ROBUST BLIND IMAGE WATERMARKING BASED ON MULTI-WAVELET TRANSFORM AND SINGULAR VALUE DECOMPOSITION
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1 Proceeding of 3th Seminar on Harmonic Analysis and Applications, January 2015 ROBUST BLIND IMAGE WATERMARKING BASED ON MULTI-WAVELET TRANSFORM AND SINGULAR VALUE DECOMPOSITION Author: Malihe Mardanpour, Mohammad Ali Zare Chahooki
2 The 3 rd Seminar on Harmonic Analysis and Applications Organized by the Iranian Mathematical Society January 21 22, 2015, Yazd University, Iran Robust blind image atermarking based on Multiavelet Transform and Singular Value Decomposition M. Mardanpour and M. A. Zare Chahooki Abstract Digital atermarking is a technique for copyright protection of multimedia products such as digital images, hich embeds a atermark into a host image. The main challenge in image atermarking is the development of ne robust methods against different attacks. This paper presents a robust blind atermarking scheme based on multiavelet transform (MWT) and singular value decomposition (SVD). By performing MWT on the host image, it as decomposed into four sub-bands and then a gray scale atermark image as embedded directly in the singular values of the lo-frequency sub-band of the host image. Since the extraction of atermark as done in the absence of original image, hence the blind scheme as achieved. Experimental results on benchmark images sho that the proposed scheme has a high transparency and is robust against various attacks. Keyords and phrases: Image atermarking, multiavelet transform(mwt), singular value decomposition(svd). M. Mardanpour, Department of Electrical and Computer Engineering, University of yazd, Yazd, Iran malihe.mardanpour@stu.yazd.ac.ir M. A. Zare Chahooki, Department of Electrical and Computer Engineering, University of yazd, Yazd, Iran chahooki@yazd.ac.ir speaker
3 Robust blind image atermarking based on Multiavelet Transform and Singular Value Decomposition Malihe Mardanpour, Mohammad Ali Zare Chahooki* Abstract Digital atermarking is a technique for copyright protection of multimedia products such as digital images, hich embeds a atermark into a host image. The main challenge in image atermarking is the development of ne robust methods against different attacks. This paper presents a robust blind atermarking scheme based on multiavelet transform (MWT) and singular value decomposition (SVD). By performing MWT on the host image, it as decomposed into four sub-bands and then a gray scale atermark image as embedded directly in the singular values of the lo-frequency sub-band of the host image. Since the extraction of atermark as done in the absence of original image, hence the blind scheme as achieved. Experimental results on benchmark images sho that the proposed scheme has a high transparency and is robust against various attacks. Keyords: image atermarking, multiavelet transform (MWT), singular value decomposition (SVD) 1. Introduction During last fe years, protection of multimedia content has been one of the interested fields of study. Attackers can easily copy and manipulate these data, so protection of digital content is an active research field [1]. Image atermarking techniques classified into to category as spatial and frequency domains. Previous orks have shon that frequency domain schemes are usually more robust than spatial ones [2]. Wavelet transform has better performance than other frequency transforms because of its multiresolution characteristic that is ell suited to the properties of human visual system (HVS) [3]. Having more performance in avelet transform, is subject to filters to combine a number of desirable properties, like compact support, orthogonality, and symmetry. But, avelets cannot have orthogonality and symmetry simultaneously. MWT has been specially designed to solve this problem [4]. Image atermarking schemes based on MWT is introduced in[2] and [5]. Recently, some researchers have used the combination of more than one transform to improve their atermarking methods. In [6] and [7] a hybrid scheme based on DWT-SVD and RDWT-SVD is proposed respectively. In this paper a atermarking scheme based on MWT and SVD is presented. To date, no study has explored the association beteen MWT ans SVD. In this paper, first e apply MWT on the host image. Then e modify singular values of LL subband directly by atermark image. The results of the proposed method (MWT-SVD) is evaluated on benchmark images. This paper is organized as follos. We describe some fundamentalconcepts in Section 2. In Section3, the MWT-SVD is discussed in detail. Experimental results are presented in Section 4. Finally, conclusions are dran in Section 5.
4 2. Background Revie In this section e discuss basic theory and concepts of our method. First MWT is illustrated, then e describe image decomposition based on MWT and finally SVD is discussed Multiavelet Transform In spite of scalar avelet transform, multiavelet transform has more than one scaling function and one avelet function. Multiavelets have more advantages than scalar ones in signal and image processing. MWT despite of scalar avelet provide features such as short support, orthogonality, symmetry, and vanishing moments simultaneously [4]. In multiavelets e have [4]: ( t) ( t) ( t) T (1) 1 2 ( t) ( t) ( t) T (2) 1 2 Where Φ(t) and ψ(t) are called multiscale and multiavelet functions respectively. As for the scalar avelets, the folloing equations must be satisfied: ( t) 2 Hk(2 t k) (3) k ( t) 2 Gk(2 t k) (4) k For multiavelets, both {H k } and {G k } are matrices of filters ith size 2*2 : h (2 k) h (2k 1) (2 ) (2 1) 0 0 Hk h 1 k h 1 k g (2 k) g (2k 1) (2 ) (2 1) 0 0 Gk g 1 k g 1 k (5) (6) here {h k (n)} and {g k (n)} are, respectively, the scaling and avelet filter sequences here h 2 k ( n) 1 and g 2 k ( n) 1,for k=1,2. n n Figure 1 shos multiavelet filter banks, hich need input ros. So e have to use an approach for vectorizing scalar input hich is called preprocessing [8].
5 Figure 1. Multiavelet filter banks using 1-level decomposition[4]. To decompose an image, e have to use 2-D MWT. It is obtained by taking the tensor product of to 1-D copies, one in x, and one in y. Figure 2 exhibits sub-bands of a decomposed image under 1-level MWT. Figure 2. Multiavelet sub-bands of 2-dimentional image using one level decomposition [1] 2.2. SVD SVD is a method used in various applications like image processing and image atermarking. The SVD of an image A ith size m m is given by A = USV T, here U and V are orthogonal matrices, and S = diag(λ i ) is a diagonal matrix of singular values λ i, i = 1,..., m, hich are arranged in decreasing order [6]. 3. The Proposed MWT-SVD atermarking scheme Hybrid approach taken here is based on the method presented by [7].To decompose image e used GHM, hich is orthogonal type of MWT. First the image is decomposed by1-level GHM, then the atermark is embedd by changing singular values of LL sub-band. Embedding 1- Image is decomposed by GHM as shon in figure 2. As a result, four sub-band LL, LH, HL, HH is achieved. 2- SVD is applied on LL sub-band. So, three matrices U, S, and V are obtained. S is the eigen values of the image and is used to embed the atermark. A = USV T (7) 3- Singular values, S, for LL sub-band is modifed directly by embedding the atermark, and T then SVD is applied to it, respectively, as: S W USV (8) Where α represents the scaling factor hich balancing beteen imperceptibility and robustness is adjusted ith it. ne T 4- The ne modified coefficients for LL sub-band is modified as: A U S V (9)
6 5- Finally, the atermarked image A W is obtained by the inverse GHM on the coefficients from step 4. Extracting 1- GHM is applied on the aermarked image A * to decompose it into four sub-band. * * * *T 2- SVD is performed on LL sub-band. A U S V (10) 3- D * is calculated from folloing equation. 4- D U S V (11) * * T * * * W is computed, hich is the extracted atermark. W D S / (12) 4. Experimental Results The proposed method is implemented using Matlab and tested on three gray scale images from benchmark images. They are of size 256*256, identified as: Lenna,Baboon and Peppers. A gray scale image of Copyright logo ith size 256*256 is used as atermark. Figure 3. images from left to right are: Lenna (59.46 db), Baboon (61.09 db), Peppers (59 db), and atermark Here, e set scale factor α=0.02. The performance of proposed atermarking method is investigated by measuring its imperceptibility and robustness through different attacks. For imperceptibility, Peek Signal to Noise Ratio(PSNR) is employed to evaluate similarity beteen original image and atermarked image. These figures ith their corresponding PSNR s are shon in figure 3. PSNR is calculated as follos: PSNR max( x( i, j)) MSE 2 10log10 (13) 1 MSE x i j y i j m* n m n 2 [ (, ) (, )] (14) i 1 j 1 For evaluating robustness Normalised Cross-Correlation(NC) is measured, hich indicates the difference beteen the original atermark and extracted one. NC is computed as: NC(, ) M N i1 j1 [(i, j) ][ (i, j) ] M N M N 2 2 [(i, j) ] [ (i, j) ] i1 j1 i1 j1 (15)
7 We run proposed atermark algorithm on tested images according to the parameter given above. Results shoed high imperceptibility of our scheme ith all tested images. In addition to the imperceptibility, our scheme achieved high robustness. This is shon in table 1 and table 2. Table 1 shos outcomes of testing robustness against various attacks. Table 1. Results of NC for different attacks in atermaking ith MWT-SVD. Attack Type Peppers Baboon Lenna Attack Type Peppers Baboon Lenna NC NC NC NC NC NC gamma correction Rotation(110 ) gamma correction Histogram Equalization Pepper & Salt JPEG Q= noise(density 0.3) Pepper & Salt JPEG Q= noise(density 0.01) Pepper & Salt JPEG Q= noise(density 0.001) speckle noise(var=0.01) Median filtering(3*3) speckle noise(var=0.04) Median filtering(5*5) Gaussian sharpening noise(m=0,var=0. 001) Gaussian Flip horizontal noise(m=0,var=0. 005) Rotation( 45 ) Flip vertical Rotation(2 ) Blurring Comparison of Results for our scheme and [7] and [9] is shon in table 2. As seen, our method is the best in terms of imperceptibility and it s robustness is better than [9] and almost better compared to [7], but it has less robustness in histogram eqalization and pepper&salt noise. Table 2. comparison of our scheme ith [7] and [9] on Lenna image. Proposed method Makbol et al.[7] Ramanjaneyulu et al.[9] attack PSNR=59.46 PSNR=54.03 PSNR=44.95 NC NC NC speckle noise(var=0.01)
8 flip horizontal flip vertical flip horizontal&vertical guassian noise(m=0,var=0.001) histogram equalization JPEG compression(q=40) median filter(3*3) Rotate( 50 ) (30 ) Pepper & Salt noise(density 0.001) concolusion Combining both multiavelet and SVD, e present a novel blind image atermarking in this paper. Watermark as embedded in singular values of LL subband of host image. Performance of the proposed method tested ith images like Lenna,Peppers and Baboon. The experimental results shoed that the proposed scheme obtained a high robustness against various attacks. In the future, e plan to use other algorithms of MWT and combine it ith SVD. Since employment of SVD-based schemes yields good results, in further researches e attempt to use extension of SVD called Bidiagonal-SVD and other factorization algorihm in combination ith MWT. References [1]H. Peng, J. Wang, and W. Wang, Image atermarking method in multiavelet domain based on support vector machines, J. Syst. Soft., vol. 83, no. 8, pp , [2]P. Kumsaat, K. Attakitmongcol, and A. Srikae, Multiavelet-based image atermarking using genetic algorithm, in TENCON IEEE Region 10 Conference, 2004, pp [3] J. P. Antoine, R. Murenzi, P. Vandergheynst, S. T. Ali, and others, To-dimensional avelets and their relatives, [4] C. V Serdean, M. K. Ibrahim, A. Moemeni, and M. M. Al-Akaidi, Wavelet and multiavelet atermarking, Image Process. IET, vol. 1, no. 2, pp , [5] N.-V. W. MARKING, MULTI-WAVELET BASED ON NON-VISIBLE WATER MARKING, [6] C.-C. Lai and C.-C.Tsai, Digital image atermarking using discrete avelet transform and singular value decomposition, Instrum. Meas. IEEE Trans., vol. 59, no. 11, pp , 2010.
9 [7] N. M. Makbol and B. E. Khoo, Robust blind image atermarking scheme based on redundant discrete avelet transform and singular value decomposition, AEU-International J. Electron.Commun., vol. 67, no. 2, pp , [8] K. Jafari-Khouzani and H. Soltanian-Zadeh, Multiavelet grading of pathological images of prostate, Biomed. Eng. IEEE Trans., vol. 50, no. 6, pp , [9] K. Ramanjaneyulu and K. Rajarajesari, Wavelet-based oblivious image atermarking scheme using genetic algorithm, IET image Process., vol. 6, no. 4, pp , Malihe Mardanpour, Department of Electrical & Computer Engineering, University of yazd, City yazd, Iran Mohammad Ali Zare Chahooki, Department of Electrical & Computer Engineering, University of yazd, City yazd, Iran
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