A Reliable SVD-DWT Based Watermarking Scheme with ... · demonstrated its high robustness against image distortion. Chih-Chin et al. [6] proposed a hybrid image watermarking scheme

A Reliable SVD-DWT Based Watermarking Scheme with Artificial Bee Colony Algorithm

Yongchang Chen1, * Weiyu Yu1，2, Jiuchao Feng1

1 Electronic and Information Engineering, South China University of Technology, Guangzhou, China

2 Provincial Key Laboratory for Computer Information Processing Technology, Soochow University, Suzhou, China

[email protected]

Abstract A robust image watermarking scheme based on singular value decomposition (SVD) and discrete

wavelet transform (DWT) with Artificial Bee Colony Algorithm is proposed in this paper. Previous SVD based watermarking algorithms have a major drawback of false positive detection. For solving this problem, the similarity measure of U matrix for ownership is checked. To achieve the highest possible robustness without losing the transparency, an adaptive scale factor is obtained by the artificial bee colony (ABC) algorithm. Experimental results demonstrate that the performance of the proposed approach outperforms the existing methods.

Keywords: Watermarking, SVD, ABC, DWT

1. Introduction

The rapid growth of information technology and wide availability of network access have increased the ease of the production and distribution of digital media. However, unrestricted copying and unauthorized manipulation of multimedia also raised concerns about multimedia copyright protection and become an issue of intellectual property rights (IPR)[1, 2, 3]. One potential and effective solution to make law enforcement and copyright protection for digital media is digital watermarking. Cox et al.[4] define digital watermarking as embedding a small amount of imperceptible secret signal (the watermark) into a kind of media (the cover), and the watermark can be detected and retrieved when necessary.

In terms of the working domain that a watermarking is embedded in, watermarking technology can be classified into two main categories: spatial-domain schemes and transform-domain schemes. The former are straightforward methods, which apply directly to the pixel values and statistical traits. Such methods are fast and convenient, but vulnerable to attacks. In contrast, the latter methods such as discrete cosine transform (DCT), discrete fourier transform (DFT), discrete wavelet transform (DWT), fractional fourier transform(FFT) and discrete fractional random transform(DFRNT) have been proven to be more robust and security against a kind of attacks, such as filtering, noise pollution and lossy compression.

As one of the most powerful analysis techniques of linear algebra, singular value decomposition (SVD) has been applied to various occasions of signal processing fields including watermarking. In 2002, Liu and Tan [5] first proposed a SVD based watermarking scheme, which takes advantages of the optimal image decomposition property of SVD for embedding a watermark in an image, and demonstrated its high robustness against image distortion. Chih-Chin et al. [6] proposed a hybrid image watermarking scheme based on SVD and DCT. Ganic et al. [7] developed a robust visual watermarks using DWT-SVD. Ouhsain et al. [8] proposed an image watermarking scheme using nonnegative matrix factorization and wavelet transform. Aslantas [9] proposed an optimal robust digital image watermarking based on SVD using differential evolution algorithm. Using tiny genetic optimization strategy, Chih-Chin et al.[10] proposed a new SVD digital watermarking scheme. The key property of these SVD-based approaches is that the singular values (SVs) of the whole cover image do not alter significantly after watermark embedding. However, in these schemes, one common strategy is used that only the SVs of the watermark are embedded into the cover image. Since the SVD subspace can preserve major information, such strategy leads to the false positive problem, i.e., any attackers who

A Reliable SVD-DWT Based Watermarking Scheme with Artificial Bee Colony Algorithm Yongchang Chen, Weiyu Yu, Jiuchao Feng

International Journal of Digital Content Technology and its Applications(JDCTA) Volume6,Number22,December 2012 doi:10.4156/jdcta.vol6.issue22.50

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has the watermarked image can easily claim their ownership of the arbitrary watermarked image without knowing the original watermark embedded in the host image [11-12]. Therefore these methods give rise to the ambiguity problem.

In 2005, Bergman et al. [13] suggested the SVD subspace U matrix as a proper embedding place of the watermark. A special care must be taken when studying on U matrix to preserve orthogonality and other features of it. The authors apply extra-processing to satisfy these requirements. In [14], the authors found that modifying the coefficients in column vector will cause less visible distortion than modifying the coefficients in row vector for U component of SVD, and similar behavior for V component of SVD. Based on this notes, Ming et al. proposed an SVD-based robust watermarking scheme, with increasing invisibility and capacity [15]. Again, Jain et al. [16] presented a singular value base watermarking scheme, where the principal components of the watermark in the original image rather than just the singular values, which enhances the security of the watermark and avoids the pitfall problem encountered by Liu and Tan [5]. In 2007, Erkan and Ziya proposed algorithms embed watermark into transform domain such as DCT and DWT for verification of watermark [17, 18]. The transform domain is chosen for embedding the watermark to have better robustness. And a threshold for the similarity measure of U matrix is used to ensure rightful ownership of the watermarked image.

In this paper, a reliable SVD-DWT based watermarking with artificial bee colony algorithm (ABC) is proposed. This algorithm makes some modification of the existing algorithm [17], and employ ABC algorithm to optimize the scaling factor. Such design keeps good robustness and the imperceptibility. When a dispute over the rightful ownership of a suspected image occurs, the similarity measure of U matrix can be revealed the rightfulness.

The rest of this paper is organized as follows. In section 2, 3 and 4, the related background knowledge are introduced. In section 5, the proposed embedding algorithm and extracting algorithm using ABC algorithm are described. Section 6 demonstrates the simulation results. Section 7 concludes this paper. 2. DWT

Based on subband coding, the DWT provides a fast computation of Wavelet Transform. The advantage of DWT is multi-resolution representation of images. That is say, it analyses the signal at different frequency bands with different resolutions by decomposing the image into an approximation and detail information, according to the user’s application. In this paper, Haar wavelet transform is used. Fig.1 show an example of performing 3-level Haar wavelet transform, where the original image is divided into ten subbands. In the first stage, the image is decomposed into four subbands LL1, HL1, LH1, and HH1. At the next level of wavelet coefficients, the subband LL1 is further decomposed into LL2, HL2, LH2, and HH2 subband. In level 3, the LL3 represents the lowest frequency subband of the original image (for a 3-level DWT), the HH3 denotes the highest frequency subband of the original image, and the middle-frequency parts at level 3 are LH3 and HL3.

Cover ImageCover Image

HL1HL1

LH1LH1

HH1HH1

LH2LH2

HL2HL2 HH2HH2

LL3 LH3

HL3 HH3

3‐DWT

Figure 1. Three level decomposition with Haar wavelet transform of the cover image


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3. SVD Based Watermarking

The SVD is a fundamental matrix decomposition technique used to diagonalizable matrices. The SVD of a N*N image matrix A is a decomposition of the form

TA USV (1)

where U and NxNV R , and NxNS R is a diagonal matrix. The elements of diagonal matrix S are only nonzero on the diagonal, and are called the singular values (SVs) of A. These SVs are arranged in decreasing order. When the rank of matrix A equal to r, 1 2( , ,..., )nS diag satisfies

1 2 1 2... ... 0r r r n .

Sine singular values is able to represent the brightness of the image, and the corresponding pair of singular vectors reflect the geometry of the image, it is evident that the SVD transform is particularly robust to geometric attacks, and very much desirable for using in watermarking fields. In the conventional SVD based watermarking scheme proposed by Liu and Tan [5], we can define the watermark as W and the cover image as A. Then the watermark embedding procedure can be described as follows [5],:

1) Perform SVD on the original image A : TA USV , where TV denotes the matrix transpose of V.

2) Apply SVD to the watermark W, and modify the S with the singular values of W: T

w w wW U S V , m wS S S , where is embedding factor.

3) Computer the watermarked image: Tm mA US V .

In general, the extraction process is the inverse of the embedding procedure. If wU , S , wV , and the

possibly distorted image dA are given, a possibly corrupted watermark *W can be extracted by the

following non-blind extraction process:

1) Apply SVD on the possible distortion watermarked image dA : * * *( )TdA U S V .

2) Obtain possible corrupted singular values of the watermark: * *( ) /wS S S .

3) Using the singular vector, Construct the visual watermark: * * Tw w wW U S V

As described in [11], the major problem in SVD based image watermarking is false positive detection problem. It is caused by embedding only the SVs of the watermark into the cover image. Since the SVD subspace can preserve major information, such strategy leads to the false positive problem. This occurs when attacks can extract any desired watermark by using U and V matrices with their own SVs without knowing the original watermark embedded in the host image. They then can claim their ownership of the watermarked image, and give rise to the ambiguity problem. As mention before, such SVD based methods [5-10] using the strategy for watermarking all exist the same problem.

4. Artifical Bee Colony Algorithm

Recently swarm intelligence has attracted attention of researchers in bio-information science. Bonabeau [19] has first defined the swarm intelligence as “any attempt to design algorithms or distributed problem-solving devices inspired by the collective behavior of social insect colonies”. Algorithms are motivated by the collective behavior of social insects (such as ant,


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bees and fish). These insects with very limited individual capability can cooperatively perform complex tasks necessary for their survival.

As for Bee colony optimization (BCO) [20], the algorithm mimics the food foraging behaviour of swarms of honey bees. A few models have been developed to model the intelligent behaviours of honeybee swarms and applied for solving combinatorial type problem. Yang [21] developed a virtual bee algorithm (VBA) to solve the numerical optimization problems. In VBA, a swarm of virtual bees are generated and started to move randomly. These bees interact when they find some target nectar corresponding to the values of food sources. The solution for the optimization problem can be obtained from the intensity of bee interactions.

Figure.2. Behavior of honey bee foraging for nectar

ABC algorithm provides a population-based search procedure where individuals called food source positions are modified by the artificial bees with time. ABC algorithm consists of three essential components [22]:

1) Food sources: The “profitability” of a food source is related to several factors such as richness of food, its closeness to the nest and the ease of extracting the energy from the source.

2) Employed bees: Leader bees are associated with a specific food source they exploited. They carry information about the specific source. They share this information with the forager bees waiting in the hive by dancing which is an example of multiple inter-action.

3) Unemployed bees: Unemployed bees include onlookers and scouts. The scouts randomly search food sources this behavior is a kind of fluctuations which is vital for self-organization; while the


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onlookers waiting in the hive find a food source by means of the information presented by employed foragers. The mean number of scouts is about 5~10% of the foragers.

Flowchart of ABC algorithm is given in Fig.2. Each cycle of the search procedure consists of three steps after initialization stage: placing the employed bees onto the food sources and calculating their nectar amounts; placing the onlookers onto the food sources and calculating the nectar amounts; and determining the scout bees and placing them onto the randomly determined food sources. 5. Proposed Method

In this section, we describe proposed method to overcome the problem mentioned above. It contains two parts. Part1 introduces the reliable SVD based watermarking. Part2 utilizes ABC algorithm to determine the optimal scaling factor. The block diagram of the proposed approach is show in Fig.3.

Figure.3. The proposed watermarking scheme

5.1. The reliable SVD based Watermarking

The proposed method can be described by two parts: the embedding algorithm and the extraction algorithm. It is transformed by three level discrete Haar wavelet transform (DWT). The SVs of the watermark are embedded into the SVs of the low frequency sub-band LL, which add more robustness against some kind of distortion.

The watermark embedding process is as follows.

1) Apply three levels DWT to the cover image A, and get LL3, HL3, LH3 and HH3 subbands.

2) Perform SVD on the watermark: Tw w wW U S V ,

Add wU to LH3 and HL3 subband coefficients: *k k u wA A U , { 3, 3}k LH HH .

3) Apply SVD to the LL3 subband. After modify the SVs of LL3 subband with the SVs of the watermark, we can get the new LL sub-band:

TL L L LA U S V , m L wS S S , '

L

TL m LA U S V . Here is embedding factor.

4) Use inverse DWT to generate the watermarked image.

In extraction, the similarity of extracted U matrix is checked with the original one. This similarity is used to determine the rightful ownership. When the similarity value threshold is hold, we can consider the false positive problem not occurring. The detail watermark extraction process is as follows


434

1) Apply three level DWT to the cover and watermarked image A, and get LL3, HL3, LH3 and

HH3 subbands respectively, i.e., *

LA , *

LHA , *

HLA , *

HHA

2) Calculate the similarity of U matrix, and then check its value with a pre-setting thresholdT . *

* ( )

2L L

wu

A AU

.

3) Apply SVD to LL subband of the cover and the watermark images, when the similarity check

is passed: * * * *

L L L L

TA U S V , TL L L LA U S V .

4) Obtain possible corrupted SVs of the watermark: * *( ) /w LS S S .

5) Use the singular vector to construct the visual watermark: * * Tw w wW U S V .

5.2. Optimization scaling factor using ABC algorithm

The scaling factor is in closely related with the robustness and transparency of the watermarked image. However, choosing the proper value of the scaling factor is a not an easy problem. In most cases, the scaling factor can be considered as image-dependent. So, in this paper, we employ ABC algorithm to find optimal factor, not usually constant value. ABC algorithm provides an optimization result from the intensity of bee interactions.

Since different watermarking application has different robustness requirement to all possible signal processing attack, the level of robustness of the watermark varies by application, i.e., we can select attack combination flexibility for optimization. In this paper, the value of is examined under six attacks. They are median filtering (MF), Gaussian blur (GB), crop (CR), noise additive (GN), JPEG (JP), resize (RZ), and histogram equalization (HE). After each iteration of ABC, the solution will update. And at the end of ABC iteration, we will obtain the near optimum scaling factor.

By applying ABC algorithm, the following components can be considered:

1) Initial population: ABC use random number generator to produce initial solutions (the values of the scaling factor) in the beginning of optimization.

2) Solution: In ABC, each member vector in the population represents a possible solution to the problem. Since we only consider one scaling factor in the LL sub-band, the variable is in a scalar form. 0 3 ( 0 to avoid the division by zero error during watermark extraction).

3) Objective function: Also referred to as fitness function. The objective function values associated with food sources, which evaluate the quality of food sources. In order to achieve the imperceptivity and robustness, we define the objective function as:

4)

* *

1

min{ / ( ( , ) ( , )}K

W i A Li

K corr W W corr A A

(2)

Where K denotes the number of attacking types. W and *iW ( A and *

LA ) are the original

watermark (cover image) and extracted watermark (watermarked image), respectively. *( , )W icorr W W is the two dimensional normalized correlation between the original watermark

W and the extracted watermark *iW (when the watermarked image is under attack type i ).


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*( , )A Lcorr A A is the two dimensional normalized correlation between the cover image A and the

watermarked image *LA .

6. Experiment results

In this section, the robustness and security of the proposed algorithm are performed. A 512x 512 8bit gray-scale cover Lena and a 64x64 8bit gray-scale watermark Cameramen are chosen to demonstrate the performance, that are shown in Fig.4 (a) and (b). The gain parameter for U matrix u is chosen as

30, because the variance of U is low. We choose 0.13 as the threshold for the similarity measure of U matrix. If the U matrix similarity is greater than the threshold, the extracted watermark can be regarded as constructed by original U and V , which will solve the ambiguity problem. The related parameters of ABC algorithm about the experiments are chosen as follows: the number of bee colony including employed bees and onlooker bees is 30, the number of food sources which equals the half of the colony size, the number of cycles for foraging is 20, and limit trials is 3.

(a) Cover image (b) Watermark image

Figure.4. Watermarked image using the proposed scheme.

As we know, there is a tradeoff between imperceptibility and robustness. A good watermarking approach should retain the image quality and provide a strong robustness. Hench the phase peak signal-to-noise ratio (PSNR) and normalized correlation are introduced to give a quantitative evaluation of the imperceptibility and robustness of the watermarking algorithm, respectively.

2

10

255PSNR 10 log ( )

MSEdB (3)

2'ij ij

ijMSE

c c

N N

(4)

where ijc and 'ijc represent the pixel values in the cover image and the embedded image, respectively,

and the image size is NN .

The similarity between the original watermark w and the extracted watermark *w is measured by means of normalized correlation. It is defined as:


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_1 1 _* *

0 0*

_1 1 1 1_2 * * 2

0 0 0 0

( )( )

( , )

[ ] [ ]

ij

ij

N N

iji j

N N N N

iji j i j

w w w w

corr w w

w w w w

(5)

Fig.5 (a) shows the watermarked Lena image. The PSNR between the original cover image and the watermarked Lena image is 31dB. This value is acceptable and the watermark image is also invisible for human visual. Fig.6 (a) is the constructed watermark from LL sub-band of the reference image Fig.5 (a) without any attack. The normalized correlation between the original watermark and the constructed watermark is 1, which means these two images are the same.

In Table 1, we compared the proposed scheme with ABC algorithm against the related SVD based watermarking schemes [17, 7] by their ability to withstand different types of attacks. We also compare it with the case of no ABC optimization ( 0.1 ). Under corresponding attacks, the attacked watermarked images and the constructed watermarks from the watermarked Lena are given in Fig.5(b)~(h) and Fig.6(b)~(h). From these results, we can see that proposed scheme performs well, especially when the watermarked Lena image distorted by crop and histogram equalization. It is evident that the proposed approach achieves a better balance between robustness and security.

The similarity measure of U matrix for ownership is calculated. In the best case (no attack), the similarity value of confusion matrices of extracted U matrix are 1, 0.0376, 0.0114, 0.0008 for different watermarks (Cameraman, Boat, Baboon, Peppers). In the worst case (crop 25%), the similarity value of confusion matrices of extracted U matrix are 0.1369, -0.0071, -0.0039, 0.008 for different watermarks (Cameraman, Boat, Baboon, Peppers). That means ambiguity problem will not occur in the approach.

(a) No Attack (b) MF(PSNR: 29.28dB (c) GB(PSNR: 25.66dB ) (d) CR(PSNR: 11.08dB )

(e) GN(PSNR: 21.59dB) (f) JP(PSNR: 29.25dB) (g) RZ (PSNR: 30.36dB ) (h) HE (PSNR: 19.58dB)

Figure 5. Watermarked Lena under several attacks


437

. (a) No Attack (b) MF (c) GB (d) CR

e) GN (f) JP (g) RZ (h) HE

Figure 6 Constructed watermark

Table 1. Robustness tests under different attacks

Attacks Proposed Algorithm with ABC

Proposed Algorithm

without ABC

Method in [15]

Method in [5]

MF 3x3 0.9999 0.9815 0.9879 Not given

GB 5x5 0.9956 0.2260 0.7805 0.9894

CR 50% 0.8465 -0.3455 Not given Not given

GN 0.3 0.9760 0.8804 0.8574 0.9942

JP 30:1 0.9999 0.9898 0.8617 0.9998

RZ 256-512 0.9998 0.9959 0.9984 0.9957

HE 0.8852 0.6597 0.8085 0.9148

7. Conclusions

In this paper, the robust image watermarking scheme matrix against false-positive problem is proposed. This proposed scheme hybrids SVD and DWT transform and use similarity measure of matrix for ownership. Moreover, ABC algorithm is employed to find optimal scaling factor so as to achieve better transparency and robustness. Simulation results show that the proposed approach outperforms the other similar algorithms. Further work of extending the method is one blind.

8. Acknowledgement

This work was supported by the National Natural Science Foundation of China (Grant No. 60972133), the Joint Fund of the National Natural Science Foundation and the Guangdong Provincial Natural Science Foundation (Grant No. U0835001), the Fundamental Research Funds of the Central Universities (Grant Nos. 2011ZM0033, 2012ZM0025) and by the fund for Higher-level Talent in Guangdong Province, China (No. X2DX-N9101070). 9. References [1] S. Kapre Bhagyashri, M. Joshi, "Robust image watermarking based on singular value

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[3] Saeed K. Amirgholipour, Ahmad R. Naghsh-Nilchi, “Robust Digital Image Watermarking Based on Joint DWT-DCT”, International Journal of Digital Content Technology and its Applications, vol.3, no.2, p42-54 2009.


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[6] L. Chih-Chin, Y. Chih-Hsiang, "A hybrid image watermarking scheme based on SVD and DCT," in Machine Learning and Cybernetics (ICMLC), 2010 International Conference on, pp. 2887-2891, 2010.

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A Reliable SVD-DWT Based Watermarking Scheme with ... · demonstrated its high robustness against image distortion. Chih-Chin et al. [6] proposed a hybrid image watermarking scheme

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