SECURE, BLIND IMAGE WATERMARKINGTECHNIQUE FOR COPYRIGHT PROTECTION

Faisal Alurki and Russell MersereauSchool of Electrical and Computer Engineering, Georgia Institute of Technology,

Atlanta, GA 30332-0250, USA.Tel: 404-894-2977; fax: 404-894-8363

e-mail: faisal,rmm@ece.gatech.edu

ABSTRACT

We present a new oblivious digital watermarkingmethod for copyright protection of still images. Thetechnique is based on decorrelating the image samplesthen embedding the watermark by taking block DCTof the decorrelated image. Watermark insertion is ob-tained by amplitude modulating the DC component ofthe DCT blocks with the watermarking bits. The tech-nique shows satisfactory robustness to Stirmark bench-mark test and other class of geometric deformations.Image decorelation is achieved using a key to increasethe security of the watermarking system. The water-mark is a readable sequence of binary digits channelencoded to increase its robustness against various typesof attacks.

1 introduction

A digital watermark is a short sequence of informationcontaining an owner identity or copyright informationembedded in a way that is difficult to erase. Digitalwatermarking has been proposed as a possible solutionfor resolving ownership and for copyright protection ofmultimedia data such as still images [1, 2]. In recentyears the field of digital watermarking have captureda lot of attention from researchers. Several techniqueshave been proposed for copyright protection of still im-ages [3, 4, 5]. These techniques demonstrate high de-gree of robustness against several types of attacks sim-ulated by the latest Stirmark benchmark. In this paperwe present a new blind digital watermarking algorithm.The technique is based on permuting the location of theimage samples, then embedding the watermark in thetransform domain of the permuted image. Watermarkinsertion is achieved by first taking a block DCT of thepermuted image then, amplitude modulating the DCcomponent of the DCT blocks. Embedding the water-mark in the DC value of a block of an image transformincreases the watermark robustness to image processingoperations, this is because the DC values of an imagetransform tend to preserve their values under image pro-cessing operations and they do not change their valuesdrastically. The watermark is embedded by amplitude

modulating the DC value in each block. After the water-mark is embedded we take the inverse block transformand use the same key to descramble, to get the wa-termarked image. The permutation operation increasesthe security of the watermark from being extracted as-suming the embedding algorithm is known, i.e., withoutknowing the key used to permute the pixels locations,an attacker cannot remove the embedded watermark.Furthermore, the system implementation complexity islow and watermark embedding and extraction is simple.

2 System Analysis

Let x(n1, n2) be some natural image to be watermarked,the image gets scrambled by a key K to get the decor-related image

∗x (n1, n2). The permutation process is

described in details in [6] . Next, we take a block DCTof

∗x (n1, n2), the blocks are chosen to be of middle size,

typically 32×32 or 64×64. The randomness introducedby the scrambling of pixel locations results in spectrumequalization or spectrum whitening of the host image.Furthermore, the scrambling operation results in a sig-nal with similar statistical properties for each block inthe transform domain. The statistical properties be-come close in similarities as the block size increases. Forexample, by selecting a blocks of size 32× 32 or 64× 64the DC components of the blocks will have similar val-ues. Figure 1 shows the magnitude of the DC values fora 64× 64 DCT blocks of the randomly scrambled image∗x (n1, n2). The figure indicates that the DC values arevery close in magnitude. For simplicity, we replace theDC values for all blocks by a constant value A close totheir values. Typically A is chosen to be the mean valueof all DC values rounded to the nearest integer multi-ple of the block size. Next, we embed the watermarkingbits, which are independent of the host image, by ampli-tude modulating the new DC component A of the DCTblocks as follows

Ai = A(1 + αdi), (1)

where Ai is the modulated DC coefficient of the ith blockα is a scaling factor controlling the strength of the wa-termark, basically α operates as a modulation index and

1

0 10 20 30 40 50 60 700

1000

2000

3000

4000

5000

6000

7000

8000

9000

Figure 1: DC components of 64 × 64 block coefficientsof scrambled image.

di is the ith watermarking bit mapped to polar format,i.e., ±1. The coefficient Ai replaces the original DCcoefficient in the corresponding block. For each block,the watermark signal is viewed as a two-dimensional im-pulse signal with amplitude Aαdi, with the impulse lo-cated at the origin, i.e., zero frequency. The inverseDCT gives the watermark signal w(n1, n2) in the spa-tial domain. w(n1, n2) has constant amplitude equalto Aαd

L , i.e., each pixel in the block will be perturbedby Aαd

L , where L is the block size. After embeddingthe watermark by amplitude modulating the DC com-ponent of the DCT blocks, we take the inverse DCT andunscramble the pixels locations using the same key toget the watermarked image x(n1, n2).

The watermarked image is expected to undergoes dif-ferent types of attacks. We model this process as a signaltravelling through a noisy channel which adds noise tothe watermarked image. Let y(n1, n2) be the receivedwatermarked image, which consist of the watermarkedimage x(n1, n2) plus some noise denoted by N(n1, n2),i.e.,

y(n1, n2) = x(n1, n2) + N(n1, n2). (2)

To recover the watermark the same key K is used topermute the received image. The permutation processdecorelates the samples of the watermarked image andthe samples of the additive noise. Therefore, the noisesamples can be thought of as a sequence of uncorrelatedrandom variables. The DCT of the received image isgiven by Y (k1, k2) = X(k1, k2)+N (k1, k2), after takingthe DCT of the received image we extract the water-marked coefficients. Let V (Yi) be a vector which rep-resent the received watermarking coefficients, which aremodeled as independent and identically distributed ran-dom variables. We model each received watermarkingcoefficient Yi as a random signal which consist of threeparts. The first part is deterministic and it is equalto the DC component A. The second part is randomand it is introduced by the watermarking sequence dwhich has amplitude equal to Aαdi. The last part is Ni,which is introduced by the processing noise. Since therandom signal Ni is the sum of uncorrelated identicallydistributed random variables, by the central limit the-

orem [7] this signal follows Gaussian distribution withzero mean and variance σ2

N which represent the noisepower. Therefore, we can model the ith received wa-termarked coefficient as a random variable consisting ofa deterministic signal perturbed by an additive randomsignal which has two components, one is discrete due tothe embedded watermark and the other is continuousGaussian noise introduced by processing operations.

To evaluate the system performance, we determinethe bit error rate (BER) due to image processing oper-ations. To do that we first try to develop an expressionfor computing the BER. The expected value of any re-ceived watermarking coefficient is given by

E{Yi} = E{A+Aαdi+Ni} = E{A}+E{Aαdi}+E{Ni}.(3)

Assuming the Gaussian noise is zero mean and thatE{d} = 0 for i.i.d watermarking bits, it follows thatE{Yi} = A, which is the original value of the DC co-efficient before being perturbed by the additive noise.Since A is much larger than the magnitude of the anywatermarking bit and larger than the magnitude of thenoise, we remove this average value to improve the de-tection of the watermark and minimize the BER. Sincethe technique is blind, the detector does not know thevalue of A and an estimate of its value must be per-formed first. This is obtained by computing the averageof the DC values of all the received watermarking co-efficients. This seems to give a good estimate for theactual value of A. Note that when using this approxi-mation we are making the assumption that the receivedimage after the decorrelation process can be modeled anergodic stochastic process [7]. In that case, we make theassumption that time averages equal ensemble averages,i.e.,

E{Yi} ≈1n

n∑

i=1

Yi = A. (4)

After removing the average value, the remaining signalYi consists of two independent random components, i.e.,Yi = Yi−A = Aαdi+Ni. These signals are independent.Therefore, their equivalent probability density functionis given by the convolution of the two densities [7]. As-suming di = ±1 equally likely the pdf of the watermarkhas the following distribution

fd(d) =12δ(x− αA) +

12δ(x + αA). (5)

Therefore, when we convolve this pdf with the Gaussiannoise, the result is the sum of two Gaussian pdf’s onewith mean αA and the other with mean −αA, i.e.,

fYi(y) ≈ 1√2πσy

e−(y−αA)2

2σy2 +

1√2πσy

e−(y+αA)2

2σy2 , (6)

where σ2y is the variance which represent the noise power

per block. The above analysis indicates that an es-timate to the probability of bit error of the proposed

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watermarking system is reduced into a simple binarydetection theory problem. In particular, we can modelthe watermarking system as a baseband binary digitalcommunication system in which we model the receivedsignal as a Gaussian random variable with mean αA andvariance σ2

y. An expression for the probability of errorfor this standard communication theory problem can beshown to be [8]

Pe =12erfc

(√

(αA)2

σ2y

)

. (7)

From this equation it is clear that in order to minimizethe probability of error, we need to maximize the energyin the watermarking bits. The energy in each water-marking bit is maximized either by increasing A or in-creasing the modulation index α. Increasing A, impliesincreasing the block size and that decreases the water-mark payload. Given some fixed block size, the onlyway to increase the watermark power is by increasingthe modulation index. However, increasing the modula-tion index is constrained by the perceptual quality of thewatermarked image. Hence, given some perceptual levelof distortion we increase the modulation index until wereach that level, i.e., we maximize α until δ(x, x) ≤ γwhere δ is some distortion measure and γ is the max-imum allowable distortion. For example in [9] it wassuggested that the peak signal to noise ratio (PSNR)between the original and the watermarked image due towatermark embedding should not exceed 38 dB.

Watermark extraction is done by first prefiltering thereceived image [5] to improve watermark detection, thenthe resulting image is decorrelated with the same key.Next, we Take block DCT of the permuted image andextract the DC value of each block. A vector Y is formedfrom those DC values. Each component Yi of Y is com-pared with some threshold τ . The value of the extractedbits are set according to the following

Yi =

{

1 if Yi ≥ τ0 if Yi < τ where τ =

∑ki=1 Yi

k(8)

where k represent the number of DC blocks.

3 EXAMPLE AND RESULTS

To test the robustness of the technique to different at-tacks, we used several test images for evaluation, in thispaper we show the result for three images: Lenna, ba-boon, cameraman. All images are gray level of size512× 512. A DCT block of size 32× 32 were used. Thevalue of α varies between 0.03− 0.04, depending on theimage texture. The watermark message size is 75 bits.The watermark is encoded using a rate 1

3 convolutionalencoder, to enhance the watermark robustness againstimage attacks. Furthermore, the encoded message waspassed through an interleaver. The purpose of the in-terleaver is to reduce the probability of having a burst

Figure 2: (a)Original Image. (b) Watermarked image.

Figure 3: Watermarked image after pinching and spher-izeing attacks.

error. The average PSNR between the original and thewatermarked images is about 38 dB. Figure 2 shows anexample of the original lenna image and the resultingwatermarked image. To test the robustness of the pro-posed watermarking scheme, we ran two different typesof experiments. The first test was the latest Stirmarkbenchmark test [10, 9]. The output results are shown inTable I, a score of “1” indicate a full recovery of the wa-termark for all levels of attacks “0” is given otherwise.For geometric attacks such as rotation, linear transfor-mation and shearing we used template technique similarto the one suggested in [11] to resynchronize the imageand recover the watermark. For high compression ra-tios such as below %20 quality factor we were not ableto recover the watermark. Watermark robustness canbe improved by increasing the modulation index, how-ever, image perceptual quality will be effected by in-creasing the value of the modulation index. currentlytesting the robustness of the technique against othertypes of benchmarks such as the checkmark proposedin http://watermarking.unige.ch/Checkmark. Anotherexperiment was conducted using the software Photoshopwhere the watermarked image was subjected to differenttypes of geometric deformation. Figures 3 to 5 show ex-amples of some geometric deformations which were ap-plied to the watermarked image For all of these attacks afull recovery of the watermark was obtained despite theseverity of the deformation. Recovery was obtained di-rectly without the need to resort to the synchronizationtemplate or any searching techniques.

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Figure 4: Watermarked image after twirling attacks.

Figure 5: Watermarked image after zigzag attack.

4 Conclusion

In this paper, we presented a new secure, oblivious dig-ital watermarking technique based on amplitude mod-ulating the DC component of DCT blocks of a decor-related image. The watermark is a sequence of binarydigits channel encoded to improve its robustness. Wehave used the latest Stirmark benchmark test as our cri-terion for examining the robustness of the watermark.Furthermore, we tested the robustness of the techniqueagainst some geometric deformations. In all these testthe technique indicates robustness against most of theattacks. Future work will concentrate on improving theover all robustness, in particular to attacks such as ran-dom bending and testing the technique against otherattacks and apply the technique for colored images.

References

[1] M. D. Swanson, M. Kobayashi, and A. H. Tew-fik, “Multimedia data embedding and watermark-ing technologies,” Proc. of IEEE, vol. 86, no. 6, pp.1064–1087, June 1998.

[2] F. Hartung and M. Kutter, “Multimedia water-marking techniques,” Proc. Of The IEEE, vol. 87,no. 7, pp. 1079–1107., July 1999.

[3] Ping. W. Wong and Edward J. Delp, Security andWatermarking of Multimedia Contents II, Volume3971, Proceeding of SPIE, Bellingham, Washing-ton, 2000.

Robustness Test Lenna Baboon Cameracolumns & rows removal 1 1 1

rotation 1 1 1JPEG compression 1 1 1

JPEG below 20% Q factor 0 1 0cropping 1 1 1

rotation-scale 1 1 1FMLR 1 1 1filtering 1 1 1

Sharpening-3-3 1 1 1scaling 1 1 1

aspect ratio 1 1 1shearing 1 1 1

linear transformation 1 1 1Stirmark random bend 0 1 0

Table 1: Scores after applying Stirmark benchmark test.

[4] Ping. W. Wong and Edward J. Delp, Security andWatermarking of Multimedia Contents III, Volume4314, Proceeding of SPIE, Bellingham, Washing-ton, 2001.

[5] G. Langelaar, I. Setyawan, and R. Lagendijk, “Wa-termarking digital image and video data,” IEEESignal Processing Magazine, vol. 17, no. 5, pp. 20–46, Sept 2000.

[6] F. Alturki and R. Mersereau, “Secure image trans-form domain technique for steganographic applica-tions.,” Proc. of IS & T/SPIE: Electronic ImagingIII International Conference on Security and Wa-termarking of Multimedia contents ,San Jose, Cal-ifornia, January 2001.

[7] A. Leon-Garcia, Probability and Random Processesfor Electrical Engineering, 2ed edition, AddisonWesley, Massachusetts, U. S. A, 1994.

[8] S. Haykin, Communication Systems, 3rd edition,John Wiley, New York, 1994.

[9] M. Kutter and F. Petitcolas, “A fair benchmarkfor image watermarking systems,” in (Wong andDelp, eds), Proceeding of the SPIE, Security andWatermarking of Multimedia Contents, vol. 3657,pp. 226–239, Jan 1999.

[10] F. Petitcolas, R. Anderson, and M. Kuhn, “Attackson copyright marking systems,” in (Aucsmith, eds)Information Hiding: Second International Work-shop, Lecture Notes in Copmuter Science,volume1525, pp. 218–238., April 1998.

[11] M. Kutter, Digital Image Watermarking: HidingInformation in Images, Ph.D. thesis, Ecole Poly-technique Federale De Lausanne, 1999.

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