J. Vis. Commun. Image R. 41 (2016) 247–259
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Geometrically resilient color image zero-watermarking algorithm based on quaternion Exponent moments q Wang Chun-peng a, Wang Xing-yuan a,⇑, Xia Zhi-qiu a, Zhang Chuan a, Chen Xing-jun b a b
Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian 116023, China Operation Software and Simulation Institute, Dalian Navy Academy, Dalian 116018, China
a r t i c l e
i n f o
Article history: Received 20 April 2016 Revised 20 September 2016 Accepted 8 October 2016 Available online 10 October 2016 Keywords: Color image Geometric attacks Quaternion Exponent moments Zero-watermarking
a b s t r a c t Although research on zero-watermarking has made great progress in recent years, most of it has been focused on grayscale images rather than color ones, and cannot resist geometric attacks efficiently. In this paper, we discuss properties of quaternion Exponent moments (QEMs) in detail and propose a robust color image zero-watermarking algorithm which is robust to geometric attacks. We first compute and select robust QEMs of the original color image, and then a binary feature image is constructed using the magnitude of the selected moments. Eventually, a bitwise exclusive-or is applied on the binary feature image and a scrambled binary logo to generate the zero-watermark image. Experimental results show that the proposed zero-watermarking algorithm is robust to both geometric attacks and common image processing attacks effectively. Compared to similar zero-watermarking algorithms and traditional watermarking algorithms based on QEMs, the proposed zero-watermarking algorithm has better performance. Ó 2016 Elsevier Inc. All rights reserved.
1. Introduction With the increase in digitalization and informatization of modern times, the protection of image copyright has become a prominent problem. As a crucial technology for image copyright protection, image watermarking technology has been extensively researched and used. Traditional watermarking algorithms [1,2] embed the information of ownership identification in the original image so that the information can be extracted in order to enforce copyright protection. However, this kind of algorithms degrades the quality of the original image and has to trade off between robustness and imperceptibility. To overcome the limitations of traditional watermarking algorithms, zero-watermarking was proposed by Wen et al. [3]. In zero-watermarking algorithms, copyright protection is achieved by extracting important features of an image and storing them in an intellectual property rights (IPR) database. These algorithms essentially embed nothing into the original image and thus have perfect imperceptibility. Compared with traditional watermarking algorithms, zero-watermarking
q
This paper has been recommended for acceptance by M.T. Sun.
⇑ Corresponding author at: School of Computer Science and Technology, Dalian University of Technology, No 2, Linggong Road, Dalian 116023, China. E-mail addresses:
[email protected] (C.-p. Wang),
[email protected] (X.-y. Wang). http://dx.doi.org/10.1016/j.jvcir.2016.10.004 1047-3203/Ó 2016 Elsevier Inc. All rights reserved.
algorithms have the following two major advantages. First, they do not degrade the quality of the original image; hence, this kind of algorithms has perfect imperceptibility. Second, they focus on how to construct watermarking information through the use of important features of the original image rather than on how to embed watermarks. Therefore, zero-watermarking algorithms do not have to deal with the reversion process from transform domain to spatial domain and the corresponding implementation speed is much greater than traditional algorithms. Moreover, due to the fact that zero-watermark information varies from image to another, so we need to establish Intellectual Property Right (IPR) database to preserve the zero-watermark information. From the properties of zero-watermarking, we know that the real applications of traditional watermarking algorithm are also suitable to zero-watermarking algorithm, including digital media copyright protection, intellectual property authentication, ID identity card authentication, trademark information security protection and so on. Moreover, for some images with higher integrity requirements, such as medical image, military image and remote sensing image, it is not suitable for the traditional watermarking algorithm to protect the copyright of them. In this case, zerowatermarking can be used to protect the copyright of them perfectly. Since the concept of zero-watermarking was proposed, some scholars conducted numerous studies on this topic and proposed
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some excellent algorithms. Wen et al. [3] constructed a zerowatermarking algorithm using high-order cumulants, which has good robustness to common signal processing and slight rotation attacks. Chen et al. [4] proposed a zero-watermarking scheme in the wavelet domain, which does not require the original image for logo verification. This scheme introduces cryptographic tools, such as digital signatures and timestamps, to make copyright proving publicly accessible. In 2008, an adaptive copyright protection scheme in the spatial domain was proposed by Chang and Lin [5]. This scheme uses edge detection based on Sobel’s algorithm to generate a verification map. Moreover, this approach adjusts the strength of watermarks through a threshold to enhance robustness. In [6], Tsai et al. presented an effective zero-watermarking algorithm for image copyright protection, which is based on an a-trimmed mean algorithm to enhance robustness and supports vector machine. Moreover, it memorizes the relationship between feature information and the watermark by using a trained SVM to authenticate the ownership of the image. Based on the foundation of [6], Tsai et al. [7] proposed a zero-watermarking scheme against geometric attacks for image authentication. This scheme finds RST invariants of images by integrating the discrete Fourier transform with the log-polar mapping. Subsequently, a trained SVM is used to memorize the relationship between the set of characteristics of RST invariants and the secret key. Moreover, the particle swarm optimization algorithm is also employed to determine a set of nearly optimal parameters of the SVM. Vellaisamy and Ramesh [8] presented an ‘inversion attack’ resilient zero-watermarking system for medical image authentication in the hybrid Contourlet transform-singular value decomposition domain. This scheme preserves the fidelity of the host image and employs a triangular number generating function and Hu’s image invariants to withstand ‘inversion attacks’. In [9], Gao and Jiang proposed a robust zerowatermarking algorithm based on Bessel-Fourier moments, which can resist various signal processing operations and geometric transformations. This scheme applies an image normalization technique to achieve invariance of translation and scaling. Subsequently, the magnitudes of Bessel-Fourier moments of normalized images are computed and are used to construct the feature image regarded as the zero-watermark. A novel zerowatermarking scheme based on the generalized Arnold transform was proposed by Lin et al. [10]. This scheme scrambles an original watermark using the generalized Arnold transform. Then, a binary matrix is obtained from the original image using quantitative embedding rules. Eventually, the zero-watermark image can be obtained through the application of a XOR operation between the watermark and the binary matrix by using spread spectrum technique. However, most of the existing zero-watermarking algorithms mentioned above mainly concentrate on resisting common image processing attacks; they cannot resist geometric attacks efficiently. Moreover, these algorithms are designed for grayscale images rather than color ones. However, color images are more common in our everyday life, and contain more information than grayscale images of the same dimensions, so it is very important to design zero-watermarking algorithms that can resist geometric attacks for color images. In this paper, a geometric attack-resistant robust color image zero-watermarking algorithm based on quaternion exponential moments is proposed. We first compute the QEMs of the original color image and select the robust moments. Then, the binary feature image is constructed by using the magnitudes of the selected moments. Subsequently, bitwise exclusive-or is applied on the binary feature image and a scrambled binary logo is applied to generate the zero-watermark. Experimental results show that the proposed algorithm can resist both geometric attacks and common image processing attacks.
The rest of the paper is organized as follows. Section 2 gives a brief introduction of quaternion representation and Exponent moments. Section 3 introduces quaternion Exponent moments and its invariants for rotation and scaling of color images, and discusses their stability. In Section 4, the zero-watermarking algorithm is presented. Experimental results are provided in detail in Section 5. Finally, Section 6 provides a summary of the paper. 2. Preliminaries 2.1. Quaternion representation Quaternions, which are a generalization of complex numbers, were introduced by Hamilton in 1843 [11]. A quaternion has one real and three imaginary parts:
q ¼ a þ bi þ cj þ dk;
ð1Þ
where a, b, c and d are real numbers, i, j and k are complex operators which satisfy the following properties: 2
2
2
i ¼ j ¼ k ¼ ijk ¼ 1 ij ¼ k; jk ¼ i; ki ¼ j
:
ð2Þ
ji ¼ k; kj ¼ i; ik ¼ j The conjugate and the magnitude of quaternion q are pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ a bi cj dk and jqj ¼ a2 þ b2 þ c2 þ d2 , respectively. A q quaternion can be considered as the combination of a scalar part and a vector part: q ¼ sðqÞ þ v ðqÞ, where sðqÞ ¼ a, v ðqÞ ¼ bi þ cj þ dk. When the scalar part is equal to zero scalar part (a ¼ 0) is called a pure quaternion, and a quaternion with unit magnitude is called a unit quaternion. The multiplication of any two quaternions q1 and q2 is not commutative, i.e. q1 q2 – q2 q1, and the multiplication of their conjugates satisfies q1 q2 ¼ q2 q1. 2.2. Exponent moments Based on the relationship between the exponential function and the triangular function, Ping et al. [12] introduced Exponent moments (EMs) by extending the concept of radial harmonic Fourier moments. Let f ðr; hÞ be a grayscale image in the polar coordinate system. The EMs of f ðr; hÞ are defined over a unit circle as:
1 4p
Enm ¼
Z
0
2p
Z
1
f ðr; hÞAn ðrÞ expðjmhÞrdrdh;
ð3Þ
0
where Enm are the EMs of order n ð1 < n < 1Þ with repetition m ð1 < m < 1Þ, and An ðrÞ is the conjugate of the radial basis pffiffiffiffiffiffiffiffi function An ðrÞ ¼ 2=r expðj2nprÞ; 0 6 r 6 1; 0 6 h 6 2p. The radial basis function An ðrÞ and the angle function expðjmhÞ constitute the function set Pnm ðr; hÞ in the polar coordinate system ðr; hÞ:
Pnm ðr; hÞ ¼ An ðrÞ expðjmhÞ:
ð4Þ
According to the characteristics of the radial basis function and the angle function, the set P nm ðr; hÞ is orthogonal in the unit circle:
Z
0
2p
Z
1
0
P nm ðr; hÞPkl ðr; hÞrdrdh ¼ 4pdnk dml ;
ð5Þ
where 4p is the normalization factor, dnk and dml are the Kronecker delta, and Pkl ðr; hÞ is the conjugate of Pkl ðr; hÞ. The image f ðr; hÞ can be reconstructed using the set Pnm ðr; hÞ as:
f ðr; hÞ ¼
þ1 X þ1 X
Enm Pnm ðr; hÞ ¼
n¼1m¼1
þ1 X þ1 X
Enm An ðrÞ expðjmhÞ:
n¼1m¼1
ð6Þ
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2.3. Computation of EMs
ELnm ¼
There are two methods to compute EMs of a grayscale image f ðp; qÞ with N N pixels in the Cartesian coordinate system, which are inscribed circle mapping method and circumscribed circle mapping method. The magnitudes of QEMs obtained by using the circumscribed circle method mapping cannot meet rotational invariance, so they are not suitable for image zero-watermarking. Accordingly, we will use the inscribed circle mapping method in this section, as shown in Fig. 1. The image is mapped onto a unit circle using the following formula:
xq ¼
2q N þ 1 ; N
yp ¼
N 1 2p ; N
ðp; q ¼ 0; 1; . . . ; N 1Þ;
where ðxq ; yp Þ is the center of a xq D2x ; xq þ D2x ½yp D2y ; yp þ D2y with Dx ¼ Dy ¼ N2 . Thus, we can obtain the discrete formula of Eq. (3):
Enm ¼
N 1 X N1 1 X
pN2 p¼0 q¼0
where r p;q ¼
ð7Þ
square
f ðp; qÞAn ðrp;q Þ expðjmhp;q Þ;
ð8Þ
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi y x2q þ y2p ; hp;q ¼ arctan xqp .
3. Quaternion Exponent moments of color images 3.1. Quaternion Exponent moments By using the quaternion representation, a color image f ðr; hÞ can be considered as an array of pure quaternion numbers [13]:
f ðr; hÞ ¼ f R ðr; hÞi þ f G ðr; hÞj þ f B ðr; hÞk;
ð9Þ
where f R ðr; hÞ, f G ðr; hÞ and f B ðr; hÞ represent the Red, Green and Blue color components of f ðr; hÞ respectively. The multiplication of quaternions is not commutative, hence there are two different definitions of QEMs [14,15] as follows.
ELnm ½f ðr; hÞ; l ¼
1 4p
ERnm ½f ðr; hÞ; l ¼
1 4p
Z
2p
1
0
0
Z
Z
2p
0
Z
1
0
An ðrÞ expðlmhÞf ðr; hÞrdrdh;
ð10Þ
An ðrÞf ðr; hÞ expðlmhÞrdrdh;
ð11Þ
where l is a pure unit quaternion. The two QEMs are formed by placing the integral kernels expðlmhÞ on the left side and right
side of a color image f ðr; hÞ. Accordingly, ELnm ½f ðr; hÞ; l and ERnm ½f ðr; hÞ; l are called left- and right-side QEMs of order n ð1 < n < 1Þ with repetition m ð1 < m < 1Þ, respectively.
Since q1 q2 ¼ q2 q1, we can obtain the relationship between right- and left-side QEMs for the same color image f ðr; hÞ as shown in Eq. (12).
ERnm ½f ðr; hÞ;
1 l ¼ 4p ¼ ¼
1 4p 1 4p
Z
2p
Z
0
Z
0 2p
Z
0
Z 0
1
1 0
2p
Z
1 0
Z 0
2p
Z 0
1
An ðrÞ expðlmhÞf ðr; hÞrdrdh
Z 2p Z 1 1 An ðrÞ expðlmhÞ½f R ðr; hÞi þ f G ðr; hÞj þ f B ðr; hÞkrdrdh 4p 0 0 Z 2p Z 1 1 ¼ An ðrÞ expðlmhÞf R ðr; hÞrdrdh i 4p 0 0 Z 2p Z 1 1 þ An ðrÞ expðlmhÞf G ðr; hÞrdrdh j 4p 0 0 Z 2p Z 1 1 þ An ðrÞ expðlmhÞf B ðr; hÞrdrdh k 4p 0 0 Z 2p Z 1 1 An ðrÞðcos mh l sin mhÞf R ðr; hÞrdrdh i ¼ 4p 0 0 Z 2p Z 1 1 þ An ðrÞðcos mh l sin mhÞf G ðr; hÞrdrdh j 4p 0 0 Z 2p Z 1 1 þ An ðrÞðcos mh l sin mhÞf B ðr; hÞrdrdh k 4p 0 0 Z 2p Z 1 1 An ðrÞ cos mhf R ðr; hÞrdrdh ¼ 4p 0 0 Z 2p Z 1 1 l An ðrÞ sin mhf R ðr; hÞrdrdh i 4p 0 0 Z 2p Z 1 1 þ An ðrÞ cos mhf G ðr; hÞrdrdh 4p 0 0 Z 2p Z 1 1 l An ðrÞ sin mhf G ðr; hÞrdrdh j 4p 0 0 Z 2p Z 1 1 An ðrÞ cos mhf B ðr; hÞrdrdh þ 4p 0 0 Z 2p Z 1 1 l An ðrÞ sin mhf B ðr; hÞrdrdh k 4p 0 0 iþjþk ¼ RealðEnm ðf R ÞÞ þ pffiffiffi ImagðEnm ðf R ÞÞ i 3 iþjþk þ RealðEnm ðf G ÞÞ þ pffiffiffi ImagðEnm ðf G ÞÞ j 3 iþjþk þ RealðEnm ðf B ÞÞ þ pffiffiffi ImagðEnm ðf B ÞÞ k 3 ¼
¼ ALnm þ iBLnm þ jC Lnm þ kDLnm ð13Þ with
ALnm ¼ p1ffiffi3 ½ImagðEnm ðf R ÞÞ þ ImagðEnm ðf G ÞÞ þ ImagðEnm ðf B ÞÞ BLnm ¼ RealðEnm ðf R ÞÞ þ p1ffiffi3 ½ImagðEnm ðf B ÞÞ ImagðEnm ðf G ÞÞ C Lnm ¼ RealðEnm ðf G ÞÞ þ p1ffiffi3 ½ImagðEnm ðf R ÞÞ ImagðEnm ðf B ÞÞ
An ðrÞf ðr; hÞ expðlmhÞrdrdh
;
DLnm ¼ RealðEnm ðf B ÞÞ þ p1ffiffi3 ½ImagðEnm ðf G ÞÞ ImagðEnm ðf R ÞÞ ð14Þ
An ðrÞexpðlmhÞf ðr; hÞrdrdh
ð12Þ
An ðrÞ expðlmhÞf ðr; hÞrdrdh
¼ ELnm ½f ðr; hÞ; l: In our paper, we will only refer to left-side QEMs, unless otherELnm
1 4p
ELnm
for abbreviation. can be wise stated, and denote them as obtained through the computation of EMs for a grayscale image [16], which is shown as follows.
pffiffiffi where l ¼ ði þ j þ kÞ= 3, f R , f G and f B represent the red, green and blue components of the color image respectively, Enm ðf R Þ, Enm ðf B Þ and Enm ðf G Þ are the corresponding EMs, RealðpÞ denotes the real part of complex number p and ImagðpÞ is the imaginary part. 3.2. Rotation invariance r
Let f ðr; hÞ ¼ f ðr; h aÞ denote the image rotated by an angle a. r Then, the QEMs of f ðr; hÞ and f ðr; hÞ have the following relation:
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(0, N − 1)
(0, 0)
1
p
( p, q )
q
yp
θ p ,q
rp ,q
( xq , y p )
xq
-1
1
(N-1,0)
-1
( N − 1, N − 1)
( N − 1, 0)
(a) Grayscale image
(b) Inscribed circle mapping
Fig. 1. Inscribed circle mapping of grayscale image.
r
ELnm ðf Þ ¼
1 4p
1 ¼ 4p ¼ ¼
1 4p 1 4p
Z
2p
Z
2p
Z
2p
Z
2p
Z
0
Z
0
Z
0
0
Z
1
1
0 1
0
0
1
0
¼ expðlmaÞ
An ðrÞ expðlmhÞf ðr; h aÞrdrdh
According to the experiments, the magnitudes of QEMs remain almost invariable under various attacks, as the corresponding mean relative errors (MRE) are less than 0.01. Therefore, they are suitable for color image zero-watermarking algorithms.
An ðrÞ expðlmða þ hÞÞf ðr; hÞrdrdh
3.5. Comparison between left- and right-side QEMs
An ðrÞ expðlmhÞf ðr; hÞrdrdh r
An ðrÞ expðlmaÞ expðlmhÞf ðr; hÞrdrdh 1 4p
Z 0
2p
Z 0
1
An ðrÞ expðlmhÞf ðr; hÞrdrdh
¼ expðlmaÞELnm ðf Þ ð15Þ r
r
where ELnm ðf Þ and ELnm ðf Þ are the QEMs of f ðr; hÞ and f ðr; hÞ respectively. Taking the norm of Eq. (15), we obtain
jELnm ðf Þj ¼ j expðlmaÞELnm ðf Þj ¼ j expðlmaÞjjELnm ðf Þj r
¼ jELnm ðf Þj:
ð16Þ
Therefore, the norms of the QEMs are invariant to image rotation. 3.3. Scale invariance Theoretically, QEMs are not invariant to image scaling, but we can achieve scale invariance by normalizing the image into a unit circle. If a color image f ðr; hÞ with a resolution of N N pixels is scaled by a factor of k ¼ N=2, the normalized color image will be 0
gðr ; hÞ ¼ f ðr=k; hÞ;
In this section, we conducted several experiments to compare left- and right-side QEMs, which defined in Eqs. (10) and (11), respectively. Fig. 3 shows the color images ‘Lena’, ‘Barbara’, ‘Mandrill’ and ‘Peppers’, each used with a resolution of 512 512 24 bit as a test image. In Table 1, jEn;m j represents the magnitude of QEM of order n with repetition m. L-QEM and R-QEM denote left- and right-side QEMs, respectively. As can be seen from Table 1, the magnitudes of left- and rightside QEMs are pairwise symmetric about jE0;0 j, so they have the same capability to describe a color image.
ð17Þ
0
where 0 6 r 6 1. In this way, the contents of the image are mapped onto the unit circle, hence the making the QEMs of the image invariant to scaling. 3.4. The stability of quaternion Exponent moments To verify the stability of QEMs, we conducted several experiments using the color image ‘Lena’ at a resolution of 512 512 24 bit by considering the magnitudes of QEMs under various attacks, as shown in Fig. 2. Here, the highest order of QEMs, (nmax ), is 3. Note that, due to the magnitude of QEM of order n ¼ 0 with repetition m ¼ 0 being very large compared to the other values (110.0119), they are not shown in the figure to preserve legibility.
4. Zero-watermarking algorithm Our zero-watermarking algorithm comprises two processes: the zero-watermark generation process and the zero-watermark verification procedure. The first process generates the zerowatermark by using the QEMs of the original color image. The second process verifies the copyright of the protected image. 4.1. Zero-watermark generation In this process, we first compute the QEMs of the original color image and select the robust moments to construct a binary feature image. Then, a bitwise exclusive-or operation is applied on the binary feature image and a scrambled binary logo is used to generate the zero-watermark. The flow chart of the zero-watermark generation process is shown in Fig. 4. Let I ¼ ff ðx; yÞ; 0 6 x; y < Ng be an original color image and L ¼ flði; jÞ; 0 6 i < P; 0 6 j < Q g be a binary logo image. The process of zero-watermark generation is summarized in detail as follows. Step 1: Scrambling the logo image. In order to improve the robustness of the whole zerowatermarking system, the logo image should be first scrambled.
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C.-p. Wang et al. / J. Vis. Commun. Image R. 41 (2016) 247–259
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2
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10
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(d) Median filtering (3×3), MRE=0.0069
22
0
40
Quaternion Exponent moments
(c) Average filtering (3×3), MRE=0.0008
0
35
10
6
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30
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25
(b) Gaussian noise (0.005), MRE=0.0016
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(a) Original image
0
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50
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25
30
35
Quaternion Exponent moments
Quaternion Exponent moments
(e) JPEG70, MRE=0.0025
(f) JPEG50, MRE=0.0051
40
Fig. 2. Stability of QEMs for color image ‘Lena’ at a resolution of 512 512 24 bit.
In our zero-watermark generation process, the binary logo image is scrambled from L to L1 ¼ fl1 ði; jÞ; 0 6 i < P; 0 6 j < Q g using the quasi-affine transform [17] with seed s1.
The quasi-affine transform is a special affine transform considering non-linear round-off situations; it includes 6 parameters a; b; c; d; e; f , and its general form is:
C.-p. Wang et al. / J. Vis. Commun. Image R. 41 (2016) 247–259 22
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(h) Scaling (1.2), MRE=0.0006
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(g) Scaling (0.5), MRE=0.0020
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(j) Rotation ( 45 ), MRE=0.0006
(i) Rotation ( 5 ), MRE=0.0002 Fig. 2 (continued)
(a) Lena
(b) Barbara
(c) Mandrill
(d) Peppers
Fig. 3. Color images used in the comparison between left- and right-side QEMs.
x0 y0
¼
x e þ ; y f d
a b c
ð18Þ
a b where the determinant of the matrix satisfies c d a b 0 0 c d ¼ 1; ðx; yÞ denotes one pixel in the logo image; and ðx ; y Þ denotes one pixel in the scrambled logo image. This transform
scrambles the logo image by changing the pixel locations. The image scrambling procedure is completed when the quasi-affine transform has traversed every pixel in the image. It is worth noting that quasi-affine transform can only effectively scramble an image when the following two conditions fulfilled: (1) the transformation is a single-valued mapping from domain ðx; yÞ to itself; (2) the transformation is a subjective mapping from domain ðx; yÞ to itself. Thus, we need to find specific
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C.-p. Wang et al. / J. Vis. Commun. Image R. 41 (2016) 247–259 Table 1 Magnitudes of left- and right-side QEMs for the color images of Fig. 3. jE1;1 j
jE1;0 j
jE1;1 j
jE0;1 j
jE0;0 j
jE0;1 j
jE1;1 j
jE1;0 j
jE1;1 j
Lena
L-QEM R-QEM
4.6476 5.0035
20.6961 19.9902
4.3870 5.4237
8.5970 8.4402
109.8930 109.8930
8.4402 8.5970
5.4237 4.3870
19.9902 20.6961
5.0035 4.6476
Barbara
L-QEM R-QEM
7.0693 7.0532
15.5319 15.4776
4.6736 4.9006
11.7488 11.5870
98.3310 98.3310
11.5870 11.7488
4.9006 4.6736
15.4776 15.5319
7.0532 7.0693
Mandrill
L-QEM R-QEM
5.0742 5.9205
10.9840 13.3173
6.7990 6.8890
7.1887 5.5517
107.5044 107.5044
5.5517 7.1887
6.8890 6.7990
13.3173 10.9840
5.9205 5.0742
Peppers
L-QEM R-QEM
3.6461 4.8924
13.9544 16.0948
6.7068 6.1722
7.4050 9.6332
93.2425 93.2425
9.6332 7.4050
6.1722 6.7068
16.0948 13.9544
4.8924 3.6461
The original color image Quasi-affine Logo image transform
Quaternion Exponent moments
Scrambled logo image
Random selection
⊕
Accurate QEMs
Feature image
Feature vector
Binarization
Zero-watermark image Fig. 4. The zero-watermark generation procedure.
values for parameters a; b; c; d; e; f to fulfill those two conditions, which further ensures the safety of the algorithm.
m=0 m=-70
m=+70
n=+70
Step 2: Computation of QEMs. The QEMs of the original color image I are computed through using Eq. (10). Step 3: Selection of robust QEMs.
n=+16 n=0
Although QEMs are stable to various attacks, the increasing moment order will result in some non-robust moments, but for zero-watermarking algorithms, only the robust moments should be used. According to the experiments on some kinds of image attacks, we select the QEMs whose magnitude variation is smaller than 2% as robust moments in this paper. In summary, robust QEMs for zero-watermarking must be selected using: ① m ¼ 0, ② If nmax > bN=32c, then bN=32c < n < bN=32c; If nmax 6 bN=32c, then nmax 6 n 6 nmax ,
m>0
n=-16
n=-70
Fig. 5. Robust QEMs for zero-watermark generation (for color images with a resolution of 512 512 24 bit).
where T is a threshold determined using Otsu’s method [18]. Step 5: Generation of verification image.
where nmax is the highest order of QEMs, while bc represents the round-down function. The shaded region of Fig. 5 shows the set S of the robust QEMs for color images with 512 512 24 bit. Here, the highest order of QEMs is set to 70. To enhance the robustness of our algorithm, we use a secret key s2 to randomly select P Q robust QEMs from S. Then, let the mag!
We then apply an XOR operation between the feature image Lf and scrambled logo image L1 to generate the zero-watermark image W, where
W ¼ XORðLf ; L1 Þ:
ð20Þ
Thus, the zero-watermark image contains the binary logo image.
nitude of the selected moments be A ¼ fA1 ; A2 ; ; APQ g. Step 6: Digital signature. Step 4: Generation of binary feature image. A is rearranged into a two-dimensional feature image LA with P Q pixels. Then, we obtain the binary feature image Lf from LA through thresholding as follows:
Lf ði; jÞ ¼
1; if LA ði; jÞ P T 0;
if LA ði; jÞ < T
;
ð0 6 i < P; 0 6 j < Q Þ;
ð19Þ
Finally, the zero-watermark image and all the security parameters are signed by the owner using a digital signature technique [4]:
DS ¼ SignOSK ðW; s1 ; s2 Þ:
ð21Þ
where SignOSK is a digital signature function that uses the owner’s private key OSK. Finally, the signature DS is registered in
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a third-part intellectual property rights (IPR) database for copyright protection.
7000
The second process is to verify the copyright of the protected image I . This is summarized in detail as follows. Step 1: Digital signature verification. In order to verify the copyright of the protected image, anyone can use the owner’s public key to verify the signature DS and to validate the security parameters W, s1 and s2 . If successful, the verification will be ‘verified’, otherwise the algorithm returns ‘fail’ and stops.
Watermark capacity (bit)
6000
4.2. Zero-watermark verification
5000
4000
3000
2000
1000
0
0
10
20
30
40
50
70
60
80
90
100
Highest order of QEMs
Step 2: Computation of QEMs. The QEMs of I are computed using Eq. (10).
Fig. 6. The relationship between the watermark capacity and highest order of QEMs.
Step 3: Selection of robust QEMs.
algorithms. Nine original color images with a resolution of 512 512 24 bit and a binary logo image with 64 64 bit were used, as shown in Fig. 7. The highest order of QEMs is set to 70. We use the Peak Signal-to-Noise Ratio (PSNR) to evaluate the quality of attacked images. The definition of PSNR for an N N image is as follows:
We use the secret key s2 to randomly select P Q robust QEMs. Then, let the magnitude of the selected moments be !
A ¼ fA1 ; A2 ; ; APQ g. Step 4: Generation of binary feature image. A is rearranged into the two-dimensional feature image LA with P Q pixels. Then, we obtain the binary feature image Lf from LA through thresholding. Step 5: Retrieving the scrambled logo image. We apply an XOR operation on the feature image Lf and zerowatermark image W to retrieve the scrambled logo image L1 :
L1 ¼ XORðLf ; WÞ:
!
2552 N2
ð22Þ
Step 6: Inversely scrambling the logo image. Finally, the retrieved logo image L1 is unscrambled to obtain the original logo image L using seed s1. 5. Experimental results To evaluate the performance of the proposed algorithm, we conducted experiments comparing our algorithm with similar zero-watermarking algorithms, and QEMs-based traditional watermarking algorithm. 5.1. Watermark capacity Watermark capacity is an important criterion to evaluate the performance of a zero-watermarking algorithm. In this paper, the watermark capacity is determined by the number of robust QEMs that can be used to construct zero-watermark image. As we know from Fig. 5, the number of robust QEMs will be determined when the size of a color image and the highest order of QEMs are given. For a color image with a resolution of 512 512 24 bit, the relationship between the watermark capacity and highest order of QEMs is shown in Fig. 6. 5.2. Watermark robustness 5.2.1. Comparison with similar zero-watermarking algorithms We first investigate the proposed zero-watermarking algorithm’s performance compared to similar zero-watermarking
PSNR ¼ 10 log PN1 PN1 x¼0
y¼0
½f ðx; yÞ f ðx; yÞ
2
dB;
ð23Þ
where f ðx; yÞ is the original image and f ðx; yÞ is the attacked image. The robustness of the proposed algorithm is evaluated using the bit error rate (BER) of the retrieved logo image, which is defined as follows:
BER ¼
B 100%; PQ
ð24Þ
where B is the number of erroneously retrieved bits and P Q is the size of logo image. In practice, a low BER indicates that the retrieved logo image resembles the original one. The robustness of the proposed algorithm was evaluated in terms of both geometric attacks and common image processing attacks. We first subjected the ‘Lena’ image to the following attacks: Attack 1: Rotation with no cropping. The image was rotated with no cropping and then resized to original size. Attack 2: Rotation with cropping. The image was rotated with cropping. Attack 3: Scaling. The image was up-scaled and then downscaled back to its original size. Attack 4: JPEG compression. We compressed the image using JPEG. Attack 5: Surround cropping. We applied surround cropping on the image. Attack 6: Gaussian noise. We added zero-mean Gaussian noise on the image. Attack 7: Salt & pepper noise. We added salt & pepper noise on the image. Attack 8: Median filtering. Median filtering was applied on the image. Attack 9: Blurring. The image was blurred. Attack 10: Sharpening. Sharpening was applied on the image. Attack 11: UnZign. The image was subjected to an UnZign attack (randomly deleting some rows and some columns, and resizing to original size).
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(a) Lena
(b) Barbara
(d) Peppers
(e) Airplane
(g) Splash
(h) Tree
(c) Mandrill
(f) Sailboat on lake
(i) San Diego
(j) Logo
Fig. 7. Test images used in the comparison between the proposed zero-watermarking algorithm and similar zero-watermarking algorithms.
Attack 12: StirMark and unZign. We consecutively applied the StirMark RBA and UnZign attacks. The corresponding attacked images are shown in Fig. 8. To achieve more precise results, one binary logo images are embedded into the nine color images and the results are obtained by averaging the BERs of nine experiment groups. Since almost all the existing zero-watermarking algorithms are designed for grayscale images rather than color ones. Experimental results are compared with three grayscale image zerowatermarking algorithms [4,5,9], which are shown in Table 2. It can be seen clearly that the proposed algorithm has a better robustness than algorithms [4,5,9] in general, only slightly worse than them on resisting a few attacks. For rotation with no cropping attacks, the proposed algorithm can only resist image rotation with small degree. When a color image is rotated with no cropping for big degree, the inscribed circle of the rotated image has large difference with that of the original image. So the QEMs of the two images are very different. This will result in the proposed algorithm has poor performance when the rotation degree gets bigger.
For rotation with cropping attacks, the proposed algorithm can resist image rotation with all degrees. When a color image is rotated with cropping for big degree, the inscribed circle of the rotated image is same with that of the original image. Thus the proposed algorithm has superb performance on resisting image rotation with cropping. For scaling attacks, when a color image with a resolution of 512 512 24 bit was up-scaled with 1.2, the size of the image should be 614.4 614.4 24 bit. However, in the computation process, the size is set to 615 615 24 bit. This process will result in computational error. And in scaling case with 1.25, 1.5, 2, there is no this kind of error. Therefore, BER is still existed in the scaling case with 1.2 but vanished in scaling case with 1.5 and 2. For other attacks, such as JPEG compression attack, noise attack and image filtering, the proposed algorithm has superb performance. 5.2.2. Comparison with traditional watermarking algorithm In this section, we present experiments conducted to compare the proposed zero-watermarking algorithm with the traditional watermarking algorithm based on QEMs [19].
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(a) Rotation 0.25 with no cropping
(e) Surround cropping (1/4)
(i) Blurring
(b) Rotation 2 with cropping
(f) Gaussian noising (0.01)
(j) Sharpening
(c) Scaling (0.25)
(d) JPEG compression (30)
(g) Salt & pepper noise (0.01)
(k) UnZign (6,6)
(h) Median filtering (3×3)
(l) StirMark RBA (1.1) + UnZign (6,6)
Fig. 8. Attacked images of color image ‘Lena’ at a 512 512 24 bit resolution.
5.2.2.1. Robust QEMs for traditional watermarking algorithm. As is known, the magnitudes of the EMs for grayscale images are symmetric at n ¼ 0; m ¼ 0. As shown in Eq. (13), QEMs are derived from EMs, therefore the magnitudes of the former have a corresponding relationship about n ¼ 0; m ¼ 0. Considering the quaternion representation of color images, it is important to note that the watermarked color image can also be represented in pure quaternion form after the image reconstruction using QEMs [19,20]. In order to obtain the pure quaternion representation of the watermarked color image, we must embed the watermark into the robust QEMs and modify the symmetric QEMs. Accordingly, in the traditional watermarking algorithm, the rule of selecting robust QEMs for watermark embedding is as follows [16]: ① n 6 0 and m ¼ 0, ② If nmax > bN=32c, then bN=32c < n < bN=32c and m > 0; If nmax 6 bN=32c, then nmax 6 n 6 nmax and m > 0. The selection of robust QEMs for watermark embedding is shown in the shaded region of Fig. 9. Here, the host images are color images with a resolution of 256 256 24 bit and the highest order of QEMs is set to 70. 5.2.2.2. The highest order of QEMs. Owing to the different rules of selecting robust QEMs, the nmax in the traditional watermarking algorithm is nearly twice as large
as the corresponding value used in the zero-watermarking algorithm for embedding the same logo image. 5.2.2.3. Computation time. In the traditional watermarking algorithm, the image reconstruction process based on QEMs must be conducted to obtain the watermarked image. Moreover, the larger value of nmax in the traditional watermarking algorithm increases run time considerably. 5.2.2.4. Quantization step. Traditional watermarking algorithms embedded a watermark into the original color image, thus degrading the original image’s quality. To achieve an appropriate watermark invisibility, a corresponding quantization step should be determined to ensure that PSNR of the watermarked image satisfies PSNR > 40 dB. 5.2.2.5. Comparison results. To achieve more precise results, in out experiments we used eight original color images with a resolution of 256 256 24 bit and one binary logo image sized 32 32 bit. The results were obtained by averaging the BERs of the eight groups of experiments. The parameters used in our experiments are shown in Table 3. The robustness of the two algorithms was compared under both geometric attacks and common image processing attacks. Figs. 10–13 show the comparison results of rotation, scaling, JPEG
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C.-p. Wang et al. / J. Vis. Commun. Image R. 41 (2016) 247–259 Table 2 Comparison of the retrieved logo image BER results between the proposed algorithm and similar zero-watermarking algorithms. Attacks
Proposed algorithm
Chen [4]
Chang [5]
Gao [9]
Rotation with no cropping
0:25 0:5 0:75 1 2
0.0122 0.0254 0.0378 0.0466 0.0750
0.0854 0.1034 0.1258 0.1465 0.1768
0.1952 0.2047 0.2256 0.2365 0.2967
0.0135 0.0278 0.0423 0.0564 0.0897
Rotation with cropping
2 5 15 30 45
0 0 0 0 0
0.1776 0.1825 0.1732 0.1754 0.1706
0.3245 0.3320 0.3215 0.3198 0.3155
0 0 0 0 0
Scaling
0.25 0.5 0.8 1.2 1.5 2.0
0.0151 0.0115 0.0068 0.0056 0 0
0.0092 0.0088 0.0075 0.0075 0.0056 0.0023
0.0117 0.0112 0.0096 0.0096 0.0088 0.0056
0.0054 0.0032 0.0020 0 0 0
JPEG compression
90 70 50 40 30 10
0 0.0034 0.0056 0.0066 0.0075 0.0156
0.0034 0.0068 0.0075 0.0092 0.0109 0.0164
0.0034 0.0048 0.0056 0.0066 0.0084 0.0164
0 0.0025 0.0068 0.0075 0.0087 0.0189
0.1242 0.0131 0.0088 0.0049 0.0125 0.0112 0.0185 0.0436
0.1978 0.0285 0.0465 0.0164 0.0075 0.0251 0.0344 0.1098
0.1601 0.0285 0.0698 0.0178 0.0092 0.0285 0.0621 0.1743
0.2112 0.0180 0.0153 0 0 0.0142 0.0142 0.1047
Surround cropping (1/4) Gaussian noise (0.01) Salt and Peppers noise (0.01) Median filtering (3 3) Blurring Sharpening UnZign (6, 6) StirMark RBA (1.1) + UnZign (6, 6)
0.04
m=0 m=-70
Proposed zero-watermarking algorithm Traditional watermarking algorithm
0.035
m=+70
n=+70
0.03
n=0 n=-8
m>0
0.025
BER
n=+8
0.02 0.015 0.01
n=-70
0.005 0
Fig. 9. Robust QEMs for traditional watermarking algorithm (for color images with a resolution of 256 256 24 bit).
0
10
20
30
40
50
60
70
80
90
Rotation angle Fig. 10. Comparison of BERs obtained after image rotation between the proposed algorithm and the traditional algorithm.
compression and PSNR attacks. Table 4 shows the comparison results of other common image processing attacks and some Stirmark attacks [21,22]. We can see clearly that the proposed zerowatermarking algorithm outperforms the traditional algorithm. Moreover, the proposed algorithm is faster than the traditional algorithm.
To summarize, the proposed zero-watermarking algorithm is robust to both geometric attacks and common image processing attacks. Compared to similar zero-watermarking algorithms and the QEMs-based traditional watermarking algorithm, the proposed zero-watermarking algorithm achieves better performance.
Table 3 Parameters used in the proposed zero-watermarking algorithm and the traditional watermarking algorithm.
Proposed zero-watermarking algorithm Traditional watermarking algorithm [19]
nmax
Running time (s)
Quantization step
PSNR
35 70
740.51 4345.64
– 0.18
– 40.7768
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C.-p. Wang et al. / J. Vis. Commun. Image R. 41 (2016) 247–259 Table 4 Comparison of BERs obtained after common image processing attacks between the proposed algorithm and the traditional algorithm.
0.3 Proposed zero-watermarking algorithm Traditional watermarking algorithm
0.25
Attacks
Proposed zerowatermarking algorithm
Traditional watermarking algorithm [19]
Luminance increasing (5) Luminance decreasing (5) Contrast increasing (10) Contrast decreasing (10) Gaussian noise (0.001) Salt and Peppers noise (0.01) Random noise (10) Average filtering (3 3) Median filtering (3 3) Gaussian filtering (3 3) Edge sharpening Blurring Mosaic (2) Add Noise 0 Add Noise 20 Self-Similarities 1 Self-Similarities 2 Self-Similarities 3 Rotation-Scale 0.25 Rotation-Scale 0.5 Rotation-Scale 0.75 Rotation-Scale 1 Rotation-Scale 2
0.0049 0.0010 0.0049 0.0020 0.0029 0.0146 0.0029 0.0117 0.0098 0.0039 0.0029 0.0039 0.0098 0.0054 0.1035 0.0078 0.0049 0.0085 0.0071 0.0129 0.0190 0.0273 0.0483
0.0566 0.0596 0.0439 0.0400 0.0273 0.0918 0.0283 0.1406 0.0781 0.0254 0.0273 0.0313 0.0996 0.0430 0.4980 0.2119 0.0557 0.3066 0.0518 0.0869 0.1455 0.2012 0.3242
BER
0.2
0.15
0.1
0.05
0 0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
Scaling factor Fig. 11. Comparison of BERs obtained after image scaling between the proposed algorithm and the traditional algorithm.
0.5 Proposed zero-watermarking algorithm Traditional watermarking algorithm
0.45 0.4 0.35
6. Conclusion
BER
0.3 0.25 0.2 0.15 0.1 0.05 0
0
10
20
30
40
50
60
70
80
90
JPEG compression factor Fig. 12. Comparison of BERs obtained after JPEG compression between the proposed algorithm and the traditional algorithm.
0.06 Proposed zero-watermarking algorithm Traditional watermarking algorithm
0.05
BER
0.04
0.03
Acknowledgment
0.02
This research is supported by the National Natural Science Foundation of China (Nos: 61672124, 61370145 and 61173183), Program for Liaoning Excellent Talents in University (No: LR2012003).
0.01
0
Existing zero-watermarking algorithms are almost entirely focused on grayscale images. However, color images are more common in our everyday life, and contain more information than grayscale images of the same dimensions. Moreover, most of the existing zero-watermarking algorithms cannot resist geometric attacks efficiently. Hence it is very important to design zerowatermarking algorithms that can resist geometric attacks for color images. In this paper, we propose a color zerowatermarking algorithm which is robust to geometric attacks based on quaternion Exponent moments. The algorithm generates the feature image by using the magnitudes of quaternion Exponent moments. Then, a bitwise exclusive-or operation is applied on the binary feature image and a scrambled binary logo to generate the zero-watermark image. Experimental results indicate that the proposed zero-watermarking algorithm resists various attacks significantly better than similar zero-watermarking algorithms and the QEMs-based traditional watermarking algorithm. Despite the usefulness of our algorithm, there are still a few limitations. Since our method is applied to the square image, it cannot resist the change of aspect ratio of the image. Moreover, the robustness of our method on resisting large scale cropping attacks is poor. In the future, we should improve our algorithm to overcome these shortcomings.
0
10
20
30
40
50
60
70
80
90
100
References
PSNR attack factor Fig. 13. Comparison of BERs obtained after PSNR attack between the proposed algorithm and the traditional algorithm.
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