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Blind image watermarking technique based on differential embedding in DWT and DCT domains
EURASIP Journal on Advances in Signal Processing volume 2015, Article number: 55 (2015)
Abstract
This paper presents a new blind and robust image watermarking scheme based on discrete wavelet transform (DWT) and discrete cosine transform (DCT). Two DCTtransformed subvectors are used to embed the bits of the watermark sequence in a differential manner. The original subvectors are obtained by the subsampling of the approximation coefficients of the DWT transform of the host image. During the extraction stage, the simple difference between the corresponding subvectors of the watermarked image, gives directly the embedded watermark sequence. Experimental results demonstrate that the proposed technique successfully fulfills the requirement of imperceptibility and provides high robustness against a number of imageprocessing attacks, such as JPEG compression, noise adding, lowpass filtering, sharpening, and bitplane removal. Our scheme exhibits also an acceptable to good performance against some geometrical attacks such as resizing and cropping.
1 Introduction
The process of embedding a watermark in a multimedia (image, audio, or video) object is termed as digital watermarking. Content providers want to embed watermarks in their multimedia objects (digital content) for several reasons like copyright protection, content authentication, tamper detection, etc [1–3]. More and more researchers are particularly attracted to the area of image watermarking because of the property of the image as it has a lot of redundant information contained in it which can be exploited to be used for watermark embedding. The embedding process is guided by the use of a secret key which decides the locations within the image where the watermark would be embedded. When the owner wants to check the watermarks in the possibly attacked and distorted digital images, s/he relies on the secret key that was used to embed the watermark. Using the secret key, the embedded watermark sequence can be extracted. In order to be successful, the watermark should be invisible and robust against common image processing operations such as additive noise, compression, cropping, filtering, and resizing [2]. If the watermark is placed in perceptually significant coefficients of the image, the robustness against image distortion is better achieved. These coefficients do not change much after common image processing and compression operations. Also, if these coefficients are destroyed, the reconstructed image is different from the original image and the digital watermark becomes irrelevant. Although, embedding the watermark in perceptually significant coefficients could alter the perceived visual quality of the image. Thus, two essential prerequisites for a powerful watermarking scheme, robustness and invisibility, conflict with each other [4].
Watermarking techniques can be broadly categorized into two distinct categories: nonblind or blind depending on whether the original image is necessary for watermark extraction or not. In realworld practices, nonblind watermarking algorithms are unsuitable for many practical applications in that they require the nonwatermarked data to be presented during extraction or detection [2].
Watermarking techniques can be also classified according to the domain in which the watermark is embedded, i.e., the spatial domain or the transform domain. While the spatial domain techniques are having least complexity and high payload, they can not withstand image compression and other common image processing attacks [2, 3]. Transform domain watermarking schemes like those based on the discrete Fourier transform (DFT) [5], the discrete cosine transform (DCT) [6], and the discrete wavelet transform (DWT) [7, 8] typically provide higher image imperceptibility and are much more robust to image manipulations. However, DWT has been used more frequently in digital image watermarking due to its time/frequency decomposition characteristics, which resemble to the theoretical models of the human visual system [8].
Further performance improvements in DWTbased digital image watermarking methods could be obtained by jointing DWT with other transformation domain so that effective watermarking approaches could be developed [9–16].
An algorithm based on joint DWT and DFT transform is proposed in [9]. In the DWT domain, a spread spectrumbased watermark is embedded in the coefficients of the LL subband while in DFT domain a template is embedded in the middle frequency component.
Zhao et al. proposed a watermarking approach implemented as a DCTDWT dual domain algorithm and applied for the protection and compression of cultural heritage imagery [10]. They employed Haar DWT domain to embed the watermark in the components of the image that are of perceptual significance. These components are identified using a blockbased (DCT) transform. They specifically demonstrated that watermark embedding in the Haar DWT domain does not interfere with watermark generation in the DCT domain.
In the algorithm proposed in [11], the watermarking was carried out through the embedding of the watermark in the first and secondlevel DWT subbands of the host image followed by the application of DCT on a selected DWT coefficient sets. It has been shown that the combination of the two transforms improved the watermarking performance considerably when compared to the DWTonly watermarking approach.
In [12], the authors proposed a watermarking scheme based on adaptive quantization index modulation and SVD in a hybrid DWT and DCT domain. The watermark bits are embedded in the singular values’ vector of blocks within low frequency subband in host image hybrid DWTDCT domain. To embed the watermark imperceptibly and robustly, they model the adaptive quantization steps by utilizing human visual system (HVS) characteristics and PSO algorithm.
In [13], Feng et al. have proposed a blind DWTDCT watermarking approach. After scrambling the binary watermark, a blockbased DCT transform of the firstlevel DWT LL subband is computed and two PNsequences of the watermark bits are embedded in the mid frequency coefficients of the corresponding DCT blocks. In the extraction process, the same steps as the embedding process is used to extract the DCT middle frequencies of the LL subband. Finally, correlation between midband coefficients and PNsequences is calculated to determine the watermarked bits.
A similar approach is presented in [14], where a multiple subbands of the thirdlevel DWT transform of a host image are used to insert the watermark instead of the firstlevel LL subband.
In the method proposed in [16], the wavelet firstlevel LL subband and the watermark image are transformed using DCT and SVD. The S vector of watermark information is embedded in the S component of the host image. Watermarked image is generated by inverse SVD on modified S vector and original U, V vectors followed by inverse DCT and inverse DWT.
Our method is also linked to schemes that use the subsampling of the image data [6, 15, 17, 18]. The subsampling techniques offer more room for watermarking by, for example, dividing the original image into subimages and applying different modifications to transformed coefficients belonging to different subimages [6, 17].
In this paper, a binary watermark sequence is embedded in the host image using DWT and DCT domains and the technique of differential embedding. The DCT is applied on two subvectors obtained by the subsampling of the DWT LL subband of the image. The differential embedding of the watermark in the resulting two DCTtransformed subvectors ensures the blind extraction of it.
To further emphasize the efficiency of combining DWT and DCT domains, we propose also a reduced DCTbased version of our method which is based on the DCT domain only. The results of comparison between the combined DWTDCT and the DCTonly methods justify the combining of DWT and DCT domains.
The rest of the paper is structured as follows. In Section 2, we present the new DWTDCT blind watermarking scheme. The reduced DCTonly method is outlined in Section 3. Numerical experimental results and comparisons with other methods are given in Section 4. Finally, we draw conclusion and suggest future work in Section 5.
2 Proposed method
2.1 The embedding process
The proposed watermark embedding scheme is shown in Fig. 1.
Let I denote the grayscale square image of size M×M to be watermarked by the bipolar {−1,1} binary sequence W of size L, the embedding process can be described as follows:

Step 1: Perform the firstlevel DWT of the input image I. This produces the approximation coefficients matrix (LL subband) and a set of detail coefficients (H L,L H, and HH subbands).

Step 2: Perform zigzag scanning [19] to convert the matrix LL into a vector of approximation coefficients x(n), n=1,…,N, where N=M.M/4. Since adjacent pixels are highly correlated in real images and the firstlevel LL subband represents a close approximation of the original image (Fig. 2); the zigzag scanning of the LL matrix helps to cluster high correlated approximation coefficients in the vector x(n).

Step 3: Decompose the vector of approximation coefficients x into two (correlated) subvectors x _{1} and x _{2} using the following subsampling operations:
$$\begin{array}{*{20}l} x_{1}(k)&=x(2k) \end{array} $$((1))$$\begin{array}{*{20}l} x_{2}(k)&=x(2k1) \end{array} $$((2))where k=1,…,N/2.

Step 4: Perform DCT on x _{1} and x _{2} to produce their DCTtransformed versions X _{1} and X _{2} (Fig. 3):
$$\begin{array}{*{20}l} X_{1}&=dct(x_{1}) \end{array} $$((3))$$\begin{array}{*{20}l} X_{2}&=dct(x_{2}) \end{array} $$((4)) 
Step 5: Insert the watermark sequence bits W(i) for i=0,2,…,L−1, in the transformed subvectors X _{1} and X _{2} using a differential embedding technique. This will produce two transformed and modified (by watermarking) subvectors \(\hat {X}_{1}\) and \(\hat {X}_{2}\) as follows:
$$ \hat{X}_{1}(i^{\prime})=\frac{1}{2}\left[X_{1}\left(i^{\prime}\right)+X_{2}\left(i^{\prime}\right)\right]+\alpha W\left(i\right) $$((5))$$ \hat{X}_{2}(i^{\prime})=\frac{1}{2}\left[X_{1}\left(i^{\prime}\right)+X_{2}\left(i^{\prime}\right)\right]\alpha W\left(i\right) $$((6))where α is the gain factor and i ^{′} are the random locations within the high energy band of X _{1} and X _{2} in which the watermark bits are embedded (Fig. 4). These locations are the elements of a vector r which can be generated using a random permutation function:
$$\begin{array}{*{20}l} i^{\prime}&=r(i) \end{array} $$((7))$$\begin{array}{*{20}l} r&=\text{RandPerm}(S,a,b) \end{array} $$((8))where S is the seed of the associated pseudo random number generator (PNRG), a and b are, respectively, the starting and the ending locations of the high energy band used to insert the watermark (Fig. 4). Therefore, the user’s secret key is k e y=(S,a,b), which prevent the watermark from tempering or unauthorized access by attackers.

Step 6: Perform the inverse DCT on \(\hat {X}_{1}\) and \(\hat {X}_{2}\):
$$\begin{array}{*{20}l} \hat{x}_{1}&=idct(\hat{X}_{1}) \end{array} $$((9))$$\begin{array}{*{20}l} \hat{x}_{2}&=idct(\hat{X}_{2}) \end{array} $$((10)) 
Step 7: Combine the two modified subvectors \(\hat {X}_{1}\) and \(\hat {X}_{2}\) using the opposite operation in (1) and (2) in order to produce the modified vector of approximation coefficients \(\hat {x}\):
$$\begin{array}{*{20}l} \hat{x}(2k)&=\hat{x}_{1}(k) \end{array} $$((11))$$\begin{array}{*{20}l} \hat{x}(2k1)&=\hat{x}_{2}(k) \end{array} $$((12))for k=1,…,N/2.

Step 8: Convert the modified vector \(\hat {x}\) into the matrix of a modified approximation coefficients \(\widehat {LL}\) using the inverse of the zigzag scan operation used instep 2.

Step 9: Construct the watermarked image \(\hat {I}\) by performing the inverse wavelet transform of the modified approximation coefficients \(\widehat {LL}\) and the sets of original detail coefficients (H L,L H, and HH subbands).

Note 1: The parameters a and b should be chosen to satisfy the following conditions:

a>0: the DCcomponents of the transformed subvectors X _{1} and X _{2} must remain unchanged in order to preserve the quality of the watermarked image;

b−a≥L: the insertion band have to be wide enough to insert all the watermark’s bits;

\(b\leq \frac {N}{2}\): the watermarking is done in the hight energy band of X _{1} and X _{2} in order to guarantee the robustness of the method.


Note 2: While the normal differential embedding would be as follows: \(\hat {X}_{1}=X_{1}+\alpha W\) and \(\hat {X}_{2}=X_{2}\alpha W\) (by omitting the insertion locations), the fact that the transformed subvectors X _{1} and X _{2} are highly correlated (as shown in Fig. 5) allow as to assume in Eqs. 5 and 6, that \(X_{1}\boldsymbol {\approx } X_{2}\boldsymbol {\approx }\frac {1}{2}\left [X_{1}+X_{2}\right ]\). This will ensure that X _{1} and X _{2} are equally contributing in the new modified ones \(\hat {X}_{1}\) and \(\hat {X}_{2}\) so that the resulting distortion on the watermarked image will be minimal. Also, it is obvious that the difference between \(\hat {X}_{1}\) and \(\hat {X}_{2}\) will give an amplified (by 2) amount of the inserted watermark sequence ( α W) which is the key feature of this differential embedding technique.
2.2 The extraction process
The watermark extraction process follows the same steps as the embedding process until step 5 where the extraction is taking place as shown in Fig. 6.
If the input image is the watermarked one, and by analogy with the embedding process, step 4 of the extraction process will give the two subvectors \(\hat {X}_{1}\) and \(\hat {X}_{2}\) in Eqs. 5 and 6, respectively. Consequently, the difference between them has a proportional relationship with the watermark sequence W:
with i=1,…,L, and i ^{′} are the random locations where the watermark bits are embedded. These locations are determined simply by recreating the vector r (Eq. 7) using the userselected secret key and the random permutation function (Eq. 8). Finally, and since the difference △_{ X }(i) might differ from + 1/ −1 values, we apply a hard limitation function on it in order to recover the original bits of the watermark:
If the watermarked image has been attacked, the proposed method is able to extract the watermark and the quality of extraction closely depends on the severity of the attack as shown in the experiments.
Notice that no threshold setting is needed at the extraction stage, which represents a great advantage compared with a lot of schemes in literature [9, 10]. Also, this watermarking approach is analogous to the technique of Differential Signaling, a method of transmitting information electrically by means of two complementary signals [20]. At the end of the connection, the receiver reads the difference between the two signals to recover the original information.
3 The DCTonly method
To justify the utility of combining DWT and DCT domains, we propose here a reduced version of our method based only on the DCT domain. Since we applied the zigzag scanning on the matrix of approximation coefficients of DWT (Section 2.1) to obtain the vector x, we choose here to apply it on the whole image (without using DWT). The flowchart of the embedding process of the DCTonly method is given in Fig. 7.
In this process, the operations are the same as described in the embedding process of the DWTDCT method (Section 2.1). Notice that all the vectors in Fig. 7 are four times the size of the corresponding vectors in the DWTDCT method. The extraction process will be the same as in Fig. 6 except that the DWT step is not needed in this case.
4 Experiment results
In this section, several experiments are conducted to evaluate the performance of the proposed watermarking scheme. The size of original cover images (baboon, bridge, jetplane, peppers, and pirate) is 512×512 pixels^{1}. The watermark is a pseudorandom binary sequence of size 256 bits, which is a usual payload [21]. To evaluate the quality of the watermarked image, the peak signal to noise ratio (PSNR) is used [10]. To evaluate the quality of extracted watermark, the bitcorrect ratio (BCR) is adopted to measure the similarity between the original watermark W and the extracted watermark \(\tilde {W}\). The use of this measure has become common recently [22], as it allows for a more detailed scale of values and is defined as the ratio of correct extracted bits to the total number of embedded bits [22]:
where ⊕ is the XOR operator. If the watermark is extracted without error the BCR value will be 100 %.
4.1 Gain factor selection
In order to select the suitable values of the gain factor α in Eqs. 5 and 6 that fulfill both the invisibility and the robustness requirements of the watermarking, we plot with respect to α the PSNR of the watermarked images (Fig. 8 a) and the BCR of the extracted watermarks (Fig. 8 b) after a standard image attack (JPEG lossy with quality factor equals to 40).
It is apparent from Fig. 8 that higher α values make lower PSNR of the watermarked images, but the similarity (BCR %) of original watermark and the extracted watermark gets better for higher values of α. The best tradeoff between visual quality and watermark robustness is achieved for the values of α in range from 0.2 to 0.3 where the PSNR values are greater than 40 dB and the BCR values are almost 100 % for all test images. In the rest of our experiments, we will set α= 0.2 as the default gain factor value.
Figure 9 shows the perceptual difference between the original test images and their watermarked versions and the corresponding PSNR measures.
From Fig. 10, we can see that PSNR of 15 watermarked images is greater than 42 dB which ensures the invisibility requirement. Notice that the watermark is extracted from all test images with no error (BCR = 100 %).
4.2 Robustness tests
4.2.1 4.2.1 Robustness against image compression
The BCR values of the extracted watermarks under JPEG lossy and JPEG2000 compression attacks are shown in Fig. 11. For JPEG lossy compression, the quality factor (Q) is varied from 10 to 70, whereas for JPEG2000 attacks, the compression ratio r [23] is varied from 0.01 to 0.1.
We can see from Fig. 11 a that the watermark is completely recovered under high strength JPEG lossy attacks (BCR = 100 for Q≥40) for all test images.
The proposed method is also robust for the practical JPEG2000 compression range of levels, i.e., r≥0.04 (Fig. 12 b) except for the textured images of Baboon and Bridge where it exhibits a lower robustness. This because, JPEG2000 compression does not necessarily provide an image of good quality in texture features [24].
4.2.2 4.2.2 Robustness against image processing attacks
In the following, we evaluate the proposed method against noise addition, low pass filtering, image enhancement, etc. Table 1 shows the BCR values of the extracted watermarks under noise addition attacks. For the three types of noises (Gaussian, salt and pepper, and speckle), we can observe that the proposed method is fairly robust against noises with medium variances, whereas for high variance noises the method presents acceptable performance since the BCR values is greater than 93 % for the majority of experiments.
Tables 2 and 3 demonstrate that the proposed method is robust against lowpass filtering, bitplane removal, gamma correction, histogram equalization, and Laplacian sharpening attacks. Notice that in bitplane removal attack, the least significant bits of the watermarked image are replaced with zeros. All these experiments show that the proposed method is robust against common imageprocessing attacks.
Figure 12 shows the visual impact of some attacks on different images. The watermark is extracted with BCR value greater than 99 % which confirms the preceding results.
4.2.3 4.2.3 Robustness against geometrical attacks
The next experiments show the robustness against some geometrical attacks on the test images.
Table 4 and Fig. 13 demonstrate that the proposed method is relatively robust against geometrical attacks. In particular, it performs well for cropping and resizing attacks but exhibits weak robustness against rotation attacks.
4.2.4 4.2.4 Robustness against watermark suppression attack
In these experiments, we suppose that the an informed attacker have partial knowledge of the embedding process and he tries to perform a successful attack that produces a smaller amount of perceptible distortion compared to its blind counterparts. In particular, we suppose that the attacker tries to obliterate the inserted watermark by erasing a portion of the two carrying subvectors \(\hat {X}_{1}\) and \(\hat {X}_{2}\) (Eqs. 5 and 6). So the attacker puts the vectors X _{1}(n)=0 and X _{2}(n) to 0 for n=1,2,…,K. (n≠0 in order to keep the DC value intact). The results of attacked images of peppers and the corresponding BCR values for different value of k are given in Fig. 14. We can see that the watermark (or a portion of it) can be successfully extracted for this type of attacks. However, once the suppression of the watermark exceeds a certain level (K>512), the image becomes no longer usable because of the high perceptible distortions.
4.3 Comparison with other methods
In this subsection, we conduct several experiments to compare the performance of the proposed DWTDCT method with two other blind watermarking approaches ([13] and [25]) and also with the reduced DCTonly method.
The approach in [25] proposed a blockbased significant difference quantization watermarking. Every seven wavelet coefficients in one subband are grouped into a block and the watermark bit is embedded into a block by quantizing the difference between two maximum wavelet coefficients. Notice that the embedding parameters in each method are adjusted to produce a watermarked image (Lena) of PSNR equal to 44 dB. The results of comparison are listed in Tables 5, 6, and 7.
From the results in Tables 5, 6, and 7, we notice the following:

 The proposed DWTDCT method outperforms the reduced DCTonly method for JPEG compression, lowpass filtering, resizing, and rotation attacks. For the rest of attacks, both techniques perform equally well. Consequently, the combination of the two transforms (DWT and DCT) is more practically helpful than the use of one domain only (DCT) especially if the watermarked images are intended to undergo these types of attacks.

 For JPEG compression, only the method in [25] performs slightly better than the proposed DWTDCT method. This is because the fact that wavelet quantization techniques are generally robust against image compression attacks [25].

 For the rest of attacks, the proposed DWTDCT method is more robust than the two methods in [13] and [25] especially for bitplane removal, gamma correction, noise addition, and for all geometrical attacks.
From the previous results, we may conclude that, overall, the proposed method has a better performance than the compared watermarking schemes ([13, 25]) and that the combination of the DWT and DCT domains is more advantageous than the use of only one frequency domain.
5 Conclusions
In this paper, a robust, yet simple watermarking scheme based on the combination of DWT and DCT domains is presented. In the embedding process, a differential technique is performed on two transformed subvectors so that the extraction of the watermark is achieved using only the difference of the corresponding watermarked subvectors.
Overall, the experimental results demonstrate that our scheme provides excellent robustness against multiple image attacks such as bitplan removal, cropping, JPEG compression, histogram equalization, lowpass filtering, and noise adding attacks. Besides, the quality of the watermarked image is satisfactory in terms of imperceptibility as the PSNR per watermarked image is over 42 dB.
We have also investigated the utility of the combination of the DWT and DCT transforms through the proposition of a relaxed version of our method based only on the DCT transform. In comparison, the DWTDCT method is more robust than the DCTonly method for a set of attacks such as JPEG compression and lowpass filtering. The results of experiments have showed also that the proposed (DWTDCT) method has stronger robustness in comparison with two existing watermarking schemes.
As a future work, we plan to extend the proposed approach to video watermarking domain. As the embedding and the extracting processes are of low complexity and do not require any specific features of the input image, the extension to video watermarking will be straightforward. Along with that, an automatic technique for the selection of the gain factor value needs to be developed to have better control on both imperceptibility and robustness of the scheme.
6 Endnote
^{1} All test images are obtained from the USCSIPI Image Database: http://sipi.usc.edu/database/.
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Benoraira, A., Benmahammed, K. & Boucenna, N. Blind image watermarking technique based on differential embedding in DWT and DCT domains. EURASIP J. Adv. Signal Process. 2015, 55 (2015). https://doi.org/10.1186/s1363401502395
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DOI: https://doi.org/10.1186/s1363401502395