A new robust watermarking scheme based on PDE decomposition *

A new robust watermarking scheme based on PDE decomposition * Noura Aherrahrou University Sidi Mohamed Ben Abdellah Faculty of Sciences Dhar El mahraz LIIAN, Department of Informatics Fez, Morocco Hamid Tairi University Sidi Mohamed Ben Abdellah Faculty of Sciences Dhar El mahraz LIIAN, Department of Informatics Fez, Morocco Abstract The Discrete Cosine Transform (DCT) based watermarking scheme is a common and popular technique that has been used for long time for image watermarking. This technique is based on embedding watermark information in the middle frequency band of the DCT blocks of the host image. In this work, we aimed to further improve the commonly used DCT based watermarking method by combining the DCT with the PDE (Partial Differential Equation) method, while the PDE is a method based on decomposing an image into its structures, textures, and noise components. To test the robustness of our developed combined method we evaluate the proposed method against Gaussian noise, JPEG compression, Salt&Pepper and Averagefilter. Our experimental results and comparison analysis demonstrated that our method has better performance in terms of invisibility and the robustness of the watermark compared to the traditional DCT based watermarking scheme. Keywords Watermarking, DCT, PDE, structure, texture, noise. I. INTRODUCTION Nowadays, with the rapid growth of network and digital technologies, there are new challenges raised in protecting the digital materials. Data security is one of the main concerns these days. To deal with the issue of data security, the concept of watermarking has been introduced. The idea of watermarking is to embed a secret message (watermark) inside an image to increase the digital data security. Different techniques have been proposed. Watermarking techniques can be categorized in different ways. They can be classified based on the type of watermark being used (the watermark can be a visually recognizable logo or a sequence of random numbers) or on the domain where the watermark is applied (spacial domain or the frequency-domain). The most popular approaches for the image watermarking are the frequency domain approaches. In these schemes, the image is being transformed via some common frequency transform and watermarking is achieved by altering the transform coefficients of the image. The transforms that are usually used are the DCT, DFT and the DWT [6]. The classic and still most popular Transform for image watermarking is that of the Discrete-Cosine-Transform (DCT). The watermark is embedded by modifying the middle frequency coefficients so that the visibility of the image will not be affected [2][3][4][5][6]. Rather than embedding the watermark to the DCT mid frequency coefficients, we propose to combine the DCT with the PDE (Partial Differential Equation) method beforehand to improve the security and robustness further. The proposed watermarking algorithm embed watermark inside each (8x8) Discrete Cosine Transform (DCT) block of the host image, this operation is done based on a secret key. The main idea of these technique is to embed a pseudo random noise sequence W into the middle frequencies (F M ) of the DCT block [2][3][4][5][6]. We can modulate a given DCT block I(x,y) using the equation shown below : { } For each 8x8 block of the image, the DCT for the block is first calculated, in that block, the middle frequency components F M are added to the pseudo random noise sequence W, multiplied by a gain factor k. coefficients in the low and high frequencies are copied over the transformed image unaffected. Each block is then inverse transformed to give us our final watermarked image I w. We define the middle-band frequencies (F M ) of an 8x8 DCT block as shown below in figure1 978-1-4799-0792-2/13/$31.00 2013 IEEE

Fig. 1. Definition of DCT Regions F L is used to denote the lowest frequency components of the block, while F H is used to denote the higher frequency components. The remainder of this paper is organized as follows: Section 2 presents our watermarking scheme based on joint DCT and PDE decomposition; Section 3 discusses and evaluates the proposed approach compared to the traditional method. II. WATERMARKING SCHEME BASED ON JOINT DCT AND PDE MODEL A. PDE decomposition model 1) Presentation Decomposing an image into meaningful components is an important and challenging inverse problem in image processing. In the last few years, different algorithms have been proposed to decompose an image f into various components representing different information in the image. In [1], J.F.Aujol and A.Chambolle propose a decomposition model which splits a grayscale image into three components: the first one, u 1, containing the structure of the image, a second one, v 2, the texture, and the third one, w 3 The decomposition is done by solving the following minimisation: Where: - - - Where J(u) is the total variation related to the extraction of the geometrical component,, are the Legendre-Fenchel transforms 4 of respectively J and B for the 1 BV is the space of bounded variations functions. This space is widely used in image processing because it is a good candidate to modelize structures in images. 2 G is the space of oscillating functions, which contains signals with large oscillations, and thus in particular textures 3 E is a Banach space to model very oscillating patterns. 4 The Legendre-Fenchel transform of F is given by ( ) where stands for L² inner product 5 6 7 extraction of texture and noise components, The bound µ controls the G norm of the oscillating component v, parameter controls the L² norm of the residual f-u-v-w, δ controls the E norm of the w component, and X is the discrete Euclidean space NxN for images of size NxN. To solve (2), J.F.Aujol and A.Chambolle consider the three following problems: v and w being fixed, they search for u as a solution of: ( u and w being fixed, they search for v as solution of: u and v being fixed, they search for w as solution of: J.F.Aujol and A.Chambolle use Chambolle_s projection algorithm [1] to compute the solution of each minimization problem. The solution of (4) is simply given by: The solution of (5) is simply given by: of f And the solution of (6) is given by: of v 2) Algorithm 1. Initialisation of w 2. Iterations 3. Stopping test ( Figure 3 shows an example of PDE decomposition.

(a) (b) (c) (d) Fig. 2. (a) the original Elaine image; (b) the sketch u of the image; (c) the texture content v; (d) the noise w B. Proposed algorithm 1) Watermark Embedding The proposed watermarking algorithm embeds watermark logo information inside each Component obtained after decomposing image using the PDE Model. Where the PDE model is based on decomposing an image into its structural part (u), textural part (v), and noise (w). This operation is done based on a secret key. Watermarked image is obtained by adding all components. The watermark embedding procedure is represented in Figure3, followed by a detailed explanation. Fig. 3. Diagram of watermark embedding method using DCT and PDE model Step1 : Read in the host image Step2 : Decomposing the host image into its structural part (u), textural part (v), and noise (w) Step3 Read in the watermark image and reshape it into a vector of zeros and ones Step4 : Re-formulate the grey-scale watermark image into a vector of zeros and ones. Step5 : Set the gain factor for embedding k Step6 : Segment each component into blocks of 8 x8 Step7 : Apply forward DCT to each of these blocks Step8 : Generate two uncorrelated pseudorandom sequences by a key. One sequence is used to embed the watermark bit 0 (PN_0) and the other sequence is used to embed the watermark bit 1 (PN_1). Number of elements in each of the two pseudorandom sequences must be equal to the number of mid-band elements of the DCTtransformed Step9 : Embed the two pseudorandom sequences, PN_0 and PN_1, with a gain factor k in the DCT coefficients. If we donate X as the matrix of the midband coefficients of the DCT transformed block, then embedding is done as follows: If the watermark bit is 0 then X =X+k* PN_0 If the watermark bit is 1 then X = X + k * PN_1 Step10 : Perform inverse DCT (IDCT) on each block to produce the watermarked component. Step11 : Watermarked image is obtained by adding all the watermarked components. 2) Watermark Extraction The watermark information can be extracted by the following steps: Step1 : Read in the watermarked image Step2 : Decomposing the watermarked image into its structural part (watermarked_u), textural part (watermarked_v), and noise (watermarked_w). Step3 : Segment the each component into blocks of 8 x8. Step4 : Perform DCT on each block. Step5 : Extract the middle band coefficients from each block. Step6 : Regenerate the two pseudorandom sequences (PN_0 and PN_1) using the same key which used in the watermark embedding procedure. Step7 : For each block calculate the correlation between the mid-band coefficients and the two generated pseudorandom sequences (PN_0 and PN_1). If the correlation with the PN_0 was higher than the correlation with PN_1, then the extracted watermark bit is considered 0, otherwise the extracted watermark is considered 1.

Step8 : The watermark is reconstructed using the extracted watermark bits, and compute the similarity between the original and extracted watermarks. Therefore, the block diagram of the extraction process is shown in Figure 4. of the watermark. For the imperceptible capability, a quantitative index, Peek Signal-to-Noise Ratio (PSNR), is employed to evaluate the difference between an original image I and a watermarked image Iw. Generally, if PSNR value is greater than 35 db, the watermarked image is within acceptable degradation levels, the watermark is almost invisible to human visual system. The effectiveness of the proposed watermarking technique for embedding is evaluated by the metric called Peek Signal-to- Noise Ratio (PSNR). Table I shows the PSNR values in attack free case for different images between an original image I and the watermarked Iw as well as between each component obtained after decomposing original image using PDE method and the corresponding watermarked. u&watermarked_u v&watermarked_v w&watermarked_w I &Iw Elaine 51.36 68.27 69.75 53.67 Lena 50.60 69.22 71.30 52.34 Peppers 71.67 73.11 75.15 67.83 TABLE I. PSNR BETWEEN THE ORIGINAL IMAGE AND THE WATERMARKED IMAGE. Fig. 4. Diagram of watermark detection method using DCT and PDE model III. RESULTS AND DISCUSSIONS In this section the results of our study are shown. Several experiments are done to evaluate the effectiveness of the presented watermarking algorithm. In this experiment, a 64x64 binary image, as shown in Figure 5(a) is taken as the watermark of images. Additionally, figure5 (b)-(d) display three 512x512 examined images. The PSNR values in Table I show that our proposed method is imperceptible (PSNR>35 db in each case). The PSNR value between the noise component (w) and the corresponding watermarked (watermarked_w) has the greatest value for the PSNR values. Thus, the noise component is the best part of an image to insert the watermark. 2) Detection The effectiveness of the proposed watermarking technique for extraction of watermark image is evaluated by measuring the correlation between the original watermark and the corresponding extracted watermark. Normalized correlation (NC) in Table II is between original watermark and extracted watermark. u & watermarked_u v & watermarked_v w & watermarked_w I & Iw (a) Elaine 0.29 0.98 1 1 Lena 0.42 0.98 1 1 Peppers 0.38 0.99 1 1 (b) (c) (d) Fig. 5. (a) The original watermark; (b) The original Elaine image; (c) The original Lena image; (d) The original Peppers image A. Image Watermarking scheme based on joint DCT and PDE Decomposition Model 1) Embedding The performance of the watermarking method under consideration is investigated by measuring the imperceptibility TABLE II. CORRELATION BETWEEN THE ORIGINAL WATERMARK AND THE CORRESPONDING EXTRACTED WATERMARK. As shown in Table II the method display good recovered watermark. Note particularly that extraction of the watermark from the watermarked noise component (watermarked_w) is done without any problem. B. Comparative Analysis 1) Robustness in Attacks free case The watermarking performance of the proposed method is compared with that of the traditional method (Based on DCT only). Besides the quantitative results in terms of the PSNR and correlation, experiments also provide visual comparison results.

Table III shows the comparison between Traditional method based on DCT only and our proposed algorithm. It is presented in terms of Peak Signal to- Noise Ratio (PSNR) and correlation between original watermark and recovered watermark for different values of k (gain factor). As can be seen from Table III, the quality of watermarked images degrades as the value of k increases. Note particularly that the value of PSNR degrades at higher k values. Without any Attacks, our technique is imperceptible and show good recovered watermark. TABLE IV. COMPARISON BETWEEN THE DIFFERENT ALGORITHMS IN ATTACK CASE. TABLE III. COMPARISON BETWEEN THE DIFFERENT ALGORITHMS IN ATTACK FREE CASE. 2) Robustness against attacks In this section, we evaluate the proposed method against Gaussian noise, JPEG compression, Salt and Pepper noises, etc. The simulation results are listed in Table IV. The performance of the proposed technique is evaluated by measuring the similarity (correlation) of the extracted watermark to the original one. In Table IV, V refers to the variance and Q refers to the quality factor. All the experiments presented in this part were carried out on the Lena image (512x512 pixels) shown in figure 6(c). IV. CONCLUSION We have presented a new robust digital image watermarking scheme based on joint DCT transform and an image decomposition model. Our scheme is shown to be resistant against several signal processing techniques, including Average filter, noise, and JPEG compression. Furthermore, we show that our algorithm lead to better performance in terms of invisibility of the watermark compared with classical and state of the art watermarking methods. REFERENCES [1] J.F. Aujol and A. Chambolle. "Dual norms and image decomposition models", International Journal of Computer Vision, 63(1): 85-104, 2005. [2] Shoemaker, C., "Hidden bits: A survey of techniques for digital watermarking", Independent study, EER 290, spring 2002. [3] Tribhuwan Kumar Tewari, Vikas Saxena, "An Improved and Robust DCT based Digital Image Watermarking Scheme", International Journal of Computer Applications IJCA 3.1 (2010). [4] S.Mansoori, AlaviKunhu, "Robust Watermarking Technique based on DCT to Protect the Ownership of DubaiSat-1 Images against Attacks", IJCSNS, VOL.12 No.6, June 2012. [5] Kaur, Blossom, Amandeep Kaur, and Jasdeep Singh. "Steganographic Approach for Hiding Image in DCT Domain." International Journal of Advances in Engineering & Technology 1 (2011): 72-78. [6] Bekkouche, S., and A. Chouarfia. "A New Watermarking Approach Combined RW/CDMA in Spatial and Frequency Domain." International Journal of Computer Science and Telecommunications 2.4 (2011): 1-8.