A NEW ROBUST IMAGE WATERMARKING ...

c ICIC International 2013 ISSN 1881-803X

ICIC Express Letters Volume 7, Number 4, April 2013

pp. 1371–1376

A NEW ROBUST IMAGE WATERMARKING ALGORITHM BASED ON DWT-SVD AND ARNOLD SCRAMBLING Cuiwei He1 , Mohammad Reza Asharif1 , Carlos Enrique Gutierrez1 Mahdi Khosravy1,2 , Katsumi Yamashita3 and Rui Chen4 1

Department of Information Engineering University of the Ryukyus No. 1, Senbaru, Nishihara, Okinawa 903-0213, Japan [email protected]; [email protected]; [email protected] 2

University for Information Science and Technology “Saint Paul the Apostle”, Ohrid, Macedonia [email protected] 3

Graduate School of Engineering Osaka Prefecture University 1-1 Gakuen-cho, Sakai, Osaka, Japan [email protected] 4

Faculty of Engineering Central South University of Forestry and Technology Changsha 410000, P. R. China [email protected]

Received June 2012; accepted August 2012 Abstract. In this paper, a new robust digital watermarking algorithm based on discrete wavelet transform (DWT), singular value decomposition (SVD) and Arnold scrambling is proposed. After decomposing the host image into 4 bands by using DWT, we apply the SVD to the LL and HH bands and embed the watermarking data by modifying the singular values. The experimental results show that it is robust to different kinds of attacks and this algorithm also has a better security than other watermarking methods. Keywords: Robust digital watermarking algorithm, Discrete wavelet transform (DWT), Singular value decomposition (SVD), Arnold scrambling

1. Introduction. With the development of the Internet and communication multimedia technology, copyright protection of multimedia has become more and more prominent. Watermarking technology, the most effective method on the issue of copyright protection, has attracted more and more attention at present. Digital watermarking is the process of embedding information into a digital signal which may be used to verify its authenticity or the identity of its owners [1]. In multimedia applications, embedded watermarks should be invisible and robust. Invisibility refers to the degree of distortion introduced by the watermark and its effect on the viewers or listeners. Robustness means the resistance of the embedded watermarking against different kinds of attacks. Currently the digital watermarking technologies can be divided into two categories by the embedding position: spatial domain and transform domain watermark. Spatial domain techniques develop earlier and are easier to implement, but are limited in robustness, while transform domain techniques, which embed watermark in the host’s transform domain, are more sophisticated and robust. As one of the typical transforms, DWT is widely used in digital watermarking. It has the ability to express the local characteristics of the signal in both spatial and temporal domains. Embedding watermarking in DWT domain is of great significance since the 1371

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JPEG2000 compression standard which based on DWT is becoming more and more popular. In recent years, SVD was started to use in watermarking as a different transform. The idea of SVD-based watermarking comes from that changing the singular values of one image slightly does not affect the image quality. Arnold scrambling method is also very popular in image watermarking application. It can improve the security of the watermarking algorithm. In this paper, we will combine DWT, SVD and Arnold scrambling method to develop a new robust watermarking algorithm. The next sections will introduce DWT, SVD and Arnold scrambling. The last part will discuss the experimental algorithm and results. 2. Digital Wavelet Transform. Although the Fourier transform has been the mainstay of the transform-based image processing since the late 1950s, a more recent transformation, called the wavelet transform, is now making it even easier to compress, transmit, and analyze many images. Unlike the Fourier transform, whose basis functions are sinusoid, wavelet transforms are based on small waves, called wavelets, of varying frequency and limited duration. In two-dimensional DWT, each level of decomposition produces four bands of data denoted by LL, HL, LH and HH. LL subband represents the lower resolution approximation image, and HL, LH, HH can show the horizontal detail, vertical detail and diagonal detail components, respectively [2]. The LL subband can further be decomposed to obtain another level of decomposition. This process is continued until the desired number of levels determined by the application is reached. Figure 1 shows two levels of decomposition.

Figure 1. The decomposition of DWT

3. Singular Value Decomposition. In linear algebra, the singular value decomposition (SVD) is a factorization of a matrix, with many useful applications in signal processing and statistics [3]. Any matrix A of size m × n can be represented as: A = UΣV T where U and V are orthogonal matrices (UU T = I, V V T = I) with size m × m and n × n respectively. Σ, with size m × n, is the diagonal matrix with r (rank of A matrix) nonzero elements called singular values of A matrix. Columns of U and V matrices are called left and right singular vectors respectively. If A is an image, the left singular vectors represent horizontal details while right singular vectors represent the vertical details of the image. Singular values come in decreasing order meaning that the importance is decreasing from the first singular value to the last one, and this feature is used in SVD based compression methods. Changing singular values slightly does not affect the image quality and singular values do not change much after the image being attacked [4]; watermarking schemes make use of these two properties.

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4. Arnold Scrambling. In this part, we mainly focus on the Arnold scrambling method which will increase the system’s security. Mathematically the two-dimensional Arnold chaotic map is defined as the following: X X Let X1 = be one element of the n × n matrix, is the coordinate of the Y Y element, then the Arnold transformation is: ′ X 1 1 X = mod n Y′ 1 2 Y ′ X Note: is the new coordinates of the element, the mod is remainder the (X + Y′ Y, X + 2Y ) and n. Actually this kind of scrambling is the shift of each pixel, since the pixel (X, Y ) moves to (X ′ , Y ′ ) after once transforming. Then we use (X ′ , Y ′ ) as the input for the next transformation. After several times’ transformation we can get one scrambled watermarking image. Another vitally important property of Arnold scrambling is that it is a kind of periodic transformation. That is when the iteration keeps on doing, the original image will be recovered. The figure below shows the period of Arnold transform for different size (N) of image. We can use this property to recover the scrambled watermarking image. We scramble the original watermark image (256×256) first, and choose the count of the scrambling as a key. Figure 2 shows the original watermarking image and the scrambled image (152 times). Table 1. Arnold transform cycle N 2 6 7 12 16 19 24 32 Period 3 12 8 12 12 9 12 24 N 35 45 48 60 64 80 96 100 Period 40 60 12 60 48 60 24 150 N 125 250 256 300 384 480 512 513 Period 250 750 192 300 96 120 384 36

Figure 2. Original watermarking image and scrambled watermarking image 5. Proposed Watermarking Algorithm. Watermarking embedding: Step 1: Apply DWT to the host image A (512 × 512) and get the 4 subbands: LL, HL, LH and HH. LL HH Step 2: Apply SVD to the subbands of LL and HH by ALL = UALL ΣLL = A VA and A HH HH HH LL HH LL HH UA ΣA VA . λi , λi (i = 1, . . ., n) are the singular values of ΣA and ΣA . Step 3: Use the Arnold scramble algorithm to scramble the watermark image and then apply SVD to the result by W = UW ΣW VWT . λW i (i = 1, . . ., n) are the singular values of ΣW .

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Step 4: Modify the singular values of the LL, HH with the singular values of scrambled W ∗HH watermark image by λ∗LL = λLL = λHH +α2×λW i i +α1×λi and λi i i . Obtain the two sets T T ∗LL LL ∗LL LL ∗HH of modified DWT coefficients by: A = UA ΣA VA and A = UAHH Σ∗HH VAHH . A Step 5: Replace the original LL and HH subbands by new subbands. Then apply the inverse DWT to get the watermarked image A∗ .

Figure 3. Watermarking embedding algorithm Watermarking extracting: Step 1: Apply DWT to the watermarked image A∗ (512 × 512) and get the 4 subbands: LL′ , HL′ , LH ′ , HH ′. ′ ′ LL′ LL′ Step 2: Apply SVD to the subbands of LL′ and HH ′ by A∗LL = UALL and ∗ ΣA∗ VA∗ ′ ′ ′ ′ ′ ′ HH LL HH LL′ A∗HH = UAHH ΣHH V . λ and λ (i = 1, . . ., n) are the singular values of Σ ∗ ∗ ∗ i i A A A∗ HH ′ and ΣA∗ . ′ 1 Step 3: Extract the singular values from LL and HH by λW = (λLL − λLL i i )/α1 and i ′ W1 W2 HH HH LL HH 2 λW = (λ − λ )/α2. Compose the Σ and Σ from λ and λ . i i i W W i i HH Step 4: Construct the two watermarking image by W LL = UW ΣLL = W VW and W HH UW ΣW VW . Step 5: Use the Arnold scramble algorithm to the result above to recover the watermarking image. Finally we choose one with best quality as the final watermarking image. 6. Experimental Results. In order to put the performance investigation of our algorithm, we calculate the PSNR (Peak Signal-to-Noise Ratio) between the original image and the watermarked image and NC (Normalized Cross-Correlation) between the original watermarking image and the extracted watermarking image. P SNR = 10 log10

A2 1 N ×M

PN PM i=1

j=1 [f (i, j)

− f ′ (i, j)]2

PM1 PM2

′ i=1 j=1 W (i, j)W (i, j) qP P NC = qP P M1 M2 M1 M2 2 ′ 2 i=1 j=1 W (i, j) i=1 j=1 W (i, j)

In our algorithm, we embed watermarking image into two subbands (LL, HH) of the original image, because watermarks inserted in the lowest frequencies (LL subband) are resistant to one group of attacks, while the watermarks embedded in highest frequencies (HH subband) are resistant to another group of attacks [5]. At last, we choose one extracted watermarking image with better quality as the final extracted result. The algorithm is tested on a variety of images, but for the sake of space, here we only give the results obtained using the 512×512 grayscale image Lena and 256×256 grayscale image Ryukyu and test the robustness under seven kinds of attack: Cropping, Gaussian

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noise, Rotation, JPEG Compression, JPEG2000 Compression, Low-pass filtering and High-pass filtering.

Figure 4. Host image and watermarking image

Figure 5. Watermarked image and extracted watermarking image

Robustness test

Figure 6. Cropping test

Figure 8. Rotation test

Figure 10. JPEG2000 compression test

Figure 7. Gaussian test

Figure 9. JPEG compression test

Figure 11. Low-pass filtering test

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Figure 12. High-pass filtering test Table 2. Experimental results Type No attack Cropping Gaussian noise Rotation JPEG compression JPEG2000 compression Low-pass filtering High-pass filtering

PSNR 32.4421 14.4778 19.8241 11.1091 30.8296 29.4387 21.2356 6.2532

NC 0.9995 0.9474 0.9974 0.9936 0.9810 0.9975 0.9976 0.9012

7. Conclusions. In this paper, we have proposed a new robust watermarking algorithm for digital image based on DWT, SVD and Arnold scrambling. Because of the Arnold scrambling, our algorithm is more secure than other algorithm. And in this paper we also combine DWT with SVD. In this way we can embed more large images as the watermarking image, and the experiment results also proved that the proposed scheme has good transparency as well as good robustness against common attacks. REFERENCES [1] Q. Liu and Q. Ai, A combination of DCT-based and SVD-based watermarking scheme, Proc. of the 7th International Conference on Signal Processing, vol.1, pp.873-876, 2004. [2] Y. Wang, J. F. Doherty and R. E. Van Dyck, A wavelet-based watermarking algorithm for ownership verification of digital images, IEEE Transactions on Image Processing, vol.11, no.2, pp.77-88, 2002. [3] K. Konstantinides and G. S. Yovanof, Improved compression performance using SVD-based filters for still images, Proc. of SPIE, San Jose, CA, vol.2418, pp.100-106, 1995. [4] R. Liu and T. Tan, An SVD-based watermarking scheme for protecting rightful ownership, IEEE Transactions on Multimedia, vol.4, no.1, pp.121-128, 2002. [5] E. Ganic and A. M. Eskicioglu, Robust DWT-SVD domain image watermarking: Embedding data in all frequencies, Proc. of the ACM Multimedia and Security Workshop (MM&SEC) Magdeburg, Germany, pp.166-174, 2004.