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Robust Image watermarking Method Using Homomorphic Block-Based KLT
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Robust image watermarking method using Homomorphic Block-Based SVD
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Hanaa A. Abdallah a , Osama S. Faragallah b,∗ , Hala S. Elsayed c , Mohiy M. hadhoud d , Abdalhameed A. Shaalan a , Fathi E. Abd El-samie b a
Faculty of Engineering, Zagazig university, Zagazig, Egypt Faculty of Electronic Engineering, Menoufia University, Menouf 32952, Egypt c Department of Electrical Engineering, Menoufia University, Shebin El-kom, Egypt d Faculty of computers and information, Menofia University, Shebin Elkom, Egypt
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Article history: Received 23 December 2014 Accepted 11 October 2015 Available online xxx
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Keywords: DWT Digital watermarking 19 Copyright protection 20 Spatial and temporal redundancy 21 Multiresolution 22 Wavelet decomposition 23 24 Q3 Attacks resilience 17 18
This paper presents two robust image watermarking methods based on the Homomorphic transform and singular value decomposition (SVD). The first method is denoted as Homomorphic-Based SVD image watermarking. It works by inserting the watermark with the SVD algorithm in the reflectance component after employing the Homomorphic transform on the image to be watermarked. The reflectance component includes most image features, and so watermarks added in this component will survive against most of the attacks. The second method is denoted as Homomorphic Block-Based SVD image watermarking. It works using the SVs after segmenting the image to be watermarked into blocks to add the watermark in each block separately. The watermark addition on a block-by-block basis makes the watermark more robust to attacks. A comparative study is done between the proposed Homomorphic-Based SVD image watermarking method, Homomorphic Block-Based SVD image watermarking method, the traditional SVD watermarking method, and other image watermarking methods. The proposed Homomorphic-Based SVD image watermarking and Homomorphic Block-Based SVD image watermarking methods are more secure and robust to various attacks, viz., JPEG compression, and scaling, cropping and Gaussian noise without degrading the watermarked image to the same level as the other technique. Superior experimental results are observed with the proposed Homomorphic-Based SVD image watermarking and Homomorphic Block-Based SVD image watermarking methods over other image watermarking schemes by Normalized Cross correlation (NC) and Peak Signal to Noise Ratio (PSNR). © 2015 Published by Elsevier GmbH.
1. Introduction
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Digital media, e.g., images, audio, and video, are readily manipulated, reproduced, and distributed over information networks. These efficiencies lead to problems regarding copyright protection. As a result, creators and distributors of digital data are hesitant to provide access to their digital intellectual property. Technical solutions for copyright protection of multimedia data are actively being pursued. Digital watermarking has been proposed as a means to identify the owner and distribution path of digital data. Watermarking is the process of encoding hidden copyright information into digital data by making small modifications to the data samples, e.g., pixels.
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∗ Corresponding author. . E-mail address: osam [email protected] (O.S. Faragallah).
Many watermark algorithms have been proposed. Some techniques modify spatial/temporal data samples [1–3], while others modify transform coefficients [4–10]. Unlike encryption, watermarking does not restrict access to the data. Once encrypted data is decrypted, intellectual property rights are no longer protected. A watermark is designed to permanently reside in the host data. When the ownership of data is in question, the information can be extracted to completely characterize the owner or distribution path. Recently, watermarking schemes based on singular value decomposition (SVD) have gained popularity due to its simplicity in implementation and some attractive mathematical features of SVD. The SVD method has drawn a significant attention in image processing, pattern recognition, and information security areas for many years. In SVD-based watermarking, several approaches are possible. A common approach is to apply the SVD to the whole cover image,
http://dx.doi.org/10.1016/j.ijleo.2015.10.050 0030-4026/© 2015 Published by Elsevier GmbH.
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and modify all the SVs to embed the watermark data. An important property of SVD watermarking is that the largest of the modified singular values (SVs) changes very little for most types of attacks. In this paper, we focus on engaging the digital watermarking techniques to protect digital multimedia intellectual copyright, and propose a new algorithm particularly for image watermarking purpose. The main contribution of this paper is to present a homomorphic image watermarking scheme based on singular value decomposition. It also gives an up-to-date overview of the field of image watermarking in the SVD domain. The proposed image watermarking scheme is robust to most types of attacks. Experimental results show that the proposed image watermarking scheme is not only robust against common image processing operations as blurring, noise adding, and JPEG compression, etc., but also robust against the desynchronization attacks such as scaling cropping, and rotation, etc. This paper is organized as follows: Section 2 describes the singular value decomposition. Section 3 presents SVD watermarking. Section 4 surveys the related work of transform domain based SVD watermarking. Section 5 explores SVD watermarking with the method of Liu. Section 6 presents the proposed SVD watermarking in the homomorphic domain. Section 7 presents the proposed block-based SVD watermarking in the homomorphic domain. Section 8 discusses simulation results. Section 9 gives a comparison between the proposed Homomorphic-Based SVD image watermarking and Homomorphic Block-Based SVD image watermarking methods and other image watermarking schemes. Section 10 presents conclusions.
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2. Singular value decomposition (SVD)
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SVD is an effective numerical analysis tool used to analyze matrices. In SVD transformation, a matrix can be decomposed into three matrices that are of the same size as the original matrix. From the view point of linear algebra, an image is an array of non negative scalar entries that can be regarded as a matrix. Without loss of generality, if A is a square image, denoted as A ∈ Rn×n , where R represents the real number domain, then SVD of A is defined as [11–14]:
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A = USVT
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(1) UT
VT
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such that U = I, where, U and V are orthogonal matrices V = I, I is an identity matrix. S = diag 1 , . . ., p . Where, p = min (m, n), 1 ≥ 2 ≥ . . . p ≥ 0, are the singular values of A. The diagonal entries are called the singular values of the matrix A, the columns of U are called the left singular vectors of A, and the columns of V are called the right singular vectors of A. This decomposition is known as the singular value decomposition (SVD) of A, and can be written as follows [11]:
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SVD (A) = [USV]
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or
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A = USVT
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Rm×n ,
where R is the matrix of real numbers, then there 1. If A ∈ exist orthogonal matrices. U [u1 , . . ., um ] ∈ Rm×n
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and
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V [v1 , . . ., vn ] ∈ Rm×n
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U AV = diag 1 , . . ., p
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TheSVs are the square roots of the Eigen values i , that is i . This, can be represented as follows [11]: i =
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(7)
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n 2. The stability of SVs: the stability of SVs indicates that, when there is a little disturbance with A, the variation of its SVs is not greater than the largest SV of the matrix [11]. Using the SVD in digital image processing has some advantages [12–14]. (a) The SVs of an image have a very good stability, when a small perturbation takes place in the image. (b) The SVs represent the algebraic image properties, which are intrinsic and not visual. The scaling property, if the SVs of Amxn are 1 , 2 ,. . ., k , the SVs of ˛ × Am×n are 1∗ , 2∗ , . . ., k∗ such that [11]:
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3. The rotation invariant property: if P is a unitary and rotating matrix, the singular values of PA (rotated matrix) are the same as those of A [11]. 4. The translation invariance property: the original image A and its rows or columns of the interchanged image have the same SVs [11]. The transposition invariance property: T
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IfAA u = u Then,
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A Av = 2v
So that A and
AT
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(9)
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have the same SVs [11].
The above mentioned stability of SVs, scaling invariance of SVs, rotational invariance of SVs, and translation and transposition invariance of SVs properties of the SVD transformation are very much desirable in image watermarking. When the watermarked image undergoes attacks like rotation, scaling, and noise addition, the watermark can be retrieved effectively from the attacked watermarked image due to the above mentioned properties. 3. SVD watermarking There are two types of SVD watermarking; watermarking of the image as a whole and block-based watermarking. 3.1. Watermarking of the image as a whole
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(2)
The SVs represent the algebraic properties of an image. These values possess an algebraic and geometric invariance to some extent. The properties of the singular values are reviewed as follows [11]:
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Such that
(4)
(5)
Liu and Tan proposed an algorithm that embeds the watermark directly to the whole image in the SVD domain [11]. This algorithm requires the SVs or the orthogonal matrices for retrieving the watermark. It is resistant to some attacks like compression, filtering, and cropping, but is not robust to attacks including rotation and translation. A method based on the SVD has also been proposed by Liu and Kong. This algorithm uses an M-sequence as the watermark. Considering the visual quality and robustness criteria, the watermark has been embedded in middle SVs maintaining the original order. This algorithm is blind, i.e., does not require the original image or any other information of the original SVs to detect the watermark. This method can resist some attacks like JPEG compression, median filtering, rescaling, Gaussian low-pass filtering, but is not robust to some other attacks including rotation, and cropping.
Please cite this article in press as: H.A. Abdallah, et al., Robust image watermarking method using Homomorphic Block-Based SVD, Optik - Int. J. Light Electron Opt. (2015), http://dx.doi.org/10.1016/j.ijleo.2015.10.050
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3.2. Block-based watermarking
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An SVD watermarking scheme has been proposed by Ganic et al. [15] where the watermark is embedded twice. In the first layer, the cover image is divided into smaller blocks and a piece of the watermark is embedded in each block. The cover image is used as a single block to embed the whole watermark in the second layer. Layer 1 allows flexibility in data capacity and Layer 2 provides additional robustness to attacks. This scheme can resist several attacks including JPEG compression, JPEG 2000, Gaussian blur, Gaussian noise, cropping, rotation, and rescaling but after each attack visual quality of the image degrades and the commercial value of the image is lost. For the rotation attack, small angles only have been tested. This scheme is not robust to translation attack. In [15], a SVD-based scheme has been proposed by Ghazi et al., where the original image is divided into blocks and then the watermark is embedded in the SVs of each block, separately. The watermark can be a pseudo random number or an image. This method is robust to several attacks such as JPEG compression, Gaussian noise, Gaussian blur, cropping, resizing, and rotation, though for rotation a small angle has been tested, and the correlation value for rotation and resizing is not good. This method is not resistant to translation attack. Zhou et al. [16] presented an algorithm in which the original image is divided into several blocks of size 8 × 8 for each block and the watermark is embedded in the SVD domain of each block of the image. The embedded watermark may be binary image, a pseudorandom number or a gray scale image. If the cover image size is not exactly divisible by 8, then it requires adjustment before embedding of watermark. Experimental results have shown that the algorithm is resistant to JPEG compression, noise, filtering, clipping, and rotation. Similarity of the original watermark and the extracted watermark has been evaluated using the correlation coefficient, which is not very satisfactory in the case of the rotation attack. Moreover, this algorithm can’t resist scaling and translation attacks.
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4. Transform domain based SVD watermarking
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Some algorithms have been presented for SVD watermarking in transform domains.
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4.1. DCT-based SVD watermarking
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A DCT-based SVD watermarking algorithm has been proposed by Sverdlov et al. [17]. The DCT is applied to the whole cover image, and the DCT coefficients are mapped to four quadrants using a zigzag sequence, and then the SVD is applied to each quadrant. These four quadrants actually represent frequency bands from the lowest to the highest. SVs of the DCT-transformed visual watermark are then used to modify the SVs of each quadrant of the cover image. It has been shown that embedding data in lowest frequencies is resilient to a set of attacks, while embedding data in the highest frequencies is resilient to another set of attacks. Robustness of this algorithm has been tested for a set of attacks including Gaussian blur, Gaussian noise, JPEG compression, JPEG 2000 compression, rescaling, cropping, histogram equalization, and gamma correction. Robustness to the rotation attack is not guaranteed. This algorithm is also not resistant to translation attack.
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4.2. DWT-based SVD watermarking
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Fig. 1. Proposed homomorphic image watermarking embedding.
Fig. 2. Proposed homomorphic image watermarking detection.
each sub-band. SVD is then applied on the watermark image and the SVs of the cover image are modified with the SVs of the watermark image. Finally, four sets of DWT coefficients are obtained and, and the Inverse DWT (IDWT) is calculated from the modified DWT coefficients to obtain the watermarked image. Robustness of this algorithm has been tested for a set of attacks including Gaussian blur, Gaussian noise, JPEG compression, JPEG 2000 compression, rescaling, cropping, histogram equalization, and gamma correction. Results have revealed that the extracted watermark from the LL band is the best in visual quality and correlation coefficient. Performance of this algorithm for sharpening, contrasting, and histogram equalization attacks is not good. 4.3. Hadamard-based SVD watermarking The Fast Hadamard Transform (FHT) has been used in SVD watermarking [18]. This algorithm first divides the cover image into blocks and applies FHT to each block. Then SVD is applied to the watermark image and the SVs of the visual watermark image are distributed over the transformed cover blocks. The main features of this algorithm are simplicity, flexibility in data embedding capacity, and real time implementation. Robustness of this scheme has been tested for several attacks including Gaussian blur, Gaussian noise, cropping, histogram equalization, gamma correction, sharpening, resizing, and rotation. Translation attack has not been considered, which is an indication of the vulnerability of this algorithm to this attack. 4.4. Zernike moments-based SVD watermarking Li et al. proposed a Zernike moments-based SVD watermarking scheme, where the Zernike moments are used to estimate the rotation angle to make the algorithm rotation invariant [19]. The cover image can be divided into blocks and the SVD is applied to each block. This algorithm is robust to rotation for even large angles, scaling, and pixel removal attacks. Visual quality of the watermarked image has been measured by the Weighted Peak Signal-to-Noise Ratio (WPSNR), and similarity of the original to the extracted watermark has been evaluated by normalized correlation. 5. SVD watermarking with the method of Liu
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A DWT-based SVD watermarking algorithm has been presented by Ganic and Eskicioglu [15]. This algorithm is very similar to the algorithm of Sverdlov et al. [17]. The cover image is first decomposed with the DWT into four sub-bands and the SVD is applied to
In the approach proposed by Liu et al. [11], the watermark W is added into the matrix S. Then, a new SVD process is performed on the new matrix S + kW to get Uw , Sw , and Vw , where k is the scale
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Fig. 3. Method of Liu (a) Original image. (b) Watermark. (c) Watermarked image without attacks PSNR = 62.65 dB. (d) Extracted watermarks cr = 0.9. Fig. 5. Block-based SVD watermarking in the homomorphic domain. (a) Original image. (b) Watermark embedded in each block in the homomorphic domain. (c) Watermarked image without attacks, PSNR = 66.5837 dB. (d) Extracted watermarks from each block. (e) Zooming of the extracted watermark which has c rmax = 0.9997. (f) Correlation coefficient between each extracted watermark and the original one.
Fig. 4. SVD watermarking in the homomorphic domain. (a) Original image. (b) Watermark (c) Watermarked image without attacks, PSNR = 65.7 dB. (d) Extracted watermark, cr = 0.9993.
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factor that controls the strength of the watermark embedded to the original image. Then, the watermarked image Fw is obtained by multiplying the matrices U, Sw , and VT . The steps of embedding the watermark are summarized as follows:
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1. The SVD is performed on the original image (F matrix).
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F =s
(11)
2. The watermark (W matrix) is added to the SVs of the original matrix. D = S + KW
(12)
3. The SVD is performed on the new modified matrix (D matrix). T D = Uw Sw Vw
(13)
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The watermarked image (Fw matrix) is obtained by using the modified matrix (Sw matrix).
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Fw = USVTw
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(14)
To extract the possibly corrupted watermark from the possibly distorted watermarked image, given Uw , S, Vw matrices and
Fig. 6. The extracted watermarks for the method of Liu after applying attacks.
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Fig. 7. Extracted watermarks for SVD watermarking in the homomorphic domain after applying attacks.
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the possibly distorted image Fw , the above steps are reversed as follows: 1. The SVD is performed on the possibly distorted watermarked image (F ∗w matrix). ∗ ∗ ∗T Fw = U ∗ Sw V
∗ T D∗ = Uw Sw Vw
W ∗ = (D∗ − S) /K
6. SVD watermarking in the homomorphic domain
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(17)
*
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3. The possibly corrupted watermark is obtained.
The refers to the corruption due to attacks.
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Fig. 8. Extracted watermarks for the block based SVD watermarking in the homomorphic domain in the presence of attacks.
2. The matrix that includes the watermark is computed.
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In general, an image can be regarded as a 2-D function of the form f(n1 , n2 ), whose values at the spatial coordinates (n1 , n2 ) are positive scalar quantities [20]. Assuming that we are dealing with grayscale images, we can say that when an image is generated from a physical process, its values are proportional to the energy radiated by a physical source. In other words, an image is an array of measured light intensities and is a function of the amount of light reflected from the objects in the scene. The intensity of pixels is the product of the incident illumination and the reflectance. The illumination is approximately constant, while the reflectance holds most of the image details. The reflectance results from the way the objects in the image reflect light, and is determined by the intrinsic
Fig. 9. Plot of the correlation coefficient for all attacks.
properties of the object itself. So, it is expected that a watermark embedded in the reflectance component can survive several attacks [20]. In the following subsections, the steps of watermark embedding in the reflectance component of an image and watermark detection are presented.
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Fig. 10. (a) Original image. (b) Watermark. (c) Watermarked image without attacks in the method of Liu with PSNR = 62.65 dB. (d) Extracted watermarks with cr = 0.9 in the method of Liu. (e) Watermarked image without attacks in homomorphic method with PSNR = 48.06 dB. (f) Recovered watermark cr = 0.995 in homomorphic method. (g) Watermarked image in block-based homomorphic method with PSNR = 48.07 dB. (h) Recovered watermarks. (i) Magnification of the watermark with cr = 0.999.
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6.1. Watermark embedding 1. The image intensities can be represented as follows [20]:(18)f(n1 , n2 ) = i(n1 , n2 )r(n1 , n2 ) where, i(n1 ,n2 ) is the light illumination and r(n1 ,n2 ) is the reflectance of the object to be imaged. 2. The homomorphic transform is performed ln[f (n1 , n2 )] = ln[i(n1 , n2 )] + ln[r(n1 , n2 )]
(19)
3. A LPF and a HPF are applied to log [f(n1 , n2)] to separate the illumination component I and the reflectance component R, respectively, for each pixel value in the form of matrices. 4. The SVD is performed on the (R matrix). R = USVT
(20)
5. The watermark (W matrix) is added to the SVs of the reflectance matrix. D = S + kW
(21)
6. The SVD is performed on the new modified matrix (D matrix). D=
T Uw Sw Vw
(22)
7. The image (Rw matrix) is obtained by using the modified matrix (Sw matrix). Rw = USVTw
(23)
8. An inverse homomorphic transform is performed on I and Rw to obtain a matrix Xw . Xw = Rw + I
(24)
Fig. 11. The extracted watermarks for the method of Liu after applying attacks.
9. The watermarked image is obtained as follows: Fw = exp(Xw )
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(25)
6.2. Watermark detection
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To extract the possibly corrupted watermark from the possibly distorted watermarked image, given Uw , S, Vw matrices and the possibly distorted image Fw , the above steps are reversed as follows: (1) The homomorphic transform is performed on the watermarked image (Fw ). (2) A HPF is used to get the possibly corrupted reflectance component R∗w . (3) The SVD is performed on the R∗w matrix. ∗ Rw = U∗ S∗w V∗T
(26)
(4) The matrix that includes the watermark is computed. ∗
D =
∗ T Uw Sw Vw
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(5) The possibly corrupted watermark is obtained. W ∗ = (D∗ − S)/k
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Fig. 12. Extracted watermarks for SVD watermarking in the homomorphic domain.
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7. Block-based SVD watermarking in the homomorphic domain
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7.1. Watermark embedding
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Fig. 13. Extracted watermarks for the block-based SVD watermarking in the homomorphic domain.
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The same steps from 1 to 4 as in Section 6.1 are applied, and then: 5. Divide the S matrix into non-overlapping blocks (Sb ). 6. The watermark (W matrix) is added to each block.
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D = Sb + kW
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(29)
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7. The watermarked blocks are combined back into a single matrix to build the Sw matrix. The same steps from 8 to 10 are applied as in Section 6.1.
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7.2. Watermark detection
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The same steps from 1 to 4 in Section 6.2 are applied and then: 5. Divide the D* into blocks Di∗ . 6. The possibly corrupted watermark is obtained.
W ∗ = Di∗ − Sb /k
Fig. 14. Plot of the correlation coefficient for all attacks.
(30)
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The * refers to the corruption due to attacks. Embedding and detecting are shown in Figs. 1–2.
8. Simulation results In this section, several experiments are carried out to compare between the methods of Liu, and the proposed method. The 512 × 512 airplane and the 512 × 512 colored baby images are used in the simulation experiments. The RGB color space is highly correlated and is not suitable for watermarking applications, except for the blue channel used by some researchers because of its low effect on human perception [21]. So we have chosen to transform the RGB color space to the Y Cb Cr color space. In this color space, most of the information is concentrated in the luminance (Y component) and less in the chrominance (Cb and Cr components). The experiments demonstrate that the watermark embedding in the luminance component (Y) has a larger effect on the human vision than human vision than embedding in the Cb and Cr components, but due to the robustness to JPEG compression; we propose watermark embedding in the Y channel. Fig. 3 shows the original image, the watermark, the watermarked image, and the extracted watermark using the method of Liu. A single watermark is used. Fig. 4 shows the original image, the watermark, the watermarked image, and extracted watermark using the proposed homomorphic method. It is clear that there is no visual difference between the original image and the watermarked image for the human vision, enforcing the fidelity of homomorphic method. We find that the PSNR in the method of Liu is 62.65 dB, and in the proposed method, the PSNR = 65.7 dB. The maximum correlation coefficient between the original transmitted watermark and any of the extracted watermarks for the block-based SVD method and the block-based SVD method in the homomorphic domain are 0.9 and 0.96, respectively. Fig. 5 shows the original image, the watermark, the watermarked image, and extracted watermark using the proposed block-based homomorphic method. It is clear that there is no visual difference between the original image and the watermarked image, enforcing the fidelity of the homomorphic method. We find that PSNR in the block-based method is 66.58 dB. The maximum correlation coefficient between the original transmitted watermark and the extracted watermark for the proposed block-based method is c rmax = 0.999. Some attacks such as Gaussian noise, cropping, compression, rotation, and resizing on the watermarked images have been applied. Figs. 6–8 show the watermarked images and the extracted watermarks under attacks for all watermarking methods. The first attack applied is the JPEG compression with quality factor 50. The second attack is resizing from 512 to 256 and back to 512 again. The third attack is addition of Gaussian noise with zero mean and 0.1 variance. The fourth attack is cropping. The fifth attack is rotation with (−3◦ ). Fig. 6 shows the extracted watermarks for the different attacks and the correlation coefficient between each extracted watermark and the original watermark for the method of Liu. The results reveal that the value of cr is more than 0.1, but less than 0.8 for each attack except for the cropping attack, which gives cr = 0.0317. Fig. 7 shows the extracted watermarks for the proposed method after applying the same attacks. In all cases, there are some extracted watermarks with cr higher than 0.6, which ensures the existence of the watermark. The figures show the superiority of the proposed method to the method of Liu in the presence of a Gaussian noise attack and a compression attack, respectively. These results reveal the ability of the proposed algorithm to extract watermarks even in the presence of severe attacks. Fig. 8 shows the extracted watermarks for the block-based SVD method in the homomorphic domain after applying the same attacks. In all cases, there are extracted watermarks with cr higher than 0.8, which ensures the
existence of the watermark. The figures show the superiority of the proposed block-based SVD watermarking method in the homomorphic domain to the method of Liu in the presence of a Gaussian noise attack, a compression attack and a cropping attack. Fig. 9 reveals the superiority of the proposed method. Simulation results on the 512 × 512 color Baby image with the method of Liu, the proposed homomorphic-based SVD image watermarking and homomorphic block-based SVD are depicted in Figs. 10–14. 9. Comparison between the proposed a comparison between the proposed homomorphic-based SVD image watermarking and homomorphic block-based SVD image watermarking methods and other schemes
=
i
428 429 430 431 432 433
435 436 437
NC(win , wout )
438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468
469
win (i, j)wout (i, j)
j
i
427
434
In order to study the performance of the proposed methods, we compared the results of the proposed block-based SVD image watermarking in the homomorphic domain and the proposed SVD image watermarking in the homomorphic domain against four image watermarking algorithms. The first method we use as reference is the one presented by Liu et al. [11], which is based on singular values decomposition (SVD). This method is denoted as Liu method, works by inserting the watermark into the whole image in the SVD domain. The method utilizes the SVs matrices for obtaining the watermark. The second method denoted as waveletbased watermarking method [22]. It is based on classifying wavelet coefficients as insignificant or significant using zero tree and then embedding a watermark in the location of insignificant coefficients or in the location of the thresholded significant coefficients at the coarser scales adjacent frames comparison in the wavelet domain. The third method denoted as DWT-Based SVD watermarking [23]. It works by decomposing the cover image with the DWT into four sub-bands and the SVD is applied to each sub-band. The SVs of the cover image are modified with the SVs of the watermark image. The fourth method denoted as DWT-based chaotic watermarking is basically based on embedding binary watermark pattern after applying a chaotic mixing method in the DWT domain [24]. The 512 × 512 Lena and Mandrill images have been used in the simulation experiments. The watermark decoder measures the normalized correlation between the transform coefficients of extracted watermark and the coefficients of the original watermark. For each method, the normalized correlation was estimated for watermarked sequences that had not gone through any type of distortion. The six watermarking schemes were able to correctly detect all of the watermarks. The normalized correlation can be estimated as: Normalized Correlation :
426
[win (i, j)]
2
(31)
470
j
where, win is the original watermark and wout is the extracted watermark, Tables 1 and 2 give normalized correlation values for Lena and Mandrill test images with all watermarking methods under different attacks. It is clear that the proposed block-based SVD image watermarking and the proposed SVD image watermarking in the homomorphic domain outperforms better than other schemes [11,22–24] under most attacks in terms of the normalized correlation between the transform coefficients of extracted watermark and the coefficients of the original watermark. From Tables 1 and 2, the obtained results reveal the superiority of watermarking in the homomorphic domain. Also, we can see that the watermark achieves the robustness to both various desynchronization attacks and common image processing operations by
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Table 1 Normalized correlation values for the extracted watermarks using different watermarking methods for the Lena image with and without attacks. Method
Wavelet-Based watermarking [23]
Liu method [11]
DWT-Based SVD Watermarking [24]
DWT-Based chaotic watermarking [25]
Homomorphicbased SVD watermarking
Homomorphicbased Block-by-block SVD watermarking
0.8500 0.7500 0.5714 0.1438 0.3017 0.1747 0.2450
0.8800 0.8100 0.6120 0.3120 0.5480 0.2310 0.3780
0.9670 0.9320 0.8740 0.6780 0.7850 0.3560 0.6210
0.9730 0.9560 0.9010 0.7560 0.8850 0.4820 0.8840
0.9853 0.9750 0.9015 0.7790 0.9234 0.5654 0.9350
0.9996 0.9940 0.9930 0.8920 0.9910 0.9770 0.9910
Attack No attack JPEG compression Q = 50% Resizing 512–256–512 Gaussian noise with variance = 0.1 Cropping Rotation Bluring
Table 2 Normalized correlation values for the extracted watermarks using different watermarking methods for the Mandrill image with and without attacks. Method
Wavelet-Based watermarking [23]
Liu method [11]
DWT-Based SVD Watermarking [24]
DWT-Based chaotic watermarking [25]
HomomorphicBased SVD watermarking
HomomorphicBased Block-by-block SVD watermarking
0.8780 0.79 0.594 0.1965 0.3756 0.1987 0.2856
0.8940 0.840 0.6590 0.4230 0.6580 0.2758 0.3960
0.9690 0.9368 0.8980 0.6880 0.7960 0.3740 0.6452
0.9690 0.9620 0.9120 0.7780 0.8970 0.4990 0.8960
0.9870 0.9730 0.9256 0.7950 0.9364 0.5960 0.9440
0.9995 0.9960 0.9925 0.9210 0.9955 0.9810 0.9925
Attack No attack JPEG compression Q = 50% Resizing 512–256–512 Gaussian noise with variance = 0.1 Cropping Rotation Bluring
484 485 486
487
488 489 490 491 492 493 494 495 496 497 498 499 500 501
502
503 504 505 506 507 508 509 510 511 512 513 514 515
incorporating the proposed block-based SVD image watermarking and the proposed SVD image watermarking in the homomorphic domain.
10. Conclusions This paper presented a homomorphic image watermarking method using the SVD algorithm. By embedding a watermark with the SVD algorithm to the reflectance component of an image after the homomorphic transform, and the modified one which embed the watermark into the SVs of the HPF of the homomorphic of the original image after dividing it into blocks. It is shown that we can transmit two images, the original image, and the watermark as a single image; the watermarked image. This can achieve a reduction in bandwidth. The experimental results show also that the blockbased SVD watermarking in the homomorphic domain has a high fidelity and robustness in the presence of different types of attacks. There is always a large probability for detecting the watermark. The results also reveal the superiority of the proposed block-based SVD watermarking in the homomorphic domain to the method of Liu.
References [1] G.C. Langelaar, I. Setyawan, R.L. Lagendijk, Watermarking digital image and video data: a state-of the-art overview, IEEE Signal Process Mag. 17 (2000) 20–46. [2] H.A. Al-Otum, A.O. Al-Taba’a, Adaptive color image watermarking based on a modified improved pixel-wise masking technique, Comput. Electr. Eng. 35 (2009) 673–695 (Elsevier). [3] W. Lu, H. Lu, F. Chung, Feature based robust watermarking using image normalization, Comput. Electr. Eng. 36 (2010) 2–18 (Elsevier). [4] M.A. Suhail, M.S. Obaidat, Digital watermarking-based DCT and JPEG model, IEEE Trans. Instrum. Meas. 52 (2003) 1640–1647. [5] X. Kang, J. Huang, Y.Q. Shi, Y. Lin, A DWT-DFT composite watermarking scheme robust to both affine transform and JPEG compression, IEEE Trans. Circuits Syst. Video Technol. 13 (2003) 776–786.
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[23] N.M. Makbol, B.E. Khoo, Robust blind image watermarking scheme based on redundant discrete wavelet transform and singular value decomposition, AEU – Int. J. Electron. Comm. 6 (2) (2013) 102–112 (February). [24] R. Reyes, C. Cruz, M. Nakano-Miyatake, H. Pérez-Meana, Digital video watermarking in DWT domain using chaotic mixtures, IEEE Lat. Am. Trans. 8 (3) (2010) 304–310.
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Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Robust image watermarking method using Homomorphic Block-Based SVD
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Hanaa A. Abdallah a , Osama S. Faragallah b,∗ , Hala S. Elsayed c , Mohiy M. hadhoud d , Abdalhameed A. Shaalan a , Fathi E. Abd El-samie b a
Faculty of Engineering, Zagazig university, Zagazig, Egypt Faculty of Electronic Engineering, Menoufia University, Menouf 32952, Egypt c Department of Electrical Engineering, Menoufia University, Shebin El-kom, Egypt d Faculty of computers and information, Menofia University, Shebin Elkom, Egypt
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a r t i c l e
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Article history: Received 23 December 2014 Accepted 11 October 2015 Available online xxx
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Keywords: DWT Digital watermarking 19 Copyright protection 20 Spatial and temporal redundancy 21 Multiresolution 22 Wavelet decomposition 23 24 Q3 Attacks resilience 17 18
This paper presents two robust image watermarking methods based on the Homomorphic transform and singular value decomposition (SVD). The first method is denoted as Homomorphic-Based SVD image watermarking. It works by inserting the watermark with the SVD algorithm in the reflectance component after employing the Homomorphic transform on the image to be watermarked. The reflectance component includes most image features, and so watermarks added in this component will survive against most of the attacks. The second method is denoted as Homomorphic Block-Based SVD image watermarking. It works using the SVs after segmenting the image to be watermarked into blocks to add the watermark in each block separately. The watermark addition on a block-by-block basis makes the watermark more robust to attacks. A comparative study is done between the proposed Homomorphic-Based SVD image watermarking method, Homomorphic Block-Based SVD image watermarking method, the traditional SVD watermarking method, and other image watermarking methods. The proposed Homomorphic-Based SVD image watermarking and Homomorphic Block-Based SVD image watermarking methods are more secure and robust to various attacks, viz., JPEG compression, and scaling, cropping and Gaussian noise without degrading the watermarked image to the same level as the other technique. Superior experimental results are observed with the proposed Homomorphic-Based SVD image watermarking and Homomorphic Block-Based SVD image watermarking methods over other image watermarking schemes by Normalized Cross correlation (NC) and Peak Signal to Noise Ratio (PSNR). © 2015 Published by Elsevier GmbH.
1. Introduction
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Digital media, e.g., images, audio, and video, are readily manipulated, reproduced, and distributed over information networks. These efficiencies lead to problems regarding copyright protection. As a result, creators and distributors of digital data are hesitant to provide access to their digital intellectual property. Technical solutions for copyright protection of multimedia data are actively being pursued. Digital watermarking has been proposed as a means to identify the owner and distribution path of digital data. Watermarking is the process of encoding hidden copyright information into digital data by making small modifications to the data samples, e.g., pixels.
27 28 29 30 31 32 33 34 35 36 37
Q2
∗ Corresponding author. . E-mail address: osam [email protected] (O.S. Faragallah).
Many watermark algorithms have been proposed. Some techniques modify spatial/temporal data samples [1–3], while others modify transform coefficients [4–10]. Unlike encryption, watermarking does not restrict access to the data. Once encrypted data is decrypted, intellectual property rights are no longer protected. A watermark is designed to permanently reside in the host data. When the ownership of data is in question, the information can be extracted to completely characterize the owner or distribution path. Recently, watermarking schemes based on singular value decomposition (SVD) have gained popularity due to its simplicity in implementation and some attractive mathematical features of SVD. The SVD method has drawn a significant attention in image processing, pattern recognition, and information security areas for many years. In SVD-based watermarking, several approaches are possible. A common approach is to apply the SVD to the whole cover image,
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and modify all the SVs to embed the watermark data. An important property of SVD watermarking is that the largest of the modified singular values (SVs) changes very little for most types of attacks. In this paper, we focus on engaging the digital watermarking techniques to protect digital multimedia intellectual copyright, and propose a new algorithm particularly for image watermarking purpose. The main contribution of this paper is to present a homomorphic image watermarking scheme based on singular value decomposition. It also gives an up-to-date overview of the field of image watermarking in the SVD domain. The proposed image watermarking scheme is robust to most types of attacks. Experimental results show that the proposed image watermarking scheme is not only robust against common image processing operations as blurring, noise adding, and JPEG compression, etc., but also robust against the desynchronization attacks such as scaling cropping, and rotation, etc. This paper is organized as follows: Section 2 describes the singular value decomposition. Section 3 presents SVD watermarking. Section 4 surveys the related work of transform domain based SVD watermarking. Section 5 explores SVD watermarking with the method of Liu. Section 6 presents the proposed SVD watermarking in the homomorphic domain. Section 7 presents the proposed block-based SVD watermarking in the homomorphic domain. Section 8 discusses simulation results. Section 9 gives a comparison between the proposed Homomorphic-Based SVD image watermarking and Homomorphic Block-Based SVD image watermarking methods and other image watermarking schemes. Section 10 presents conclusions.
83
2. Singular value decomposition (SVD)
55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81
91
SVD is an effective numerical analysis tool used to analyze matrices. In SVD transformation, a matrix can be decomposed into three matrices that are of the same size as the original matrix. From the view point of linear algebra, an image is an array of non negative scalar entries that can be regarded as a matrix. Without loss of generality, if A is a square image, denoted as A ∈ Rn×n , where R represents the real number domain, then SVD of A is defined as [11–14]:
92
A = USVT
84 85 86 87 88 89 90
(1) UT
VT
100
such that U = I, where, U and V are orthogonal matrices V = I, I is an identity matrix. S = diag 1 , . . ., p . Where, p = min (m, n), 1 ≥ 2 ≥ . . . p ≥ 0, are the singular values of A. The diagonal entries are called the singular values of the matrix A, the columns of U are called the left singular vectors of A, and the columns of V are called the right singular vectors of A. This decomposition is known as the singular value decomposition (SVD) of A, and can be written as follows [11]:
101
SVD (A) = [USV]
102
or
103
A = USVT
93 94 95 96 97 98 99
104 105 106 107
108 109
(3)
Rm×n ,
where R is the matrix of real numbers, then there 1. If A ∈ exist orthogonal matrices. U [u1 , . . ., um ] ∈ Rm×n
111
and
112
V [v1 , . . ., vn ] ∈ Rm×n
T
U AV = diag 1 , . . ., p
113
(6)
TheSVs are the square roots of the Eigen values i , that is i . This, can be represented as follows [11]: i =
⎡
⎢ S=⎢ ⎣
⎤
1 ..
⎥ ⎥ ⎦
.
(7)
114 115 116
117
n 2. The stability of SVs: the stability of SVs indicates that, when there is a little disturbance with A, the variation of its SVs is not greater than the largest SV of the matrix [11]. Using the SVD in digital image processing has some advantages [12–14]. (a) The SVs of an image have a very good stability, when a small perturbation takes place in the image. (b) The SVs represent the algebraic image properties, which are intrinsic and not visual. The scaling property, if the SVs of Amxn are 1 , 2 ,. . ., k , the SVs of ˛ × Am×n are 1∗ , 2∗ , . . ., k∗ such that [11]:
∗
|˛| (1 , 2 , . . ., k ) = 1∗ , 2∗ , . . ., k
(8)
3. The rotation invariant property: if P is a unitary and rotating matrix, the singular values of PA (rotated matrix) are the same as those of A [11]. 4. The translation invariance property: the original image A and its rows or columns of the interchanged image have the same SVs [11]. The transposition invariance property: T
2
IfAA u = u Then,
T
A Av = 2v
So that A and
AT
118 119 120 121 122 123 124 125 126 127
128 129 130 131 132 133 134 135
(9)
136
(10)
137
have the same SVs [11].
The above mentioned stability of SVs, scaling invariance of SVs, rotational invariance of SVs, and translation and transposition invariance of SVs properties of the SVD transformation are very much desirable in image watermarking. When the watermarked image undergoes attacks like rotation, scaling, and noise addition, the watermark can be retrieved effectively from the attacked watermarked image due to the above mentioned properties. 3. SVD watermarking There are two types of SVD watermarking; watermarking of the image as a whole and block-based watermarking. 3.1. Watermarking of the image as a whole
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147 148
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(2)
The SVs represent the algebraic properties of an image. These values possess an algebraic and geometric invariance to some extent. The properties of the singular values are reviewed as follows [11]:
110
Such that
(4)
(5)
Liu and Tan proposed an algorithm that embeds the watermark directly to the whole image in the SVD domain [11]. This algorithm requires the SVs or the orthogonal matrices for retrieving the watermark. It is resistant to some attacks like compression, filtering, and cropping, but is not robust to attacks including rotation and translation. A method based on the SVD has also been proposed by Liu and Kong. This algorithm uses an M-sequence as the watermark. Considering the visual quality and robustness criteria, the watermark has been embedded in middle SVs maintaining the original order. This algorithm is blind, i.e., does not require the original image or any other information of the original SVs to detect the watermark. This method can resist some attacks like JPEG compression, median filtering, rescaling, Gaussian low-pass filtering, but is not robust to some other attacks including rotation, and cropping.
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3.2. Block-based watermarking
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An SVD watermarking scheme has been proposed by Ganic et al. [15] where the watermark is embedded twice. In the first layer, the cover image is divided into smaller blocks and a piece of the watermark is embedded in each block. The cover image is used as a single block to embed the whole watermark in the second layer. Layer 1 allows flexibility in data capacity and Layer 2 provides additional robustness to attacks. This scheme can resist several attacks including JPEG compression, JPEG 2000, Gaussian blur, Gaussian noise, cropping, rotation, and rescaling but after each attack visual quality of the image degrades and the commercial value of the image is lost. For the rotation attack, small angles only have been tested. This scheme is not robust to translation attack. In [15], a SVD-based scheme has been proposed by Ghazi et al., where the original image is divided into blocks and then the watermark is embedded in the SVs of each block, separately. The watermark can be a pseudo random number or an image. This method is robust to several attacks such as JPEG compression, Gaussian noise, Gaussian blur, cropping, resizing, and rotation, though for rotation a small angle has been tested, and the correlation value for rotation and resizing is not good. This method is not resistant to translation attack. Zhou et al. [16] presented an algorithm in which the original image is divided into several blocks of size 8 × 8 for each block and the watermark is embedded in the SVD domain of each block of the image. The embedded watermark may be binary image, a pseudorandom number or a gray scale image. If the cover image size is not exactly divisible by 8, then it requires adjustment before embedding of watermark. Experimental results have shown that the algorithm is resistant to JPEG compression, noise, filtering, clipping, and rotation. Similarity of the original watermark and the extracted watermark has been evaluated using the correlation coefficient, which is not very satisfactory in the case of the rotation attack. Moreover, this algorithm can’t resist scaling and translation attacks.
200
4. Transform domain based SVD watermarking
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Some algorithms have been presented for SVD watermarking in transform domains.
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4.1. DCT-based SVD watermarking
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A DCT-based SVD watermarking algorithm has been proposed by Sverdlov et al. [17]. The DCT is applied to the whole cover image, and the DCT coefficients are mapped to four quadrants using a zigzag sequence, and then the SVD is applied to each quadrant. These four quadrants actually represent frequency bands from the lowest to the highest. SVs of the DCT-transformed visual watermark are then used to modify the SVs of each quadrant of the cover image. It has been shown that embedding data in lowest frequencies is resilient to a set of attacks, while embedding data in the highest frequencies is resilient to another set of attacks. Robustness of this algorithm has been tested for a set of attacks including Gaussian blur, Gaussian noise, JPEG compression, JPEG 2000 compression, rescaling, cropping, histogram equalization, and gamma correction. Robustness to the rotation attack is not guaranteed. This algorithm is also not resistant to translation attack.
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4.2. DWT-based SVD watermarking
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3
Fig. 1. Proposed homomorphic image watermarking embedding.
Fig. 2. Proposed homomorphic image watermarking detection.
each sub-band. SVD is then applied on the watermark image and the SVs of the cover image are modified with the SVs of the watermark image. Finally, four sets of DWT coefficients are obtained and, and the Inverse DWT (IDWT) is calculated from the modified DWT coefficients to obtain the watermarked image. Robustness of this algorithm has been tested for a set of attacks including Gaussian blur, Gaussian noise, JPEG compression, JPEG 2000 compression, rescaling, cropping, histogram equalization, and gamma correction. Results have revealed that the extracted watermark from the LL band is the best in visual quality and correlation coefficient. Performance of this algorithm for sharpening, contrasting, and histogram equalization attacks is not good. 4.3. Hadamard-based SVD watermarking The Fast Hadamard Transform (FHT) has been used in SVD watermarking [18]. This algorithm first divides the cover image into blocks and applies FHT to each block. Then SVD is applied to the watermark image and the SVs of the visual watermark image are distributed over the transformed cover blocks. The main features of this algorithm are simplicity, flexibility in data embedding capacity, and real time implementation. Robustness of this scheme has been tested for several attacks including Gaussian blur, Gaussian noise, cropping, histogram equalization, gamma correction, sharpening, resizing, and rotation. Translation attack has not been considered, which is an indication of the vulnerability of this algorithm to this attack. 4.4. Zernike moments-based SVD watermarking Li et al. proposed a Zernike moments-based SVD watermarking scheme, where the Zernike moments are used to estimate the rotation angle to make the algorithm rotation invariant [19]. The cover image can be divided into blocks and the SVD is applied to each block. This algorithm is robust to rotation for even large angles, scaling, and pixel removal attacks. Visual quality of the watermarked image has been measured by the Weighted Peak Signal-to-Noise Ratio (WPSNR), and similarity of the original to the extracted watermark has been evaluated by normalized correlation. 5. SVD watermarking with the method of Liu
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A DWT-based SVD watermarking algorithm has been presented by Ganic and Eskicioglu [15]. This algorithm is very similar to the algorithm of Sverdlov et al. [17]. The cover image is first decomposed with the DWT into four sub-bands and the SVD is applied to
In the approach proposed by Liu et al. [11], the watermark W is added into the matrix S. Then, a new SVD process is performed on the new matrix S + kW to get Uw , Sw , and Vw , where k is the scale
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Fig. 3. Method of Liu (a) Original image. (b) Watermark. (c) Watermarked image without attacks PSNR = 62.65 dB. (d) Extracted watermarks cr = 0.9. Fig. 5. Block-based SVD watermarking in the homomorphic domain. (a) Original image. (b) Watermark embedded in each block in the homomorphic domain. (c) Watermarked image without attacks, PSNR = 66.5837 dB. (d) Extracted watermarks from each block. (e) Zooming of the extracted watermark which has c rmax = 0.9997. (f) Correlation coefficient between each extracted watermark and the original one.
Fig. 4. SVD watermarking in the homomorphic domain. (a) Original image. (b) Watermark (c) Watermarked image without attacks, PSNR = 65.7 dB. (d) Extracted watermark, cr = 0.9993.
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factor that controls the strength of the watermark embedded to the original image. Then, the watermarked image Fw is obtained by multiplying the matrices U, Sw , and VT . The steps of embedding the watermark are summarized as follows:
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1. The SVD is performed on the original image (F matrix).
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F =s
(11)
2. The watermark (W matrix) is added to the SVs of the original matrix. D = S + KW
(12)
3. The SVD is performed on the new modified matrix (D matrix). T D = Uw Sw Vw
(13)
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The watermarked image (Fw matrix) is obtained by using the modified matrix (Sw matrix).
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Fw = USVTw
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(14)
To extract the possibly corrupted watermark from the possibly distorted watermarked image, given Uw , S, Vw matrices and
Fig. 6. The extracted watermarks for the method of Liu after applying attacks.
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Fig. 7. Extracted watermarks for SVD watermarking in the homomorphic domain after applying attacks.
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the possibly distorted image Fw , the above steps are reversed as follows: 1. The SVD is performed on the possibly distorted watermarked image (F ∗w matrix). ∗ ∗ ∗T Fw = U ∗ Sw V
∗ T D∗ = Uw Sw Vw
W ∗ = (D∗ − S) /K
6. SVD watermarking in the homomorphic domain
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(17)
*
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3. The possibly corrupted watermark is obtained.
The refers to the corruption due to attacks.
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Fig. 8. Extracted watermarks for the block based SVD watermarking in the homomorphic domain in the presence of attacks.
2. The matrix that includes the watermark is computed.
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(15)
In general, an image can be regarded as a 2-D function of the form f(n1 , n2 ), whose values at the spatial coordinates (n1 , n2 ) are positive scalar quantities [20]. Assuming that we are dealing with grayscale images, we can say that when an image is generated from a physical process, its values are proportional to the energy radiated by a physical source. In other words, an image is an array of measured light intensities and is a function of the amount of light reflected from the objects in the scene. The intensity of pixels is the product of the incident illumination and the reflectance. The illumination is approximately constant, while the reflectance holds most of the image details. The reflectance results from the way the objects in the image reflect light, and is determined by the intrinsic
Fig. 9. Plot of the correlation coefficient for all attacks.
properties of the object itself. So, it is expected that a watermark embedded in the reflectance component can survive several attacks [20]. In the following subsections, the steps of watermark embedding in the reflectance component of an image and watermark detection are presented.
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Fig. 10. (a) Original image. (b) Watermark. (c) Watermarked image without attacks in the method of Liu with PSNR = 62.65 dB. (d) Extracted watermarks with cr = 0.9 in the method of Liu. (e) Watermarked image without attacks in homomorphic method with PSNR = 48.06 dB. (f) Recovered watermark cr = 0.995 in homomorphic method. (g) Watermarked image in block-based homomorphic method with PSNR = 48.07 dB. (h) Recovered watermarks. (i) Magnification of the watermark with cr = 0.999.
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6.1. Watermark embedding 1. The image intensities can be represented as follows [20]:(18)f(n1 , n2 ) = i(n1 , n2 )r(n1 , n2 ) where, i(n1 ,n2 ) is the light illumination and r(n1 ,n2 ) is the reflectance of the object to be imaged. 2. The homomorphic transform is performed ln[f (n1 , n2 )] = ln[i(n1 , n2 )] + ln[r(n1 , n2 )]
(19)
3. A LPF and a HPF are applied to log [f(n1 , n2)] to separate the illumination component I and the reflectance component R, respectively, for each pixel value in the form of matrices. 4. The SVD is performed on the (R matrix). R = USVT
(20)
5. The watermark (W matrix) is added to the SVs of the reflectance matrix. D = S + kW
(21)
6. The SVD is performed on the new modified matrix (D matrix). D=
T Uw Sw Vw
(22)
7. The image (Rw matrix) is obtained by using the modified matrix (Sw matrix). Rw = USVTw
(23)
8. An inverse homomorphic transform is performed on I and Rw to obtain a matrix Xw . Xw = Rw + I
(24)
Fig. 11. The extracted watermarks for the method of Liu after applying attacks.
9. The watermarked image is obtained as follows: Fw = exp(Xw )
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(25)
6.2. Watermark detection
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To extract the possibly corrupted watermark from the possibly distorted watermarked image, given Uw , S, Vw matrices and the possibly distorted image Fw , the above steps are reversed as follows: (1) The homomorphic transform is performed on the watermarked image (Fw ). (2) A HPF is used to get the possibly corrupted reflectance component R∗w . (3) The SVD is performed on the R∗w matrix. ∗ Rw = U∗ S∗w V∗T
(26)
(4) The matrix that includes the watermark is computed. ∗
D =
∗ T Uw Sw Vw
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(5) The possibly corrupted watermark is obtained. W ∗ = (D∗ − S)/k
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(28)
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Fig. 12. Extracted watermarks for SVD watermarking in the homomorphic domain.
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7. Block-based SVD watermarking in the homomorphic domain
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7.1. Watermark embedding
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Fig. 13. Extracted watermarks for the block-based SVD watermarking in the homomorphic domain.
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The same steps from 1 to 4 as in Section 6.1 are applied, and then: 5. Divide the S matrix into non-overlapping blocks (Sb ). 6. The watermark (W matrix) is added to each block.
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D = Sb + kW
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(29)
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7. The watermarked blocks are combined back into a single matrix to build the Sw matrix. The same steps from 8 to 10 are applied as in Section 6.1.
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The same steps from 1 to 4 in Section 6.2 are applied and then: 5. Divide the D* into blocks Di∗ . 6. The possibly corrupted watermark is obtained.
W ∗ = Di∗ − Sb /k
Fig. 14. Plot of the correlation coefficient for all attacks.
(30)
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The * refers to the corruption due to attacks. Embedding and detecting are shown in Figs. 1–2.
8. Simulation results In this section, several experiments are carried out to compare between the methods of Liu, and the proposed method. The 512 × 512 airplane and the 512 × 512 colored baby images are used in the simulation experiments. The RGB color space is highly correlated and is not suitable for watermarking applications, except for the blue channel used by some researchers because of its low effect on human perception [21]. So we have chosen to transform the RGB color space to the Y Cb Cr color space. In this color space, most of the information is concentrated in the luminance (Y component) and less in the chrominance (Cb and Cr components). The experiments demonstrate that the watermark embedding in the luminance component (Y) has a larger effect on the human vision than human vision than embedding in the Cb and Cr components, but due to the robustness to JPEG compression; we propose watermark embedding in the Y channel. Fig. 3 shows the original image, the watermark, the watermarked image, and the extracted watermark using the method of Liu. A single watermark is used. Fig. 4 shows the original image, the watermark, the watermarked image, and extracted watermark using the proposed homomorphic method. It is clear that there is no visual difference between the original image and the watermarked image for the human vision, enforcing the fidelity of homomorphic method. We find that the PSNR in the method of Liu is 62.65 dB, and in the proposed method, the PSNR = 65.7 dB. The maximum correlation coefficient between the original transmitted watermark and any of the extracted watermarks for the block-based SVD method and the block-based SVD method in the homomorphic domain are 0.9 and 0.96, respectively. Fig. 5 shows the original image, the watermark, the watermarked image, and extracted watermark using the proposed block-based homomorphic method. It is clear that there is no visual difference between the original image and the watermarked image, enforcing the fidelity of the homomorphic method. We find that PSNR in the block-based method is 66.58 dB. The maximum correlation coefficient between the original transmitted watermark and the extracted watermark for the proposed block-based method is c rmax = 0.999. Some attacks such as Gaussian noise, cropping, compression, rotation, and resizing on the watermarked images have been applied. Figs. 6–8 show the watermarked images and the extracted watermarks under attacks for all watermarking methods. The first attack applied is the JPEG compression with quality factor 50. The second attack is resizing from 512 to 256 and back to 512 again. The third attack is addition of Gaussian noise with zero mean and 0.1 variance. The fourth attack is cropping. The fifth attack is rotation with (−3◦ ). Fig. 6 shows the extracted watermarks for the different attacks and the correlation coefficient between each extracted watermark and the original watermark for the method of Liu. The results reveal that the value of cr is more than 0.1, but less than 0.8 for each attack except for the cropping attack, which gives cr = 0.0317. Fig. 7 shows the extracted watermarks for the proposed method after applying the same attacks. In all cases, there are some extracted watermarks with cr higher than 0.6, which ensures the existence of the watermark. The figures show the superiority of the proposed method to the method of Liu in the presence of a Gaussian noise attack and a compression attack, respectively. These results reveal the ability of the proposed algorithm to extract watermarks even in the presence of severe attacks. Fig. 8 shows the extracted watermarks for the block-based SVD method in the homomorphic domain after applying the same attacks. In all cases, there are extracted watermarks with cr higher than 0.8, which ensures the
existence of the watermark. The figures show the superiority of the proposed block-based SVD watermarking method in the homomorphic domain to the method of Liu in the presence of a Gaussian noise attack, a compression attack and a cropping attack. Fig. 9 reveals the superiority of the proposed method. Simulation results on the 512 × 512 color Baby image with the method of Liu, the proposed homomorphic-based SVD image watermarking and homomorphic block-based SVD are depicted in Figs. 10–14. 9. Comparison between the proposed a comparison between the proposed homomorphic-based SVD image watermarking and homomorphic block-based SVD image watermarking methods and other schemes
=
i
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In order to study the performance of the proposed methods, we compared the results of the proposed block-based SVD image watermarking in the homomorphic domain and the proposed SVD image watermarking in the homomorphic domain against four image watermarking algorithms. The first method we use as reference is the one presented by Liu et al. [11], which is based on singular values decomposition (SVD). This method is denoted as Liu method, works by inserting the watermark into the whole image in the SVD domain. The method utilizes the SVs matrices for obtaining the watermark. The second method denoted as waveletbased watermarking method [22]. It is based on classifying wavelet coefficients as insignificant or significant using zero tree and then embedding a watermark in the location of insignificant coefficients or in the location of the thresholded significant coefficients at the coarser scales adjacent frames comparison in the wavelet domain. The third method denoted as DWT-Based SVD watermarking [23]. It works by decomposing the cover image with the DWT into four sub-bands and the SVD is applied to each sub-band. The SVs of the cover image are modified with the SVs of the watermark image. The fourth method denoted as DWT-based chaotic watermarking is basically based on embedding binary watermark pattern after applying a chaotic mixing method in the DWT domain [24]. The 512 × 512 Lena and Mandrill images have been used in the simulation experiments. The watermark decoder measures the normalized correlation between the transform coefficients of extracted watermark and the coefficients of the original watermark. For each method, the normalized correlation was estimated for watermarked sequences that had not gone through any type of distortion. The six watermarking schemes were able to correctly detect all of the watermarks. The normalized correlation can be estimated as: Normalized Correlation :
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[win (i, j)]
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(31)
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j
where, win is the original watermark and wout is the extracted watermark, Tables 1 and 2 give normalized correlation values for Lena and Mandrill test images with all watermarking methods under different attacks. It is clear that the proposed block-based SVD image watermarking and the proposed SVD image watermarking in the homomorphic domain outperforms better than other schemes [11,22–24] under most attacks in terms of the normalized correlation between the transform coefficients of extracted watermark and the coefficients of the original watermark. From Tables 1 and 2, the obtained results reveal the superiority of watermarking in the homomorphic domain. Also, we can see that the watermark achieves the robustness to both various desynchronization attacks and common image processing operations by
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Table 1 Normalized correlation values for the extracted watermarks using different watermarking methods for the Lena image with and without attacks. Method
Wavelet-Based watermarking [23]
Liu method [11]
DWT-Based SVD Watermarking [24]
DWT-Based chaotic watermarking [25]
Homomorphicbased SVD watermarking
Homomorphicbased Block-by-block SVD watermarking
0.8500 0.7500 0.5714 0.1438 0.3017 0.1747 0.2450
0.8800 0.8100 0.6120 0.3120 0.5480 0.2310 0.3780
0.9670 0.9320 0.8740 0.6780 0.7850 0.3560 0.6210
0.9730 0.9560 0.9010 0.7560 0.8850 0.4820 0.8840
0.9853 0.9750 0.9015 0.7790 0.9234 0.5654 0.9350
0.9996 0.9940 0.9930 0.8920 0.9910 0.9770 0.9910
Attack No attack JPEG compression Q = 50% Resizing 512–256–512 Gaussian noise with variance = 0.1 Cropping Rotation Bluring
Table 2 Normalized correlation values for the extracted watermarks using different watermarking methods for the Mandrill image with and without attacks. Method
Wavelet-Based watermarking [23]
Liu method [11]
DWT-Based SVD Watermarking [24]
DWT-Based chaotic watermarking [25]
HomomorphicBased SVD watermarking
HomomorphicBased Block-by-block SVD watermarking
0.8780 0.79 0.594 0.1965 0.3756 0.1987 0.2856
0.8940 0.840 0.6590 0.4230 0.6580 0.2758 0.3960
0.9690 0.9368 0.8980 0.6880 0.7960 0.3740 0.6452
0.9690 0.9620 0.9120 0.7780 0.8970 0.4990 0.8960
0.9870 0.9730 0.9256 0.7950 0.9364 0.5960 0.9440
0.9995 0.9960 0.9925 0.9210 0.9955 0.9810 0.9925
Attack No attack JPEG compression Q = 50% Resizing 512–256–512 Gaussian noise with variance = 0.1 Cropping Rotation Bluring
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incorporating the proposed block-based SVD image watermarking and the proposed SVD image watermarking in the homomorphic domain.
10. Conclusions This paper presented a homomorphic image watermarking method using the SVD algorithm. By embedding a watermark with the SVD algorithm to the reflectance component of an image after the homomorphic transform, and the modified one which embed the watermark into the SVs of the HPF of the homomorphic of the original image after dividing it into blocks. It is shown that we can transmit two images, the original image, and the watermark as a single image; the watermarked image. This can achieve a reduction in bandwidth. The experimental results show also that the blockbased SVD watermarking in the homomorphic domain has a high fidelity and robustness in the presence of different types of attacks. There is always a large probability for detecting the watermark. The results also reveal the superiority of the proposed block-based SVD watermarking in the homomorphic domain to the method of Liu.
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