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Geometrically resilient digital watermarking scheme based on radial harmonic Fourier moments magnitude
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International Journal of Electronics and Communications (AEÜ) journal homepage: www.elsevier.com/locate/aeue
Geometrically resilient digital watermarking scheme based on radial harmonic Fourier moments magnitude
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Yang Hong-Ying a,∗∗ , Wang Xiang-Yang a,b,∗ , Wang Pei a , Niu Pan-Pan a a
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School of Computer and Information Technology, Liaoning Normal University, Dalian 116029, PR China Provincial Key Laboratory for Computer Information Processing Technology, Soochow University, 215006, PR China
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a r t i c l e
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i n f o
a b s t r a c t
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Article history: Received 23 January 2014 Accepted 14 October 2014
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Keywords: Image watermarking Geometrical transformations Radial harmonic Fourier moments Moment magnitude distribution Adaptive quantization
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1. Introduction
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It is still a challenging work to design a robust image watermarking scheme to resist geometrical transformations. In this paper, we analyze the geometric invariant properties of radial harmonic Fourier moments (RHFMs), and propose a new geometrically resilient digital image watermarking scheme based on RHFMs magnitudes. Firstly, the binary watermark image is encrypted by Arnold transform, and the RHFMs of the host image are computed. Then, the accurate and robust RHFMs are selected according to the moment magnitude distribution. Finally, the encrypted watermark is embedded by quantizing the magnitudes of the selected RHFMs, and the watermarked image is obtained by adding the compensation image to the original host image. Experimental results show that the proposed RHFMs based image watermarking scheme outperforms other moments based watermarking methods, and is robust to a wide range of attacks, e.g., median filtering, random noise addition, JPEG compression, rotation, and scaling, etc. © 2014 Published by Elsevier GmbH.
Distribution channels such as digital music downloads, image/video-on-demand, and multimedia social networks pose new challenges to the design of content protection measures aimed at preventing copyright violations. Digital watermarking has been considered a potential solution to providing further protection of digital content. The close integration of the hidden signal, i.e., digital watermark, with the host media (such as video, image, audio, and text) can be used for declaring/verifying the ownership of the content, controlling the software/hardware operations or for the trailer tracking purposes [1]. In most of the related applications, the digital watermark signal has to be robust against the “watermark attacks,” including lossy compression, signal processing procedures and even malicious watermark-removal operations, etc. For still images, the requirement of digital watermark surviving geometrical transformations is necessary since such manipulations as rotation, scaling and translation are common. Nevertheless, these procedures cause challenging synchronization problems for watermark detection. Special care has to be taken so that the embedded
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∗ Corresponding author at: Provincial Key Laboratory for Computer Information Processing Technology, Soochow University, 215006, PR China. ∗∗ Corresponding author. E-mail addresses: yhy [email protected] (Y. Hong-Ying), [email protected] (W. Xiang-Yang).
watermark can survive such attacks to achieve the related functionalities in the target application [2,3]. In the last decade, researchers have made the great efforts in developing image watermarking to resist geometrical transformations, and several geometrically invariant image watermarking approaches have been developed. These schemes can be roughly divided into Exhaustive search, Spread spectrum modulation, Template insertion, Feature-based embedding, and Invariant domain [4,5]. 1.1. Exhaustive search Since the hidden signal usually exists in the geometrically distorted watermarked image, exhaustive geometrical search is a feasible solution if a known hidden signal is the searched target [3]. Lichtenauer et al. [6] examined the false positive watermark detection of this methodology to show its feasibility. One challenge is to determine all the possible geometrical distortions in advance. The computational cost in the large search space and the dramatic increase of the false alarm probability during the search process are concerns of the exhaustive search. 1.2. Spread spectrum modulation It is probably the most popular approach for data hiding, which spreads the digital watermark over the host image. Spread spectrum embedding could be implemented by two main ways, namely
http://dx.doi.org/10.1016/j.aeue.2014.10.012 1434-8411/© 2014 Published by Elsevier GmbH.
Please cite this article in press as: Hong-Ying Y, et al. Geometrically resilient digital watermarking scheme based on radial harmonic Fourier moments magnitude. Int J Electron Commun (AEÜ) (2014), http://dx.doi.org/10.1016/j.aeue.2014.10.012
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additive and multiplicative spread spectrum embedding [7]. The additive spread spectrum scheme uniformly spreads the watermark bit over the host image while the multiplicative spread spectrum spreads the watermark bit according to the host contents. Since the original host image is generally not available at the watermark decoder side, blind decoders are usually employed. Its robustness against common image processing operations and some geometric distortion, and its simple decoder structure make spread spectrum attractive for image watermarking. Despite these advantages of spread spectrum modulation, the interference effect of the host image, which causes the watermark decoding performance degradation, is a major concern of the spread spectrum modulation [8,9].
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1.3. Template insertion
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Employing synchronization templates may be a more flexible approach. The template is usually the repeated structure or tiling of signals that will help to reflect the distortion or manipulation applied on the image. The watermark detector can reverse the geometrical operation according to the extracted template for the watermark detection [10,11]. The detection of template is based on local autocorrelation. However, the embedded template signal is unfortunately, for both watermarker and attacker, easily detectable and removed, which causes inevitably problems for the watermark detection [12].
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1.4. Feature-based embedding
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It is a new watermark resynchronization techniques, which uses image content to recover the watermark after geometrical transformations. For feature-based embedding schemes, the basic strategy is to bind a watermark with the geometrically invariant image features, so the detection of the watermark can be conducted with the help of features [13]. However, some drawbacks indwelled in current feature-based schemes restrict the performance of watermarking system. First, the image feature extraction is usually sensitive to image modification. Second, watermark capacity is often limited, because the watermark is embedded into the feature based on local regions [3,14–16].
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1.5. Invariant domain
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The obvious way to achieve resilience against geometric distortions is to use an invariant domain. In [17–21], the watermark was embedded in an affine-invariant domain by using Fourier–Mellin transform, generalized Radon transform, singular value, polar harmonic transform, and histogram shape respectively. Despite that they are robust against geometrical transformations, these techniques usually suffer from implementation issues. Invariant image moments is another kind of invariant domain for embedding the robust watermark. Image moments are efficient image content descriptors, which have the advantage to fully reconstruct the initial image after the embedment of the watermark information. Moreover, the invariant properties of the moments to remain unchanged under common geometric transformations significantly increase the robustness of the watermarks in such kind of attacks. Yap et al. [22] constructed a new method that gives the opportunity to control the insertion of the watermark not only by adjusting the embedding strength but also by defining its embedment location by controlling the Krawtchouk moment parameters. Xin et al. [23] proposed an image watermarking method by using Zernike moments (ZMs) and pseudo-Zernike moments (PZMs). In order to reduce the effects of computational errors and make ZMs suitable for image watermarking, Fahmy et al. [24] proposed to use
Bspline interpolation to interpolate between image pixels. Due to the smooth and robust performance of Bspline interpolation, significant image quality improvements can be achieved. Zhu et al. [25] first presented an approach of RST invariant analysis for images. This approach achieves a set of completely invariant descriptors from the complex moments of the original image’s Radon projection. Then, they proposed a watermarking scheme which can resist global geometric transforms. Elshoura and Megherbi [26] present an empirical comparative study of Tchebichef and ZMs in image watermarking applications. In particular, they consider the case of moment-based watermarking schemes involving moment watermarks being embedded in a given carrier image moments. Zhang et al. [27] proposed a new watermarking approach which allows watermark detection and extraction under affine transformation attacks. The novelty of the approach stands on a set of affine invariants derived from Legendre moments. Watermark embedding and detection are directly performed on this set of invariants. Singh and Ranade [28] proposed an invariant image watermarking based on a recently introduced set of polar harmonic transforms and angular radial transforms, and presented their comparative analysis with state-of-art approaches based on ZMs and PZMs. In paper [29], an image adaptive technique for high capacity watermarking scheme is introduced, in which accurate and fast radial harmonic Fourier moments is utilized. The high embedding capacity is achieved by improving the hiding ratio after reducing inaccuracies in the computation of moments. The binary watermark is embedded by performing the conditional quantization of selected moments magnitudes to minimize the spatial distortion added to the host image. Papakostas et al. [30] included a theoretical analysis and performance investigation of representative moment-based watermarking systems. Through a designed set of specific experiments, the influence of moment order and moment family (ZMs, PZMs, Wavelet, Krawtchouk, Tchebichef, Legendre, Fourier–Mellin) on each methods’ performance is investigated and evaluated by applying geometric and signal processing attacks through the well-known benchmark Stirmark. Moreover, a comparative study regarding to methods’ robustness, imperceptibility and algorithms’ efficiency is achieved. Generally, moments based image watermarking approaches can resist geometrical transformations, but they are often faced with the problems of numerical instability of high order moments and computation errors, which inevitably degrade digital watermark recovery performance. In 2003, Ren et al. [31] suggested to use triangular functions as radial kernels, and introduced new orthogonal moments named radial harmonic Fourier moments (RHFMs). Compared with other orthogonal moments, RHFMs has a better image reconstruction, lower noise sensitivity, and magnitude invariance to geometrical transformations. Besides, the RHFMs is free of numerical instability issues so that high order moments can be obtained accurately. So, RHFMs are more suitable for robust digital image watermarking. In this paper, we propose a new robust image watermarking based on RHFMs magnitudes, which can achieve both geometric invariance and high capacity data hiding. The novelty of the proposed algorithm includes: (1) The accurate and robust RHFMs selection strategy is discussed; (2) A new RHFMs magnitudes based robust image watermarking is proposed. The rest of this paper is organized as follows. Section 2 recalls the preliminary about the radial harmonic Fourier moments (RHFMs). Section 3 analyzes the rotation, scaling, and translation (RST) invariant property of RHFMs magnitudes. Section 4 discusses the robust image watermarking using RHFMs magnitudes. Simulation results in Section 5 will show the performance of our scheme. Finally, Section 6 concludes this presentation.
Please cite this article in press as: Hong-Ying Y, et al. Geometrically resilient digital watermarking scheme based on radial harmonic Fourier moments magnitude. Int J Electron Commun (AEÜ) (2014), http://dx.doi.org/10.1016/j.aeue.2014.10.012
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Fig. 1. Some examples of reconstructed images (moment orders K = 10, 15, 20, 25, 30, 35, 40, 45, 50): (a) ZMs for standard gray image “Lena”, (b) RHFMs for standard gray image “Lena”, (c) ZMs for standard gray image “Barbara”, (d) RHFMs for standard gray image “Barbara”.
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2. Radial harmonic Fourier moments (RHFMs) The radial harmonic Fourier moments (RHFMs) belongs to the class of orthogonal moments, and supports inherent features like magnitude invariance, minimum information redundancy, and lower noise sensitivity. Furthermore, RHFMs is free of numerical instability issues so that high order moments can be obtained accurately. RHFMs has shown a promising behavior at a variety of applications like in image description, tumor cell recognition, character recognition, etc [31,32]. The RHFMs, Mn,l , of order n ≥ 0 with repetition |l|≥0 for a continuous image function, f(r, ), in the polar domain are defined over a unit disk as follows 1 2
Mn,l =
2
1
∗
f (r, )[Hn,l (r, )] rdrd 0
(1)
0
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f (r, ) =
+∞ +∞
(5)
Mn,l Rn (r)exp(il)
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211
n=0 l=−∞
where Mn,l is the RHFMs of order n with repetition l. Following the principle of orthogonal function, the image function f(r, ) can be reconstructed approximately by limited orders of RHFMs (n ≤ nmax , l ≤ lmax ). The more orders used, the more accurate the image description
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where [·]∗ denotes the complex conjugate and the basis Hn,l (r, ) can be decomposed into radial and circular components Hn,l (r, ) = Rn (r)eil
(2)
with the radial kernel being a complex exponential in the radial direction
Rn (r) =
⎧ ⎪ 1 ⎪ while n = 0 ⎪ ⎪ r ⎪ ⎪ ⎪ ⎨
2 sin((n + 1)r) r
while n is odd
⎪ ⎪ ⎪ ⎪ ⎪ ⎪ 2 ⎪ ⎩ cos(nr) while n is even
(3)
r
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where 2 is the normalization factor, ın,n and ıl,l are the Kronecker ∗ symbols, and [Hn ,l (r, )] is the conjugate of Hn ,l (r, ). The image (gray image) f(r, ) can be decomposed with the set of Hn,l (r, ) as
The RHFMs kernel function is orthogonal in the interior of the unit circle and satisfies the condition
2
1
∗
Hn,l (r, )[Hn ,l (r, )] rdrd = 2ın,n ıl,l
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0
0
(4)
f (r, ) =
+∞ +∞
lmax
nmax
Mn,l Rn (r)exp(il) ≈
n=0 l=−∞
Mn,l Rn (r)exp(il)(6)
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n=0 l=−lmax
where f (r, ) is the reconstructed image. The basis functions Rn (r)exp(il) of the RHFMs are orthogonal over the interior of the unit circle, and each order of the RHFMs makes an independent contribution to the reconstruction of the image. Fig. 1 gives some examples of image reconstruction using ZMs and RHFMs for standard gray image “Lena” and “Barbara” (moment orders K = 10, 15, 20, 25, 30, 35, 40, 45, 50). It can be observed that (1) the reconstructed images using RHFMs show more visual resemblance to the original image in the early orders. The edges of the reconstructed images are also better defined with less jaggedness; (2) the numerical stability of ZMs breaks down when the number of moments is increased up to 45, but RHFMs gives better reconstruction results when compared to ZMs.
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3. Geometric invariance of radial harmonic Fourier moments
=
Here we will derive and analyze the rotation, scaling, and translation (RST) invariant property of radial harmonic Fourier moments (RHFMs) [23,33].
=
1 2 k2 2
2
k
f 0
0
2
r k
, R∗n
r
k
exp(−il)rdrd
1
f (, )Rn∗ ()exp(−il)dd = k2 Mn,l (f ) 0
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(8)
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3.1. Translation invariance Translation invariance can be achieved by putting the origin of coordinate system at the image centroid. The common centroid (xc , yc ) of gray image can be defined as follows m1,0 (f ) xc = , m0,0 (f )
m0,1 (f ) yc = m0,0 (f )
where m0,0 (f), m1,0 (f), and m0,1 (f) are respectively the zero-order and first-order geometric moment for gray image. Let the origin of the coordinate system be located at (xc , yc ), the central RHFMs, which are invariant to image translation, can be obtained as follows ¯ n,l = M
1 2
2
1
∗
¯ ¯ r¯ d¯r d¯ f (¯r , )[H r , )] n,l (¯ 0
0
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¯ is the image pixel coordinate representation in polar where (¯r , ) form by locating the origin at (xc , yc ). All the RHFMs calculated in this new coordinate system are translation invariant.
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3.2. Rotation invariance
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Let fr (r, ) = f(r, + ˛) denote the rotation change of an image f(r, ) by the angle ˛, then RHFMs of f(r, + ˛) and f(r, ) have the following relations M n,l (f r ) =
=
1 2
1 = 2
1 2 2
2
0
0
1
f (r, )Rn∗ (r)exp(−il( − ˛))rdrd 0
0
2
1
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= Mn,l (f )exp(il˛)
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f (r, )Rn∗ (r)exp(−il)rdrd × exp(il˛) 0
yn =
n − N/2 N/2
Fig. 2 shows the magnitude distribution of RHFMs Mn,l (n = 0, 1, 2 ; l = −2, − 1, 0, 1, 2) for standard gray image “Barbara” under various common image processing operations and geometrical transformations. It can be seen that the RHFMs magnitudes of image have good robustness against common image processing operations and geometrical transformations. 4. Robust image watermarking approach based on RHFMs magnitudes In this paper, we propose a geometrically resilient digital image watermarking approach, in which the watermark information is embedded into original host image by adaptively quantizing the RHFMs magnitudes. In the decoder, the digital watermark can be retrieved from the robust RHFMs magnitudes. The diagram of our image watermark embedding framework is shown in Fig. 3.
Let I = {f(x, y), 0 ≤ x < M, 0 ≤ y < N)} represent a host digital image (gray image), and f(x, y) denotes the pixel value at position (x, y). W = {w(i, j) ∈ {0, 1}, 0 ≤ i < P, 0 ≤ j < Q } is a binary watermark image to be embedded within the host image. The digital watermark embedding can be summarized as follows:
0
2
m − M/2 , M/2
4.1. Watermark embedding
1
f (r, + ˛)Rn∗ (r)exp(−il)rdrd
xm =
0
(7)
where Mn,l (fr ) and Mn,l (f) are the RHFMs of fr (r, ) and f(r, ), respectively. According to Eq. (7), we know that a rotation of the image by an angle ˛ induces a phase shift eil˛ of the Mn,l (f). Taking the norm on both sides of Eq. (7), we have
4.1.1. Step 1: watermark preprocessing In order to dispel the pixel space relationship of the binary watermark image, and improve the robustness of the whole digital watermark system, watermark scrambling algorithm is used at first. In our watermark embedding scheme, the binary watermark image is scrambled from W to W1 by using Arnold transform, where
|Mn,l (f r )| = |Mn,l (f )exp(il˛)| = |Mn,l (f )|| exp(il˛)| = |Mn,l (f )|
W1 = {w1 (i, j) ∈ {0, 1}, 0 ≤ i < P, 0 ≤ j < Q } Then, it is transformed into a one-dimensional sequence of ones and zeros as follows
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So, the rotation invariance can be achieved by taking the norm of the images’ RHFMs. In other words, the RHFMs magnitude |Mn,l (f)| are invariant with respect to rotation transform.
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3.3. Scaling invariance
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2
1
f s (r, )Rn∗ (r)exp(−il)rdrd
s
0
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0
299
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w2 (k) ∈ {0, 1}}
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by the factor k, then RHFMs of f((r/k), ) and f(r, ) have the following relations
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W2 = {w2 (k) = w1 (i, j), 0 ≤ i < P, 0 ≤ j < Q, k = i × Q + j, Let fs (r, ) = f((r/k), ) denote the scaling change of an image f(r, )
1 M n,l (f ) = 2
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0
257
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1
f r (r, )Rn∗ (r)exp(−il)rdrd
1 = 2
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Obviously, Mn,l (f)/k2 is the scaling invariant RHFMs of the scaled image fs (r, ). We know that, the RHFMs magnitudes will be invariant to scaling if the computation area can be made to cover the same content. In practice, this condition is met because the RHFMs is defined on the unit disk. Given an image defined on a discrete domain f(m, n), where m = 0, . . ., M − 1 and n = 0, · · · , N − 1, we can map the image to a unit-disk domain of (xm , yn ) ∈ [−1, 1] × [−1, 1] with
4.1.2. Step 2: the RHFMs computation of the original host image The RHFMs of the original host image are computed (see Section 2).
Please cite this article in press as: Hong-Ying Y, et al. Geometrically resilient digital watermarking scheme based on radial harmonic Fourier moments magnitude. Int J Electron Commun (AEÜ) (2014), http://dx.doi.org/10.1016/j.aeue.2014.10.012
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Fig. 2. The magnitude distribution of RHFMs for image Barbara under various common image processing operations and geometric transformations: (a) no attack, (b) median filtering, (c) Gaussian noise, (d) JPEG 50, (e) edge sharpening, (f) rotation, (g) scaling and (h) translation.
Please cite this article in press as: Hong-Ying Y, et al. Geometrically resilient digital watermarking scheme based on radial harmonic Fourier moments magnitude. Int J Electron Commun (AEÜ) (2014), http://dx.doi.org/10.1016/j.aeue.2014.10.012
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Digital Watermark
Original Image
RHFMs Computation
RHFMs Selection
Watermark Embedding
New RHFMs Reconstruction
Watermarked Image
Image Combination Original RHFMs Reconstruction
Difference Image Computation
Fig. 3. Watermark embedding framework.
Table 1 The RHFMs magnitudes for an image with constant gray scale 168.
321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341
n
l=0
l = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
0 1 2 3 4 5 6 7 8 9 10
111.8329 28.5816 6.7219 15.5927 2.8296 10.7925 1.7219 8.2735 1.2301 6.7167 0.9615
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
4.1.3. Step 3: accurate and robust RHFMs selection The RHFMs are defined for analog images. For digital images, the moments can only be obtained approximately, and the invariance of the moments is also achieved approximately. For geometrically resilient image watermarking, only the accurate and robust moments should be used. In order to select the accurate RHFMs, we compute the RHFMs on a 128 × 128 image with constant gray scale 168, and the RHFMs magnitudes are listed in Table 1. From Table 1, it could be concluded that the RHFMs magnitudes with repetition l = 0, are not zero. Some of them even have significant values. This shows that the RHFMs with repetitions l = 0, are not accurate, so they cannot be used to encode watermark bits. As a result, the accurate RHFMs that can be used for watermark / 0} .In order to evaluate the embedding is denoted by S = {Mn,l , l = invariance of the RHFMs, we performed some simulations. For rotation, the image is rotated by angles from 0◦ to 180◦ with the interval 10◦ , and the average value and the standard deviation of the RHFMs magnitudes are computed. Then / is calculated to evaluate the invariance of the moments, which indicates the percentage of spread of the RHFMs magnitudes from their average values [34].
For scaling, the image is scaled with factors from 0.5 to 2 with interval 0.1. Fig. 4 show the invariance of the RHFMs, where about 50 lower order moments are employed in the experiment. From Fig. 4, we know that / is almost evenly distributed for both low order and high order moments, and this show that RHFMs has better geometric invariance. According to the accuracy and geometric invariance of RHFMs, we determined the accurate and robust RHFMs for watermarking as follows: (1) The RHFMs with repetitions l = 0, are reduced because they are not accurate; (2) For the conjugated moment pairs, only the RHFMs with positive repetition is used. As a result, the final moment set used for watermark embedding in the proposed scheme are as follows S = {Mn,l , l > 0}
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4.1.4. Step 4: digital watermark embedding Once the accurate and robust RHFMs are determined, the binary watermark sequence is then embedded by modifying the RHFMs magnitudes. For the binary watermark sequence W2 = w2 (k), 0 ≤ k < P × Q , a secret key K is first employed to randomly select P × Q RHFMs M(k)(0 ≤ k < P × Q) from the moments set S. Then the watermark bits are embedded by modifying the RHFMs magnitudes by using the following quantization function [35]
|M(k)| ⎧ ⎪ ⎨ 2 ∗ round 2 + 2 if w2 (k) = 1 |M (k)| =
⎪ ⎩ 2 ∗ round M(k)| − if w (k) = 0 2 (0 ≤ k < P × Q )
2
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364
2
where |M(k)| is the old RHFMs magnitudes of host image, |M (k)| is the new RHFMs magnitudes, round(·) denotes round operator, and is the watermark embedding strength.
Fig. 4. The geometric invariance of the RHFMs: (a) rotation invariance of the RHFMs and (b) scale invariance of the RHFMs.
Please cite this article in press as: Hong-Ying Y, et al. Geometrically resilient digital watermarking scheme based on radial harmonic Fourier moments magnitude. Int J Electron Commun (AEÜ) (2014), http://dx.doi.org/10.1016/j.aeue.2014.10.012
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Fig. 5. The host images used in experiment: (a) Lena, (b) Barbara, (c) Mandrill, (d) Peppers, (e) Couple, (f) Fishing boat, (g) Clock, (h) Girl, (i) Stream and bridge and (j) Aerial.
Fig. 6. Digital watermarks A through J used in experiments.
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4.1.5. Step 5: RHFMs reconstructing and obtaining the watermarked image The watermarked image is composed of two parts. One part is the components contributed by those unchanged RHFMs, which is
where the second term is the components contributed by the selected RHFMs before they are changed
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P×Q −1
dM (·) = 372
drem (r, ) = d(r, ) − dM (r, )
(9)
Mni ,li Hni ,li (·) + Mni ,−li Hni ,−li (·)
(10)
i=0
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Fig. 7. The watermark embedding examples by using different scheme: (a) The watermarked image for our method, (b) The absolute difference between origin image and watermarked image for our scheme, (c) The absolute difference between origin image and watermarked image for scheme [18], (d) The absolute difference between origin image and watermarked image for scheme [23].
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The other part is the components contributed by those modified RHFMs
P×Q −1 378
dM˜ (·) =
˜ n ,−l Hn ,−l (·) ˜ n ,l Hn ,l (·) + M M i i i i i i i i
(11)
i=1 379 380
381
Therefore we obtain the watermarked image by combining the two parts ˜ ) = drem (r, ) + d ˜ (r, ) d(r, M
(12)
4.2. Watermark extraction The watermark extraction procedure in the proposed scheme neither needs the original image nor any other side information. Let I* denote the watermarked image, the main steps of watermark extraction can be described as follows: 4.2.1. Step 1: the RHFMs computation of the watermarked image The RHFMs of the watermarked image are computed (see Section 2).
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Fig. 8. The attacked watermarked image and the extracted watermark using the proposed scheme: (a) JPEG 20, BER = 0.02, (b) JPEG 40, BER = 0, (c) median filtering (4 × 4), BER = 0.07, (d) random noise (5%), BER = 0.08, (e) rotation (45◦ ), BER = 0.05 and (f) scaling (0.7), BER = 0.05.
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4.2.2. Step 2: accurate and robust RHFMs selection With the same key K as in the process of watermark insertion, we locate the RHFMs M*(k)(0 ≤ k < P × Q) that carry the watermark information.
4.2.3. Step 3: one-dimensional binary sequence extraction The one-dimensional binary sequence is extracted from the selected RHFMs magnitudes
|M ∗ (k)|
⎧ ⎪ >0 ⎨ 1 if |M ∗ (k)| − 2 ∗ round 2 w∗ (k) =
⎪ ⎩ 0 if |M ∗ (k)| − 2 ∗ round |M ∗ (k)| ≤ 0 2
(0 ≤ k < P × Q )
398 399
where W ∗ = {w∗ (k), 0 ≤ k < P × Q } dimensional binary sequence.
is
the
extracted
one-
4.2.4. Step 4: obtaining the binary watermark image The one-dimensional binary sequences W* is rearranged to form the binary image, and the watermark image
Average PSNR (no attack) (dB)
A B C D E F G H I J
43.43 43.15 44.03 43.68 44.45 43.61 43.36 43.24 44.04 44.23
401 402
ˆ = {w(i, ˆ j), 0 ≤ i < P, 0 ≤ j < Q } W
403
can be obtained by descrambling.
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5. Simulation results
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We test the proposed watermarking scheme on ten popular test images. Ten test images from USC-SIPI image database, each of dimensions 512 × 512 × 8bit, are shown in Fig. 5, referred to as “Lena”, “Barbara”, “Mandrill”, “Peppers”, “Couple”, “Fishing boat”, “Clock”, “Girl”, “Stream and bridge”, and “Aerial”, respectively, in the sequel. And ten test watermarks, each of dimensions 32 × 32, are shown in Fig. 6, hereinafter referred to as watermarks A–J, respectively. The embedding strength = 0.2. Also, the experimental results are compared with schemes in [18,23]. In this work, the watermarking performance is evaluated from two aspects, namely invisibility and robustness. Here we use peek
Table 2 The average performance of the proposed watermarking method. Watermark
400
Average BER JPEG 20
JPEG 40
Median filtering (4 × 4)
Random noise (5%)
Rotation 10◦
Rotation 45◦
Scaling 0.7
Scaling 1.5
0.02 0.01 0.02 0.02 0.01 0.02 0.01 0.01 0.02 0.02
0 0 0 0 0 0 0 0 0 0
0.06 0.05 0.05 0.06 0.05 0.06 0.05 0.05 0.06 0.06
0.07 0.07 0.06 0.06 0.05 0.06 0.06 0.07 0.06 0.06
0.04 0.05 0.05 0.04 0.05 0.05 0.04 0.05 0.05 0.04
0.05 0.04 0.06 0.06 0.04 0.06 0.05 0.05 0.04 0.04
0.05 0.06 0.06 0.04 0.04 0.05 0.06 0.06 0.05 0.04
0.09 0.07 0.07 0.06 0.08 0.08 0.07 0.08 0.08 0.08
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Table 3 The PSNR for various watermarking methods (dB).
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Image
Proposed scheme
Scheme [23]
Scheme [18]
Lena Barbara Mandrill Peppers
43.96 44.25 43.75 43.87
41.07 41.63 40.90 41.46
43.56 43.65 42.97 43.22
signal-to-noise ratio (PSNR) to measure the watermark invisibility. It is defined as
419
PSNR(I, I ∗ ) = 10 log
2552 × M × N
M−1 N−1 x=0
420 421 422 423
424
425 426 427 428 429 430
y=0
2 [f (x, y) − f ∗ (x, y)]
where I is the original image and I* is the watermarked version, M × N is the size of digital image. Also, watermark robustness was measured as the bit error rate (BER) of extracted watermark, its definition is
attacks. Table 2 gives the average values of the PSNRs obtained after embedding a particular watermark in the ten test images, as well as the average values of the BER obtained under various attacks. 5.1. Watermark invisibility Fig. 7(a) shows the watermarked image Lena, Barbara, Mandrill, and Peppers using the proposed scheme. Fig. 7(b)–(d) are the absolute difference between origin image and watermarked image for the diffrent scheme, multiplied by 5 for better display. Table 3 gives the PSNR of different watermarking schemes. From Table 3, we can know that the proposed scheme is better than schemes [18,23] in terms of the transparency. 5.2. Robustness to various attacks
Table 4 The watermark detection results for standard gray image Lena.
Table 5 The watermark detection results for standard gray image Peppers.
Attacks
No attack
Scheme [23]
Scheme [18]
ZMs
PZMs
PECT
PST
PCT
0
0
0
0
0
Proposed scheme
Attacks
0
No attack
433
435 436 437 438 439 440 441
442
where B is the number of erroneously detected bits, P × Q is the watermark image dimensions. Each of the ten test watermarks was embedded in the ten test images using the proposed watermarking method. A total of 10 × 10 = 100 watermarked images were generated and for each watermarked image, the digital was extracted under various
B × 100% P×Q
432
434
Simulation results, which are obtained by the proposed watermarking scheme, for some common image processing operations and geometrical transformations are shown in Fig. 8. Table 4 and Table 5 show the results of comparison with schemes [18,23]. It is clear that the proposed scheme outperforms scheme [18,23] under most attacks in terms of BER. In sum, the above experimental results confirm the validity of our approach and its higher robustness against geometric transformations compared to alternative watermarking methods in the literature. This is because that the RHFMs are free of numerical instability and the RHFMs magnitudes is invariant to
BER =
431
Scheme [23]
Scheme [18]
Proposed scheme
ZMs
PZMs
PECT
PST
PCT
0
0
0
0
0
0
0.04 0.01 0.03 0.03
0.02 0 0 0
0.03 0.04 0.04 0.05
0.01 0 0 0
0.0508 0 0 0
JPEG compression 20 0.02 40 0.03 60 0.04 80 0.02
0.04 0.03 0.03 0.03
0.01 0 0 0
0.04 0.03 0.03 0.04
0.02 0 0.01 0.01
0.0273 0 0 0
JPEG compression 20 0.06 0 40 60 0 0 80
Median filtering 0.17 2×2 4×4 0.20 0.35 6×6 0.49 8×8
0.18 0.16 0.32 0.39
0.19 0.12 0.46 0.54
0.22 0.13 0.37 0.48
0.14 0.19 0.35 0.46
0.4336 0.4219 0.4375 0.4609
Median filtering 0.30 2×2 0.41 4×4 0.51 6×6 0.55 8×8
0.25 0.34 0.44 0.54
0.13 0.18 0.31 0.45
0.21 0.19 0.38 0.37
0.24 0.23 0.37 0.47
0.3672 0.3945 0.4609 0.5156
Random noise addition 0.03 0.02 1% 0.05 0.05 2% 0.10 0.10 3% 0.32 0.21 4% 0.43 0.52 5%
0 0.01 0.04 0.22 0.38
0.03 0.07 0.09 0.33 0.46
0 0.02 0.09 0.23 0.39
0 0 0 0 0
Random noise addition 1% 0.01 0.03 0.03 0.02 2% 0.30 0.19 3% 0.39 0.39 4% 0.45 0.52 5%
0 0.03 0.17 0.28 0.48
0.03 0.09 0.20 0.40 0.43
0 0.02 0.22 0.38 0.45
0 0 0 0 0
Rotation 5◦ 10◦ 15◦ 20◦ 25◦ 30◦ 35◦ 40◦ 45◦
0.52 0.47 0.43 0.31 0.20 0.46 0.35 0.35 0.48
0.49 0.47 0.41 0.32 0.15 0.40 0.33 0.36 0.44
0.53 0.37 0.36 0.23 0.01 0.37 0.20 0.24 0.31
0.52 0.40 0.37 0.20 0.04 0.39 0.20 0.38 0.36
0.56 0.51 0.46 0.28 0.08 0.46 0.38 0.35 0.44
0 0 0 0 0 0 0 0 0
Rotation 5◦ 10◦ 15◦ 20◦ 25◦ 30◦ 35◦ 40◦ 45◦
0.48 0.48 0.48 0.43 0.19 0.54 0.53 0.44 0.50
0.49 0.55 0.57 0.41 0.21 0.57 0.59 0.34 0.54
0.47 0.52 0.52 0.22 0.03 0.52 0.36 0.33 0.50
0.50 0.55 0.59 0.21 0.04 0.62 0.40 0.45 0.63
0.43 0.44 0.50 0.31 0.07 0.46 0.46 0.44 0.47
0 0 0 0 0 0 0 0 0
Scaling 0.5 0.7 0.9 1.1 1.3 1.5
0.32 0.26 0.20 0.16 0.18 0.23
0.32 0.29 0.19 0.17 0.18 0.17
0.05 0.03 0.04 0.08 0.08 0.12
0.14 0.05 0.08 0.09 0.12 0.13
0.29 0.18 0.10 0.08 0.09 0.13
0.1211 0 0.0352 0.0742 0 0
Scaling 0.5 0.7 0.9 1.1 1.3 1.5
0.41 0.33 0.24 0.26 0.28 0.34
0.34 0.25 0.26 0.26 0.32 0.33
0.13 0.05 0.08 0.17 0.17 0.20
0.20 0.19 0.23 0.21 0.23 0.22
0.31 0.18 0.17 0.18 0.23 0.28
0.1445 0 0.0703 0.0859 0 0
Mean BER
0.24
0.23
0.17
0.19
0.21
0.0671
Mean BER
0.31
0.31
0.22
0.27
0.25
0.0697
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geometric transformation, so RHFMs are more suitable for robust image watermarking. 6. Conclusion
477
Geometric transformations are the Achilles heel for many watermarking schemes. It is a challenging work to design a robust image watermarking scheme against geometric transformations. In this paper, we investigated the geometric invariant properties of radial harmonic Fourier moments (RHFMs), and proposed a new geometrically resilient image watermarking scheme based on RHFMs magnitudes. In the interest of better robustness and imperceptibility, the binary watermark image is first encrypted by Arnold transform, then the RHFMs of the host image are computed, and finally the digital watermark is embedded by quantizing the RHFMs magnitudes. Moreover, a detailed method has been designed to select the accurate and robust RHFMs. The experimental results demonstrate that the proposed watermarking scheme can survive common image processing operations, such as JPEG compression, median filtering, random noise addition and so on. Furthermore, the proposed scheme possesses good robustness against geometric transformations such as rotation, scaling, etc, simultaneously. However, the proposed algorithm is vulnerable to local image cropping attack. Accordingly, further work will be focused on improving the resistance to local image cropping attack for the watermarked digital image.
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Acknowledgements
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This work was supported by the National Natural Science Foundation of China under Grant No. 61472171 and 61272416, the Open Project Program of Jiangsu Key Laboratory of Image and Video Understanding for Social Safety (Nanjing University of Science and Technology) under Grant No. 30920130122006, the Open Foundation of Zhejiang Key Laboratory for Signal Processing under Grant No. ZJKL 4 SP-OP2013-01, the Open Foundation of Provincial Key Laboratory for Computer Information Processing Technology (Soochow University) under Grant No. KJS1325, the Open Project Program of the State Key Lab of CAD&CG (Grant No. A1425), Zhejiang University, and Liaoning Research Project for Institutions of Higher Education of China under Grant No. L2013407.
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References
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[1] Bianchi T, Piva A. Secure watermarking for multimedia content protection: a review of its benefits and open issues. IEEE Signal Process Mag 2013;30(2):87–96. [2] Lin P, Lee J, Chang C. Protecting the content integrity of digital imagery with fidelity preservation. ACM Trans Multimed Comput Commun Appl 2011;7(3):1–15. [3] Su P, Chang Y, Wu C C. Geometrically resilient digital image watermarking by using interest point extraction and extended pilot signals. IEEE Trans Inf Forensics Secur 2013;8(12):1897–908. [4] Cheddad A, Condell J, Curran K. Digital image steganography: survey and analysis of current methods. Signal Process 2010;90(3):727–52. [5] Zheng D, Liu Y, Zhao J, Saddik AE. A survey of RST invariant image watermarking algorithms. ACM Comput Surv 2007;39(2):1–91. [6] Lichtenauer J, Setyawan I, Kalker T, Lagendijk R. Exhaustive geometrical search and the false positive watermark detection probability. Proc SPIE Secur Watermarking Multimed Contents V 2003;5020:203–14.
11
[7] Valizadeh A, Wang ZJ. An improved multiplicative spread spectrum embedding scheme for data hiding. IEEE Trans Inf Forensics Secur 2012;7(4):1127–43. [8] Maity SP, Maity S. Collusion resilient spread spectrum watermarking in M-band wavelets using GA-fuzzy hybridization. J Syst Softw 2013;86(1):47–59. [9] Li M, Michel KK, Dimitris AP, Stella NB, Michael JM. Extracting spreadspectrum hidden data from digital media. IEEE Trans Inf Forensics Secur 2013;8(7):1201–10. [10] Kaur M, Kaur P. Robust watermarking into the color models based on the synchronization template. In: International conference on information and multimedia technology (ICIMT 09). 2009. p. 296–300. [11] Zhao Y, Ni R, Zhu. Z. RST transforms resistant image watermarking based on centroid and sector-shaped partition. Sci China Inf Sci 2012;55(3):650–62. [12] Herrigel A, Voloshynovsky S, Rytsar Y. The watermark template attack. Proc SPIE Secur Watermarking Multimed Contents III 2008;4314:394–405. [13] Seo JS, Yoo. CD. Image watermarking based on invariant regions of scale-space representation. IEEE Trans Signal Process 2006;54(4):1537–49. [14] Tian H, Zhao Y, Ni R, Qin L, Li. X. LDFT-based watermarking resilient to local desynchronization attacks. IEEE Trans Cybern 2013;43(6):2190–201. [15] Gao XB, Deng C, Li. XL. Geometric distortion insensitive image watermarking in affine covariant regions. IEEE Trans Syst Man Cybern Part C: Appl Rev 2010;40(3):278–86. [16] Yuan XC, Pun CM, Chen. PCL. Geometric invariant watermarking by local Zernike moments of binary image patches. Signal Process 2013;93(7):2087–95. [17] Manoochehri M, Pourghassem H, Shahgholian G. A novel synthetic image watermarking algorithm based on discrete wavelet transform and Fourier–Mellin transform. In: 2011 IEEE 3rd international conference on communication software and networks (ICCSN). 2011. p. 265–9. [18] Tsougenis ED, Papakostas GA, Koulouriotis DE, Tourassis VD. Towards adaptivity of image watermarking in polar harmonic transforms domain. Opt Laser Technol 2013;54:84–97. [19] Ali M, Ahn. CW. An optimized watermarking technique based on self-adaptive DE in DWT–SVD transform domain. Signal Process 2014;94:545–56. [20] Coatrieux G, Pan W, Cuppens-Boulahia N, Cuppens F. Reversible watermarking based on invariant image classification and dynamic histogram shifting. IEEE Trans Inf Forensics Secur 2013;8(1):111–21. [21] Mohammad AA. A new digital image watermarking scheme based on Schur decomposition. Multimed Tools Appl 2012;59(3):851–83. [22] Yap PT, Paramesran R. Local watermarks based on Krawtchouk moments. In: 2004 IEEE region 10 conference TENCON. 2004. p. 73–6. [23] Xin Y, Liao S, Pawlak M. Circularly orthogonal moments for geometrically robust image watermarking. Pattern Recognit 2007;40(12):3740–52. [24] Fahmy MF, Raheem GMA, Thabet MA. A Zernike moment based rotational invariant watermarking scheme. In: The 30th national radio science conference (NRSC), 16–18 April 2013. 2013. p. 228–35. [25] Zhu H, Liu M, Li Y. The RST invariant digital image watermarking using Radon transforms and complex moments. Digit Signal Process 2010;20(6): 1612–28. [26] Elshoura SM, Megherbi DB. Analysis of noise sensitivity of Tchebichef and Zernike moments with application to image watermarking. J Vis Commun Image Represent 2013;24(5):567–78. [27] Zhang H, Shu H, Coatrieux G. Affine Legendre moment invariants for image watermarking robust to geometric distortions. IEEE Trans Image Process 2011;20(8):2189–99. [28] Singh C, Ranade SK. Rotation invariant moments and transforms for geometrically invariant image watermarking. J Electron Imaging 2013;22(1): 013034. [29] Chandan Singh, Ranade Sukhjeet K. A high capacity image adaptive watermarking scheme with radial harmonic Fourier moments. Digit Signal Process 2013;23(5):1470–82. [30] Papakostas GA, Koulouriotis DE, Tourassis VD. Performance evaluation of moment-based watermarking methods: a review. J Syst Softw 2012;85(8):1864–84. [31] Ren H, Ping Z, Bo W, Wu W. Multidistortion-invariant image recognition with radial harmonic Fourier moments. J Opt Soc Am A 2003;20(4):631–7. [32] Hoang TV, Tabbone S. Generic polar harmonic transforms for invariant image description. In: The 18th IEEE international conference on image processing (ICIP). 2011. p. 845–8. [33] Chen BJ, Shu HZ, Zhang H. Quaternion Zernike moments and their invariants for color image analysis and object recognition. Signal Process 2012;92(2):308–18. [34] Li L, Li S, Abraham A, Pan J. Geometrically invariant image watermarking using polar Harmonic transforms. Inf Sci 2012;199(15):1–19. [35] Li X. Optimization analysis of formulas for quantization-based image watermarking. Opto-Electron Eng 2010;37(2):96–102.
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International Journal of Electronics and Communications (AEÜ) journal homepage: www.elsevier.com/locate/aeue
Geometrically resilient digital watermarking scheme based on radial harmonic Fourier moments magnitude
1
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Yang Hong-Ying a,∗∗ , Wang Xiang-Yang a,b,∗ , Wang Pei a , Niu Pan-Pan a a
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b
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School of Computer and Information Technology, Liaoning Normal University, Dalian 116029, PR China Provincial Key Laboratory for Computer Information Processing Technology, Soochow University, 215006, PR China
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a r t i c l e
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i n f o
a b s t r a c t
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Article history: Received 23 January 2014 Accepted 14 October 2014
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Keywords: Image watermarking Geometrical transformations Radial harmonic Fourier moments Moment magnitude distribution Adaptive quantization
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1. Introduction
13 14 15 16 17
It is still a challenging work to design a robust image watermarking scheme to resist geometrical transformations. In this paper, we analyze the geometric invariant properties of radial harmonic Fourier moments (RHFMs), and propose a new geometrically resilient digital image watermarking scheme based on RHFMs magnitudes. Firstly, the binary watermark image is encrypted by Arnold transform, and the RHFMs of the host image are computed. Then, the accurate and robust RHFMs are selected according to the moment magnitude distribution. Finally, the encrypted watermark is embedded by quantizing the magnitudes of the selected RHFMs, and the watermarked image is obtained by adding the compensation image to the original host image. Experimental results show that the proposed RHFMs based image watermarking scheme outperforms other moments based watermarking methods, and is robust to a wide range of attacks, e.g., median filtering, random noise addition, JPEG compression, rotation, and scaling, etc. © 2014 Published by Elsevier GmbH.
Distribution channels such as digital music downloads, image/video-on-demand, and multimedia social networks pose new challenges to the design of content protection measures aimed at preventing copyright violations. Digital watermarking has been considered a potential solution to providing further protection of digital content. The close integration of the hidden signal, i.e., digital watermark, with the host media (such as video, image, audio, and text) can be used for declaring/verifying the ownership of the content, controlling the software/hardware operations or for the trailer tracking purposes [1]. In most of the related applications, the digital watermark signal has to be robust against the “watermark attacks,” including lossy compression, signal processing procedures and even malicious watermark-removal operations, etc. For still images, the requirement of digital watermark surviving geometrical transformations is necessary since such manipulations as rotation, scaling and translation are common. Nevertheless, these procedures cause challenging synchronization problems for watermark detection. Special care has to be taken so that the embedded
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∗ Corresponding author at: Provincial Key Laboratory for Computer Information Processing Technology, Soochow University, 215006, PR China. ∗∗ Corresponding author. E-mail addresses: yhy [email protected] (Y. Hong-Ying), [email protected] (W. Xiang-Yang).
watermark can survive such attacks to achieve the related functionalities in the target application [2,3]. In the last decade, researchers have made the great efforts in developing image watermarking to resist geometrical transformations, and several geometrically invariant image watermarking approaches have been developed. These schemes can be roughly divided into Exhaustive search, Spread spectrum modulation, Template insertion, Feature-based embedding, and Invariant domain [4,5]. 1.1. Exhaustive search Since the hidden signal usually exists in the geometrically distorted watermarked image, exhaustive geometrical search is a feasible solution if a known hidden signal is the searched target [3]. Lichtenauer et al. [6] examined the false positive watermark detection of this methodology to show its feasibility. One challenge is to determine all the possible geometrical distortions in advance. The computational cost in the large search space and the dramatic increase of the false alarm probability during the search process are concerns of the exhaustive search. 1.2. Spread spectrum modulation It is probably the most popular approach for data hiding, which spreads the digital watermark over the host image. Spread spectrum embedding could be implemented by two main ways, namely
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additive and multiplicative spread spectrum embedding [7]. The additive spread spectrum scheme uniformly spreads the watermark bit over the host image while the multiplicative spread spectrum spreads the watermark bit according to the host contents. Since the original host image is generally not available at the watermark decoder side, blind decoders are usually employed. Its robustness against common image processing operations and some geometric distortion, and its simple decoder structure make spread spectrum attractive for image watermarking. Despite these advantages of spread spectrum modulation, the interference effect of the host image, which causes the watermark decoding performance degradation, is a major concern of the spread spectrum modulation [8,9].
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1.3. Template insertion
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Employing synchronization templates may be a more flexible approach. The template is usually the repeated structure or tiling of signals that will help to reflect the distortion or manipulation applied on the image. The watermark detector can reverse the geometrical operation according to the extracted template for the watermark detection [10,11]. The detection of template is based on local autocorrelation. However, the embedded template signal is unfortunately, for both watermarker and attacker, easily detectable and removed, which causes inevitably problems for the watermark detection [12].
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1.4. Feature-based embedding
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It is a new watermark resynchronization techniques, which uses image content to recover the watermark after geometrical transformations. For feature-based embedding schemes, the basic strategy is to bind a watermark with the geometrically invariant image features, so the detection of the watermark can be conducted with the help of features [13]. However, some drawbacks indwelled in current feature-based schemes restrict the performance of watermarking system. First, the image feature extraction is usually sensitive to image modification. Second, watermark capacity is often limited, because the watermark is embedded into the feature based on local regions [3,14–16].
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1.5. Invariant domain
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The obvious way to achieve resilience against geometric distortions is to use an invariant domain. In [17–21], the watermark was embedded in an affine-invariant domain by using Fourier–Mellin transform, generalized Radon transform, singular value, polar harmonic transform, and histogram shape respectively. Despite that they are robust against geometrical transformations, these techniques usually suffer from implementation issues. Invariant image moments is another kind of invariant domain for embedding the robust watermark. Image moments are efficient image content descriptors, which have the advantage to fully reconstruct the initial image after the embedment of the watermark information. Moreover, the invariant properties of the moments to remain unchanged under common geometric transformations significantly increase the robustness of the watermarks in such kind of attacks. Yap et al. [22] constructed a new method that gives the opportunity to control the insertion of the watermark not only by adjusting the embedding strength but also by defining its embedment location by controlling the Krawtchouk moment parameters. Xin et al. [23] proposed an image watermarking method by using Zernike moments (ZMs) and pseudo-Zernike moments (PZMs). In order to reduce the effects of computational errors and make ZMs suitable for image watermarking, Fahmy et al. [24] proposed to use
Bspline interpolation to interpolate between image pixels. Due to the smooth and robust performance of Bspline interpolation, significant image quality improvements can be achieved. Zhu et al. [25] first presented an approach of RST invariant analysis for images. This approach achieves a set of completely invariant descriptors from the complex moments of the original image’s Radon projection. Then, they proposed a watermarking scheme which can resist global geometric transforms. Elshoura and Megherbi [26] present an empirical comparative study of Tchebichef and ZMs in image watermarking applications. In particular, they consider the case of moment-based watermarking schemes involving moment watermarks being embedded in a given carrier image moments. Zhang et al. [27] proposed a new watermarking approach which allows watermark detection and extraction under affine transformation attacks. The novelty of the approach stands on a set of affine invariants derived from Legendre moments. Watermark embedding and detection are directly performed on this set of invariants. Singh and Ranade [28] proposed an invariant image watermarking based on a recently introduced set of polar harmonic transforms and angular radial transforms, and presented their comparative analysis with state-of-art approaches based on ZMs and PZMs. In paper [29], an image adaptive technique for high capacity watermarking scheme is introduced, in which accurate and fast radial harmonic Fourier moments is utilized. The high embedding capacity is achieved by improving the hiding ratio after reducing inaccuracies in the computation of moments. The binary watermark is embedded by performing the conditional quantization of selected moments magnitudes to minimize the spatial distortion added to the host image. Papakostas et al. [30] included a theoretical analysis and performance investigation of representative moment-based watermarking systems. Through a designed set of specific experiments, the influence of moment order and moment family (ZMs, PZMs, Wavelet, Krawtchouk, Tchebichef, Legendre, Fourier–Mellin) on each methods’ performance is investigated and evaluated by applying geometric and signal processing attacks through the well-known benchmark Stirmark. Moreover, a comparative study regarding to methods’ robustness, imperceptibility and algorithms’ efficiency is achieved. Generally, moments based image watermarking approaches can resist geometrical transformations, but they are often faced with the problems of numerical instability of high order moments and computation errors, which inevitably degrade digital watermark recovery performance. In 2003, Ren et al. [31] suggested to use triangular functions as radial kernels, and introduced new orthogonal moments named radial harmonic Fourier moments (RHFMs). Compared with other orthogonal moments, RHFMs has a better image reconstruction, lower noise sensitivity, and magnitude invariance to geometrical transformations. Besides, the RHFMs is free of numerical instability issues so that high order moments can be obtained accurately. So, RHFMs are more suitable for robust digital image watermarking. In this paper, we propose a new robust image watermarking based on RHFMs magnitudes, which can achieve both geometric invariance and high capacity data hiding. The novelty of the proposed algorithm includes: (1) The accurate and robust RHFMs selection strategy is discussed; (2) A new RHFMs magnitudes based robust image watermarking is proposed. The rest of this paper is organized as follows. Section 2 recalls the preliminary about the radial harmonic Fourier moments (RHFMs). Section 3 analyzes the rotation, scaling, and translation (RST) invariant property of RHFMs magnitudes. Section 4 discusses the robust image watermarking using RHFMs magnitudes. Simulation results in Section 5 will show the performance of our scheme. Finally, Section 6 concludes this presentation.
Please cite this article in press as: Hong-Ying Y, et al. Geometrically resilient digital watermarking scheme based on radial harmonic Fourier moments magnitude. Int J Electron Commun (AEÜ) (2014), http://dx.doi.org/10.1016/j.aeue.2014.10.012
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Fig. 1. Some examples of reconstructed images (moment orders K = 10, 15, 20, 25, 30, 35, 40, 45, 50): (a) ZMs for standard gray image “Lena”, (b) RHFMs for standard gray image “Lena”, (c) ZMs for standard gray image “Barbara”, (d) RHFMs for standard gray image “Barbara”.
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186 187 188 189 190 191 192 193 194 195 196
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2. Radial harmonic Fourier moments (RHFMs) The radial harmonic Fourier moments (RHFMs) belongs to the class of orthogonal moments, and supports inherent features like magnitude invariance, minimum information redundancy, and lower noise sensitivity. Furthermore, RHFMs is free of numerical instability issues so that high order moments can be obtained accurately. RHFMs has shown a promising behavior at a variety of applications like in image description, tumor cell recognition, character recognition, etc [31,32]. The RHFMs, Mn,l , of order n ≥ 0 with repetition |l|≥0 for a continuous image function, f(r, ), in the polar domain are defined over a unit disk as follows 1 2
Mn,l =
2
1
∗
f (r, )[Hn,l (r, )] rdrd 0
(1)
0
205
f (r, ) =
+∞ +∞
(5)
Mn,l Rn (r)exp(il)
207 208 209 210
211
n=0 l=−∞
where Mn,l is the RHFMs of order n with repetition l. Following the principle of orthogonal function, the image function f(r, ) can be reconstructed approximately by limited orders of RHFMs (n ≤ nmax , l ≤ lmax ). The more orders used, the more accurate the image description
212 213 214 215 216
where [·]∗ denotes the complex conjugate and the basis Hn,l (r, ) can be decomposed into radial and circular components Hn,l (r, ) = Rn (r)eil
(2)
with the radial kernel being a complex exponential in the radial direction
Rn (r) =
⎧ ⎪ 1 ⎪ while n = 0 ⎪ ⎪ r ⎪ ⎪ ⎪ ⎨
2 sin((n + 1)r) r
while n is odd
⎪ ⎪ ⎪ ⎪ ⎪ ⎪ 2 ⎪ ⎩ cos(nr) while n is even
(3)
r
204
where 2 is the normalization factor, ın,n and ıl,l are the Kronecker ∗ symbols, and [Hn ,l (r, )] is the conjugate of Hn ,l (r, ). The image (gray image) f(r, ) can be decomposed with the set of Hn,l (r, ) as
The RHFMs kernel function is orthogonal in the interior of the unit circle and satisfies the condition
2
1
∗
Hn,l (r, )[Hn ,l (r, )] rdrd = 2ın,n ıl,l
206
0
0
(4)
f (r, ) =
+∞ +∞
lmax
nmax
Mn,l Rn (r)exp(il) ≈
n=0 l=−∞
Mn,l Rn (r)exp(il)(6)
217
n=0 l=−lmax
where f (r, ) is the reconstructed image. The basis functions Rn (r)exp(il) of the RHFMs are orthogonal over the interior of the unit circle, and each order of the RHFMs makes an independent contribution to the reconstruction of the image. Fig. 1 gives some examples of image reconstruction using ZMs and RHFMs for standard gray image “Lena” and “Barbara” (moment orders K = 10, 15, 20, 25, 30, 35, 40, 45, 50). It can be observed that (1) the reconstructed images using RHFMs show more visual resemblance to the original image in the early orders. The edges of the reconstructed images are also better defined with less jaggedness; (2) the numerical stability of ZMs breaks down when the number of moments is increased up to 45, but RHFMs gives better reconstruction results when compared to ZMs.
Please cite this article in press as: Hong-Ying Y, et al. Geometrically resilient digital watermarking scheme based on radial harmonic Fourier moments magnitude. Int J Electron Commun (AEÜ) (2014), http://dx.doi.org/10.1016/j.aeue.2014.10.012
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3. Geometric invariance of radial harmonic Fourier moments
=
Here we will derive and analyze the rotation, scaling, and translation (RST) invariant property of radial harmonic Fourier moments (RHFMs) [23,33].
=
1 2 k2 2
2
k
f 0
0
2
r k
, R∗n
r
k
exp(−il)rdrd
1
f (, )Rn∗ ()exp(−il)dd = k2 Mn,l (f ) 0
273
(8)
274
0 275
236
237 238 239
240
241 242 243 244 245
246
3.1. Translation invariance Translation invariance can be achieved by putting the origin of coordinate system at the image centroid. The common centroid (xc , yc ) of gray image can be defined as follows m1,0 (f ) xc = , m0,0 (f )
m0,1 (f ) yc = m0,0 (f )
where m0,0 (f), m1,0 (f), and m0,1 (f) are respectively the zero-order and first-order geometric moment for gray image. Let the origin of the coordinate system be located at (xc , yc ), the central RHFMs, which are invariant to image translation, can be obtained as follows ¯ n,l = M
1 2
2
1
∗
¯ ¯ r¯ d¯r d¯ f (¯r , )[H r , )] n,l (¯ 0
0
249
¯ is the image pixel coordinate representation in polar where (¯r , ) form by locating the origin at (xc , yc ). All the RHFMs calculated in this new coordinate system are translation invariant.
250
3.2. Rotation invariance
247 248
251 252 253
254
255
256
Let fr (r, ) = f(r, + ˛) denote the rotation change of an image f(r, ) by the angle ˛, then RHFMs of f(r, + ˛) and f(r, ) have the following relations M n,l (f r ) =
=
1 2
1 = 2
1 2 2
2
0
0
1
f (r, )Rn∗ (r)exp(−il( − ˛))rdrd 0
0
2
1
258
= Mn,l (f )exp(il˛)
261 262 263
f (r, )Rn∗ (r)exp(−il)rdrd × exp(il˛) 0
yn =
n − N/2 N/2
Fig. 2 shows the magnitude distribution of RHFMs Mn,l (n = 0, 1, 2 ; l = −2, − 1, 0, 1, 2) for standard gray image “Barbara” under various common image processing operations and geometrical transformations. It can be seen that the RHFMs magnitudes of image have good robustness against common image processing operations and geometrical transformations. 4. Robust image watermarking approach based on RHFMs magnitudes In this paper, we propose a geometrically resilient digital image watermarking approach, in which the watermark information is embedded into original host image by adaptively quantizing the RHFMs magnitudes. In the decoder, the digital watermark can be retrieved from the robust RHFMs magnitudes. The diagram of our image watermark embedding framework is shown in Fig. 3.
Let I = {f(x, y), 0 ≤ x < M, 0 ≤ y < N)} represent a host digital image (gray image), and f(x, y) denotes the pixel value at position (x, y). W = {w(i, j) ∈ {0, 1}, 0 ≤ i < P, 0 ≤ j < Q } is a binary watermark image to be embedded within the host image. The digital watermark embedding can be summarized as follows:
0
2
m − M/2 , M/2
4.1. Watermark embedding
1
f (r, + ˛)Rn∗ (r)exp(−il)rdrd
xm =
0
(7)
where Mn,l (fr ) and Mn,l (f) are the RHFMs of fr (r, ) and f(r, ), respectively. According to Eq. (7), we know that a rotation of the image by an angle ˛ induces a phase shift eil˛ of the Mn,l (f). Taking the norm on both sides of Eq. (7), we have
4.1.1. Step 1: watermark preprocessing In order to dispel the pixel space relationship of the binary watermark image, and improve the robustness of the whole digital watermark system, watermark scrambling algorithm is used at first. In our watermark embedding scheme, the binary watermark image is scrambled from W to W1 by using Arnold transform, where
|Mn,l (f r )| = |Mn,l (f )exp(il˛)| = |Mn,l (f )|| exp(il˛)| = |Mn,l (f )|
W1 = {w1 (i, j) ∈ {0, 1}, 0 ≤ i < P, 0 ≤ j < Q } Then, it is transformed into a one-dimensional sequence of ones and zeros as follows
267
So, the rotation invariance can be achieved by taking the norm of the images’ RHFMs. In other words, the RHFMs magnitude |Mn,l (f)| are invariant with respect to rotation transform.
268
3.3. Scaling invariance
264 265 266
269 270 271
272
2
1
f s (r, )Rn∗ (r)exp(−il)rdrd
s
0
278 279 280 281 282 283
284
285 286 287 288 289 290
291 292
293 294 295 296 297 298
0
299
300 301 302 303 304
305 306 307 308 309 310 311
312
313 314
315
w2 (k) ∈ {0, 1}}
316
317
by the factor k, then RHFMs of f((r/k), ) and f(r, ) have the following relations
277
W2 = {w2 (k) = w1 (i, j), 0 ≤ i < P, 0 ≤ j < Q, k = i × Q + j, Let fs (r, ) = f((r/k), ) denote the scaling change of an image f(r, )
1 M n,l (f ) = 2
276
0
257
260
1
f r (r, )Rn∗ (r)exp(−il)rdrd
1 = 2
259
Obviously, Mn,l (f)/k2 is the scaling invariant RHFMs of the scaled image fs (r, ). We know that, the RHFMs magnitudes will be invariant to scaling if the computation area can be made to cover the same content. In practice, this condition is met because the RHFMs is defined on the unit disk. Given an image defined on a discrete domain f(m, n), where m = 0, . . ., M − 1 and n = 0, · · · , N − 1, we can map the image to a unit-disk domain of (xm , yn ) ∈ [−1, 1] × [−1, 1] with
4.1.2. Step 2: the RHFMs computation of the original host image The RHFMs of the original host image are computed (see Section 2).
Please cite this article in press as: Hong-Ying Y, et al. Geometrically resilient digital watermarking scheme based on radial harmonic Fourier moments magnitude. Int J Electron Commun (AEÜ) (2014), http://dx.doi.org/10.1016/j.aeue.2014.10.012
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Fig. 2. The magnitude distribution of RHFMs for image Barbara under various common image processing operations and geometric transformations: (a) no attack, (b) median filtering, (c) Gaussian noise, (d) JPEG 50, (e) edge sharpening, (f) rotation, (g) scaling and (h) translation.
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Digital Watermark
Original Image
RHFMs Computation
RHFMs Selection
Watermark Embedding
New RHFMs Reconstruction
Watermarked Image
Image Combination Original RHFMs Reconstruction
Difference Image Computation
Fig. 3. Watermark embedding framework.
Table 1 The RHFMs magnitudes for an image with constant gray scale 168.
321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341
n
l=0
l = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
0 1 2 3 4 5 6 7 8 9 10
111.8329 28.5816 6.7219 15.5927 2.8296 10.7925 1.7219 8.2735 1.2301 6.7167 0.9615
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
4.1.3. Step 3: accurate and robust RHFMs selection The RHFMs are defined for analog images. For digital images, the moments can only be obtained approximately, and the invariance of the moments is also achieved approximately. For geometrically resilient image watermarking, only the accurate and robust moments should be used. In order to select the accurate RHFMs, we compute the RHFMs on a 128 × 128 image with constant gray scale 168, and the RHFMs magnitudes are listed in Table 1. From Table 1, it could be concluded that the RHFMs magnitudes with repetition l = 0, are not zero. Some of them even have significant values. This shows that the RHFMs with repetitions l = 0, are not accurate, so they cannot be used to encode watermark bits. As a result, the accurate RHFMs that can be used for watermark / 0} .In order to evaluate the embedding is denoted by S = {Mn,l , l = invariance of the RHFMs, we performed some simulations. For rotation, the image is rotated by angles from 0◦ to 180◦ with the interval 10◦ , and the average value and the standard deviation of the RHFMs magnitudes are computed. Then / is calculated to evaluate the invariance of the moments, which indicates the percentage of spread of the RHFMs magnitudes from their average values [34].
For scaling, the image is scaled with factors from 0.5 to 2 with interval 0.1. Fig. 4 show the invariance of the RHFMs, where about 50 lower order moments are employed in the experiment. From Fig. 4, we know that / is almost evenly distributed for both low order and high order moments, and this show that RHFMs has better geometric invariance. According to the accuracy and geometric invariance of RHFMs, we determined the accurate and robust RHFMs for watermarking as follows: (1) The RHFMs with repetitions l = 0, are reduced because they are not accurate; (2) For the conjugated moment pairs, only the RHFMs with positive repetition is used. As a result, the final moment set used for watermark embedding in the proposed scheme are as follows S = {Mn,l , l > 0}
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4.1.4. Step 4: digital watermark embedding Once the accurate and robust RHFMs are determined, the binary watermark sequence is then embedded by modifying the RHFMs magnitudes. For the binary watermark sequence W2 = w2 (k), 0 ≤ k < P × Q , a secret key K is first employed to randomly select P × Q RHFMs M(k)(0 ≤ k < P × Q) from the moments set S. Then the watermark bits are embedded by modifying the RHFMs magnitudes by using the following quantization function [35]
|M(k)| ⎧ ⎪ ⎨ 2 ∗ round 2 + 2 if w2 (k) = 1 |M (k)| =
⎪ ⎩ 2 ∗ round M(k)| − if w (k) = 0 2 (0 ≤ k < P × Q )
2
356 357 358 359 360 361 362 363
364
2
where |M(k)| is the old RHFMs magnitudes of host image, |M (k)| is the new RHFMs magnitudes, round(·) denotes round operator, and is the watermark embedding strength.
Fig. 4. The geometric invariance of the RHFMs: (a) rotation invariance of the RHFMs and (b) scale invariance of the RHFMs.
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Fig. 5. The host images used in experiment: (a) Lena, (b) Barbara, (c) Mandrill, (d) Peppers, (e) Couple, (f) Fishing boat, (g) Clock, (h) Girl, (i) Stream and bridge and (j) Aerial.
Fig. 6. Digital watermarks A through J used in experiments.
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4.1.5. Step 5: RHFMs reconstructing and obtaining the watermarked image The watermarked image is composed of two parts. One part is the components contributed by those unchanged RHFMs, which is
where the second term is the components contributed by the selected RHFMs before they are changed
373 374
P×Q −1
dM (·) = 372
drem (r, ) = d(r, ) − dM (r, )
(9)
Mni ,li Hni ,li (·) + Mni ,−li Hni ,−li (·)
(10)
i=0
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Fig. 7. The watermark embedding examples by using different scheme: (a) The watermarked image for our method, (b) The absolute difference between origin image and watermarked image for our scheme, (c) The absolute difference between origin image and watermarked image for scheme [18], (d) The absolute difference between origin image and watermarked image for scheme [23].
376 377
The other part is the components contributed by those modified RHFMs
P×Q −1 378
dM˜ (·) =
˜ n ,−l Hn ,−l (·) ˜ n ,l Hn ,l (·) + M M i i i i i i i i
(11)
i=1 379 380
381
Therefore we obtain the watermarked image by combining the two parts ˜ ) = drem (r, ) + d ˜ (r, ) d(r, M
(12)
4.2. Watermark extraction The watermark extraction procedure in the proposed scheme neither needs the original image nor any other side information. Let I* denote the watermarked image, the main steps of watermark extraction can be described as follows: 4.2.1. Step 1: the RHFMs computation of the watermarked image The RHFMs of the watermarked image are computed (see Section 2).
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Fig. 8. The attacked watermarked image and the extracted watermark using the proposed scheme: (a) JPEG 20, BER = 0.02, (b) JPEG 40, BER = 0, (c) median filtering (4 × 4), BER = 0.07, (d) random noise (5%), BER = 0.08, (e) rotation (45◦ ), BER = 0.05 and (f) scaling (0.7), BER = 0.05.
390 391 392 393
394 395 396
397
4.2.2. Step 2: accurate and robust RHFMs selection With the same key K as in the process of watermark insertion, we locate the RHFMs M*(k)(0 ≤ k < P × Q) that carry the watermark information.
4.2.3. Step 3: one-dimensional binary sequence extraction The one-dimensional binary sequence is extracted from the selected RHFMs magnitudes
|M ∗ (k)|
⎧ ⎪ >0 ⎨ 1 if |M ∗ (k)| − 2 ∗ round 2 w∗ (k) =
⎪ ⎩ 0 if |M ∗ (k)| − 2 ∗ round |M ∗ (k)| ≤ 0 2
(0 ≤ k < P × Q )
398 399
where W ∗ = {w∗ (k), 0 ≤ k < P × Q } dimensional binary sequence.
is
the
extracted
one-
4.2.4. Step 4: obtaining the binary watermark image The one-dimensional binary sequences W* is rearranged to form the binary image, and the watermark image
Average PSNR (no attack) (dB)
A B C D E F G H I J
43.43 43.15 44.03 43.68 44.45 43.61 43.36 43.24 44.04 44.23
401 402
ˆ = {w(i, ˆ j), 0 ≤ i < P, 0 ≤ j < Q } W
403
can be obtained by descrambling.
404
5. Simulation results
405
We test the proposed watermarking scheme on ten popular test images. Ten test images from USC-SIPI image database, each of dimensions 512 × 512 × 8bit, are shown in Fig. 5, referred to as “Lena”, “Barbara”, “Mandrill”, “Peppers”, “Couple”, “Fishing boat”, “Clock”, “Girl”, “Stream and bridge”, and “Aerial”, respectively, in the sequel. And ten test watermarks, each of dimensions 32 × 32, are shown in Fig. 6, hereinafter referred to as watermarks A–J, respectively. The embedding strength = 0.2. Also, the experimental results are compared with schemes in [18,23]. In this work, the watermarking performance is evaluated from two aspects, namely invisibility and robustness. Here we use peek
Table 2 The average performance of the proposed watermarking method. Watermark
400
Average BER JPEG 20
JPEG 40
Median filtering (4 × 4)
Random noise (5%)
Rotation 10◦
Rotation 45◦
Scaling 0.7
Scaling 1.5
0.02 0.01 0.02 0.02 0.01 0.02 0.01 0.01 0.02 0.02
0 0 0 0 0 0 0 0 0 0
0.06 0.05 0.05 0.06 0.05 0.06 0.05 0.05 0.06 0.06
0.07 0.07 0.06 0.06 0.05 0.06 0.06 0.07 0.06 0.06
0.04 0.05 0.05 0.04 0.05 0.05 0.04 0.05 0.05 0.04
0.05 0.04 0.06 0.06 0.04 0.06 0.05 0.05 0.04 0.04
0.05 0.06 0.06 0.04 0.04 0.05 0.06 0.06 0.05 0.04
0.09 0.07 0.07 0.06 0.08 0.08 0.07 0.08 0.08 0.08
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Table 3 The PSNR for various watermarking methods (dB).
417 418
Image
Proposed scheme
Scheme [23]
Scheme [18]
Lena Barbara Mandrill Peppers
43.96 44.25 43.75 43.87
41.07 41.63 40.90 41.46
43.56 43.65 42.97 43.22
signal-to-noise ratio (PSNR) to measure the watermark invisibility. It is defined as
419
PSNR(I, I ∗ ) = 10 log
2552 × M × N
M−1 N−1 x=0
420 421 422 423
424
425 426 427 428 429 430
y=0
2 [f (x, y) − f ∗ (x, y)]
where I is the original image and I* is the watermarked version, M × N is the size of digital image. Also, watermark robustness was measured as the bit error rate (BER) of extracted watermark, its definition is
attacks. Table 2 gives the average values of the PSNRs obtained after embedding a particular watermark in the ten test images, as well as the average values of the BER obtained under various attacks. 5.1. Watermark invisibility Fig. 7(a) shows the watermarked image Lena, Barbara, Mandrill, and Peppers using the proposed scheme. Fig. 7(b)–(d) are the absolute difference between origin image and watermarked image for the diffrent scheme, multiplied by 5 for better display. Table 3 gives the PSNR of different watermarking schemes. From Table 3, we can know that the proposed scheme is better than schemes [18,23] in terms of the transparency. 5.2. Robustness to various attacks
Table 4 The watermark detection results for standard gray image Lena.
Table 5 The watermark detection results for standard gray image Peppers.
Attacks
No attack
Scheme [23]
Scheme [18]
ZMs
PZMs
PECT
PST
PCT
0
0
0
0
0
Proposed scheme
Attacks
0
No attack
433
435 436 437 438 439 440 441
442
where B is the number of erroneously detected bits, P × Q is the watermark image dimensions. Each of the ten test watermarks was embedded in the ten test images using the proposed watermarking method. A total of 10 × 10 = 100 watermarked images were generated and for each watermarked image, the digital was extracted under various
B × 100% P×Q
432
434
Simulation results, which are obtained by the proposed watermarking scheme, for some common image processing operations and geometrical transformations are shown in Fig. 8. Table 4 and Table 5 show the results of comparison with schemes [18,23]. It is clear that the proposed scheme outperforms scheme [18,23] under most attacks in terms of BER. In sum, the above experimental results confirm the validity of our approach and its higher robustness against geometric transformations compared to alternative watermarking methods in the literature. This is because that the RHFMs are free of numerical instability and the RHFMs magnitudes is invariant to
BER =
431
Scheme [23]
Scheme [18]
Proposed scheme
ZMs
PZMs
PECT
PST
PCT
0
0
0
0
0
0
0.04 0.01 0.03 0.03
0.02 0 0 0
0.03 0.04 0.04 0.05
0.01 0 0 0
0.0508 0 0 0
JPEG compression 20 0.02 40 0.03 60 0.04 80 0.02
0.04 0.03 0.03 0.03
0.01 0 0 0
0.04 0.03 0.03 0.04
0.02 0 0.01 0.01
0.0273 0 0 0
JPEG compression 20 0.06 0 40 60 0 0 80
Median filtering 0.17 2×2 4×4 0.20 0.35 6×6 0.49 8×8
0.18 0.16 0.32 0.39
0.19 0.12 0.46 0.54
0.22 0.13 0.37 0.48
0.14 0.19 0.35 0.46
0.4336 0.4219 0.4375 0.4609
Median filtering 0.30 2×2 0.41 4×4 0.51 6×6 0.55 8×8
0.25 0.34 0.44 0.54
0.13 0.18 0.31 0.45
0.21 0.19 0.38 0.37
0.24 0.23 0.37 0.47
0.3672 0.3945 0.4609 0.5156
Random noise addition 0.03 0.02 1% 0.05 0.05 2% 0.10 0.10 3% 0.32 0.21 4% 0.43 0.52 5%
0 0.01 0.04 0.22 0.38
0.03 0.07 0.09 0.33 0.46
0 0.02 0.09 0.23 0.39
0 0 0 0 0
Random noise addition 1% 0.01 0.03 0.03 0.02 2% 0.30 0.19 3% 0.39 0.39 4% 0.45 0.52 5%
0 0.03 0.17 0.28 0.48
0.03 0.09 0.20 0.40 0.43
0 0.02 0.22 0.38 0.45
0 0 0 0 0
Rotation 5◦ 10◦ 15◦ 20◦ 25◦ 30◦ 35◦ 40◦ 45◦
0.52 0.47 0.43 0.31 0.20 0.46 0.35 0.35 0.48
0.49 0.47 0.41 0.32 0.15 0.40 0.33 0.36 0.44
0.53 0.37 0.36 0.23 0.01 0.37 0.20 0.24 0.31
0.52 0.40 0.37 0.20 0.04 0.39 0.20 0.38 0.36
0.56 0.51 0.46 0.28 0.08 0.46 0.38 0.35 0.44
0 0 0 0 0 0 0 0 0
Rotation 5◦ 10◦ 15◦ 20◦ 25◦ 30◦ 35◦ 40◦ 45◦
0.48 0.48 0.48 0.43 0.19 0.54 0.53 0.44 0.50
0.49 0.55 0.57 0.41 0.21 0.57 0.59 0.34 0.54
0.47 0.52 0.52 0.22 0.03 0.52 0.36 0.33 0.50
0.50 0.55 0.59 0.21 0.04 0.62 0.40 0.45 0.63
0.43 0.44 0.50 0.31 0.07 0.46 0.46 0.44 0.47
0 0 0 0 0 0 0 0 0
Scaling 0.5 0.7 0.9 1.1 1.3 1.5
0.32 0.26 0.20 0.16 0.18 0.23
0.32 0.29 0.19 0.17 0.18 0.17
0.05 0.03 0.04 0.08 0.08 0.12
0.14 0.05 0.08 0.09 0.12 0.13
0.29 0.18 0.10 0.08 0.09 0.13
0.1211 0 0.0352 0.0742 0 0
Scaling 0.5 0.7 0.9 1.1 1.3 1.5
0.41 0.33 0.24 0.26 0.28 0.34
0.34 0.25 0.26 0.26 0.32 0.33
0.13 0.05 0.08 0.17 0.17 0.20
0.20 0.19 0.23 0.21 0.23 0.22
0.31 0.18 0.17 0.18 0.23 0.28
0.1445 0 0.0703 0.0859 0 0
Mean BER
0.24
0.23
0.17
0.19
0.21
0.0671
Mean BER
0.31
0.31
0.22
0.27
0.25
0.0697
Please cite this article in press as: Hong-Ying Y, et al. Geometrically resilient digital watermarking scheme based on radial harmonic Fourier moments magnitude. Int J Electron Commun (AEÜ) (2014), http://dx.doi.org/10.1016/j.aeue.2014.10.012
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G Model AEUE 51306 1–11
ARTICLE IN PRESS Y. Hong-Ying et al. / Int. J. Electron. Commun. (AEÜ) xxx (2014) xxx–xxx
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geometric transformation, so RHFMs are more suitable for robust image watermarking. 6. Conclusion
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Geometric transformations are the Achilles heel for many watermarking schemes. It is a challenging work to design a robust image watermarking scheme against geometric transformations. In this paper, we investigated the geometric invariant properties of radial harmonic Fourier moments (RHFMs), and proposed a new geometrically resilient image watermarking scheme based on RHFMs magnitudes. In the interest of better robustness and imperceptibility, the binary watermark image is first encrypted by Arnold transform, then the RHFMs of the host image are computed, and finally the digital watermark is embedded by quantizing the RHFMs magnitudes. Moreover, a detailed method has been designed to select the accurate and robust RHFMs. The experimental results demonstrate that the proposed watermarking scheme can survive common image processing operations, such as JPEG compression, median filtering, random noise addition and so on. Furthermore, the proposed scheme possesses good robustness against geometric transformations such as rotation, scaling, etc, simultaneously. However, the proposed algorithm is vulnerable to local image cropping attack. Accordingly, further work will be focused on improving the resistance to local image cropping attack for the watermarked digital image.
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Acknowledgements
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This work was supported by the National Natural Science Foundation of China under Grant No. 61472171 and 61272416, the Open Project Program of Jiangsu Key Laboratory of Image and Video Understanding for Social Safety (Nanjing University of Science and Technology) under Grant No. 30920130122006, the Open Foundation of Zhejiang Key Laboratory for Signal Processing under Grant No. ZJKL 4 SP-OP2013-01, the Open Foundation of Provincial Key Laboratory for Computer Information Processing Technology (Soochow University) under Grant No. KJS1325, the Open Project Program of the State Key Lab of CAD&CG (Grant No. A1425), Zhejiang University, and Liaoning Research Project for Institutions of Higher Education of China under Grant No. L2013407.
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References
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[1] Bianchi T, Piva A. Secure watermarking for multimedia content protection: a review of its benefits and open issues. IEEE Signal Process Mag 2013;30(2):87–96. [2] Lin P, Lee J, Chang C. Protecting the content integrity of digital imagery with fidelity preservation. ACM Trans Multimed Comput Commun Appl 2011;7(3):1–15. [3] Su P, Chang Y, Wu C C. Geometrically resilient digital image watermarking by using interest point extraction and extended pilot signals. IEEE Trans Inf Forensics Secur 2013;8(12):1897–908. [4] Cheddad A, Condell J, Curran K. Digital image steganography: survey and analysis of current methods. Signal Process 2010;90(3):727–52. [5] Zheng D, Liu Y, Zhao J, Saddik AE. A survey of RST invariant image watermarking algorithms. ACM Comput Surv 2007;39(2):1–91. [6] Lichtenauer J, Setyawan I, Kalker T, Lagendijk R. Exhaustive geometrical search and the false positive watermark detection probability. Proc SPIE Secur Watermarking Multimed Contents V 2003;5020:203–14.
11
[7] Valizadeh A, Wang ZJ. An improved multiplicative spread spectrum embedding scheme for data hiding. IEEE Trans Inf Forensics Secur 2012;7(4):1127–43. [8] Maity SP, Maity S. Collusion resilient spread spectrum watermarking in M-band wavelets using GA-fuzzy hybridization. J Syst Softw 2013;86(1):47–59. [9] Li M, Michel KK, Dimitris AP, Stella NB, Michael JM. Extracting spreadspectrum hidden data from digital media. IEEE Trans Inf Forensics Secur 2013;8(7):1201–10. [10] Kaur M, Kaur P. Robust watermarking into the color models based on the synchronization template. In: International conference on information and multimedia technology (ICIMT 09). 2009. p. 296–300. [11] Zhao Y, Ni R, Zhu. Z. RST transforms resistant image watermarking based on centroid and sector-shaped partition. Sci China Inf Sci 2012;55(3):650–62. [12] Herrigel A, Voloshynovsky S, Rytsar Y. The watermark template attack. Proc SPIE Secur Watermarking Multimed Contents III 2008;4314:394–405. [13] Seo JS, Yoo. CD. Image watermarking based on invariant regions of scale-space representation. IEEE Trans Signal Process 2006;54(4):1537–49. [14] Tian H, Zhao Y, Ni R, Qin L, Li. X. LDFT-based watermarking resilient to local desynchronization attacks. IEEE Trans Cybern 2013;43(6):2190–201. [15] Gao XB, Deng C, Li. XL. Geometric distortion insensitive image watermarking in affine covariant regions. IEEE Trans Syst Man Cybern Part C: Appl Rev 2010;40(3):278–86. [16] Yuan XC, Pun CM, Chen. PCL. Geometric invariant watermarking by local Zernike moments of binary image patches. Signal Process 2013;93(7):2087–95. [17] Manoochehri M, Pourghassem H, Shahgholian G. A novel synthetic image watermarking algorithm based on discrete wavelet transform and Fourier–Mellin transform. In: 2011 IEEE 3rd international conference on communication software and networks (ICCSN). 2011. p. 265–9. [18] Tsougenis ED, Papakostas GA, Koulouriotis DE, Tourassis VD. Towards adaptivity of image watermarking in polar harmonic transforms domain. Opt Laser Technol 2013;54:84–97. [19] Ali M, Ahn. CW. An optimized watermarking technique based on self-adaptive DE in DWT–SVD transform domain. Signal Process 2014;94:545–56. [20] Coatrieux G, Pan W, Cuppens-Boulahia N, Cuppens F. Reversible watermarking based on invariant image classification and dynamic histogram shifting. IEEE Trans Inf Forensics Secur 2013;8(1):111–21. [21] Mohammad AA. A new digital image watermarking scheme based on Schur decomposition. Multimed Tools Appl 2012;59(3):851–83. [22] Yap PT, Paramesran R. Local watermarks based on Krawtchouk moments. In: 2004 IEEE region 10 conference TENCON. 2004. p. 73–6. [23] Xin Y, Liao S, Pawlak M. Circularly orthogonal moments for geometrically robust image watermarking. Pattern Recognit 2007;40(12):3740–52. [24] Fahmy MF, Raheem GMA, Thabet MA. A Zernike moment based rotational invariant watermarking scheme. In: The 30th national radio science conference (NRSC), 16–18 April 2013. 2013. p. 228–35. [25] Zhu H, Liu M, Li Y. The RST invariant digital image watermarking using Radon transforms and complex moments. Digit Signal Process 2010;20(6): 1612–28. [26] Elshoura SM, Megherbi DB. Analysis of noise sensitivity of Tchebichef and Zernike moments with application to image watermarking. J Vis Commun Image Represent 2013;24(5):567–78. [27] Zhang H, Shu H, Coatrieux G. Affine Legendre moment invariants for image watermarking robust to geometric distortions. IEEE Trans Image Process 2011;20(8):2189–99. [28] Singh C, Ranade SK. Rotation invariant moments and transforms for geometrically invariant image watermarking. J Electron Imaging 2013;22(1): 013034. [29] Chandan Singh, Ranade Sukhjeet K. A high capacity image adaptive watermarking scheme with radial harmonic Fourier moments. Digit Signal Process 2013;23(5):1470–82. [30] Papakostas GA, Koulouriotis DE, Tourassis VD. Performance evaluation of moment-based watermarking methods: a review. J Syst Softw 2012;85(8):1864–84. [31] Ren H, Ping Z, Bo W, Wu W. Multidistortion-invariant image recognition with radial harmonic Fourier moments. J Opt Soc Am A 2003;20(4):631–7. [32] Hoang TV, Tabbone S. Generic polar harmonic transforms for invariant image description. In: The 18th IEEE international conference on image processing (ICIP). 2011. p. 845–8. [33] Chen BJ, Shu HZ, Zhang H. Quaternion Zernike moments and their invariants for color image analysis and object recognition. Signal Process 2012;92(2):308–18. [34] Li L, Li S, Abraham A, Pan J. Geometrically invariant image watermarking using polar Harmonic transforms. Inf Sci 2012;199(15):1–19. [35] Li X. Optimization analysis of formulas for quantization-based image watermarking. Opto-Electron Eng 2010;37(2):96–102.
Please cite this article in press as: Hong-Ying Y, et al. Geometrically resilient digital watermarking scheme based on radial harmonic Fourier moments magnitude. Int J Electron Commun (AEÜ) (2014), http://dx.doi.org/10.1016/j.aeue.2014.10.012
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