An indirect watermark hiding in discrete cosine transform–singular value decomposition domain for copyright protection

Digital image watermarking has emerged as a promising solution for copyright protection. In this paper, a discrete cosine transform (DCT) and singular value decomposition (SVD) based hybrid robust image watermarking method using Arnold scrambling is proposed and simulated to protect the copyright of natural images. In this proposed scheme, before embedding, watermark is scrambled with Arnold scrambling. Then, the greyscale cover image and encrypted watermark logo are decomposed into non-overlapping blocks and subsequently some selected image blocks are transformed into the DCT domain for inserting the watermark blocks permanently. For better imperceptibility and effectiveness, in this proposed algorithm, watermark image blocks are embedded into singular values of selected blocks by multiplying with a feasible scaling factor. Simulation result demonstrates that robustness is achieved by recovering satisfactory watermark data from the reconstructed cover image after applying common geometric transformation attacks (such as rotation, flip operation, cropping, scaling, shearing and deletion of lines or columns operation), common enhancement technique attacks (such as low-pass filtering, histogram equalization, sharpening, gamma correction, noise addition) and jpeg compression attacks.


Introduction
Nowadays with the advancement of high-speed communication network and personal computers, access, transmission, saving and distribution of digital data (such as images, video, audio and using two or three transform domain techniques. These hybrid domain techniques provide better results than their single counterpart. In addition to this, the application of SVD mechanism in one single image requires huge computation [12]. So hybrid domain watermarking scheme is becoming more effective than pure SVD. Makbol & Khoo [12] present a new hybrid image watermarking scheme based on the redundant discrete wavelet transform (RDWT) and SVD. But, it is shown by Ling et al. [13] that the robust blind image watermarking scheme based on RDWT and SVD [12] has a fundamental flaw in its design that undermines the security of its scheme against the false positive problem. A non-blind DCT-SVD based hybrid domain watermarking is presented in [14]. In this technique, discrete cosine transform (DCT) is applied to the cover image at first, and then coefficients are scanned in zigzag order. Then SVs of the cover image are modified with the SVs of DCT transformed visual watermark. Its main disadvantage lies in its computational value. A DWT-SVD based watermarking scheme is proposed in [15]. After decomposing the cover image into four sub-bands, SVs of each sub-band are modified by SVs of watermark data in this technique. A DWT-SVD based watermarking technique is proposed in [16]. An RDWT and SVD based hybrid watermarking scheme is proposed in [17]. Rastegar et al. [18] proposed hybrid domain watermarking technique using SVD and radon transform. In [19], a new hybrid, secure and robust image watermarking scheme based on the integer wavelet transform (IWT) and SVD is proposed. In this work, authors raise the issue of the false positive problem for most of the SVD based watermarking schemes. Two reasons for this problem are also discussed in this paper: (i) Reason 1: For watermark embedding, the modification of the SVs of the host with the SVs of the watermark. (ii) Reason 2: Use of the following equation in embedding process: In watermark embedding step, embed the watermark into the SVs of cover image by multiplying with a scaling factor of α. In the next step, apply SVD to obtain U W , V W and V T W matrices and keep U W and V T W as secret keys for extraction purpose (as U and V preserve major information of an image). Therefore, illegitimate user can allege ownership using counterfeited U C and V T C . Modern researchers suggest lots of solutions for the above stated security concerns. In [19], it has been solved by adopting a digital signature into the watermarked image. In another research work, Loukhaoukha et al. [20] encrypted the watermark before inserting it into the cover object. This encryption policy is adopted in this proposed method. The literature survey suggests that robustness of image watermarking scheme can be improved with the proper combination of SVD and suitable transform domain technique. To improve the effectiveness of watermarking scheme, in this proposed hybrid domain technique SVD is combined with block based DCT, and SVs of an image are modified with Arnold scrambled watermark data and not with the watermark SVs.
After this introductory section, the rest of the paper is organized as follows. Preliminaries of the DCT and SVD and Arnold scrambling are presented in §2. The proposed watermark embedding and extraction algorithms are described in §3. Experimental results are furnished in §4. Finally, conclusions are drawn in §5.

Preliminaries
In the proposed robust image watermarking scheme, the greyscale encrypted watermark information is embedded in SVD domain. To make the scheme robust, watermark embedding process is developed in the DCT-SVD based hybrid domain. So in this section, DCT and SVD and Arnold scrambling are briefly explained.

Block based discrete cosine transform
DCT [21] is one of the popular and widely used signal decompositions and compression techniques that transform a signal from spatial domain representation into a spectral representation with an inherent ability to exhibit excellent energy compaction for the signal or image. It basically transforms the signal as a sum of sinusoids of varying magnitudes and frequencies. This transformation is used for transferring pixel values of the image from one domain to the other. DCT transformation consists of one DC coefficient and AC coefficients. Most of the information of transformed image stored in few low level frequency coefficients lies on the upper top left corner of the image. DC coefficient is the average of the pixels of the image and AC coefficients contain the significant information of the image, but less than that of DC component. In block based DCT, the input image, f of size M × N is decomposed into non-overlapping blocks of size m × n and then each block f b is transformed into corresponding DCT coefficients according to the following equation: In block based DCT, significant information of the image decreases while traversing from one coefficient to another coefficient in zigzag order. Therefore, few upper coefficients of zigzag order are sufficient to represent an approximate image. Actually block based DCT produces three different frequency bands, namely high, middle and low frequency bands, as signal energies. In general, modification of low frequency band distorted the perceptual quality of the image as it contains maximum image information, while high frequency band can be removed by compression. That is why DCT based watermarking scheme is actually developed on using middle band frequency as it is less perceptible on modification. The top upper left DCT component of block based DCT image is F(0, 0), the average intensity of the image, and also known as the DC coefficient or the energy of the image. The other components of the DCT image are called AC coefficients with different low level values. In this proposed scheme, every coefficient of selected block is modified (figure 1).

Singular value decomposition
In the linear algebra, SVD is a stable and reliable orthogonal matrix decomposition method which splits the system optimally in such a way that each linearly independent set persists with its own energy contribution [22]. In image processing, digital Image A of size n × n can be decomposed by its SVD as follows: A = USV T (2.4) = u 11 u 12 · · · u 1n u 21 u 22 · · · u 2n . . . . . . . . . . . . u n1 un 2 · · · u nn where U, left singular matrix, is an n × n matrix with orthogonal columns, i.e. U T U = I n , where I n is the n × n identity matrix. V, right singular matrix, is an n × n orthogonal matrix, i.e. V T = V −1 . S is an n × n diagonal matrix with non-negative SVs entries and these singular values are in sorted order or satisfying the condition σ 11 > σ 22 > · · · > σ nn . The superscript T denotes the transpose of the matrix. Owing to their attractive properties, SVD factorization methods efficiently compress an image matrix to a smaller sized matrix with almost identical representation of its energy compaction properties [23]. Main features of SVD based methods to apply in watermarking schemes are [23,24] as follows: (i) The SVs of an image have a very good stability. Let X, Y ∈ R m×n and their corresponding SVs are σ 1 , σ 2 , σ 3 , . . . , σ n and τ 1 , τ 2 , τ 3 , . . . , τ n , respectively, and they satisfied the condition |σ i − τ i | ≤ X − Y 2 , i.e. SVs of an image have so much stability that the addition of disturbance to the SVs is not greater than 2-norm of disturbance matrix. So, when a small perturbation is added to an image, its SVs do not change significantly; (ii) The SVs of an image exhibit proportionality property. The SVs of X(σ 1 , σ 2 , σ 3 , . . . , σ n ) and the SVs of kX(σ 1 , σ 2 , σ 3 , . . . , σ n ) are related as k (σ 1 , σ 2 , σ 3 , . . . , σ n ) = (σ 1 , σ 2 , σ 3 , . . . ., σ n ) means proportion invariance of SV must depend on the standardization of SV. (iii) The SVs of an image show transpose property. X and its transposed X T have same number of SVs. (iv) X and its flipped versions about vertical axis and about horizontal axis have the same number of non-zero SVs. (v) X and its rotated version (by an arbitrary angle) have the same number of non-zero SVs. (vi) Suppose, X ∈ R m×n has the SVs σ 1 , σ 2 , σ 3 , . . . , σ n , then its scaled version X s (s = scaling factor) has the σ i × (L r L c ) where i ranges from 1,2, . . . ,n. and L r and L c are the scaling factors of rows and columns. (vii) Both the matrix A and its translated counterpart A T have the same non-zero singular values. (viii) For SVD decomposition, the size of matrices can be either square or rectangle.
(ix) Each singular value specifies the luminance of an image layer, while the corresponding pair of singular vectors specifies the geometry of the image.

Arnold scrambling
In order to expand the robustness of the algorithm and provide extra security to the embedded watermark, Arnold scrambling is employed in the pre-processing step of the proposed method. The classical Arnold scrambling jumbles up the pixel positions of the host image to generate a chaotic image and thus takes the responsibility to act as a secondary encryption technique. Eventually, the watermark is shared out in all space of the host image as space locations of watermark pixels are disturbed by scrambling method. This muddled watermark cannot be recovered without proper information about the scrambling algorithm, even if the attacker successfully extracts the watermark from cover image. Hence, scrambling transformation improves the security of the embedded watermark and increases the robustness of the proposed method. Two-dimensional Arnold scrambling transformation is defined as follows: where i, j is the pixel coordinate of the original space; i , j is the pixel coordinate after iterative computation scrambling and N is the size of the watermark. To restore the original watermark, the corresponding inverse transformation formula can be defined as

Proposed scheme
In this section, DCT-SVD based proposed watermarking scheme is elaborated in detail.

Watermark embedding procedure
Assume I represents the cover image of size M × N and W represents the watermark image of size M1 × N1 (figure 2). To embed W into the I, proposed DCT-SVD based watermark embedding method steps are as follows: Step 1: Block processing of cover image: The cover image I is divided into 8 × 8 non-overlapping blocks according to the following equation: and I_b p is the divided 8 × 8 non-overlapping cover image block where 1 ≤ p ≤ nob.
Step 2: Selection of 8 × 8 cover image block for watermark component embedding: For security and authentication purposes, selection of watermark embedding position in cover image is one of the main concerns in the watermarking schemes. In this proposed scheme, one 8 × 8 non-overlapping cover image block is selected after four 8 × 8 non-overlapping cover image block and it starts from I_b 1 (1st 8 × 8 non-overlapping cover image block). In other words, in each four 8 × 8 non-overlapping cover image blocks, the first block is selected for watermark module embedding purpose, i.e. I_b 1 (1st 8 × 8 nonoverlapping cover image block), I_b 5 (5th 8 × 8 non-overlapping cover image block), I_b 9 (9th 8 × 8 non-overlapping cover image block), . . . and so on till total 8 × 8 non-overlapping cover image block is traversed. So number of selected 8 × 8 non-overlapping cover image block for watermark component embedding is equal to nob/4 or 1/4th of total number of 8 × 8 non-overlapping cover image block. Keep these watermark embedding block values as the secret keys.
(For this proposed embedding algorithm, watermark size is considered as 1/4th of cover image. So, embedded blocks are selected one among four successive blocks. If watermark size is 1/2 of cover image, embedded blocks are selected one among two successive blocks. Similarly, if watermark size is 3/4th of cover image, embedded blocks are selected three among four successive blocks. In this way, if watermark size is equal to the cover image, all the cover image blocks are needed for watermark embedding purpose. So in this proposed method, watermark embedding capacity can be varied according to the size of watermark image.) Step 3: DCT transformation of selected 8 × 8 cover image blocks: As discussed above, hybrid domain watermarking scheme provides better result than its single domain counterpart. So apply the DCT transformation to each selected 8 × 8 non-overlapping cover image block for watermark section embedding according to the following equation: where I_b dct p is the DCT transformed 8 × 8 cover image block where 1 ≤ p ≤ nob/4.
Step 4: Encrypting and block processing the watermark: At first, greyscale watermark W is encrypted to AW by Arnold scrambling technique. Then, scrambled watermark AW is partitioned into 8 × 8 nonoverlapping blocks according to the following equation:  Step 5: SVD transformation of DCT transformed cover image block: Apply SVD to each DCT transformed 8 × 8 cover image blocks according to the following equation: Step 6: Watermark embedding: Embed the 8 × 8 non-overlapping scrambled watermark blocks into the SVs of DCT-SVD transformed 8 × 8 cover image blocks (S p ) by multiplying with a scaling factor of α according to the following equation: Step 7: SVD transformation of watermark embedded SVs: Apply SVD to each watermark embedded 8 × 8 SVs block according to the following equation: Step 8: Inverse SVD transformation of SVD transformed watermark embedded SVs: Apply inverse SVD to the SVD transformed watermark embedded 8 × 8 SVs blocks according to the following equation: where 1 ≤ p ≤ w nob Step 9: Inverse DCT transformation to each inverse SVD applied block: Apply inverse DCT to each inverse SVD transformed 8 × 8 blocks according to the following equation:

Watermark extracting procedure
Assume I_attack represents the modified watermarked image of size M × N (figure 3). To recover watermark image of size M1 × N1 from modified watermarked image, proposed DCT-SVD based watermark extracting technique steps are as follows: Step 1: Block processing of modified watermarked image: The modified watermarked image I_attack is divided into 8 × 8 non-overlapping blocks according to the following equation: Step 3: DCT transformation of selected 8 × 8 modified watermarked image blocks: Apply the DCT transformation to each selected 8 × 8 non-overlapping modified watermarked image block for watermark section extracting according to the following equation: (3.10) where I_attackbdct p is the dct transformed 8 × 8 modified watermarked image block, where 1 ≤ p ≤ nob/4.
Step 4: SVD transformation of DCT transformed modified watermarked image blocks: Apply SVD to each DCT transformed 8 × 8 modified watermarked image blocks according to the following equation: where 1 ≤ p ≤ nob/4.
Step 5: Inverse SVD transformation of DCT-SVD transformed modified watermarked image blocks: Inverse SVD is applied to the 8 × 8 DCT-SVD transformed modified watermarked image blocks according to the following equation: where 1 ≤ p ≤ w nob Step 6: Encrypted watermark extracting: Extract the 8 × 8 non-overlapping modified scrambled watermark blocks using the 8 × 8 modified watermarked image blocks (MSW p ), SVs of DCT-SVD transformed 8 × 8 cover image blocks (S p ) and value of α according to the following equation: Step 7: Recovering the watermark: Merge the recovered 8 × 8 modified scrambled watermark blocks into one block to produce scrambled watermark. Watermark is recovered after applying Arnold scrambling in the following step.

Experimental result
To evaluate the performance of the proposed schemes, a number of experiments are performed in the Matlab platform on four standard greyscale benchmark images of size 512 × 512, namely Lena, Baboon, Barbara and Pepper images and a 256 × 256 logo image taken as a watermark image. The proposed DCT-SVD based watermarking schemes are tested with various experiments in terms of imperceptibility, robustness, security and capacity analysis.

Imperceptibility analysis
To calculate the imperceptibility/invisibility analysis, alteration of perceptual image quality (by the proposed watermarking method) should be determined. The peak signal-to-noise ratio (PSNR) is used to find perceptual similarity between a host image and a watermarked image. In an effective invisible watermarking algorithm (i) watermark should be imperceptible/invisible from human visual system (HVS) and should check with (ii) standard benchmark PSNR. PSNR values are presented in decibel (dB). For optimized imperceptibility, the minimum acceptable value of PSNR is 38 dB as suggested by Kutter & Petitcolas [25]. This convention is dubious because PSNR is not a meaningful constraint in the context of geometric distortions [26]. PSNR can be defined as follows: where the mean square error (MSE) between host image x and the watermarked imagex is defined as follows: where the notations M and N represent the width and height of an image, respectively; x ij is the pixel intensity value of coordinate (i, j) of the original image; andx ij is the corresponding value of watermarked image. Basically, PSNR has been computed to compare the visual quality between cover image and watermarked image after embedding the watermark.

Robustness analysis
The robustness indicates that the watermarked object should resist against some watermark removal intentional/unintentional attacks. To measure the robustness property of proposed method, bit error rate (BER) and normalized correlation (NC) value between the original watermark and extracted distorted watermark (without attack/after applying different types of attack) is compared. and where M and N represent the width and height of the watermark image, respectively; w(i,j) = the pixel intensity value at coordinate (i,j) of original watermark,w(i, j) = the pixel intensity value at coordinates (i,j) of extracting watermark, µ w = mean of the original watermark, μw = mean of the extracted watermark. BER

Security analysis
As discussed in the introduction section, there are at least three serious drawbacks in SVD based algorithm: (i) lower invisibility, (ii) false positive detection problem and (iii) diagonal line. To overcome lower invisibility and diagonal line, SVs of cover image are modified to embed watermark instead of watermark SVs. Recently, scientists have proposed lots of ways to solve the false positive detection problem. In [20], Loukhaoukha et al. suggest to encrypt the watermark before inserting it into the cover object. In this proposed scheme, this encryption policy is employed to overcome the false positive detection issue. So, watermark logo is encrypted in this technique using Arnold scrambling before inserting into SVs of host image.

Capacity analysis
For this proposed embedding algorithm, watermark size is considered as 128 × 128. So, embedded blocks are selected one among four successive blocks. If watermark size is 256 × 256, embedded blocks are selected one among two successive blocks. Similarly, if watermark size is 384 × 384, embedded blocks are selected three among four successive blocks. In this way, if watermark size is 512 × 512, all the cover image blocks are needed for the watermark embedding purpose. So in this proposed method, watermark embedding capacity can be varied. For performance evaluation and fair benchmarking, the proposed technique is verified against various attacks. In [26], Stirmark benchmark is represented as a watermarking scheme benchmark where different types of image watermarking scheme attacks are divided into categories such as signal enhancement, compression, scaling, cropping, shearing, rotation, linear transformations, other geometric transformations and random geometric distortions. These attacks are divided into three sections according to their properties as described in [25]. As a representative, Lena image figure has been shown under different types of attacks.

Enhancement technique attacks
(i) Low-pass filtering: Low-pass filtering operation is used to remove high frequency noise from a signal. To prove the robustness of the proposed technique against low-pass filter, Gaussian low-pass filtering attack with six different size parameters (2 × 2, 3 × 3, 5 × 5, 7 × 7, 9 × 9, 11 × 11) are applied on selected standard test images. With the increment of filter order size, high frequency components of watermarked image are attenuated by the low-pass filtering operation. Modified watermarked image under Gaussian low-pass filtering attack (3 × 3) and its corresponding recovered watermark logo are presented in figure 5a. BER and NC values of recovered watermark, from table 2, conclude that recovered watermark data of this proposed method survive the Gaussian low-pass manipulation filtering attack. Data from table 2 establish the consistency of recovered watermark data in the Gaussian low-pass filtering attack. (ii) Median filtering: In common image enhancement application, a median filter is not often used to achieve blurring rather than it is used in the noise reduction process. Basically, median filter modifies the centre pixel value of the window with the middle value of the sorted pixel values. The proposed scheme is examined against median filtering attacks with different window sizes. Recovered watermark logo and its corresponding median filtering (

Noise addition attack
(viii) Noise addition: Most addressed non-geometrical attack in signal processing is the addition of additive noise and uncorrelated multiplicative noise. The proposed scheme is tested against salt and peppers, speckle and Gaussian noise.
Salt and pepper noise is caused by pixel's error at the time of data transmission. In salt and pepper noise, corrupted pixel values are either set to zero or maximum value or single bits flipped over. This pixel's value modification gives the image salt and pepper-like appearance where noise density is calculated by the alteration of percentage of pixels. This method is tested against salt and pepper noise with six different noise densities. Salt and pepper noise modified watermarked image with noise density 0.01 is shown in figure 5i. In salt and pepper noise, inverse proportionality of NC and proportionality of BER of recovered watermark with noise density is given in table 8. Speckle noise is one of the multiplicative noises where speckle exists inherently as a granular noise. The variance of a single pixel is equal to the variance of the local area that is centred on that pixel. This method is tested against speckle noise under six different noise variances. Manipulated watermarked image by speckle noise with variance = 0.01 is portrayed in figure 5j. NC values of recovered watermark exhibit inverse proportionality with speckle image noise variance where BER shows proportionality characteristic. This is tabulated in table 9.
Gaussian noise is one of the commonly used statistical noise processing operations. The amount of noise is varied by its variance with zero mean.       For example, scaling of the image is a normal scenario for scanning of a hard copy image. So, the proposed scheme is tested against scaling operation to prove the robustness. At first, the image is resized by multiplying by a scaling factor. Then again the image is scaled back to its original size. As a representative, one watermarked image and corresponding recovered logo under this scaling geometric attack are represented in figure 5n. NC and BER values of recovered watermark images are given in table 13. (xii) Deletion of lines or columns: Very frequently some part of the image is removed or deleted intentionally or unintentionally. This is one of the geometric transformation attacks that have been widely used against some simple copyright protection watermarking systems. Sometimes, this deletion of lines or columns has the same effect as image scaling. The proposed technique is verified against this type of attack for better robustness. In this experiment, some lines (rows) or columns of watermarked images are deleted.

Compression attack
(xv) JPEG compression: JPEG compression is one of the most widely used common manipulation/ compression attacks. Any effective watermark should be rigid to some degree of compression. The proposed scheme is checked against JPEG compression by changing quality factor. One compression attack image (quality factor = 50) along with recovered logo is given in figure 5r.

Combinational attack
For robustness test, some combination of above discussed attacks is applied to all the standard test images. There can be lots of combinational attacks, but some of the different combinational attacks are presented as follows:   (xvi) Combinational attack: For robustness clarity, combination of one enhancement technique attack (histogram equalization) and one geometric attack (cropping (128 × 128 by white)); combination of one enhancement technique attack (histogram equalization) and one noise addition attack (salt and pepper noise (density = 0.01)); combination of one enhancement technique attack (histogram equalization) and one compression attack (JPEG compression Q = 50); combination of one noise addition attack (salt and pepper noise (density = 0.01)) and one geometric attack (cropping (128 × 128 by white)); combination of one noise addition attack (salt and pepper noise (density = 0.01)) and one compression attack (JPEG compression Q = 50); combination of one compression attack (JPEG compression Q = 50) and one geometric attack (cropping (128 × 128 by white)) are applied on watermarked images of the proposed scheme (as given in table 18). For combinational attack, two of the attack images of this combinational attack are portrayed in figure 5s,t. Recovered watermarks for these attacks are also given in the same figure (figure 5s,t).

Comparative analysis
The proposed scheme is compared with some existing algorithm in tabular format with some predefined attacks. Then individual comparison is done with some existing methods as graphical plot (figures 6-10).
Better results are shown as bold data in table 19.

Conclusion
In this paper, a DCT-SVD based robust hybrid image watermarking scheme using Arnold scrambling has been proposed. Special attention is given to security issues such as (i) lower invisibility, (ii) false positive detection problem and (iii) diagonal line problem of SVD-based watermarking algorithms. The proposed scheme is tested against common image manipulation attacks, geometric transformation attacks and compression attacks to confirm the imperceptibility and robustness property effectively. Experimental results section establishes the supremacy of the hybrid domain watermarking technique over their single counterpart. This scheme is compared with some existing schemes in terms of various attacks and in terms of different watermarking embedding characteristics (as presented in table 20). This comparative analysis confirms the superiority of this proposed scheme.