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Abstract:This paper gives the choice of watermark domain in presence of the lossy compression. It is assumed that separation of watermark embedding domain from the processing (compression or decompression) domain improves the embedding capacity of the image. Improvement in the embedding capacity ultimately results into the improved robustness of the technique. We worked mainly with grey scale images in five different transform domains namely; pixel, DCT, DWT, FFT and Hadamard. We find that though the capacity of Hadamard and Wavelet transforms are very superior considering the hiding room of the image, the use of same transforms for embedding and processing purpose give better results for the robustness. We have tried to estimate the capacity measures for two popular compressions, JPEG and QSWT and found that the matching of watermarking and compression domain (i.e. DCT for JPEG and Wavelet for QSWT) result towards better hiding capacities as well as higher co-relation factor.

Keywords: Steganography, Watermark, Data Hiding.

1. Introduction:

The fast growth of digital networks, and the ever decreasing cost of computers, printers and digital transmission have made digital media increasingly popular over the conventional analog media. However, digital media also causes extensive opportunities for mass piracy of copyrighted material. Figure 1 shows few examples of the real frauds and forgeries recently happened in India.

Figure 1: Examples of Frauds and Forgeries.

It is therefore very important to have ways and means to detect copyright violations and control access to digital media. In this paper we have given the idea of Steganography, which hides the watermarks into the information as digital stamps for authentication. Techniques such as Steganogphy and Data Hiding help to establish the integrity and the authenticity of the information. [1]

Figure 2 gives us the general idea of watermarking process. The information of the multimedia on the Internet can get separated into individual streams like audio, text or video containing still images.

Figure 2: Overview of Watermarking Process.

We have worked with still images. We tried with the grey scale images because the ratio of added information to adding information is very low for grey scale images. If we take care of robustness at low ratio factors, definitely it will perform well for color images having higher ratios.

In [2] we tried to give the estimation of number of bits that can be hidden and retrieved successfully with an arbitrary low probability of bit error i.e. ‘watermark capacity’[3].

While working with transform domains, we decomposed original image into distinct bands, as shown in figure 3. The lower frequency bands are very noisy due to high image content. While the higher frequency bands are very sensitive to the image noise and are likely to be eliminated in the compression or decompression process. So we have to strike some compromise at middle frequency bands only.

As the band capacities change according to the band variances, the overall sum of the capacities of decomposed bands allows drastic increase in the data hiding capacity. The simulations were taken for four different transformations like DCT, DWT, FFT, & Hadamardand concluded that Hadamard and DWT give better results for hiding and are proved to be good watermark embedding domains.

Figure 3: Decomposition of data hiding

channel into parallel sub channels.

s-signature, s*-corrupted signature

I-image noise, P-processing noise.

Considering the basic concepts implemented in the technique given in [2] we extended further.

For experiment, we separated the watermarking domain from the compression domain. And focused on the situation in which watermarked signal undergo lossy compression involving quantization in a specified domain. As practical compression is the most common form of the incidental distortion, it limits the robustness or capacity of data hiding or watermarking scheme[4].

2.0 Joint watermarking in compression scenario:

The block diagram of a typical watermark embedding scheme in the presence of lossy compression is shown in Figure 4. There are three basic stages:

1) Watermark embedding.

2) Lossy compression.

3) Watermark detection.

Figure 4: Joint watermarking in the compression

Scenario.

Figure shows that the watermark and compression domains are separated. The idea of separate domains may improve the channel capacity. This will also answer our fundamental question, ‘For lossy compression involving in a specific transform domain, what domain is best suited for reliable watermark embedding and extraction?’

Generally, the embedding process occurs in a watermark domain. An orthogonal transformation T_w is applied to the host image I. The transformation decomposes the host image I into coefficients to which the watermark is embedded. Taking the inverse transform produces watermarked image I_w in pixel domain which is designed to be perceptually identical to the original image I. Most commonly used transforms include discrete cosine transform (DCT), wavelet transforms, the Hadamard transform, the discrete sine transform, the discrete Fourier transform (DFT) and the Karhunen Loeve transform (KLT)[5].

We consider the situation in which such compression is applied after watermark embedding. Lossy compression is a quantization process in a compression domain T_c such as DCT domain for JPEG. The resulting compressed watermarked image is .

At the receiver, the hidden message w* is extracted from the “corrupted” watermarked image in the watermark domain. The existence of the original watermark w within is detected by calculating the correlation between the original watermark w and the extracted watermark w*.

If the correlation coefficient is above a given threshold the watermark is considered to be detected, otherwise, the watermark is considered not to be present in the image.

2.1 Compression Attack Model:

The lossy compression we consider here, involves quantization of signal coefficients in a compression domain such as the DCT domain (for JPEG). We denote the associated transformation from the pixel domain to the compression domain with Tc. Both the host image signal and the watermark signal pass through a quantizer, as shown in Figure 5, where w is the watermark information and I is the host image in the Tc domain.

Figure 5: Quantizer. The watermark w and the host image I jointly undergo quantization to produce watermarked quantized signal ?.

The existence of a nonlinear element such as a quantizer in the watermark channel makes it difficult to analyze the relationship between the original watermark and extracted watermark. However, since watermark detection involves computing the correlation coefficient between the original and extracted watermark (i.e., the input and the output of the watermark channel), we treat this channel as a black box and propose a more tractable linear model which still captures the essential characteristics of the effect of compression on w in terms of correlation [6].

Suppose I and w are two independent random variables with zero mean. The transform Tc coefficient value of the watermarked image prior to quantization is given by,

y = I + w eq. 1

Let ? be the quantization step. Then the quantized coefficient is given as follows,

? = [y]_? = round(y/?)? eq. 2

Where round(.) denotes the rounding to the nearest integer, and [.]? denotes quantization operation with step ?.

Our mathematical additive model for quantization is to replace ? with y’ where,

y’=?w +?I eq. 3

Where ? and ? are two parameters set such that the output of the novel additive model has the same power E{ ? ²}, and the same correlation to w, E{w ? }.

That is, ? and ? are set such that,

E{ y’²} = E{ ? ²} eq. 4

E{wy’} = E{w ? } eq. 5

It can be shown that following assignments obey equations 4 and 5.

eq. 6

The given model essentially tries to account for the varying degree of effect of the quantization process on the host and watermark components of y. Clearly, because w is much lower in amplitude than I for transparency of the watermark, the influence of w after quantization on ? will be much smaller if not negligible than the influence on I Thus, we expect ? to be smaller than ?.

2.2 The Scheme:

In this section we incorporate the novel linear quantization model discussed in Section 2.0 into our analysis framework. Figure 6 shows an overall representation of the watermarking and quantization-based compression process. Spread spectrum watermarking occurs in the Tw domain and compression in the Tc domain where Tw and Tc are both orthogonal transformation matrices.

Figure 6: Representation of overall watermarking in compression process.

Although an image is often represented by a two-dimensional signal, for our purposes we regard the image signal as a one-dimensional sequence acquired by a column-wise reordering operation. After column by column scanning, each 8 x 8 block field is regarded as a 64 x 1 vector. Let n = 64 be the length of the vector [8].

Suppose I = [i1; i2; _ _ _ ; in]^T is an image block in the pixel domain,

X = [x1; x2; _ _ _ ; xn]^T is the image coefficient in the compression domain,

and W = [w1; w2; _ _ _ ; wn]^T is the watermark signal in the watermark domain.

From Figure 6 , we can see that,

X = T_c I

V = T_cT_w ^–1 W eq. 7

In practical lossy compression, the quantization is applied to all coefficients in varying degrees depending on a quantization table. By modeling the quantization of coefficient i using parameters ??_i and ?_i we can establish a relationship between the watermark signal embedded and its extracted version after quantization.

For practical calculations approximating a non linear quantizer as linear model, we can obtain ,

? = AV + BX eq. 8

Where A and B are vectors containing ? and ? values for individual channels.

Considering T = T_cT_w ^–1

We have

? = T^-1 ? = T^-1 AT_w + T^-1 BX eq. 9

It is of great interest to determine the best transformation domain in which robust watermark embedding methods can be devised given that compression occurs in some other domain. We can attempt to investigate analytically the choice of watermark domain for high capacity data embedding in the presence of compression.

The channel efficiency depends on the dependence between watermark inputs in different channels. Here we considered two extreme cases of watermark input dependence,

(1) Fully dependent watermark inputs.

(2) Independent watermark inputs.

To calculate the capacity, we make the following assumptions:

• The image signal I is Gaussian distribution, so X, Y are all normally distributed random variables whose variances can be derived from I.

• In channel i, the watermark signal component w_i is also Gaussian distributed with variance ?²_wi

Case1: Fully dependent watermark inputs

Suppose w1,w2,……. wn are fully dependent, namely for all i, wi = ?_wi u where u is a standard normal distribution N(0,1) and ?_wi is the amplitude of watermark signal in channel i. This corresponds to the situation in which the watermark is repeated throughout the signal. We can exploit the full correlation and treat the watermark components from other channels wj for all j ? i as equivalent to the input signal wi.

Case2: Independent watermark inputs

Suppose wi and wj for i ? j are independent. This corresponds to the situation in which one long spread spectrum watermark sequence is embedded. For channel i, other watermark signals wj, j ? i are regarded as noise.

2.3 Channel Efficiency :

We implemented spread spectrum watermarking on various 256 x 256 grey scale still test images in five different domains. Since efficiency is a theoretical measure, we estimate the efficiency of the channel by formula ,

C= 0.5* log2(1/(1-?2)) eq.10

where ? is the correlation co-efficient between the original watermark and the extracted watermark. It is observed that ,the capacity of the channel is proportional to the efficiency of the channel.

2.4 JND Threshold :

An effective watermark must withstand image compression, because images placed on the Internet or in databases are almost always compressed – sometimes to a very low data rate. Since compression tends to weaken a watermark in an image, it is important to find ways to maximize the amount of watermark that remains in the image after compression. The image adaptive watermarking methods use the visual models to define the threshold.

Specifically, visual models allow the user to raise or lower the amplitude of the watermark according to the image content (hence the name, image adaptive). These visual models provide thresholds for how much a given transform coefficient can change, before such changes are noticeable under standard viewing conditions. These thresholds are known as just-noticeable difference (JND) values. The larger the JND values, the more coarsely a coefficient can be quantized without noticeable visual distortion. In the same way, larger JND values allow us to imperceptibly add a larger-amplitude watermark to the transform coefficients [7].

The above scenario is tested with following two algorithms for co-relation factor.

1. DCT based Interblock Co-relation method [9].

2. QSWT – Qualified Significant Wavelet

Tree method [10].

3. Conclusion :

Figure 7 gives the example of invisible watermarking in our college laboratory. Perceptually the watermarked image is not degraded.

(a) (b) (c)

Figure 7: Invisible watermarking

a) Original Image b) Watermark logo

c) Watermarked image with

MSE=0.45 and PSNR=57.2

Chart1 shows the channel efficiency for case1 as discussed in section 2.3 . We can see that Hadamard and Wavelet transforms are better for robust data hiding than other transforms. In particular Hadamard transform is the best when JPEG compression occurs in the very common range of JPEG Quality 60 to 100.

Chart1

Chart2 shows the channel efficiency for case2 as per section 2.3. It is observed that the efficiency of DCT domain is improved if the watermark inputs are independent. The Hadamard transform is also giving better results as expected. But it is suggested that [] for more robustness and for improved channel capacity choose watermark domain to be the same as the compression domain. (i.e. DCT for JPEG and DWT for EZW or QSWT)

Chart2

The results in the chart3 show the co-relation values for watermark embedding and extraction in two domains. The watermarked image is allowed to pass through JPEG compression with different quality factors.

It is observed that for JPEG compression DCT domain watermark embedding gives better co-relation factor which is almost 0.9 for all quality factors. The DWT domain watermark embedding results into comparatively poor co-relation factor which is nearly 0.75 for all quality factors. In contrast to this if we apply compression using significant wavelet tree, it results into almost 1.0 as the co-relation factor for the DWT watermark embedding domain.

This indicates that the complementary transforms will result in superior capacity performance. But the use of same embedding domain as the compression domain will improve the robustness of the technique.

Chart3

Acknowledgements:

The first author is working as Young Scientist for the project in the area of digital image watermarking supported by Department of Science and Technology, Delhi, India.

References:

[1] I. J. Cox, J. Killian, T. Leighton, and T. Shamoon. ‘Secure spread spectrum watermarking for multimedia.’ Technical Report 95-10, NEC Research Insitute, 1995.

[2] S. Shefali, S M Deshapande ‘Mathematical model for Capacity estimates for data hiding techniques under lossy compression’ International conf. on mathematics and computer sci. IMTGT 06, June Malaysia.

[3] M. Barni, F. Bartolini, A. De Rosa ‘Capacity of the Watermark-Channel: How Many Bits Can Be Hidden Within a Digital Image?’ Proc. of S P I E , Vol. 3657, Jan 1999.

[4] Chuhong Fei, Deepa Kundur and Raymond Kwong ‘The Choice of Watermark Domain in the Presence of Compression.’ IEEE, conf. on IT, Coding and Computing April 2001.

[5] Ramkumaar & Ali Akansu. ‘Capacity estimates for data hiding in compressed images’ IEEE tr. On Image processing, Vol10, no.8, August 2001.

[6] W. Stallings, Network Security Essentials: Applications and Stardands. Prentice Hall, 2000.

[7] Alghoniemy & Tewfik ‘Geometric invariance in image watermarking,’ IEEE Tr. On Image Proc. ol. 13,No.2 Feb 2004.

[8] S. D. Servetto, C. I. Podilchuk and K. Ramchan-dran, ‘Capacity Issues in Digital Image Watermarking’,Proc. IEEE International Conf on Image Processing,Chicago, IL, 4-7, Oct 1998.

[9] W. R. Bender, D. Gruhl, and N. Morimoto, ‘Techniques for data hiding,’ Proc. SPIE: Storage and Retrieval of Image and Video Database, vol. 2420, pp. 164–173, Feb. 1995.

[10] C.-T. Hsu and J.-L. Wu, ‘Multiresolution watermarking for digital images,’ IEEE Trans. Consumer Electron., vol. 45, Aug. 1998.

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