Digital watermarking has gained importance in recent years in copyright protection and multimedia authentications. In this paper an attempt is made to study the approach of combined DWT-DCT watermarking technique on satellite and bio-medical images. The method provides improved imperceptibility and robustness to the cover images. In the first step, the cover image is decomposed into two levels by DWT transform. Then DCT of the HL (or HH) sub band of the DWT coefficients is computed. The watermark is embedded in the form of a PN (pseudo random) sequence into the DWT sub band after computing DCT. The technique is tested on cover image LENA (512x512, 8-bit gray scale) with a binary watermark of size 50x20. The watermarked images are tested for robustness against JPEG compression and other image processing attacks. Experimental results show that combining the two transforms improved the performance when compared to only DWT transform methods.
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Digital watermarking refers to techniques used to protect digital data by imperceptibly embedding information (watermark) into the original data in such a way that it always remains present. For a digital watermarking method to be effective, it should be imperceptible and robust to common image manipulations such as compression, filtering, rotation, scaling, and cropping attacks among many other digital signal processing operations. Current digital image watermarking techniques can be grouped in to two major classes: spatial-domain and frequency domain techniques. Frequency domain watermarking techniques have proved to be more effective with respect to achieving the imperceptibility and robustness requirements of digital watermarking algorithms.
Commonly used frequency-domain transforms are the Discrete Wavelet Transform (DWT), the Discrete Cosine Transform (DCT) and Discrete Fourier Transform (DFT). However, DWT has been used in digital image watermarking more frequently due to its excellent spatial localization and multi-resolution characteristics, which are similar to the theoretical models of the human visual system (HVS). Further performance improvements in DWT-based digital image watermarking algorithms could be obtained by combining DWT with DCT. This is based on the fact that combined transforms could compensate for the drawbacks of each other, resulting in effective watermarking. Watermarking is done by altering the wavelets coefficients of selected DWT sub bands (HL or HH), followed by the application of DCT transform on selected sub bands.
2. DCT and DWT TRANSFORMS
The DCT and DWT transforms have been extensively used in many digital signal processing applications. In this section, we introduce the two transforms and outline their relevance to the implementation of digital watermarking.
2.1. DCT Transform: The discrete cosine transform (DCT) is a technique for converting a signal into elementary frequency components. It represents an image as a sum of sinusoids of varying magnitudes and frequencies. With an input image f, the DCT coefficients for the transformed output image, T, are computed according to Eqn.1 given below. Here, f, is the input image with MxN pixels, f(m,n) is the intensity of the pixel in row m and column n of the image, T(u,v) is the DCT coefficient in row u and column v of the DCT matrix.
The image is reconstructed by applying inverse DCT operation according to equation 2).
f(x,y) is the original cover image and
F(x,y) is the watermarked image
The block-based DCT transform segments an image in to non overlapping blocks and applies DCT to each block. This will yield three frequency sub bands: low frequency sub band, mid-frequency sub band and high frequency sub band. DCT watermarking is based on two facts. The first is that much of the signal energy lies at low frequencies sub band which contains the most important visual parts of the image. The second fact is that the high frequency components of the image are usually removed through compression and noise attacks. The watermark is therefore embedded by modifying the coefficients of the middle frequency sub band so that the visibility of the image will not be affected and the watermark will not be destroyed by compression.
Fig.1. Watermark embedding procedure using combined DWT-DCT method
2.2 DWT Transform:
For 2-D images, applying DWT corresponds to processing the image by 2-D filters in each dimension. The filters divide the input image into four non-overlapping multi-resolution sub bands: LL1, LH1, HL1 and HH1. The sub band LL1 represents the coarse-scale DWT coefficients while the sub bands LH1, HL1 and HH1 represent the fine-scale DWT coefficients. To obtain the next coarse scale wavelet coefficients, the sub band LL1 is further decomposed.
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Due to its excellent spatial frequency localization properties, the DWT is very much suitable to identify the areas in the cover image where a watermark can be embedded effectively. In particular, this property allows the exploitation of the masking effect of the HVS such that if a DWT coefficient is modified, only the region corresponding to that coefficient will be modified. In general most of the image energy is concentrated at the lower frequency sub bands LL, and therefore embedding watermarks in these sub bands may degrade the image significantly. Embedding in the low frequency sub bands, however, could increase robustness significantly. On the other hand, the high frequency sub bands HH include the edges and textures of the image and the human eye is not generally sensitive to changes in such sub bands. This allows the watermark to be embedded without being perceived by the human eye. The compromise adopted by many DWT-based watermarking algorithm, is to embed the watermark in the middle frequency sub bands LH and HL where acceptable level of imperceptibility and robustness could be achieved.
Fig.2. Two Level DWT decomposition of the original image
3. DWT-DCT METHOD
3.1. Watermark Embedding
The watermark embedding is performed with the following steps (Fig.1)
Step 1: Read in the cover image f(x,y).
Step 2: Apply DWT to decompose the f into four non-overlapping multi-resolution sub bands: LL1, HL1, LH1, and HH1.
Step 3: Apply DWT to sub band HL1 to get four smaller sub bands: LL2, HL2, LH2, and HH2. Choose the HL2 sub band (Fig. 2a), or apply DWT to sub band HH1 to get four smaller sub bands: LL2, HL2, LH2, HH2. Choose HH2 sub band as shown in Fig. 2b.
Step 4: Divide the sub band HL2 (or HH2) into 4x4 blocks.
Step 5: Perform DCT on each 4x4 block in the chosen sub band (HL2 or HH2).
Step 6: Read in the binary watermark image.
Step 7: Generate two uncorrelated pseudorandom (PN) sequences. One sequence is used to embed the watermark bit 0 (PN0) and the other sequence is used to embed the watermark bit 1 (PN1). The number of elements in each of the two pseudorandom sequences must be equal to the number of mid-band elements of the DCT-transformed DWT sub bands.
Step 8: Embed the pseudorandom sequences PN0, PN1, with gain factor k in the DCT transformed 4x4 blocks of the selected DWT sub bands of the cover image. Embedding is applied only to the mid-band DCT coefficients. If X is the matrix of the mid band coefficients of the DCT transformed block, then embedding is done as follows:
If the watermark bit is 0 then,
X¢ = X + k * PN_0 (3)
Otherwise, if the watermark bit is 1 then,
X¢ = X + k * PN_1 (4)
Where X¢ is the watermarked DCT block
Step 9: Apply inverse DCT (IDCT) to each 4x4 block after its mid-band coefficients have been modified by embedding the watermark bits.
Step 10: Apply the inverse DWT (IDWT) to produce the watermarked cover image.
3.2 Watermark Extraction
The watermark extraction procedure is shown in Fig. 3, and described in detail in the following steps. In the proposed combined DWT-DCT algorithm watermarking algorithm, the original cover image is not required to extract the watermark.
Step 1: Read in the watermarked cover image
Step 2: Apply DWT to decompose the watermarked image into four non-overlapping multi-resolution sub bands: LL1, HL1, LH1, and HH1
Step 3: Apply DWT to HL1 to get four smaller sub bands, and choose the sub band HL2, as shown in Fig. 2 a. or, apply DWT to the HH1 sub band to get four smaller sub bands, and choose the HH2 sub band, as shown in Fig. 2b.
Step 4: Divide the sub band HL2 (or HH2) into 4´4 blocks.
Step 5: Apply DCT to each block in the chosen sub band (HL2 or HH2), and extract the mid-band coefficients of each DCT transformed block.
Step 6: Regenerate the two pseudorandom sequences (PN0 and PN1) using the same seed used in the watermark embedding procedure.
Step 7: For each block in the sub band HL2 (or HH2), calculate the correlation between the mid-band coefficients and the two generated pseudorandom sequences (PN0 and PN1). If the correlation with the PN0 was higher than the correlation with PN1, then the extracted watermark bit is considered 0, otherwise the extracted watermark is considered 1.
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Step 8: Reconstruct the watermark using the extracted watermark bits, and compute the similarity between the original and extracted watermarks.
Fig.3. Watermark extraction procedure
4. PERFORMANCE EVALUATION
The performance of combined DWT-DCT image watermarking algorithms is evaluated on the cover image 'HEAD' with a 50x20 binary image 'SVEC' as the watermark image. The two images are shown in Fig. 4 and 5, respectively. Watermarking algorithms are usually evaluated with respect to two metrics: imperceptibility and robustness .
Imperceptibility: It refers to the perceived quality of the cover image in the presence of the watermark. As a measure of the quality of a watermarked image, the peak signal to noise ratio (PSNR) is typically used. PSNR in decibels (dB) is given below in Eqn. 4
Robustness: It is a measure of the immunity of the watermark against attempts to tamper or degrade it, with different types of digital signal processing attacks. In this work, experiments are conducted for robustness to compression and resizing.
Fig. 4 (a) Watermarked image of 'head-mri' (512x512,bmp) subjected to JPEG compression attack, at gain k=10 (b) Original Watermark SVEC (30x20) and (c) Recovered Watermark with JPEG compression at gain, k=10
Fig. 5 (a) Watermarked image of 'weather-map' (512x512,bmp) subjected to JPEG compression attack, at gain k=10 (b) Original Watermark SVEC (30x20) and (c) Recovered Watermark with JPEG compression at gain, k=10
The similarity between the original watermark and the extracted watermark is measured using the correlation factor C, is given below in Eqn.6.
N is the number of pixels in the watermark, are the original and extracted watermark images respectively. The correlation values C will lie between 0 to 1.
5. EXPERIMENTAL RESULTS
Experiments have been conducted on MRI-scan image of HEAD(512x152, 8-bit gray scale). Applying the DWT on the image produced four 256x256 sub bands: LL1, LH1, HL1 and HH1. Since embedding the watermark beyond the first DWT level is more effective, the watermark is embedded in HL2 (or HH2). The selected 128´128 sub band is divided into 4´4 blocks giving a total of 1024 blocks. The DCT transform is then applied to each 4x4 block in the chosen sub band, after which the watermark was embedded according to Eqn. 3 and 4.
Table1 shows the correlation values between the original watermark and the watermarks extracted from sub band HH2 after being subjected to different levels of JPEG compression. The correlation values given in Table 2 indicate clearly that the combined DWT-DCT watermarking algorithm is robust against the compression attack. The compression effect has also been tested in the HL2 sub band and the results verified. It was observed that the results are better regardless of whether the watermark was embedded in HL2 or HH2. Fig.4 and Fig.5 show the extracted watermarks from HH2 with various levels of JPEG compression on themedical image 'head-mri' and satellite image 'weather-map'..
The imperceptibility of combined DWT-DCT algorithm is evaluated by measuring PSNR for the HH2 sub band. The PSNR values obtained are 46.19, 40.17, 36.65, 34.15 and 32.21 for k values ranging from 10 to 50.
In this paper, a combined DWT-DCT digital image watermarking algorithm has been described and tested on the cover image LENA. Watermarking was done by embedding the watermark in the second level DWT sub band HH2 of the cover image, followed by the application of DCT on the selected DWT sub bands. The combination of the two transforms improved the imperceptibility of the watermarked image by maintaining the robustness to attacks.