A novel approach for watermark embedding Текст научной статьи по специальности «Медицинские технологии»

UDC 681.324

A NOVEL APPROACH FOR WATERMARK EMBEDDING

BEHJAT FOROUZANDEH, KAMAL ABDI,

AMIRALI SHIRAZI BEHESHTI, LEYLA S. GHAZANFARI, SHOHREH SHARIFMANSOURI

Many watermarking methods use correlation detection for extraction of watermark. The decision threshold of correlation is chosen based on error probability appeared in detection process. Attacks on watermarked image usually cause fluctuation in error probability, precision, extracted energy, and length for a blind DWT-based watermarking algorithm by investigating the alteration rate of energy and the length of the detected watermark. The new algorithm can address fairly good optimization on the above issues. The extracted results are used in a novel embedding approach in which the DWT-coefficients of the image, in each sub-band, are separated into dominant and non-dominant groups. A sequence of a random generator output, referred to as signature data, is then embedded into these coefficients to obtain the watermarked image. Experimental results demonstrate that the proposed method has better robustness compared to other similar methods.

1. Introduction

With the rapid spread of computer networks and increasing the availability of digital data such as multimedia services on the internet there is a pressing need to manage and protect the illegal duplication of data. One approach to address this problem involves adding an invisible structure to a host image to ‘’mark’’ ownership of it. These structures are known as digital watermarks. To be effective, a watermark must be imperceptible within its host, discrete to prevent unauthorized removal, easily extracted by the owner, and robust to incidental and intentional distortions. In many watermarking algorithms the presence of a watermarking, will be tested by using statistical estimation. The result will be compare with a threshold value. The reason for using a threshold value arises from error probability appearing. Generally, two kinds of error are possible, false positive and false negative [1]. The detector commits a false positive if the presence of a watermark in the object is confirmed, while the contrary is true and commits a false negative at the event that the absence of a watermark is being confirmed and the contrary is true. The threshold value should be computed in a manner to minimize these two errors. There is, however, a trade-off in between, that is, the increase of the threshold level can deteriorate false negative detection while at the same time alleviating false positive detection. In [2], the threshold value is described as the average of the expected values of the extracted correlation with correct and incorrect keys. In [3], the threshold value is estimated in the similar manner of [2]. Another method for estimating the threshold value is based upon Gaussian false positive model [4]. In this method, the integration of the Gaussian distribution is computed in order to estimate the false positive to obtain the threshold value. Another threshold value is also been 48

proposed in [5], which indeed enjoys high accuracy, however, contains complex mathematical expressions. This fact therefore makes it rather problematic to use. Here, we modified the two proposed methods in [2] and [3], by introducing a novel Successful Detection Percentage (SDP), which can be used as an appropriate criterion for measuring the robustness of the extracted watermark even under heavy attacks. The modified method is not only computationally efficient, in comparison with those in [4], [5], but also has better accuracy compared with those of the [2] and [3]. In many watermarking methods, the whole coefficients of watermark are embedded into a specified frequency band. Usually a constant strength value (a ) is chosen without considering the amount of each frequency coefficient in the selected frequency band of the host image [6], [7]. This method can cause some nonoptimizations in the robustness of the watermark. In the proposed method, high and low amplitude coefficients are separated by a threshold value. The value of a then is adjusted proportionally in each part. Therefore, while keeping the quality of the image at the desirable level, the robustness of watermark will also be preserved. The details of embedding scheme are discussed in section 2. Section 3 describes the modified detection scheme in DWT domain. In section 4 the SDP criterion is illustrated. Section 5 summarizes the work. Experimental results are tabulated in section 6.

2. Watermark embedding

The embedding scheme commonly used is of the form [6], [7].

y = x + awk. (1)

Where x is the DWT coefficients vector of the host image, w k is the watermark vector that is generated from a pseudo random generator with a secret key, k, and a is the global factor which refers to the embedding strength. The corresponding DWT coefficients vector of the watermarked image is denoted as y . In [6], [7] the value of a is set to be a constant value for all coefficients of a DWT sub-band of image in which the watermark is embedded. Therefore, the optimum trade-off between imperceptibility and robustness of watermark is not provided. In [2], the watermark is only embedded to the large DWT coefficients of a given sub-band, this leads to the desirable characteristics, but the scheme is not synchronize and in some cases, resulted in invalid detections. Here, we eliminate these problems by estimating a threshold that is used for separating the dominant coefficients from nondominant coefficients in selected DWT sub-band. Therefore instead of using a global factor, a , two different factors are used. In this case by saving the fidelity of image, the robus- tness of watermarked image will be increased. In each sub-band of wavelet decomposition the large amplitude coefficients represent the dominant coefficients. As shown in Figure 1, most of the coefficients which represent the nondominant coefficient have amplitude near to zero.

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Fig. 1. Histogram of DWT coefficients

In each sub-band, the dominant coefficients play a major role in modeling the relevant characteristics of image. Generally the nondominant coefficients in each subband, are the projection of dominant coefficients at the same locations, in other sub-bands. In fact, in images with high activity features, these coefficients are near to zero and vice versa. On the other hand, in a specified subband with the small deviation values of DWT coefficients, there are a large and less number of nondominant and dominant coefficients respectively. Therefore, a threshold value for separating the dominant and nondominant coefficient can be estimated based on the deviation values of DWT coefficients in sub-bands. Thus by using this threshold the watermark can be embedded to dominant coefficients with higher strength.

LL0 HL1 HL0

LH1 HH1

LH0 HH0

Fig. 2. A DWT two level decomposition

Here, after two-level decomposition, as shown in Figure 2, the watermark is embedded to high resolution diagonal sub-bands (HH0 , HH1). In order to threshold estimation first, the ratio of nondominant coefficients in a given subband, nk is defined as follow:

nk

________°Xl_________

c HH,l +c LH,l +c HL,l

x Mk,l

(2)

[xi +a1-wk,i, tf|xi| > Tk; yi і + -fi і < T (4)

[xi +a2.wk,i, if|xi| < Tk.

First each sub-band is segmented into several nonoverlapping rectangles with equal sizes. Then, the salience S (which is a numerical measure of perceptual importance) of each of these localized segments is computed using information about HVS [8], then, the SNR for different thresholds is computed by altering the value of a , as keeping the average, minimum and maximum values of S, unchanged. (in order to saving the quality of image). Finally the threshold value which is pointed to minimum SNR, would be selected. In Table 1, the SNR values for different thresholds are shown for lenna’s image after 1’st level decomposition, in LH0 DWT band.

Table 1. Result of SNR for Lenna image. The estimated threshold value is denoted by *

0.021 0.023 0.0255* 0.15 T

0.010 0.015 0.015 0.033 a1

0.01 0.01 0.01 0.01 a2

31.244 27.776 27.750 28.153 SNR

627.46 626.66 626.62 638.59 Smax

88.108 90.207 90.204 90.203 Save

2.9648 2.9648 2.9648 2.9648 Smin

3. Correlation detection

The correlation of the modified coefficients y i with the vector of random sequence wki can be written as follows :

M

correlation(k) = £ yi.wki/M (5)

i=1

Statistically the above correlation has a peak value only when the random sequences is generated with correct key, k. This value is usually compared to a threshold, T, to showing the validity of extraction. In [3] the threshold

for detection is chosen as a /3, which is precise for spatial domain methods. In [2], it is chosen as a / 2 for DWT domain methods. The value is estimated as the average of expected values of correlation for the correct and non correct keys. Here the threshold is as in [2].

4. Evaluation of SDP

The precision of the detection after each attack is examined by a new factor named SDP.

For k= HH,LH,HL and l=1,2 where, ст^,і and sk,l are the

deviation and numbers of DWT coefficients in sub-band k at l’th level decomposition, respectively. [.] is the integer function. Then, the threshold Tk is obtained as:

Tk =

xnk + xnk +1 2

(3)

*

Where xnk is the nk’th DWT coefficient in sub-band k, after sorting the DWT coefficients from the smaller to higher amplitudes. Finally by using Tk , the embedding process is expressed as the following form:

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After estimating the correlation between the watermarked image and the set of watermarks generated by pseudo random generator the successful detection percentage, SDP, for detected watermark is obtained as:

SDP = mm(^ ,Щ (6)

p1 p2 ' W

Where, P1, P2, are the difference between the maximum correlation and the threshold Td after using the correct and non-correct keys respectively. P’i and P’2 denote the estimated value of P1 and P2 after attack. The negative

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values of SDP, indicate on invalid detection, which can help us to determine whether the M and a have appropriate values. The direct effects of M and a over the correlation results are well demonstrated by the SDP factor in Figures 3, 4, and 5. Figure 3 shows the correlation result

for watermark with M=1630 and a = 0.08. In Figure 4, with the M=273 and the same a value, SDP is negative and therefore, the detection result is invalid. Figure 5, shows the result for a = 0.15 with the same M as in Figure 4. In this case the detection is valid.

0.08 і---1----1----1----1----1----1-----1----1----1---1

0.07 - -

0.06 • -

0.05 • -

0.04--------------------------------------------------

0.03 - -

0.02 - -

.0.02 1--1----1----1-----1----1----1----1----1-----1----1

0 100 200 300 400 500 600 700 800 900 1000

Fig. 3. Correlation for M=1630 , a = 0.08

0.15

0.1

-0.1 1------1-------1-------1-------1-------1------1-------1-------1-------1-------1

0 100 200 300 400 500 600 700 800 900 1000

Fig. 5. Correlation for M=273, a = 0.15

Also we can evaluate SDP analytically with more accuracy as below:

f

SDP = min

cor(w k )| after attack

cor(wk)beforeattack

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a/2 a/2 - 5a' " -a/2 ’ a/2-5a

(7)

Where, - 5a to 5a is the span in which 99% of statistical results with Gaussian distribution are placed in. a and a' are standard deviation for 999 samples of correlation response for incorrect keys before and after attack respectively.

5. Experimental results

To illustrate the effectiveness of the proposed method for watermark detection and robustness to attacks, the method is applied on several images such as Lenna image. Only the results of application on 256 x 256 grayscale Lenna are shown here. In our experiments, W contains 1000 available watermark vectors. One of the watermark vectors with key=400 is selected and embedded in the DWT coefficients of the image using schemes (1) and (4). Embedding is done in coefficients HH0, HL0, LH0, HH1, HL1, LH1. Only the results of embedding in HH0 and HH1 are tabulated here. In the proposed method, in order to satisfy the imperceptibility of the watermark and to save the fidelity of the image, the strength values ( a ) are estimated with respect to HVS scheme in [8]. Simulation results were conducted to demonstrate the robustness of the technique under JPEG compression, blurring, cropping, and salt-&-pepper noise that followed by median filtering. The robustness oftechnique is evaluated by the scheme (6). In each table in order to showing the accuracy of the estimated threshold two different thresholds are also used. In Table 2 and Table 6, the effect of compression on the SDP of correlation coefficients for HH0 and HH1 bands are pointed. The SDP in scheme (4) remains high in HH1 and acceptable in HH0 even under compression ratios of Q=20 while the SDP for scheme (1) is under zero. In Table 3 and Table 7 the effect of blurring attack by using 1.5 x 1.5 and 5.5 x 5.5 masks are shown. In Table 4 and Table 8 the watermarked image is cropped to retain 252 x 252 and 128 x 128 pixels at the center. Lastly

Table 2. SDP versus JPEG quality factor (Q) for estimated (Est) simulated (Sim) and non threshold

values in Ho band

T Q 01/02 SDP

Est 0.01568 80 0.03443/0.01 17.9480

Sim 0.012 80 0.03443/0.01 22.1233

Sim 0.0118 80 0.011/0.01 6.3342

Non - 80 0.01/0.01 -13.8486

Est 0.01568 20 0.03443/0.01 5.2256

Sim 0.012 20 0.03443/0.01 8.4354

Sim 0.0118 20 0.011/0.01 -16.6277

Non - 20 0.01/0.01 -42.4480

Table 3. SDP versus blurring mask for estimated (Est) simulated (Sim) and non threshold values in Ho band.

T W 01/02 SDP

Est 0.01568 1.5 0.03443/0.01 75.3621

Sim 0.012 1.5 0.03443/0.01 72.8453

Sim 0.0118 1.5 0.011/0.01 68.9208

Non - 1.5 0.01/0.01 75.1096

Est 0.01568 5.5 0.03443/0.01 1.9943

Sim 0.012 5.5 0.03443/0.01 0.5892

Sim 0.0118 5.5 0.011/0.01 -4.7576

Non - 5.5 0.01/0.01 1.3905

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Table 4. The watermarked image is cropped to retain 252 252 and 128128 pixels at the center in Ho band

T W 01/02 SDP

Est 0.01568 252 0.03443/0.01 96.1417

Sim 0.012 252 0.03443/0.01 96.2843

Sim 0.0118 252 0.011/0.01 96.2531

Non - 252 0.01/0.01 95.4148

Est 0.01568 128 0.03443/0.01 57.2645

Sim 0.012 128 0.03443/0.01 46.6949

Sim 0.0118 128 0.011/0.01 25.5496

Non - 128 0.01/0.01 27.5275

Table 5. SDP versus noise density of salt and pepper (N.D) for estimated (Est) simulated (Sim) and non threshold values in Ho band

T N.D 01/02 SDP

Est 0.01568 0.01 0.03443/0.01 9.6425

Sim 0.012 0.01 0.03443/0.01 10.6355

Sim 0.0118 0.01 0.011/0.01 8.3562

Non - 0.01 0.01/0.01 8.0012

Est 0.01568 0.05 0.03443/0.01 6.1160

Sim 0.012 0.05 0.03443/0.01 6.9887

Sim 0.0118 0.05 0.011/0.01 4.7341

Non - 0.05 0.01/0.01 4.8223

Table 6. SDP versus JPEG quality factor (Q) for estimated (Est) simulated (Sim) and non threshold

values in D1 band

T Q 01/02 SDP

Est 0.02156 80 0.0415/0.02 55.9263

Sim 0.03 80 0.0553/0.02 56.4182

Sim 0.005 80 0.022/0.02 24.0995

Non - 80 0.02/0.02 33.3520

Est 0.02156 20 0.0415/0.02 14.9020

Sim 0.03 20 0.0553/0.02 13.1835

Sim 0.005 20 0.022/0.02 -10.2552

Non - 20 0.02/0.02 -1.2559

Table 7. SDP versus blurring mask for estimated (Est) simulated (Sim) and non threshold values in D1 band

T W 01/02 SDP

Est 0.02156 1.5 0.0415/0.02 63.2415

Sim 0.03 1.5 0.0553/0.02 60.8303

Sim 0.005 1.5 0.022/0.02 58.0323

Non - 1.5 0.02/0.02 63.0323

Est 0.02156 5.5 0.0415/0.02 -3.0946

Sim 0.03 5.5 0.0553/0.02 -11.2445

Sim 0.005 5.5 0.022/0.02 -23.2606

Non - 5.5 0.02/0.02 -2.1163

in Table 5 and Table 9 the watermarked image is first corrupted by salt and pepper noise with intensity of 0.01 and 0.05, and then smoothened by a 2 x 2 median filter [9]. Generally our experiment results reveal that the proposed scheme is more effective when the watermarked image is JPEG compressed and cropped or when it corrupted by salt and pepper noise and then median filtered. However, in the blurred watermarked image the scheme (1) has better detection capability. In this case further investigations will be needed to improve the performance.

Table 8. The watermarked image is cropped to retain 252 252 and 128 128 pixels at the center in D1 band

T W 01/02 SDP

Est 0.021568 252 0.0415/0.02 97.4821

Sim 0.03 252 0.0553/0.02 97.5750

Sim 0.005 252 0.022/0.02 97.3272

Non - 252 0.02/0.02 96.6333

Est 0.021568 128 0.0415/0.02 39.6192

Sim 0.03 128 0.0553/0.02 36.8658

Sim 0.005 128 0.022/0.02 31.4998

Non - 128 0.02 27.8434

Table 9. SDP versus noise density of salt and pepper (N.D) for estimated (Est) simulated (Sim) and non threshold values in D1 band

T N.D 01/02 SDP

Est 0.02156 0.01 0.0415/0.02 64.7547

Sim 0.03 0.01 0.0553/0.02 61.2911

Sim 0.005 0.01 0.022/0.02 50.7173

Non - 0.01 0.02/0.02 50.66110

Est 0.02156 0.05 0.0415/0.02 55.8567

Sim 0.03 0.05 0.0553/0.02 48.8087

Sim 0.005 0.05 0.022/0.02 43.5098

Non - 0.05 0.02/0.02 41.0788

References: 1. Lichtenauer J., SetyawanI., Kalker T., Lagendijk R. Exhustive geometrical search and the false positive watermark detection probability // Philips research lab. The Netherlanls, 2003. 2. DugadR., Ratakonda K., and Ahuja N. A new wavelet-based scheme for watermarking images // Image Proc. 1998, ICIP 98 Proc., 1998. 3. Chun-Shien Lu. Multimedia sequrity // Hershey, London, Melbourne, Singapore, 2005. 4. CoxI.J., LeightonF.T., and Shamoon T. Secure spread spectrum watermarking for multimedia // IEEE Trans. image Proc., 1997. 5. Piper A. Choice of false positive model for threshold selection in watermark detection of scaled content // Int. Conf. 2003. 6. Mehul R, Priti R. Discrete wavelet transform based multiple watermarking scheme // Proc. of the IEEE, 2003. 7. George M., Chouinard J.Y. and Georganas N. Digital watermarking of images and video using direct sequence spread spectrum techniques”, IEEE, Canadian conference May, 1999. 8. Kundur D.and Hatzinakas D. A Robust digital image watermarking method using wavelet based fusion”, Proc. of the IEEE, 1997. 9. Matlab: Image Proc. Toolbox User’s Guide, The Math Works Inc, 1993.

Поступила в редколлегию 18.07.2006

Рецензент: д-р техн. наук, проф. Хаханов В.И.

Behjat Forouzandeh, School of Electrical and Computer Engineering University of Tehran, Iran.

Kamal Abdi, School of Electrical and Computer Engineering University of Tehran, Iran.

Amirali Shirazi Beheshti, School of Electrical and Computer Engineering University of Tehran, Iran.

Leyla S. Ghazanfari, PhD student of School of Electrical and Computer Engineering University of Tehran, Iran.

Shohreh Sharifmansouri, School of Electrical and Computer Engineering University of Tehran, Iran.

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