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Dual watermarking scheme for copyright protection and authentication.

1. Introduction

In the recent years, the advance of editing software and the popularity of the Internet, illegal operations, such as duplication, modification, forgery and others in digital media, have become easy, fast and difficult to prevent. Therefore, the protection of the intellectual property rights of digital media has become an urgent matter. One of the solution for this is Digital Watermarking. Digital watermarking has been demonstrated to be very useful in identifying the source, creator, owner, distributor, or authorized consumer of a document or an image. It can be used for tracking the images that were illegally distributed. Watermarking, when complemented with encryption, can serve for many purposes, such as copyright protection, broadcast monitoring, and data authentication. There are many watermarking algorithms proposed in literature. Some of them operate either in the frequency domain or in the spatial domain[1,2,3,4,5]. Xia et al. [1] have added a pseudo random sequence to the largest coefficients of the detail bands: perceptual considerations are taken into account by setting the amount of modification proportional to the strength of the coefficient itself. Watermark detection is achieved through comparison with the original un-watermarked image. Zhang et al. [2] and Wang et al. [3] proposed wavelet tree based watermarking algorithms. Dawei et al. [4] proposed a new technique in which wavelet transform applies locally, based on chaotic logistic map, and embeds the watermark. Meerwald et al. [5] gives detail survey on wavelet based watermarking techniques.

In the recent years, a new transform is introduced for watermarking namely Singular Value Decomposition (SVD)[6,7]. In the SVD domain, a common approach is to modify the singular values by the singular values of a visual watermark. This transform is introduced for Square matrices by Beltrami in 1873 and Jordan in 1874, and extended to rectangular matrices by Eckart and Young in the 1930s. SVD is one of the most useful tools of linear algebra with several applications in image and signal processing.

To improve the robustness and protection, the concept of dual watermarking[8,9,10,11] is introduced by Swanson et al. [8]. Mohanty et al. [9] presented a dual watermarking scheme which is the combination of visible and invisible watermarking scheme. For embedding, they have used Discrete Cosine Transform (DCT). Hu et al. [10] have presented a new scheme in which again the authors embed a visible and an invisible watermark using DWT. When the visible watermarked image is in question, the invisible watermark can provide rightful ownership.

In this paper, we present a new Dual Watermarking Scheme based on DWT-SVD. Both Discrete Wavelet Transform (DWT) and Singular Value Decomposition (SVD) have been used as a mathematical tool to embed watermark in the image. In the proposed technique, two watermarks are embedded in the host image such that both the watermarks are invisible. First watermark is called Primary Watermark, which is a gray scale digital image. Second watermark is called secondary watermark, which is a gray scale meaningful logo instead of randomly generated Gaussian noise type watermark. The secondary watermark is embedded into primary watermark and the resultant watermarked image is used as watermark for the host image. An efficient watermarking extraction scheme is introduced for finding both primary and secondary watermarks. The primary watermark is easy to detect in all the cases but sometimes secondary one is severely distorted. The rest of the paper is organized as follows. The SVD transform are explained in Section 2. In section 3, proposed embedding and extraction algorithms are introduced. The experimental results are presented in section 4. Finally, the concluding remarks are given in section 5.

2. Singular value decomposition

Let A be a general real matrix of order m x n. The singular value decomposition (SVD) of A is the factorization

A = U * S * [V.sup.T] (1)

where U and V are orthogonal matrices, and

S = diag ([[sigma].sub.1], [[sigma].sub.2], ..., [[sigma].sub.r] (2)

where [[sigma].sub.i] , i=1(1)r are the singular values of the matrix A with r = min(m,n) and satisfying

[[sigma].sub.1] [greater than or equal to] [[sigma].sub.2] ... [greater than or equal to] ... [greater than or equal to] [[sigma].sub.r] (3)

If A is complex matrix, then SVD is

A = U * S * [V.sup.T] (4)

where U and V are unitary matrices and S is as before with real diagonal elements. The first r columns of V are called right singular vectors and the first r columns of U are called left singular vectors.

Use of SVD in digital image processing has some advantages. First, the size of the matrices from SVD transformation is not fixed. It can be a square or a rectangle. Second, singular values in a digital image are less affected if general image processing is performed. Third, singular values contain intrinsic algebraic image properties.

3. Proposed Algorithm

In this section, we have discussed some motivating factors in design of our approach to watermarking. We have used DWT and SVD to develop the algorithm. This scheme inherits advantages of both DWT and SVD, i.e. robustness and watermark capacity. Let us consider F is the host image. W1 and W2 are the primary and secondary watermarks. The host image and primary watermark are gray scale images of size M x N and [M.sub.1] x [N.sub.1] respectively. Secondary watermark is a gray scale meaningful logo of size [M.sub.1]/2x[N.sub.1]/2. We embed secondary watermark into the primary watermark. The resultant watermarked primary watermark is used as a watermark for the host image. Block diagram of the proposed dual watermarking scheme is shown in figure 1.

3.1 Watermark Embedding

3.1.1 Embedding Secondary Watermark

The embedding technique for secondary watermark is given as follows:

* Perform 1-level discrete wavelet transform on the primary watermark. Let us denote each sub-band with [W1.sup.theta] where [theta][member of]{LL, LH, HL, HH} represents the orientation.

* Perform SVD transform on secondary watermark, W2 = [U.sub.W2][S.sub.W2][V.sup.T.sub.W2]

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

* Perform SVD transform on approximation and all the detail parts,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

* Modify the singular values of approximation and all the detail parts with the singular values of the secondary watermark as

[[sigma].sup.*.sub.[theta]] = [[sigma].sub.[theta]] + [[alpha].sub.[theta]][[sigma].sub.W2]]

* Obtain modified approximation and all the detail parts as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

* Performing 1-level inverse discrete wavelet transform to get watermarked primary watermark.

3.1.2 Embedding Primary Watermark

The resultant watermarked primary watermark image (obtain from the previous sub-section) is the watermark for the host image and it is used for the following embedding algorithm. Let us denote watermarked primary watermark image by [bar.W1].

* Perform l-level discrete wavelet transform on the host image. Let us denote each sub-band with [f.sup.1.sub.[theta]] where [theta][member of]{LL, LH, HL, HH} represents the orientation and l gives the level of the orientation.

* The details and approximation sub-images of the host image are segmented into non overlapping rectangles of size [M.sub.1] x [N.sub.1] using ZIG-ZAG sequence (see figure 2).

We denote these segmented rectangles by [f.sup.l,m.sub.[theta]] where M=1,2,[2.sup.2], ... [2.sup.M+N-2l]

* Perform SVD transform on new primary watermark,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

* Perform SVD transform on all non overlapping rectangles,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

* Modify the singular values of all non overlapping rectangles with the singular values of the new primary watermark as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Obtain all modified non overlapping rectangles:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

* After embedding, reconstruct approximation and all the detail parts using De-ZIG-ZAG sequence.

* Perform l-level inverse discrete wavelet transform to get watermarked image.

3.2 Watermark Extraction

The objective of the watermark extraction is to obtain the estimate of the watermark. For watermark extraction from watermarked image, primary watermark, U and V components of secondary watermark and host image are needed. However in practical applications (in some cases) it is not possible to access the original image. We consider those applications where the original host image is available. The extraction process is formulated as follows:

3.2.1 Extracting Primary Watermark

The extracting process for primary watermark is as follows:

* Perform l-level discrete wavelet transform on the host as well as watermarked image. Let us denote each sub-band with [f.sup.l.sub.[theta]] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] for host and watermarked image respectively where [theta][member of]{LL, LH, HL, HH} represents the orientation and l gives the level of orientation.

The detail and approximation sub-images of the host as well as watermarked image is segmented into nonoverlapping rectangles of size [M.sub.1] x [N.sub.1] using ZIG-ZAG sequence. We denote these segmented rectangles by [f.sup.l,m.sub.[theta]] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] for host and watermarked image respectively, where m=1,2,[2.sup.2], ... [2.sup.M + N - 21]

* Perform SVD transform on all non overlapping rectangles of both the images,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Extract singular values of primary watermark from all non overlapping rectangles as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

* Obtain all estimate of primary watermark,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

* We select this primary watermark estimate as our detected watermark which has the greatest correlation coefficient and denoted by [[bar.W1].sub.det].

3.2.2 Extracting Secondary Watermark

In this section we extract secondary watermark from the image which we have got from the previous sub section [[bar.W1].sub.det].

* Perform 1-level discrete wavelet transform on the primary watermark and [[bar.W1].sub.det]. Let us denote each sub-band with [W1.sup.[theta]] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] respectively, where [theta][member of]{LL, LH, HL, HH} represents the orientation.

* Perform SVD transform on approximation and all the detail parts of both images,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

* Extract singular values of secondary watermark from approximation and all detail parts,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

* Obtain all estimate of secondary watermark

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

* After detecting all estimate of secondary watermark, sum up all these estimates and it is given by

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

* Normalizing [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] between [0, 1] and scale it between [0, 255].

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

4. Results and Discussion

We demonstrate our proposed algorithm using MATLAB. We have taken different 8-bit gray scale images as original (host) image namely Fruits, Mandrill, Parrot and Pepper of size 512x512. Different 8-bit gray scale images namely Lady, Lena, Cameraman, House of size 128x128 are used as primary watermarks and Circle, IIT, Star, CVGIP LAB gray scale logos are used as secondary watermark, which are of size 64x64. For embedding, the watermarked primary watermark into the host image, we have used 2-level of decomposition using Daubechies filter bank. We have embeded watermarked primary watermark 16 times in the host image. In the extraction, we only select an image whose correlation coefficient is the greatest among all. This image is being used as detected primary watermark and used for extracting secondary watermark. All original, watermarked images and extracted watermarks are shown in figures 3, 4 and 5 respectively. The watermarked image quality is measured using PSNR (Peak Signal to Noise Ratio). The PSNR values for all watermarked images are given in the table 1. If we observe original and watermarked images, we cannot find any perceptual degradation. For further analysis, Mandrill and Fruits Images are used since they have maximum and minimum PSNR values among all the experimental images.

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

[FIGURE 5 OMITTED]

To investigate the robustness of the algorithm, the watermarked image is attacked by Average and Median Filtering, Gaussian noise addition, JPEG and JPEG 2000 compression, Rotation, Resizing, Cropping and Histogram Equalization attacks. After these attacks on the watermarked image, the extracted watermarks are compared with the original one. To verify the presence of watermark, different measures can be used to show the similarity between the original and the extracted singular values. In our proposed algorithm, correlation coefficient is given by:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)

where w and [bar.w] are the original and extracted watermark and r = min(M,N), (M,N is the size of w). The value of [rho] lies between [-1, 1]. If the value of [rho] is equal to 1 then we can say the extracted singular values are just equal to original one. If the value [rho] of is -1 then the constructed watermark looks like negative thin film. Figures 6 and 7 show the correlation coefficient for all extracted 16 patterns of primary and seondary watermarks for all the experimental images.

[FIGURE 6 OMITTED]

[FIGURE 7 OMITTED]

Watermark extracted after applying 11 x 11 averaging and median filtering are shown in figures 8 and 9 respectively. It can be observed that after applying these filters, images are very much degraded and huge data is lost but extracted primary and secondary watermarks are still recognizable.

Results for additive Gaussian noise is shown in figure 10 and it is very clear from the figure that this algorithm is also standwith this attack. In figure 10, watermarks extracted form 70% additive Gaussian noise attacked image are shown.

The another most common manipulation in digital image is image compression. To check the robustness against Image Compression, the watermarked image is tested by JPEG and JPEG 2000 compression attacks. Results for JPEG (50:1) and JPEG 2000 (75:1) are shown in figure 11 and 12 respectively.

[FIGURE 8 OMITTED]

[FIGURE 9 OMITTED]

[FIGURE 10 OMITTED]

[FIGURE 11 OMITTED]

[FIGURE 12 OMITTED]

[FIGURE 13 OMITTED]

[FIGURE 14 OMITTED]

In figures 13 and 14, results for resizing and rotation attacks are given. First, the size of watermarked image is reduced to 128x128 and then again expanded to its original size i.e. 512x512. For rotation, watermarked image is rotated by 30[degrees] and then both the watermarks are extracted (shown in figure 13).

Cropping is another most common manipulation in digital image. To check the robustness against cropping attack, the 50% area of the watermarked image is cropped and then watermarks are extracted which are shown in figure 14. In figure 15, results for histogram equalization are shown.

[FIGURE 15 OMITTED]

[FIGURE 16 OMITTED]

The correlation coefficient for the extracted primary and secondary watermarks after all attacks are respectively given in tables 2 and 3. The correlation coefficient, given in tables is maximum among 16 extracted patterns of both the watermarks. With respect to geometrical attacks, including rotation, translation and scaling, our algorithm is robust since the following properties hold:

* Rotation: given an image I and its rotated [I.sup.r,] both have the same singular values.

* Translation: given an image I and its translated [I.sup.T,] both have the same singular values.

* Scaling: given an image I and its scaled [I.sup.S], if I has the singular values [[sigma].sub.i], then [I.sup.S] has the singular values [[sigma].sub.i.sup.*] [square root of [L.sub.R][L.sub.C]] where [L.sub.R] and [L.sub.C] are the scaling factor of rows and columns respectively. If rows (columns) are mutually scaled, [I.sup.S] has the singular values [[sigma].sub.i.sup.*] [square root [L.sub.R]]([[sigma].sub.i.sup.*]] [square root [L.sub.C]]).

5. Conclussions

A dual watermarking scheme is presented in which the watermarks are either a gray scale image or visually meaningful gray scale logo instead of a noise type Gaussian sequence. For the extraction of watermarks, a reliable watermark extraction scheme is constructed for both primary and secondary watermarks. Robustness of this method is carried out by a variety of attacks. The algorithm uses DWT variety of time-frequency decomposition for images, and modifies its singular value matrix with the singular value matrix of the watermark before re-constituting the signal. The left and right singular vectors must be available at the receiver. The dual watermarking algorithm presented in this paper is useful for detection of ownership of digital images and detection of manipulation in the images.

Acknowledgment

One of the authors, Gaurav Bhatnagar, gratefully acknowledges the financial support of the Council of Scientific and Industrial Research, New Delhi, India through his Junior Research Fellowship (JRF) scheme (CSIR Award no.: 09/143(0559)/2006-EMR-I) for his research work. The author, Dr. Balasubramanian Raman, gratefully acknowledges the financial support of Sponsored Research and Industrial Consultancy (SRIC), Indian Institute of Technology Roorkee, India under the grant numbers MHR03-05-802. He also acknowledges the financial support of Department of Science and Technology(DST), India under his fast track project for young scientist (DST-302-MTD) to carry out this research work.

References

[1] Xia, X., Boncelet, C.G., Arce, G. R. (1997). A multi-resolution watermark for digital images. In: Proceedings 4th IEEE Int. Conf. Image Processing 97, 3 p. 548-551, Santa Barbara, CA.

[2] Zhang, X.D., Feng, J., Lo, K.T. (2003). Image watermarking using tree-based spatial-frequency feature of wavelet transform, Journal of Visual Communication and Image Representation, 14 474-491.

[3] Wang, S.H., Lin, Y.P. (2004) Wavelet tree quantization for copyright protection watermarking. IEEE Transactions on Image Processing 13 (2) 154-165.

[4] Dawei, Z., Guanrong, C., Wenbo, L. (2004) A chaos-based robust wavelet domain watermarking algorithm. J. Chaos Solitons Fractals 22 47-54.

[5] Meerwald, P., Uhl, A. (2001) A survey of wavelet Domain Watermarking Algorithms. In: Proceedings of SPIE, Electronic Imaging, Security and Watermarking of Multimedia Contents III, 4314, San Jose, CA, USA.

[6] Liu, R., Tan, T. (2002) An SVD Based Watermarking Scheme for Protecting Rightful Ownership, IEEE Transactions on Multimedia, 4 (1) 121-128.

[7] Ganic, E., Eskicioglu, A. M. (2005) Robust Embedding of Visual Watermarks Using DWT-SVD, Journal of Electronic Imaging 14 (4) 2004.

[8] Swanson, M.D., Zhu, B.B., Tewfik, A.H. (1998) Robust audio watermarking using perceptual masking, Signal processing Elesvier. 66. 337-355.

[9] Mohanty, S.P., Ramakrishnan, K.R., Kankanhalli, M. (1999) A Dual Watermarking Technique for Images. In: Proceedings of the seventh ACM international conference on Multimedia, p. 49-51, Orlando, Florida, USA.

[10] Hu, Y., Kwong, S., Huang, J. (2004) Using Invisible Watermarks to Protect Visibly Watermarked Images, In: Proceedings of the International Symposium on Circuits and Systems 5 p. 584-587.

[11] Zhu, B.B., Swanson, M.D., Tewfik, A.H. (2004) When seeing isn't believing, IEEE Signal Processing Magazine, 21 40-49.

Gaurav Bhatnagar *, Balasubramanian Raman *, K. Swaminathan ([dagger]) Department of Mathematics,

* Indian Institute of Technology Roorkee, Roorkee-247 667, India.

([dagger]) Indian Institute of Technology Madras, Chennai-600 036, India. goravdma@gmail.com, balarfma@iitr.ernet.in, kswamy@iitm.ac.in

Author biographies

Gaurav Bhatnagar is a Ph.D student and member of the Computer Vision, Graphics and Image Processing Laboratory in the Department of Mathematics at Indian Institute of Technology Roorkee since July 2006. He received his B.Sc from C.C.S University in 2003 and M.Sc in Applied Mathematics from Indian Institute of Technology Roorkee in 2005. So far he has published one paper in International Journal and 6 papers in Conference Proceedings. His areas of research include Image Analysis, Image Fusion, Biometrics, Wavelet Analysis, Cryptography and Digital Watermarking.

Dr. Balasubramanian Raman is an Assistant Professor and head of the Computer Vision, Graphics and Image Processing Laboratory in the Department of Mathematics at Indian Institute of Technology Roorkee since February 2006. He is listed in Marquis Who's Who in the World 2006, 2007 and 2008 respectively. So far he has published 13 papers in International Journals, 27 papers in Conference Proceedings, a Book Chapter and a Technical report. His areas of research include Computer Vision, Graphics, Satellite Image Analysis, Scientific Visualization, Imaging Geometry, Reconstruction problems, Biometrics and Watermarking.

Dr. K. Swaminathan is senior scientific officer in the Department of Mathematics at Indian Institute of Technology Madras. So far he has published 16 papers in international journals and 14 papers in Conference Proceedings. His areas of research include Fluid Dynamics, Allication to Ocean Engineering and Naval Architecture, Control Systems of Sea going Vessels, Signal and Image Processing.
Table 1. PSNR for all the experimental (Host) images

 PSNR
Watermarked
Images Fruits Mandrill Parrot Pepper

Primary
 35.4974 41.9187 36.1185 35.5663
Watermark
Host Image 39.0977 43.2093 40.8390 41.5979

Table 2. Correlation coefficients for Fruits image

Attacks
 Primary Secondary

Average Filtering 0.5944 0.5523
Median Filtering 0.5175 0.5668
Additive Gaussian Noise 0.5891 0.6461
JPEG Compression 0.9993 0.8188
JPEG 2000 0.9989 0.8140
 Compression
Resize 0.9695 0.5428
Rotation 0.6915 0.5491
Cropping 0.8863 0.5694
Histogram Equalization 0.9763 0.9729

Table 3. Correlation coefficients for Mandrill image

Attacks [rho]

 Primary Secondary

Average Filtering 0.4971 0.3350
Median Filtering 0.5388 0.3369
Additive Gaussian Noise 0.4728 0.3527
JPEG Compression 0.9887 0.7393
JPEG 2000 0.9729 0.6217
 Compression
Resize 0.7776 0.2863
Rotation 0.5627 0.4040
Cropping -0.5366 0.3249
Histogram Equalization 0.7527 0.4523
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Author:Bhatnagar, Gaurav; Raman, Balasubramanian; Swaminathan, K.
Publication:Journal of Digital Information Management
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Date:Feb 1, 2009
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