserting watermark; the logistic with the same initial condition K 2. 4) Recover the watermark by using the equation (5). Fig. 8. (a) (b) (a)the original image of Lena. (b) The original binary watermark. V. EVALUATION CRITERIA OF A WATERMARKING SYSTEM The peak signal-to-noise ratio (PSNR) is used to evaluate the similarity between the attacked and the original images. The PSNR is defined by P SNR = 10.log 10 ( MN max X 2 (i,j) i,j [X(i,j) X (i,j)] 2 The normalized correlation coefficient (NC) is another criterion used to evaluate the existence and the quality of the extracted watermark. When we use a watermark image A of dimension N 1 xn 2, it is defined by ) (a) (b) NC = N1 i=1 N1 N2 [M(i,j) M (i,j)] i=1 j=1 N2 N1 N2 j=1 [M(i,j)]2 [M (i,j)] 2 i=1 j=1 Fig. 9. (a) Watermarked Lena with PSNR=42.05dB. (b) The extracted watermark with NC=1.
Fig.8 show the original image and the original watermark; Fig.9 show the watermarked image and the extracted watermark. The PSNR between the original and the watermarked images is 42.05, and we can hardly perceive the change of the original image. Also the extracted watermark is identical to the inserted watermark. TABLE IV COMPARISON WITH RINALDI MUNIR ALGORITHM. TABLE I CROPPING. Table I presents a different locations and percentage of cropping applied to the watermarked Lenna image. We can see that the watermarking algorithm is very robust to cropping attack. The spread spectrum watermark allows us to have more chance to extract the pixels after this type of attacks. TABLE II SCALING THE IMAGE. Table II presents a scaling attack, an image of size 512 x 512 is first scaled to 256 x 256 then the scaled image is opened and resized back to 512 x 512. Table III presents a rotation attack obtained by rotating the watermarked image with low angle then cropping the image to obtain the same size of the original image, the rotation is positive when it is done in the sense of the clock wise. TABLE III ROTATING THE IMAGE. B. Comparison with Rinaldi Munir Algorithm We compare the proposed method with R.munir and al[2] using the Lena image. The watermark consists of 256 bits 1 and 256 bits 0. The results are shown in Table IV; the PSNR of the proposed method is better than those of [2], however it is far better for cropping, scaling and rotation with degree of 0.25, but it is not so good for the rotation attacks with degree greater than 0.75. VII. CONCLUSION In this paper, a spread spectrum watermarking in middle frequency scheme was proposed. This scheme, firstly, use the logistic map to determine the secret position, in the 8 x 8 DCT block coefficients, this secret positions belong to the middle frequency in the aim to improve the invisibility of the watermark without degrading similarity. The extraction of watermark depends on private keys of logistic map used in the embedding algorithm. Simulations confirmed that this scheme has high fidelity and is robust against geometric attacks and geometric transformations. furthermore, the one who don t know the key can t know the position of the watermark embedded in, and the watermark is not easy to be extracted or modified, so this scheme is secure. REFERENCES [1] F. Hartung, and B. Girod, Fast Public-Key Watermarking of Compressed Video, Proceedings of the International Conference on Image Processing,1997. [2] R. Munir and al, Secure Spread Spectrum Watermarking Algorithm Based on Chaotic Map for Still Images, Proceedings of the International Conference on Electrical Engineering and Informatics, Institut Teknologi Bandung, Indonesia June 17-19, 2007. [3] S. H. Wang and Y. P. Lin, Wavelet tree quantization for copyright protection watermarking, IEEE Trans. Image Processing, vol. 13, pp. 154-165, Feb. 2004. [4] B.K.Lien and W.H. Lin, A watermarking method based on maximum distance wavelet tree quantization, In Conf, 2006. [5] E.Li, H.Liang et X.Niu, An integer wavelet based multiple logowatermarking scheme, IEEE, In Proc, 2006. [6] W.H.Lin, Y.R.Wang et S.J.Horng, A Blind Watermarking Scheme Based on Wavelet Tree Quantization, IEEE, In Proc, 2008. [7] Yanling Wang et XiuhuaJi, A New Algorithm For Watermarking Based On DCT and Chaotic Scrambling, IEEE, In Proc, 2009. [8] Zhao Yantao et al, A robust chaos-based DCT-domain watermarking algorithm, IEEE,In Proc, 2008. [9] J. Cox and al, Secure Spread Spectrum Watermarking for Multimedia, IEEE Transactions On Image Processing,VOL. 6, NO. 12, December 1997. [10] A.Briassouli and al, Hidden Messages in Heavy-Tails: DCT-Domain Watermark Detection Using Alpha-Stable Models, IEEE Transaction Multimedia,VOL. 7, NO. 4, August 2005.