Abstract: In this study, we proposed a robust quantization based digital image watermarking for copy right protection in DCT-SVD domain. The proposed watermarking algorithm which combines both merits of the algorithm based on Discrete Cosine Transform (DCT) and algorithm based on Singular Value Decomposition (SVD). The watermark is embedded by applying a quantization index modulation process on largest singular values of image blocks in the DCT domain. To avoid visual degradation of watermarked image, we have enhanced a model to take into consideration blocks statistics of the host image. Watermark detection is efficient and blind in the sense only the quantization parameters but not the original image is required. Experimental results show that the proposed method is more robust than SVD and DCT-SVD methods.
INTRODUCTION
Digital watermarking describes the technologies that embed information, for example a number or a text or an image, into the digital media, such as images, video and audio to protect the copyright, benefit of the investor and legal rights of owners. Watermarking techniques can be classified into two categories: spatial domain and transform domain techniques. Transform domain techniques have been found to offer several advantages over spatial domain methods, in terms of perceptibility and robustness (Barni et al., 1998, 2001; Chu, 2003; Wang et al., 2002).
In recent years, SVD was started to use in watermarking as a different transform. The idea behind using SVs to embed the watermark comes from the fact that changing SVs slightly does not affect the image quality. Using SVD in digital image processing has some advantages. First, the size of the matrices from SVD transformation is not fixed and can be a square or a rectangle. Second, singular values in a digital image are less affected if general image processing is performed. Third, singular values contain intrinsic algebraic image properties. So SVD has been exploited in several image watermarking methods either combined with transform domain like DCT or DWT (Lu et al., 2007; Liu and Ai, 2004; Huang and Guan, 2004; Ganic and Eskiciogulu, 2005) or on the spatial domain (Sun et al., 2002; Lee et al., 2005; Mohan et al., 2008; Chang et al., 2005). In the embedding stage of the method introduced by Liu and Ai (2004) the host image (256x256 pixels) is divided in to square bocks of size 8x8 pixels and then DCT is applied in each block. They selected midband coefficients size of 4x4 and computed the SVD of each selected matrix and before embedding the watermark in to S matrix, they also partitioned original watermark size of 128x128 grayscale image in to 4 by 4 blocks. But this method is non-blind in nature. Sun et al. (2002) have proposed a technique based on quantization of largest singular values of image blocks in the spatial domain. Lee et al. (2005) presented a secure SVD-based content authentication watermarking scheme by embedding watermark into maximum singular values of randomly ordered block.
In spite of the fact that the methods (Sun et al., 2002; Lee et al., 2005) have a good localization but the perceptual quality of watermarked image is not so good even at high PSNR. That is because of they apply the same or fixed quantization step size for all blocks in spatial domain which may have different characteristics. In this study, we proposed a robust and blind watermarking technique. In watermark casting process, we quantize the largest singular values of blocks in DCT domain by using quantization index modulation process. To achieve a better transparency, robustness against various image distortions and to enhance security of watermarking the quantization step is calculated based on the statistics of host image blocks. An improved method is proposed to compute the statistics of the image blocks in DCT domain. The block size, together with the quantization parameters would determine how well a block could be modeled statistically leading to a unified framework for controlling the transparency, robustness against image distortions and lead to be more secured. Furthermore, since the watermark embedding is based on the quantization of the biggest SV of blocks where the quantization parameters are modeled by the block statistics in the DCT domain, it is, thus, impossible to extract the watermark without the quantization parameters.
QUANTIZATION BASED WATERMARK SCHEME IN DCT-SVD DOMAIN
The watermarking embedding procedure describes below:
| • | Step 1: The original host image Y is first partitioned in to non overlapping blocks size of 8x8 then DCT is applied on each block (B matrix) |
| • | Step 2: The quantization step Qi for ith blocks can be computed with the following formulas: |
| • | Step 3: Perform SVD on each block to (B matrix) get matrices U, S and V |
| • | Step 4: Perform watermark embedding as follows. Let Si be largest singular values of each 8x8 DCT block in vector form and let the watermark image W (i, j) be W, embedding the watermark is used the following specific rule: |
| • | Step 5: Apply reverse SVD procedure to Siw and get B* and perform inverse DCT on B* to obtain the watermarked image Y* |
| (1) |
| (2) |
where, mi and δi are the mean value and standard deviation of ith block in DCT domain and take into account structural and background statistics of block. Parameters Qm and QM represented the minimum and maximum quantization steps values respectively. Where as Smin and Smax are minimum and maximum values of ith blocks in DCT domain. These quantization parameters are saved as secret key for watermark recovery. It is noteworthy that our proposed formula for obtaining block values Si is different from the formula that has been proposed by Bao and Ma (2005).
| (3) |
| (4) |
In the watermark extraction process, segmented watermarked image in to 8 by 8 blocks then perform DCT on each block. Then apply SVD on each DCT block and selected largest singular values of blocks and quantized and we used the following formula:
| (5) |
RESULTS
Here, some experiments are carried out to demonstrate the effect of proposed method and we choose a binary watermark image of size 32x32. A set of 512x12 pixels grayscale images of Lena, Barbara and Baboon are used as the host images. In watermark casting, the minimum and maximum of quantization steps are set to be values of 40 and 68, respectively. Figure 1a and b show the host images of Lena and Baboon images and their corresponding watermarked images in Fig. 1c and d with PSNR values of 47.5932 dB and 47.5391 dB, respectively and this indicated that the perceptual quality of watermarked images are very good and Fig. 1e shows original watermark image.
Invisibility
To evaluate the invisibility of the watermark, we test the proposed scheme
on different standard images. Table 1 shows the PSNR values
of different watermarked images and are found to be above 43 dB, signifying
that the quality of the host images are not much degraded.
Robustness
To test the robustness of the proposed scheme, some typical signal processing
attacks, such as filtering, scaling, salt and pepper noise, cropping, JPEG compression
and rotation tampering are performed. Figure 2a-d
show the extracted watermark image against salt and pepper noise with noise
density of 0.1, 0.2, 0.3 and 0.4% and Fig. 3a-c
shows recover watermark after applying JEPG compression with different quality
factors (rang from 30 to 100%). It can be seen that the proposed method is very
robust against JPEG compression. The watermarked image is attacked by Low Pass
Filtering (LPF) and the watermarked image is scaled down by 0.5 and the image
is rescaled to the original size before watermark extraction and the extracted
watermark is shown in Fig. 4a-c and it can
be seen clearly that the extracted watermark has good similarity with the original
watermark.
| Fig. 1: | (a, b) original image and (c, d) watermarked image and (e) original watermark image, respectively |
| Fig. 2: | Extracted watermark (a-d) from Salt and Pepper noise with density 0.1, 0.2, 0.4 and 0.3%, respectively |
| Table 1: | PSNR values of the watermarked images (dB) |
The watermarked image is attacked by rotation and rotated by 10°, 20°, 40° and 60° and rotated back to their original position and as shown in Fig. 5a-d the extracted watermark can be identified easily and shows good similarity with the original watermark, where as Fig. 6a-c give results for mid-filter, tampering and cropping, respectively. And also Lena watermarked image is tested under attacks of histogram equalization, intensity adjustment, gamma correction and cropping and the result shows in Table 2.
| Fig. 3: | Extracted watermark (a-c) from JPEG compression with quality factor 30, 40 and 60%, respectively |
| Fig. 4: | (a) Extract watermark from LPF and (b) resized by 0 .5 |
| Fig. 5: | Extracted watermark (a-d) from rotation attacks by 10°, 20°, 40° and 60°, respectively |
| Fig. 6: | Extracted watermark, (a) mid-filtered, (b) Tampering and (c) cropping |
To test the extracted watermark quality we used Normalized Cross (NC) correlation metric which can be defined:
| (6) |
where, W (i, j) represent the original binary watermark and We (i, j) is the extracted watermark. Table 2 shows the NC values for Lena and Baboon images for various attacks.
| Table 2: | Robustness experimental results for Lena and Baboon images |
| Table 3: | Robustness performance comparisons with pure SVD method |
| Table 4: | Robustness performance comparisons with DCT-SVD |
As Table 2 is shown that the proposed method is highly robust for image processing attacks but for histogram equalization, intensity adjustment and cropping attacks the proposed method is not that much good.
Table 3 and 4 show the NC values for various types of attacks and it can be observed that the proposed method has higher NC values than SVD and DCT-SVD method, respectively; hence this indicated that the proposed method has better performance and is more robust against attacks than SVD and DCT-SVD method.
However, Table 3 and 4 show the shortcoming of our proposed method. This scheme failed passing some geometry distortion such as cropping and also fails for Gaussian noise.
DISCUSSION
We proposed watermarking algorithm which combines both merits of the algorithm based on Discrete Cosine Transform (DCT) and algorithm based on Singular Value Decomposition (SVD). To achieve a better transparency, robustness against various image distortions and to enhance security of watermarking the quantization step is calculated based on the statistics of host image blocks. As we have seen above the proposed method is very robust for various image processing attacks like scaling, JPEG compression and rotation, salt and pepper, median filtering and so on. However, the method fails for some attacks like cropping; Gaussian noise and the NC values are below 0.5. An improved method is proposed to compute the statistics of the image blocks in DCT domain. The block size, together with the quantization parameters would determine how well a block could be modeled statistically leading to a unified framework for controlling the transparency, robustness against image distortions and lead to be more secured.
CONCLUSION
In this study, a robust watermarking, method is proposed based on DCT and SVD, which can resist image processing attacks such as noise, JPEG compression, filtering and rotation and so on. An improved model is employed to consider statistics of blocks in the DCT domain. And comparative experiment with pure SVD and DCT-SVD are made. Results show that the proposed method is more robust against attacks than pure SVD and DCT-SVD method.
ACKNOWLEDGMENTS
This study was supported by National Natural Science Foundation of China (60736016, 60873198), Scientific Research Fund of Hunan Provincial Education Department of China (08C018) and National Basic Research Program of China (2006CB303000, 2009CB326202).