A Reliable Image Watermarking Scheme Based on Redistributed Image Normalization and SVD

1Department of Natural and Applied Science, Glocal University, Saharanpur-247122, India 2Department of Computer Engineering, Sungkyunkwan University, Suwon-440746, Republic of Korea 3Department of Applied Science and Engineering, IIT Roorkee-247667, India 4Laboratoire Images, Signaux et Systèmes Intelligents (LiSSi, EA 3956), Université Paris-Est Créteil Val de Marne, 61 avenue du Général de Gaulle, 94010 Créteil, France


Introduction
Digital watermarking [1,2] is the process of insertion of digital watermark in media content and its extraction, if required, for authentication or ownership verification of media content.A digital watermark is a piece of information that is hidden directly in media content, in such a way that it is imperceptible to a human observer but easily detected by a computer [3].Different types of digital watermarking methods for digital contents have been developed that are classified into different categories depending upon the use and the requirement of information required for the extraction/detection of watermark.To check the authenticity of a digital content fragile watermarking is used while, for the purpose of copyright protection, robust watermarking is utilized.This classification is application-dependent.Based on the information required for the extraction/detection process watermarking schemes can be classified into blind, semiblind, and nonblind categories.Also, one more categorization is possible depending upon the domain of embedding of watermark: spatial and frequency.A detailed review of watermarking schemes can be found in [4,5].
In a robust image watermarking scheme, a trade-off always exists among the two conflicting objectives, imperceptibility (also known as perceptual transparency) and robustness.So, the main goal of a robust image watermarking scheme is to produce the watermarked image with low quality degradation and high robustness.Increasing the amount of embedding information in an image may enhance its robustness to intentional or unintentional distortions applied to the image while simultaneously scarifying its imperceptibility and vice versa.Therefore, in order to improve these objectives, researchers have proposed several watermarking schemes implemented in spatial as well as transformed domain that find a compromise between these two objectives.The spatial domain watermarking techniques directly embed the watermark into the host image by altering the pixel values [6][7][8][9].These methods generally are less robust to image and signal processing attacks and required low computational efforts, while frequency domain methods transform the representation of spatial domain into the frequency domain and then modify its frequency coefficients to embed the watermark.There are many transform domain watermarking techniques such as discrete cosine transforms (DCT) [10,11], discrete Fourier transforms (DFT) [12][13][14], discrete wavelet transforms (DWT) [15][16][17], and singular value decomposition (SVD) [2,[18][19][20].These methods typically provide higher image imperceptibility and are much more robust to image manipulations, but the computational cost is higher than spatial domain watermarking methods.The performance of watermarking methods was further improved by combining two or more transformations [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36].The idea was based on the fact that combined transforms could compensate for the drawbacks of each other, resulting in effective watermarking.
The singular value decomposition (SVD) is extensively used in image watermarking field in recent years due to its features.However, various researchers pointed out the false positive detection problem in most of the SVD-based algorithms [33,[37][38][39][40].To counter this problem, numerous researchers have proposed improved versions of SVD-based image watermarking schemes.A robust image watermarking scheme based on SVD that embeds the entire watermark is given in [19].There are two versions of this scheme depending on the implementation of SVD, to entire cover image and block-wise.The imperceptibility of an image watermarking scheme using block based SVD proposed in [18] is improved by incorporating compensation operation.According to this scheme, the damage in the quality due to insertion of the watermark in the left singular vector matrix is compensated by modifying the right singular vector matrix.The host image is segmented into nonoverlapping blocks of size 4 × 4; then the embedding blocks are selected at random.The watermark bits are embedded by modifying the coefficients in the first column of the left singular vector matrix of the target blocks.The different regions within an image have different local features, so some visual models such as human visual system (HVS) may be incorporated in finding the suitable embedding regions to improve robustness while maintaining imperceptibility.Based on this concept, a blind SVD-based watermarking scheme is presented in [34].The host image is segmented into nonoverlapping blocks of size 8 × 8; then the embedding blocks are selected based on the sum of visual and edge entropies.The watermark bits are embedded by modifying the coefficients in the first column of the left singular vector matrix of the target blocks.The above mentioned SVD-based watermarking schemes embed the entire watermark within the cover image.It has improved the reliability of the watermarking but sacrificed the transparency.Also, these schemes are applicable only for the black and white watermark.If the watermark image is grayscale, then encode it to binary before embedding.A watermarking scheme proposed in [41] is based on the fact that SVD subspace (left and right singular vectors) can preserve a significant amount of information about an image.Therefore, it embeds the principal component, multiplication of left singular vector matrix and the singular value matrix, of watermark into the host image instead of singular values of the watermark.On the same concept, Run et al. [36] introduced an image watermarking scheme embedding the principal component of the watermark in frequency domain (DCT and DWT domains, resp.).Also, an optimization technique is applied to get the optimal scaling factors for embedding.Guo and Prasetyo [33] have extended this principal component concept to the block based watermarking.For convenience, this "false positive free SVD-based watermarking" scheme is abbreviated as "FPF-SVD-W" and used throughout the paper.The low frequency subband of the DWT transformed image is segmented into nonoverlapping blocks equal to the size of the watermark.Then the largest singular value of each block is modified by adding to it a scalar multiple of the corresponding element of the principal component matrix of the watermark.This reliable SVD-based watermarking scheme has solved the false positive detection problem and shown the resistance against some image manipulation attacks.It is not robust against some special distortions, such as image rotation in integer multiple of ninety degrees and image flipping (rows/columns).It is also realized from this scheme that a single scaling factor is not suitable to scale all the elements of the principal component matrix of the watermark.As the largest singular values from each block of the image have a different tolerance limit of modification to embed the watermark, it results in some visible distortions in the watermarked image with single scaling factor.
The focus of this research is on imperceptibility and robustness improvement of the reliable SVD-based image watermarking FPF-SVD-W.This paper proposes a novel and efficient and reliable SVD-based image watermarking scheme by incorporating the redistributed image normalization and variable scaling factor.To make the proposed scheme resilient against the attacks, such as rotation in an integer multiple of ninety degrees and image flipping, which change the locations of the pixels but do not make any changes to the pixel's intensity of the image, redistributed image normalization is utilized.To mitigate the problem of visible distortions in the watermarked image, a variable scaling factor in employed depending on the coefficient's magnitude to be embedded.In the proposed scheme the host image is redistributed and then some normalization operators are applied.Subsequently, the low frequency subband of the DWT transformed image is segmented into nonoverlapping blocks and SVD is applied to each block to get the largest singular value.The watermark is shuffled by using the piecewise linear chaotic map [35,42] and then the elements of the principal component matrix of the watermark are embedded into the blocks by modifying the largest singular value of the corresponding blocks.The performance of the proposed scheme has been analyzed using several cover and watermark images and fifteen distortion attacks.Experimental results indicate that the proposed scheme not only gives the best results, but also outperforms the other SVD-based scheme FPF-SVD-W.The rest of the paper is organized as follows.A brief review of the components of the proposed scheme is given in Section 2. The watermarking scheme FPF-SVD-W is discussed in detail in Section 3. Section 4 describes the proposed scheme.The experimental results are analyzed in Section 5. Finally, Section 6 draws the conclusions based on this research.

Piecewise Linear Chaotic Map (PWLCM).
To enhance the confidentiality of the watermarking scheme, encryption of the watermark must be done before embedding into cover image.There are several chaotic maps that can be used for encryption; piecewise linear chaotic map (PWLCM) [35,42] is one of them that recently has gained popularity due to its simplicity in representation and efficiency in implementation, as well as good dynamical behavior.Since the chaotic signal generally has good invariance to disturbance due to the low correlation between the initial parameters, it has been widely utilized for encryption and data hiding applications.The PWLCM, mathematically, is described in where  ∈ (0, 0.5) is control parameter and considered as secret key.The most attractive features of PWLCM are its extreme sensitivity to initial conditions and the outspreading of orbits over the entire space.It is a noninvertible transformation of unit interval onto itself.
The encryption process of an image () of size  ×  based on this map is performed by implementing the steps given in Algorithm 1.An illustration of output of Algorithm 1 is given in Figure 1, by considering the different cases.

Singular Value Decomposition (SVD).
The singular value decomposition (SVD) [18][19][20] is a numerical analysis technique based on a theorem of linear algebra that decomposes a rectangular matrix into the product of three matrices: an orthogonal matrix (), a diagonal matrix (), and the transpose of an orthogonal matrix ().It may be considered as a method of transforming correlated data set into uncorrelated one that better explains the various relationships among the original data.Due to the unique features and attractive properties such as stability with little disturbance, SVD has been used in many signal and image processing applications such as image watermarking, image hiding, image compression, and noise reduction.The digital image is also a kind of signal which can be viewed as a matrix.According to the theory, the SVD of a rectangular matrix  of order  ×  is represented mathematically as where   =   and   =   ; the columns of  are orthonormal eigenvectors of   , the columns of  are orthonormal vectors of   , and  is a diagonal matrix containing the square roots of the eigenvalues from  or  in descending order.If  ( ≤ ) is the rank of the matrix  then the elements of the diagonal matrix  satisfy the relation (3) and the matrix  can be written as (4): where   and V  are the th eigenvector of  and  and   is the th singular value.
Algorithm 1 (shuffling of an image by PWLCM).Consider the following steps.
Step 3. Perform vectorization operation which converts the image () into a vector .
Step 4. Copy the pixel values from vector  to another vector  such that  = ().
Step 5. Finally, the encrypted image (EI) is obtained by reshaping  back to an  ×  matrix.

Discrete Wavelet Transform (DWT).
The temporal resolution (i.e., it captures both frequency and location or time information) advantage of DWT [15,21,28] over more traditional transforms, such as the Fourier transform, makes it a versatile mathematical transform having numerous applications in different areas including image and signal processing.Wavelet transform has recently become an important tool in image processing and watermarking due to its good energy compaction properties.The basic idea of discrete wavelet transform (DWT) is to separate frequency detail and is based on small waves, called wavelets, of varying frequency and limited duration.In DWT, a time scale representation of digital signal is obtained using digital filtering techniques.The signal to be analyzed is passed through filters with different cutoff frequencies at different scales.Each level of decomposition of DWT decomposes an image into four subbands, namely , , , and .The lower resolution approximation subband () that contains a rough description of the image is obtained by passing the digital signal through a low-low filter in both directions.The  and  subbands are obtained by passing through a low-pass filter in one direction and through a high-pass filter in another direction.The  subband is high-pass filtered in both directions and contains the high-frequency components along the diagonals.After the image is processed by the wavelet transform, most of the information contained in the original image is concentrated into the  image. contains mostly the vertical detail information which corresponds to horizontal edges. represents the horizontal detail information from the vertical edges.The low-pass subband can further be decomposed to obtain another level of decomposition.This process is continued until the desired number of levels determined by the application is reached.

The (FPF-SVD-W) Scheme and Its Weakness
This section provides the detail of the scheme proposed by Guo and Prasetyo [33] and then analyzes its weakness.

The "FPF-SVD-W" Scheme.
Let  be a grayscale cover image of size  × , and let  be the visual grayscale watermark of size  × .This scheme embeds the principal component of the watermark into the singular value matrix of the cover image composed by the largest singular values of the blocks.

Watermark Embedding. (E1)
The SVD is performed on the watermark image  as follows: (E2) The watermark principal component is obtained by multiplying the matrices   and   : Let the value in principal component matrix at location (, ) be denoted by   (, ), where ,  = 1, 2, . . ., .
(E5) The SVD is applied for each image block (, ) to get the largest singular value  max (, ): where  = diag(  ) and  = 1, 2, . . ., .The watermark principal component is embedded into the host image by modifying the largest singular value.(E6) The watermark principal component is embedded into the largest singular value of host image for each image block (, ) using the following formula: where   max (, ) denotes the distorted largest singular value in image block (, ).
(E7) Inverse SVD is performed on each image block (, ) as where   = diag(  max ,   ) for  = 2, . . ., . (E8) The distorted  subband image is obtained as (E9) The watermarked image is reconstructed by performing 1-level inverse DWT (IDWT) as The singular vector matrix    of the watermark and the largest singular value  max (, ), where ,  = 1, 2, . . ., , of each block of the cover image are kept safe for the watermark extraction.

Watermark Extraction.
In the watermark extraction process, the watermark  * is extracted from the possibly corrupted watermarked image  *  by using the side information that is kept safe in embedding process (   and  max (, )) by employing the following steps.
(X4) Corrupted principal component is obtained as (X5) The extracted watermark is obtained as

Weakness Analysis of the "FPF-SVD-W" Scheme.
To analyze the weakness of the scheme grayscale square images of sizes 512 and 64 are considered as cover and watermark images, respectively.These two images are given in Figure 2.This scheme has solved the false positive detection problem that occurred in some previous SVD-based watermarking schemes [22,27].It has given the competitive results in comparison to other watermarking schemes in terms of imperceptibility and robustness.It is obvious from the SVD properties that singular values are invariant to the operations of flipping and rotation of the matrix in integer multiple of ninety degrees.In other words, singular values of a matrix, singular values of its rotated version obtained by rotating in integer multiple of ninety degrees, and singular values of row/column flipping matrix are the same.So the watermarking scheme that applies the SVD to entire cover image will be resistant to rotation and flipping attacks.But in the scheme FPF-SVD-W, SVD is implemented block-wise, and these blocks are not invariant to these operations.So, this scheme is not resistant to these types of attacks.Watermarked image, distorted watermarked images under these operations, and extracted watermarks from these images are given in Figure 3. From this figure, it is clear that the scheme is not robust to these attacks.
In singular value decomposition (SVD) the singular values are in descending order of the rows from top to bottom.The columns of the singular vector matrix  are orthonormal vectors.The principal component matrix is obtained by the multiplication of these two matrices.The absolute value of the columns of this matrix decreases from left to right.There is a huge difference in the absolute values of the columns at left and right.This situation is illustrated in Figure 4 by taking a square matrix of order three.Therefore, a single constant scaling factor would not be suitable for the embedding principal component matrix of the watermark.It will introduce the visible distortions on the left side of the image that is shown in Figure 5.To obtain the good imperceptibility this scaling factor must be a variable depending on the columns of the principal component matrix that are being embedded.

The Proposed Scheme
This section is devoted to the mathematical formulation of the proposed watermarking scheme and its components.

Redistributed Image Normalization.
The purpose of redistributed image normalization is to obtain the invariant blocks under the rotation and flipping operations.The location of pixel values in a block may vary, but the elements of the blocks remain the same.To achieve it, pixels' locations of the image are redistributed and then some normalization procedures are performed.Mathematically, it is formulated as follows.
Let  be the image of size  ×  that is divided into four Redistribute the original image (), using the distribution relation given in (18) to obtain the redistributed image (RI):   To show this visually, we have taken an example of a square matrix of order 4 that is shown in Table 1.The block size is taken 2 × 2 to show the singular values of the blocks by applying SVD to both original and normalized versions, respectively.From this table it is clear that the singular values of the blocks of redistributed image are invariant under the operation of rotation and flipping.

Scaling Factor.
The scaling factor in watermarking determines the watermark strength and plays an important role to control the robustness and watermark imperceptibility.A small value of the scaling factor favors the watermark imperceptibility, but the watermarked image is less robust to A single constant scaling factor cannot be suitable to modify the coefficients having huge difference in absolute values.To maintain the balance between the imperceptibility and robustness the scaling factor corresponding to the large coefficient values must be small, whereas the scaling factor corresponding to the small coefficient values must be large [23].From Figure 4, it is clear that the scaling factor must increase from left to right depending on the columns of the watermark being embedded, because the absolute coefficient values in the columns of principal component matrix being embedded decrease from left to right.Therefore, in the proposed watermarking scheme a variable scaling factor in the range [ min = 0.25,  max = 1.0] depending on the columns of the watermark of size  ×  is utilized to achieve a better performance: (E3) Obtain the watermark principal component by multiplying matrices   and   : Let   (, ) be the principal component in pixel position (, ), where ,  = 1, 2, . . ., .
(E4) Apply the redistributed image normalization process on the cover image () to obtain the normalized cover image RI and use the flag to keep the transpose record.
(E7) Apply SVD for each image block (, ) to get the largest singular value  max (, ): where  = diag(  ) and  = 1, 2, . . ., .The watermark principal component is embedded into the host image by modifying the largest singular value.
(E8) Embed the watermark principal component into the largest singular value of host image for each image block (, ) using the following formula: where   max (, ) denotes the distorted largest singular value in image block (, ) and   is the scaling factor that is determined by (19).
(E9) Perform inverse SVD on each image block (, ) as where   = diag(  max ,   ) for  = 2, . . ., . (E10) Obtain the distorted  subband image as (E11) Perform 1-level inverse DWT on wavelet subbands replacing  subband by   as (E12) Apply the inverse redistributed image normalization process on the image obtained in step (E9) to obtain the watermarked image   .Now, we have to decide depending on the flag whether a transpose is required or not.The normalization step is done depending on flag (E4) and fresh calculation of  11 ,  12 ,  21 , and  22 values is not required.Finally, redistribute the modified RI  to get the watermarked image.
(X5) Obtain corrupted principal component as where   is the scaling factor given in (19).(X6) Obtain the extracted watermark as (X7) Apply the PWLCM on extracted watermark to get the embedded watermark.
The average of PSNR values of the watermarked images obtained by the proposed scheme is 34.5769 while in case of FPF-SVD-W it is 30.8663.Also, the average PSNR over all the test images corresponding to each embedded watermarks is plotted for both the schemes in Figure 7. From this figure, it is clear that the PSNR values obtained by the proposed scheme are quite high in comparison to FPF-SVD-W in all the cases.A high PSNR value is the indication of better quality of the watermarked image under consideration.It is shown that the variable scaling factor has increased the imperceptibility to a great extent of the proposed scheme.
For the robustness experiments the distortions are applied on watermarked images that are described above.The normalized correlation values corresponding to each of the watermarks are given in Tables 2-4.These tables show that the performance of the proposed scheme is quite satisfactory in all the cases except gamma correction case, where its performance is poor.It is due to the insertion of watermark data into low frequencies.For the robustness comparison of the proposed scheme with the FPF-SVD-W, the average of normalized correlation (NC) values of extracted watermarks over the test images obtained in each case is given in Table 5.The best results are highlighted in bold for each case.From Table 5 it is clear that the performance of the proposed scheme is quite better in comparison to the FPF-SVD-W scheme.In case of rotation and flipping, especially, the proposed scheme has given best performance, while the performance of FPF-SVD-W scheme is worse.For the visual that are used for watermarking.The invariance is in the sense that the location of the pixels in a block may vary but the elements are always the same.The SVD operation is then applied to these blocks to get the largest singular value from each block that is invariant to the rotation and flipping attacks.Then the principal component of the watermark image is embedded into these largest singular values by employing a variable scaling factor.The scaling factor varies in a specified range depending on the magnitude of embedding coefficient.To investigate the robustness of the scheme several attacks are applied to seriously distort the watermarked image.Numerical and pictorial representation of the results has shown the efficiency of the proposed scheme.In most of the cases watermark is extracted with high correlation value.The experimental results compared with the other SVD-based watermarking scheme (FPF-SVD-W) have also represented the better performance of the proposed scheme.The imperceptibility of the proposed scheme has increased to a great extent by employing a variable scaling factor in comparison to FPF-SVD-W scheme that has used constant scaling factor.Thus, the proposed scheme has satisfied the robustness, and imperceptibility, requirements that are essential for a robust watermarking scheme.The proposed scheme has proven its reliability for grayscale image watermarking; as a future work it can be extended to the video watermarking and color image watermarking.Due to the reliability of the proposed scheme, it may have the application in various areas, such as fingerprinting and medical image watermarking.

Figure 1 :
Figure 1: Illustration of PWLCM with different cases.

Figure 4 :
Figure 4: Illustration of SVD and its principal component.

Figure 5 :
Figure 5: Illustration of visible distortion caused by embedding the watermark by zooming the portions of watermarked image.

Table 1 :
Illustration of invariant features of the redistributed normalization.

Table 2 :
Correlation values of the extracted watermarks by the proposed scheme corresponding to WM1.

Table 3 :
Correlation values of the extracted watermarks by the proposed scheme corresponding to WM2.

Table 4 :
Correlation values of the extracted watermarks by the proposed scheme corresponding to WM3.

Table 6 :
Extracted watermarks from the watermarked images that are distorted by various attacks.

Table 7 :
Extracted watermarks from the watermarked images that are distorted by various attacks.