Hybrid Image Watermarking Scheme using SVD and PDFB based Contourlet Transform Swanirbhar Majumder1
Monjul Saikia 1
Tirtha Sankar Das2
Subir Kumar Sarkar2
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1
North Eastern Regional Institute of Science and Technology (Deemed University), Arunachal Pradesh, India 2 Jadavpur University, Kolkata, West Bengal, India
Abstract— Copyright protection of intellectual property is a very large and growing business. This is due to the easier availability of all multimedia data with just a click of a mouse, resulting to the increase of piracy. Watermarking is one of the popular methods of authentication to help protect intellectual property rights. Of the various forms of multimedia data image is one of the most popular variant. Here a method of digital image watermarking is presented using singular value decomposition (SVD) which one of the very popular mathematical computation tools. Along with it a lot of transforms have been used earlier like discrete wavelet transform (DWT), DCT, Fourier transform, etc. to provide hybrid techniques. But here an unconventional transform introduced in the middle of this decade, called contourlet transform (CT) has been used. This transform being similar to DWT fits well to provide a robust watermarking scheme along with the SVD. Here the combination of pyramidal and directional filter bank (PDFB) in CT has been used. Keywords—Watermarking, Singular Value Decomposition (SVD), Contourlet Transform, Pyramidal and Directional Filter Bank (PDFB).
I.
INTRODUCTION
The increasing use of Internet has made the duplication of digital media easy. Due to the demands from a national security point of view, preventing the leakage of multimedia information is crucial to the global economy [1]. The copyright industries are experiencing a substantial decline in income and job positions, largely attributed to piracy [2]. One solution for copyright protection and content integrity authentication is digital watermarking technology. This should satisfy mainly two properties. Firstly the quality of original media should not be affected and be visually imperceptible. Secondly it must be robust enough to survive compression and noise that normally effect internet transmission [3]. Singular value decomposition (SVD), is a generalization of the eigen-value decomposition, is used to analyze rectangular matrices (the eigen-value decomposition is defined only for squared matrices). It has been used widely in field of image compression and watermarking either individually or in hybrid form with other popular transforms like discrete cosine transform (DCT), discrete wavelet transform (DWT), and many more. The main idea of the SVD is to decompose a rectangular matrix into three simple matrices (two orthogonal matrices and one diagonal matrix) [4] [5].
Contours are used for wavelet decomposition mainly for embedding and encoding as they are two dimensional linear singularities. This makes them very good for robust digital watermarking. The popular discrete wavelet transform (DWT) is not optimal in this as it is based on tensor product [6][7]. This led to development of several mutiscale directional transforms to capture smooth contours in natural images like contourlet, as it provided different and flexible number of directions at each scale [8]. Another variant of non-redundant contourlet transform known as wavelet-based contourlet transform (WBCT) which has been applied in image watermarking to withstand geometrical and non-geometrical attacks [9] [10]. In this paper, we present a non-blind robust watermarking technique which utilizes the advantages of singular value decomposition and the PDFB based Contourlet transform both [11]. The binary bits of the logo to be watermarked is scrambled in four different ways and embedded into the Eigen value matrix after the SVD vectors for each of the subband blocks in PDFB based Contourlet domain are generated. The complexity and pay load parameters of the system are no doubt high but are so embedded on image characteristics of energy distribution to increase robustness. Results show that the proposed scheme has good visual quality along with its robust characteristics [12]. With respect to the two previous works done in this line last year using the same hybrid combination of SVD and CT here the imperceptibility of the logo has been analyzed in much more detail [13] [14]. The 22 imperceptibility quality metrics presented here are PSNR (Peak Signal to Noise Ratio), UIQI (Universal Image Quality Index), SSIM (Structural Similarity Index Measure), MSSIM (Mean Structural Similarity Index Measure), MD (Maximum Difference), AD (Average Absolute Difference), NAD (Normalized Average Absolute Difference), MSE (Mean Square Error), NMSE (Normalized Mean Square Error), SNR (Signal To Noise Ratio), WSNR (Weighted Signal to Noise Ratio), IF (Image Fidelity), HS (Histogram Similarity), KLD (Kullback Leibler Divergence), LMSE (Laplacian Mean Square Error), SC (Structural Content), PQS (Picture Quality Scale), VSNR (Vertex Signal to Noise Ratio), VIF (Visual Information Fidelity), IFC (Independent Feature Component), NQM (Noise Quality Measure), and VIFP (Visual Information Fidelity Pixel) [15] [16].
II.
PDFB BASED CONTOURLET TRANSFORM
Contourlet transform (CT) has inherent characteristics of directionality and anisotropy, which makes it better than the popular discrete wavelet transform (DWT). The CT used here makes full use of combination with a Pyramidal and a Directional Filter Bank thereby called the pyramidal directional filter bank (PDFB). Here specifically the pyramidal filter and the directional filter both have been taken to be of the ladder structure. Moreover the vector of number of directional filterbank decomposition level at each pyramidal level i.e. from course to finer scale has been taken to be four specifically. The dual set of ladder based filter bank structures help in obtaining sparse expansion of typical images having smooth contours. The point discontinuities are taken care of by the Pyramidal filter bank based on Laplacian, while the linking of these to the liner structures is achieved via the Directional Filter Bank (DFB). As shown in figure 1 the first stage of the PDFB based CT is pyramidal filter bank the output of which is fed in cascade to the directional filter bank.
Figure 3: Single level Pyramidal Reconstruction.
The dual set of ladder based filter bank structures help in obtaining sparse expansion of typical images having smooth contours. The point discontinuities are taken care of by the Pyramidal filter bank based on Laplacian, while the linking of these to the liner structures is achieved via the Directional Filter Bank (DFB). As shown in figure 1 the first stage of the PDFB based CT is pyramidal filter bank the output of which is fed in cascade to the directional filter bank. In the first pyramidal stage for image X(i,j), it is down sampled to generate low pass image labeled to be as XL0(i,j). Here the prediction error is taken as the de-correlated band pass image XH0(i,j) given is equation 1 as the difference of the original image X(i,j) and the predicted image X*L0(i,j). This can be repeated by applying the equation 1 iteratively on XL0(i,j)to get XL1(i,j), XL2(i,j), …. XLN(i,j) as shown in figure 2. Here N represents the pyramidal level number. The reconstruction from the band pass image XH0(i,j) is shown in figure 3. XH0(i,j)= X(i,j)- X*L0(i,j)
(1)
Figure 1: Pyramidal and Directional Filter Bank of Contourlet Transform
The band pass image XH0(i,j) obtained via pyramidal decomposition in the next stage is processed by the directional filter bank (DFB) so that they together form the PDFB of the CT. The DFB is implemented by using k-level binary tree decomposition that leads to 2k sub-bands as in figure 4 to capture high frequency using quincunx filter bank with fan filters [11].
Figure 2: Single level Pyramidal Decomposition.
Figure 4: DFB frequency partitioning for k=3 i.e 2k=8 subbands.
III.
WATERMARKING METHODOLOGY
The 256 x 256 ‘Lena’ image has been used here as the host image and the logo to be watermarked is 32 x 32 and has the initials ‘ECE JU’. Firstly the host image undergoes PDFB based CT. Passing through the pyramidal filter bank produces a low pass image. This image is further passed through the directional filter bank which decomposes for k=4, i.e. 24=16 different frequency partitioning are generated, as in figure 5. The 256x256 host image is hereby decomposed to 16 subband images out of which half are horizontal and rest vertical decompositions. They generate eight 32x128 and eight 128x32 sub band images. These 16 sub band images consisting of the coefficient matrices are grouped in four groups consisting of four coefficient matrices each. The 32x32 logo is scrambled by randomization with four different ‘seeds’ or initiating values to produce 4 different watermarks. It is a similar approach like a PN sequence for imperceptibility of the logo for attacks and detection by individual key which may be later be used for fingerprinting and colluder identification. The 4 groups of 4 coefficient matrices each are taken one at a time and to each group a scrambled logo is added after multiplying it with a particular ‘key’ to reduce the intensity of the scrambled logo. This addition is done after each of the coefficient matrixes, either 32x128 or 128x32 undergoes SVD operation to produce the eigen matrix. They are denoted as SVD11, SVD12, SVD13, and SVD14 for first group and so on for groups 2 and 3, till SVD44 for group 4. In addition the new set of 16 Eigen values deduced are undergone SVD operation again for the second time to generate singular Eigen matrices. These new set of matrices in groups of four are denoted as SVD*11, SVD*12, SVD*13, and so on till SVD*43 and SVD*44 as shown in figure 5. These 16 undergo multiplication with the respective U and V orthogonal square matrices that generated during the first SVD operation to produce the 16 SVD domain watermarked coefficient matrices. This is followed by the PDFB reconstruction to generate the watermarked image. The whole operation is shown in figure 5. The watermark detection procedure is just the reverse operation of the embedding. The original image is required to detect the logo. The watermarked stego image is first resized to the original image size (in case image resizing has occurred in transmission). Then on both the stego and the original image, 4 level PDFB is undergone to achieve 16 different coefficient matrices of 32x128 or 128x32 as in the earlier embedding procedure. Then SVD operation is undergone on all 16 matrices of both the images to generate the singular matrices for all. This results to 32 singular value Eigen matrices with 16 (SVD11, SVD12, SVD13, ….. SVD44) for the watermarked stego image and 16 (SVD*11, SVD*12, SVD*13, ….. SVD*44) for the original image. The difference of these 16 sets of singular matrices are calculated and grouped 4 at a time, thus 4 groups of 4 matrices in each group is obtained. The differences of each set of intensities are multiplied by the reciprocal of ‘key’ and de-randomized by the respective ‘seed’ to retrieve the logo. So the best of the 4 logos generated is taken to be the detected logo as shown in figure 6.
IV.
RESULTS AND DISCUSSION
The ‘Lena’ host image of size 256x256 watermarked using the SVD and PDFB based CT is tested for various popular attacks. The imperceptibility quality of the watermarked image can be analyzed based on the 22 quality metrics (PSNR, UIQI, SSIM, MSSIM, MD, AD, NAD, MSE, NMSE, SNR, WSNR, IF, HS, KLD, LMSE, SC, PQS, VSNR, VIF, IFC, NQM and VIFP) enlisted in Table I. The best detected logo after each attack has been checked for the Normalized Correlation (NC) with respect to the original logo. If it has the threshold of 0.25 and below then the detection is considered as futile. The various attacks used are as in Table II. The best detection was achieved for Image crop and sharpening and to some extent for Gaussian filtering and salt and pepper noise. While average results were achieved for histogram equalization, mean filtering and JPEG compression with quality factor 30. In case of the other three attacks, the logo was detected but just having the letters ‘ECE JU’ identifiable with the worst being the ‘scale and rotate’ attack. TABLE I.
IMPERCEPTIBILITY QUALITY METRIC VALUES OBTAINED
Metric PSNR (Peak Signal to Noise Ratio) UIQI (Universal Image Quality Index) SSIM (Structural Similarity Index Measure) MSSIM (Mean Structural Similarity Index Measure) MD (Maximum Difference) AD (Average Absolute Difference) NAD (Normalized Average Absolute Difference) MSE (Mean Square Error) NMSE (Normalized Mean Square Error) SNR (Signal To Noise Ratio) WSNR (Weighted Signal to Noise Ratio) IF (Image Fidelity) HS (Histogram Similarity) KLD (Kullback Leibler Divergence) LMSE (Laplacian Mean Square Error) SC (Structural Content) PQS (Picture Quality Scale) VSNR (Vertex Signal to Noise Ratio) VIF (Visual Information Fidelity) IFC (Independent Feature Component) NQM (Noise Quality Measure) VIFP (Visual Information Fidelity Pixel) TABLE II.
Value 49.0613 dB 0.9998 0.9948 0.9997 10 0.41335 0.0033331 0.80714 4.57x10-5 43.4023 dB 69.1774 dB 0.99995 2090 0.00088016 0.016761 0.99992 5.292668 39.5822 dB 0.998 23.2611 46.7116 0.9546
PERFORMANCE FOR DIFFERENT ATTACKS
Sl. No. Major Attack Type Normalized Correlation 1 Histogram Equalization 0.47 2 Mean filter( 3x3) 0.54 3 Median filter( 4x4) 0.28 4 Median filter( 5x5) 0.29 5 JPEG Compression (QF 30) 0.54 6 Scale and Rotation (1°) 0.25 7 Gaussian filtering 0.83 8 Salt and Pepper Noise 0.89 9 Image Sharpening 0.92 10 Image crop (1/4th) 0.95
V.
CONCLUSION
In this paper a novel hybrid watermarking scheme is presented with the used of singular value decomposition (SVD) with the pyramidal directional filter bank (PDFB) based contourlet transform (CT). This method could withstand some of the very popular attacks so as to prove its robustness. The future work to be included is to check its robustness for geometric attacks.
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Figure 5: Watermark embedding procedure.
Figure 6: Watermark detection procedure.
