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Embedding Multiple Watermarks in the DFT DomainUsing Low and High Frequency Bands

Emir Ganic, Scott D. Dexter, Ahmet M. EskiciogluDepartment of Computer and Information Science, CUNY Brooklyn College

2900 Bedford Avenue, Brooklyn, NY 11210, USAeganic@brooklyn.cuny.edu, {dexter, eskicioglu}@sci.brooklyn.cuny.edu

ABSTRACT

Although semi-blind and blind watermarking schemes based on Discrete Cosine Transform (DCT) or DiscreteWavelet Transform (DWT) are robust to a number of attacks, they fail in the presence of geometric attacks such asrotation, scaling, and translation. The Discrete Fourier Transform (DFT) of a real image is conjugate symmetric,resulting in a symmetric DFT spectrum. Because of this property, the popularity of DFT-based watermarking hasincreased in the last few years. In a recent paper, we generalized a circular watermarking idea to embed multiplewatermarks in lower and higher frequencies. Nevertheless, a circular watermark is visible in the DFT domain,

providing a potential hacker with valuable information about the location of the watermark. In this paper, our focusis on embedding multiple watermarks that are not visible in the DFT domain. Using several frequency bands

increases the overall robustness of the proposed watermarking scheme. Specifically, our experiments show that thewatermark embedded in lower frequencies is robust to one set of attacks, and the watermark embedded in higherfrequencies is robust to a different set of attacks.

Keywords: semi-blind image watermarking, classification of image watermarking schemes, Discrete FourierTransform, frequency band, multimedia, owner identification, copy control, geometric attacks, multiple watermarks.

1. INTRODUCTION

Encryption and watermarking are two groups of complementary technologies that have been identified by content providers to protect multimedia data [1,2,3]. Watermark embedding and detection are sometimes considered to beanalogous to encryption and decryption [4]:

Encryption makes multimedia content unintelligible through a reversible mathematical transformation. Insymmetric key encryption, which is commonly used for protecting multimedia elements, each encryptiontransformation E K is defined by an encryption algorithm E and a key K . Given a plaintext M , the transformation

produces the ciphertext C = E K ( M ). Each decryption transformation D K is defined with a decryption algorithm D and the key K . For a given K , D K = E K

-1 such that D K ( E K ( M )) = M .

Watermarking embeds data directly into a multimedia element. The embedding transformation E K is defined byan embedding algorithm E and a key K . In watermarking, the usual approach is to use a symmetric keyalthough there is a recent trend to use asymmetric techniques. Given a cover image I and a watermark W , thetransformation produces the watermarked image I W = E K ( I,W ). Each detection (or extraction) transformation D K is defined with a detection (or extraction) algorithm D and the key K . For a given K and the watermarked image

I W , the watermark is either detected or extracted: W = D K ( I W ).

In digital distribution networks, copyrighted multimedia content is commonly protected by encryption:

Cable, satellite, and terrestrial distribution: A conditional access (CA) system provides the encryptiontechnology to control access to digital television services. Authorized users can use the appropriate decoderequipped with the means to decrypt the programs.

Internet distribution: Digital Rights Management (DRM) refers to the protection, distribution, modification,and enforcement of the rights associated with the use of digital content. The primary responsibilities of a DRMsystem include secure delivery of content, prevention of unauthorized access, enforcement of usage rules, andmonitoring of the use of content.

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Distribution in digital home networks: A digital home networks is a cluster of consumer electronics devices(e.g., DTV, DVD player, DVCR, and STB) that are interconnected. The multimedia content is encrypted intransmission across each digital interface, and on storage media.

A digital watermark is a pattern of bits inserted into a multimedia element such as a digital image, an audio or videofile. The name comes from the barely visible text or graphics imprinted on stationery that identifies the

manufacturer of the stationery. There are several proposed or actual watermarking applications [4]: broadcastmonitoring, owner identification, proof of ownership, transaction tracking, content authentication, copy control, anddevice control. In particular, watermarking appears to be useful in plugging the analog hole in consumer electronicsdevices [5]. In applications such as owner identification, copy control, and device control, the most important

properties of a watermarking system are robustness, invisibility, data capacity, and security.

In a classification of image watermarking schemes, several criteria can be used. Table 1 shows four of them typeof domain, type of watermark, type of scheme, and type of information needed in the detection or extraction process.

Table 1. Classification of image watermarking schemes

Criterion Class Brief descriptionPixel Pixels values are modified to embed the

watermark.Domain type

Transform Transform coefficients are modified to embed thewatermark. Recent popular transforms areDiscrete Cosine Transform (DCT), DiscreteWavelet Transform (DWT), and Discrete FourierTransform (DFT).

Pseudo random number (PRN) sequence(having a normal distribution with zeromean and unity variance)

Allows the detector to statistically check the presence or absence of a watermark. A PRNsequence is generated by feeding the generatorwith a secret seed.

Watermark type

Visual watermark The watermark is actually reconstructed, and itsvisual quality is evaluated.

Reversible Exact restoration of the original unwatermarked

image is possible

Scheme type

Irreversible The distortion in the watermarked image is small but irreversible.

Non-blind Both the original image and the secret key(s)Semi-blind The watermark and the secret key(s)

Information type

Blind Only the secret key(s)

2. EMBEDDING MULTIPLE WATERMARKS IN THE DFT DOMAIN

DCT or DWT domain semi-blind watermarking schemes [6,7] have been shown to be robust against a number ofattacks. If a geometric attack (e.g., rotation, translation, and scaling) is tried, however, the location of the transform

coefficients will change, resulting in a weaker detection. Because of the properties of the DFT, recent research hasan emphasis on DFT-based watermarking [8,9,10].

It is possible to embed a circularly symmetric watermark in the DFT domain using the additive formula

M w(u,v) = M (u,v) + W (u,v),

where M denotes the magnitudes of DFT coefficients of the cover image, is the scaling factor, and W is thecircular watermark:

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Solachidis and Pitas [11] embed the watermark

0, if r < R1 and r > R2

W (r , ) =

1, if R1 < r < R2

in a ring covering the middle frequencies, where r = sqrt( u2+v2) and = arctan( v/u).

Licks and Jordan [12] embed a circular watermark defined as

n, if u2 + v2 = R2

W (u,v) =

0, otherwise

where n is the output from a pseudo random number (PRN) generator, and R is the radius of the watermarkinsertion circle.

In both of the above papers, the presence of the watermark is detected using the correlation

= =

= N

u

N

vw vu M vuW c

1 1

* ),(),( ,

where N x N is the size of the cover image, and ),(* vu M w are the magnitudes of DFT coefficients of the watermarked(and possibly attacked) image. The decision rule regarding the existence of a watermark is given by

H 0: the image is watermarked with W if c T H 1: the image is not watermarked with W if c < T

The threshold T is computes as T = ( 0 + 1)/2, where 0 and 1 are the expected values of the Gaussian probabilitydensity functions (pdfs) associated with the hypotheses H 0 and H 1, respectively.

Recent work [13,14] on DWT-based watermarking indicates that embedding a watermark in low frequencies isrobust to one set of attacks whereas embedding a watermark in high frequencies is robust to another set of attacks.Mehul and Priti [13] perform a two level decomposition of the cover image, and embed the visual watermarks intoLL2 and HH2 bands, respectively. In the DWT domain, the magnitudes of coefficients in the LL2 band are higherthan the magnitudes of coefficients in the HH2 band. This difference was not taken into consideration indetermining the value of the scaling factor. The authors have implemented the scheme using a scaling factor of 0.1for both bands, resulting in a highly visible distortion in all areas of the image. Tao and Eskicioglu [14] generalizethis scheme by embedding the same watermark in all four bands using first and second level decompositions. Intheir implementation, the scaling factor is larger for the lower frequency band, not causing any visible distortion inthe image. According to their results, the watermark embedded in the lowest frequencies is robust against JPEGcompression, blurring, adding Gaussian noise, rescaling, rotation, cropping, pixelation, and sharpening, and thewatermark embedded in the highest frequencies is robust against histogram equalization, intensity adjustment, andgamma correction.

We extended the multiple watermarking idea by inserting two circular watermarks in the DFT domain [15]. Nevertheless, although the insertion of a circular watermark is simple and convenient, the modified magnitudes ofthe coefficients become visible in the transform domain, giving the hacker valuable information about the locationof the watermark. An example of this visibility is given in Figure 1. The 256x256 cover image Lena iswatermarked using a circular watermark with a radius of 100 pixels, and the scaling factor 2000. Hence, thecoefficients can be modified for malicious purposes in an attempt to remove or weaken the embedded information.In this paper, we propose a watermarking scheme that does not make the location of the watermark visible in theDFT domain.

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(a) (b)

Figure 1. Embedding a circular watermark in the DFT domain.(a) Watermarked Lena, (b) Magnitudes of DFT coefficients

Watermark Embedding

1. Compute the DFT of the N x N cover image.

2. Obtain the magnitudes of DFT coefficients.

3. Divide the N x N matrix of magnitudes into four ( N /2)x( N /2) matrices M ul, M ur , M ll, M lr .4. Embedding in the upper left ( N /2)x( N /2) matrix M ul.

a. Define two frequency bands, one high and one low, based on the DFT coefficients. b. Choose a block size k , and a PRN sequence of length m, where k xm is the band size.c. Create a watermark matrix W by placing one component of the PRN sequence in each block in each

frequency band. The location in each block is randomly selected.d. Choose the scaling factor l for the low frequency band to be larger than the scaling factor h for the

high frequency band: l > h.e. Add W to M ul.

5. Copy the modified coefficients in the upper left matrix M ul to the lower right matrix M lr .

6. Embedding in the upper right ( N /2)x( N /2) matrix M ur .

a. Use the same frequency bands in step 4(a). b. Use the same block size in step 4(b), and a different PRN sequence of the same length.c. Create a watermark matrix W by placing one component of the PRN sequence in each block in each

frequency band. The location in each block is randomly selected.d. Use the scaling factor l for the low frequency band and the scaling factor h for the high frequency

band in step 4(d).e. Add W to M ur .

7. Copy the modified coefficients upper right matrix M ur to the lower left matrix M ll.

8. Obtain the DFT coefficients of the entire image using the magnitudes in matrices M ul, M ur , M ll, M lr , and thecorresponding angles.

9. Apply inverse DFT to get the watermarked image.

Watermark Detection

1. Compute = =

= N

u

N

v

w vu M vuW c1 1

* ),(),( , where ),(* vu M w are the magnitudes of DFT coefficients of the watermarked

(and possibly attacked) image.

2. If c T, the image is watermarked with W ; if c < T, the image is not watermarked with W .

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3. EXPERIMENTS

The 256x256 test image Lena was watermarked using the algorithm proposed in Section 2. The original image, thewatermarked image, and their DFT magnitudes are given in Figure 2. For a 256x256 image, the DFT coefficients inthe first and 129 th rows are not symmetric with any other row, and the DFT coefficients in the first and 129 th columns are not symmetric with any other column. This gives us 127x127 (16,129) magnitudes that can be

modified in each of the four matrices.

(a) (b) (c) (d)

Figure 2. (a) Original Lena, (b) the DFT magnitudes of original Lena, (c) Watermarked Lena,(d) the DFT magnitudes of watermarked Lena.

In the experiments, the DFT coefficients in each matrix were put in a zig-zag order to define the two frequency bands as follows: The high frequency band was chosen using the first 5,000 highest frequency DFT coefficients,and the low frequency band was chosen using the DFT coefficients from 10,001 to 15,000. The block size k was100, and the length of the PRN sequence was 50. Since the magnitudes of lower frequency DFT coefficients arehigher than the magnitudes of higher frequency DFT coefficients, the scaling factor for each of the two bands wasdetermined by taking this difference into consideration. The scaling factor for the higher frequency band was 3000,and the scaling factor for the lower frequency band was 7000.

The locations of the modified DFT coefficients are given in Figure 3. It should be noted that the locations used inthe upper left area are different from the locations used in the upper right area.

(a) (b) (c)

Figure 3. (a) the modified DFT coefficients in the high frequency band,(b) the modified DFT coefficients in the low frequency band,(c) the modified DFT coefficients in both of the frequency bands.

The watermarked image was subjected to the same Matlab attacks in [5] (i.e., JPEG compression, Gaussian noise,low pass filtering, resizing, histogram equalization, contrast adjustment, gamma correction, rotation, cropping, andscaling). The attacked images and the attack parameters are shown in Figure 4. For the rotation attack, we assumedthat the image was rotated by a degree that can be represented as an integer. Hence, to obtain the maximumcorrelation, the image was rotated by one degree in each run. In the worst case scenario, the image will have to berotated 180 times to find the highest correlation.

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JPEG (quality factor = 50) Noise (mean = 0, variance = 0.005) Low pass filtering (window size = 3x3)

Resize (256 128 256) Histogram equalization (automatic) Contrast adjustment ([l=0 h=0.8],[b=0 t =1])

Gamma correction (1.5) Rotation (4 0) Cropping (32 pixels on each side)

Scale (256x256 512x512)

Figure 4. Attacks on the watermarked image

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We obtained the empirical pdf of each attacked image using 200 watermarked images, each with a different seed togenerate the pseudo random number (PRN) sequence for both watermarks. The correlation process was also appliedto a non-watermarked image for each of the 200 PRN sequences. We then computed the threshold T for each attackusing the formula by T = ( 0 + 1)/2. The pdfs for the unattacked image and the ten attacks are shown in Figure 5.

Unattacked Image JPEG compression Gaussian noise Low-pass filtering

H i g h

F r e q u e n c y

-0.2 0 0.2 0.4 0.6 0.8 1 1.20

2

4

6

8

10

12

14

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0. 30

5

10

15

-0.2 -0.1 0 0.1 0.2 0.3 0.4 0. 50

2

4

6

8

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12

14

16

18

-0.2 -0.1 0 0.1 0.2 0.3 0.4 0.50

2

4

6

8

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12

14

L o w

F r e q u e n c y

-0.4 -0.2 0 0.2 0.4 0.6 0.8 10

5

10

15

-0 .3 - 0. 2 - 0. 1 0 0 .1 0 .2 0 .3 0 .4 0 .5 0 .6 0. 70

2

4

6

8

10

12

14

16

-0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.60

2

4

6

8

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12

-0. 3 - 0. 2 - 0. 1 0 0.1 0. 2 0. 3 0. 4 0. 5 0.60

2

4

6

8

10

12

Resizing Scaling Rotation Cropping

H i g h

F r e q u e n c y

-0. 2 -0. 15 -0. 1 -0. 05 0 0. 05 0. 1 0.15 0. 20

2

4

6

8

10

12

14

-1 -0. 8 - 0. 6 - 0. 4 -0. 2 0 0 .2 0 .4 0. 6 0. 8 1

0

1

2

3

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5

6

7

8

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10

-1 -0.8 -0.6 -0. 4 -0. 2 0 0. 2 0. 4 0. 6 0. 8 10

2

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12

-0 .2 - 0. 1 0 0 .1 0 .2 0 .3 0 .4 0 .5 0. 6 0. 7 0.80

2

4

6

8

10

12

14

L o w

F r e q u e n c y

-0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.50

2

4

6

8

10

12

14

-1 -0. 8 - 0. 6 - 0. 4 -0. 2 0 0 .2 0 .4 0. 6 0. 8 1

0

2

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12

14

-1 -0.8 -0.6 -0. 4 -0. 2 0 0. 2 0. 4 0. 6 0. 8 10

2

4

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12

-0. 3 - 0. 2 - 0. 1 0 0.1 0. 2 0. 3 0. 4 0. 5 0.60

1

2

3

4

5

6

7

8

9

10

Histogram equalization Intensity adjustment Gamma correction

H i g h

F r e q u e n c y

-0.4 -0.2 0 0.2 0.4 0.6 0.8 10

2

4

6

8

10

12

14

16

-0.2 0 0.2 0.4 0.6 0.8 1 1. 20

2

4

6

8

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12

14

-0.4 -0.2 0 0.2 0.4 0.6 0.8 10

2

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L o w

F r e q u e n c y

-0.4 -0.2 0 0.2 0.4 0.6 0.8 10

2

4

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8

10

12

14

-0.4 -0.2 0 0.2 0.4 0.6 0.8 10

2

4

6

8

10

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16

-0.4 -0.2 0 0.2 0.4 0.6 0.8 10

2

4

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10

12

14

Figure 5. Probability density functions (pdfs)

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The percentages of false negatives and false positives, and the threshold values for the 200 decisions are given inTables 2 and 3, respectively.

Table 2. Thresholds and percentage of false negatives

High frequency band Low frequency bandAttacks\Frequency Bands T % T %

Unattacked image 0.297 0.25 0.280 0.00

JPEG compression 0.018 22.75 0.200 0.25

Gaussian noise 0.060 12.25 0.189 0.00

Low pass filtering 0.166 6.75 0.144 1.00

Resizing -0.006 25.00 0.123 2.25

Scaling 0.156 18.50 0.264 12.25

Rotation 0.101 16.75 0.088 18.50

Cropping 0.307 0.00 0.164 2.50Histogram equalization 0.282 0.75 0.275 0.00

Intensity adjustment 0.304 0.00 0.279 0.00

Gamma correction 0.291 0.50 0.275 0.00

Table 3. Thresholds and percentages of false positives

High frequency band Low frequency bandAttacks\Frequency BandsT % T %

Unattacked image 0.297 0.00 0.280 0.00JPEG compression 0.018 23.00 0.200 0.50

Gaussian noise 0.060 9.75 0.189 0.00

Low pass filtering 0.166 1.75 0.144 3.00

Resizing -0.006 24.00 0.123 4.25

Scaling 0.156 21.75 0.264 19.50

Rotation 0.101 18.50 0.088 19.25

Cropping 0.307 0.00 0.164 1.25

Histogram equalization 0.282 0.00 0.275 0.00

Intensity adjustment 0.304 0.00 0.279 0.00

Gamma correction 0.291 0.00 0.275 0.00

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4. CONCLUSIONS

We presented a semi-blind watermarking scheme that is more secure and robust than a circular watermarkingscheme. Our results can be summarized as follows:

The scaling factor for embedding the watermark in each of the two frequency bands can determined by the

relative magnitudes of the DFT coefficients of the cover image. The magnitudes of lower frequency DFTcoefficients are higher than the magnitudes of higher frequency DFT coefficients. It is therefore possible toassign a larger scaling factor for the lower frequency band using a certain percentage of the magnitudes.

If the watermark is embedded in higher frequencies, the percentages of false negatives are higher for one groupof attacks (i.e, JPEG compression, Gaussian noise, low pass filtering, resizing, and scaling), and lower foranother group of attacks (i.e., rotation and cropping). The percentages for the remaining attacks (i.e., histogramequalization, contrast adjustment, and gamma correction) are almost identical for both of the frequency bands,

being either zero or close to zero.

If the watermark is embedded in lower frequencies, the percentages of false negatives are lower for one groupof attacks (i.e, JPEG compression, Gaussian noise, low pass filtering, resizing, and scaling), and higher foranother group of attacks (i.e., rotation and cropping).

Similar results were obtained for false positives. With respect to the percentages of false negatives, the onlyexception is low pass filtering even though the percentages for high and low frequency bands are close to eachother.

If the smaller percentage is taken for a given attack, we obtain the following table. Note that for a majority ofthe attacks, the percentages are either zero or close to zero.

False negatives False positivesAttacks\Frequency BandsT % T %

Unattacked image 0.280 0.00 0.280 0.00

JPEG compression 0.200 0.25 0.200 0.50

Gaussian noise 0.189 0.00 0.189 0.00

Low pass filtering 0.144 1.00 0.166 1.75

Resizing 0.123 2.25 0.123 4.25

Scaling 0.264 12.25 0.264 19.50

Rotation 0.101 16.75 0.101 18.50

Cropping 0.307 0.00 0.307 0.00

Histogram equalization 0.275 0.00 0.275 0.00

Intensity adjustment 0.279 0.00 0.2790.00

Gamma correction 0.275 0.00 0.275 0.00

In our experience, when a circular watermark is embedded in a cover image, it introduces two major drawbacks:(a) The location of the watermark is visible in the DFT domain, and (b) some of the false negatives and false

positives are rather high, going up to 55% [15]. With the proposed scheme, the location of the watermark isdefinitely not visible, and the highest percentage computed in the experiments is 25%.

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In the proposed semi-blind image watermarking scheme, the watermark detector correlates the magnitudes of the ofDFT coefficients of the watermarked (and possibly attacked) image with the components of the watermark. It isimportant to note that the determination of a threshold relies on a prior knowledge of the nature of the attack. One

possible avenue of research is to observe how the DFT coefficients are modified after each attack, and train thedetector based on this modification.

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