Embedding Multiple Watermarks in the DFT Domain Using Low and High Frequency Bands Emir Ganic, Scott D. Dexter, Ahmet M. Eskicioglu Department of Computer and Information Science, CUNY Brooklyn College 2900 Bedford Avenue, Brooklyn, NY 11210, USA
[email protected], {dexter, eskicioglu}@sci.brooklyn.cuny.edu ABSTRACT Although semi-blind and blind watermarking schemes based on Discrete Cosine Transform (DCT) or Discrete Wavelet Transform (DWT) are robust to a number of attacks, they fail in the presence of geometric attacks such as rotation, 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 has increased in the last few years. In a recent paper, we generalized a circular watermarking idea to embed multiple watermarks 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 focus is 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 the watermark embedded in lower frequencies is robust to one set of attacks, and the watermark embedded in higher frequencies is robust to a different set of attacks. Keywords: semi-blind image watermarking, classification of image watermarking schemes, Discrete Fourier Transform, 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 be analogous to encryption and decryption [4]: •
Encryption makes multimedia content unintelligible through a reversible mathematical transformation. In symmetric key encryption, which is commonly used for protecting multimedia elements, each encryption transformation EK is defined by an encryption algorithm E and a key K. Given a plaintext M, the transformation produces the ciphertext C = EK(M). Each decryption transformation DK is defined with a decryption algorithm D and the key K. For a given K, DK = EK-1 such that DK(EK(M)) = M.
•
Watermarking embeds data directly into a multimedia element. The embedding transformation EK is defined by an embedding algorithm E and a key K. In watermarking, the usual approach is to use a symmetric key although there is a recent trend to use asymmetric techniques. Given a cover image I and a watermark W, the transformation produces the watermarked image IW = EK(I,W). Each detection (or extraction) transformation DK is defined with a detection (or extraction) algorithm D and the key K. For a given K and the watermarked image IW, the watermark is either detected or extracted: W = DK(IW).
In digital distribution networks, copyrighted multimedia content is commonly protected by encryption: •
Cable, satellite, and terrestrial distribution: A conditional access (CA) system provides the encryption technology to control access to digital television services. Authorized users can use the appropriate decoder equipped 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 DRM system include secure delivery of content, prevention of unauthorized access, enforcement of usage rules, and monitoring of the use of content.
1
•
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 in transmission 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 video file. 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]: broadcast monitoring, owner identification, proof of ownership, transaction tracking, content authentication, copy control, and device control. In particular, watermarking appears to be useful in plugging the analog hole in consumer electronics devices [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 type of 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 Domain type
Class Pixel Transform
Watermark type
Pseudo random number (PRN) sequence (having a normal distribution with zero mean and unity variance) Visual watermark
Scheme type
Information type
Brief description Pixels values are modified to embed the watermark. Transform coefficients are modified to embed the watermark. Recent popular transforms are Discrete Cosine Transform (DCT), Discrete Wavelet Transform (DWT), and Discrete Fourier Transform (DFT). Allows the detector to statistically check the presence or absence of a watermark. A PRN sequence is generated by feeding the generator with a secret seed. The watermark is actually reconstructed, and its visual quality is evaluated.
Reversible
Exact restoration of the original unwatermarked image is possible
Irreversible
The distortion in the watermarked image is small but irreversible.
Non-blind Semi-blind Blind
Both the original image and the secret key(s) The watermark and the secret key(s) 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 of attacks. 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 has an 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 Mw(u,v) = M(u,v) + αW(u,v), where M denotes the magnitudes of DFT coefficients of the cover image, α is the scaling factor, and W is the circular watermark:
2
Solachidis and Pitas [11] embed the watermark 0, if r < R1 and r > R2 W(r,θ) = ±1, if R1 < r < R2 in a ring covering the middle frequencies, where r = sqrt(u2+v2) and θ = 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 watermark insertion circle.
In both of the above papers, the presence of the watermark is detected using the correlation N
c=
N
∑∑ W (u, v)M
* w (u , v)
,
u =1 v =1
where NxN is the size of the cover image, and M w* (u , v) 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 H0: the image is watermarked with W if c ≥ T H1: the image is not watermarked with W if c < T The threshold T is computes as T = (µ0 + µ1)/2, where µ0 and µ1 are the expected values of the Gaussian probability density functions (pdfs) associated with the hypotheses H0 and H1, respectively. Recent work [13,14] on DWT-based watermarking indicates that embedding a watermark in low frequencies is robust 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 into LL2 and HH2 bands, respectively. In the DWT domain, the magnitudes of coefficients in the LL2 band are higher than the magnitudes of coefficients in the HH2 band. This difference was not taken into consideration in determining the value of the scaling factor. The authors have implemented the scheme using a scaling factor of 0.1 for both bands, resulting in a highly visible distortion in all areas of the image. Tao and Eskicioglu [14] generalize this scheme by embedding the same watermark in all four bands using first and second level decompositions. In their implementation, the scaling factor is larger for the lower frequency band, not causing any visible distortion in the image. According to their results, the watermark embedded in the lowest frequencies is robust against JPEG compression, blurring, adding Gaussian noise, rescaling, rotation, cropping, pixelation, and sharpening, and the watermark embedded in the highest frequencies is robust against histogram equalization, intensity adjustment, and gamma 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 of the coefficients become visible in the transform domain, giving the hacker valuable information about the location of the watermark. An example of this visibility is given in Figure 1. The 256x256 cover image Lena is watermarked using a circular watermark with a radius of 100 pixels, and the scaling factor 2000. Hence, the coefficients 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 the DFT domain.
3
(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 NxN cover image.
2.
Obtain the magnitudes of DFT coefficients.
3.
Divide the NxN matrix of magnitudes into four (N/2)x(N/2) matrices Mul, Mur, Mll, Mlr.
4.
Embedding in the upper left (N/2)x(N/2) matrix Mul. 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 kxm 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 αl for the low frequency band to be larger than the scaling factor αh for the high frequency band: αl > αh. e. Add W to Mul.
5.
Copy the modified coefficients in the upper left matrix Mul to the lower right matrix Mlr.
6.
Embedding in the upper right (N/2)x(N/2) matrix Mur. 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 αl for the low frequency band and the scaling factor αh for the high frequency band in step 4(d). e. Add W to Mur.
7.
Copy the modified coefficients upper right matrix Mur to the lower left matrix Mll.
8.
Obtain the DFT coefficients of the entire image using the magnitudes in matrices Mul, Mur, Mll, Mlr, and the corresponding angles.
9.
Apply inverse DFT to get the watermarked image.
Watermark Detection N
1.
Compute c =
N
∑∑ W (u, v)M
* w (u , v)
, where M w* (u , v) are the magnitudes of DFT coefficients of the watermarked
u =1 v =1
(and possibly attacked) image. 2.
If c ≥ T, the image is watermarked with W; if c < T, the image is not watermarked with W.
4
3. EXPERIMENTS The 256x256 test image Lena was watermarked using the algorithm proposed in Section 2. The original image, the watermarked image, and their DFT magnitudes are given in Figure 2. For a 256x256 image, the DFT coefficients in the first and 129th rows are not symmetric with any other row, and the DFT coefficients in the first and 129th 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 was 100, and the length of the PRN sequence was 50. Since the magnitudes of lower frequency DFT coefficients are higher than the magnitudes of higher frequency DFT coefficients, the scaling factor for each of the two bands was determined 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 in the 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, and scaling). The attacked images and the attack parameters are shown in Figure 4. For the rotation attack, we assumed that the image was rotated by a degree that can be represented as an integer. Hence, to obtain the maximum correlation, the image was rotated by one degree in each run. In the worst case scenario, the image will have to be rotated 180 times to find the highest correlation. 5
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 (40)
Cropping (32 pixels on each side)
Scale (256x256 → 512x512)
Figure 4. Attacks on the watermarked image
6
We obtained the empirical pdf of each attacked image using 200 watermarked images, each with a different seed to generate the pseudo random number (PRN) sequence for both watermarks. The correlation process was also applied to a non-watermarked image for each of the 200 PRN sequences. We then computed the threshold T for each attack using the formula by T = (µ0 + µ1)/2. The pdfs for the unattacked image and the ten attacks are shown in Figure 5. Unattacked Image
JPEG compression
14
Gaussian noise
15
14
16
12
High Frequency
Low-pass filtering
18
12
14 10
10 10
12
8
10
8
6
8
6
5
6
4
4 4
2
0 -0.2
2
2
0
0.2
0.4
0.6
0.8
1
1.2
15
0 -0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
16
0 -0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
0 -0.2
12
12
10
10
8
8
6
6
4
4
2
2
-0.1
0
0.1
0.2
0.3
0.4
0.5
Low Frequency
14 12 10 10 8 6 5 4 2 0 -0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0 -0.3
-0.2
-0.1
0
Resizing
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 -0.2
-0.1
0
Scaling
14
0.1
0.2
0.3
0.4
0.5
0.6
0 -0.3
-0.2
-0.1
Rotation
10
0
0.1
0.2
0.3
0.4
0.5
0.6
Cropping
12
14
9
High Frequency
12
12
10
8 10
10
7 8 6
8
8
5 6
6 6
4 4
3
4
4
2 2
2
2
1 0 -0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
0 -1
14
14
12
12
10
10
8
8
6
6
4
4
2
2
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0 -1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
12
0 -0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
10
Low Frequency
9 10
8 7
8 6 6
5 4
4
3 2
2 1
0 -0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
0 -1
High Frequency
Histogram equalization
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0 -1
Intensity adjustment
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0 -0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
Gamma correction
16
14
14
14
12
12
10
10
8
8
6
6
4
4
12 10 8 6 4 2
2 0 -0.4
Low Frequency
-0.8
-0.2
0
0.2
0.4
0.6
0.8
1
0 -0.2
2
0
0.2
0.4
0.6
0.8
1
1.2
0 -0.4
14
16
14
12
14
12
-0.2
0
0.2
0.4
0.6
0.8
1
-0.2
0
0.2
0.4
0.6
0.8
1
12 10
10 10
8
8 8
6
6 6
4
4 4
2
0 -0.4
2
2
-0.2
0
0.2
0.4
0.6
0.8
1
0 -0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0 -0.4
Figure 5. Probability density functions (pdfs)
7
The percentages of false negatives and false positives, and the threshold values for the 200 decisions are given in Tables 2 and 3, respectively. Table 2. Thresholds and percentage of false negatives
Attacks\Frequency Bands
High frequency band
Low frequency band
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
Histogram equalization
0.282
0.75
0.275
2.50 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
Attacks\Frequency Bands
High frequency band
Low frequency band
T
%
T
%
Unattacked image
0.297
0.00
0.280
0.00
JPEG 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
0.164
1.25
Histogram equalization
0.282
0.00 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
8
4. CONCLUSIONS We presented a semi-blind watermarking scheme that is more secure and robust than a circular watermarking scheme. 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 DFT coefficients are higher than the magnitudes of higher frequency DFT coefficients. It is therefore possible to assign 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 group of attacks (i.e, JPEG compression, Gaussian noise, low pass filtering, resizing, and scaling), and lower for another group of attacks (i.e., rotation and cropping). The percentages for the remaining attacks (i.e., histogram equalization, 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 group of attacks (i.e, JPEG compression, Gaussian noise, low pass filtering, resizing, and scaling), and higher for another group of attacks (i.e., rotation and cropping).
•
Similar results were obtained for false positives. With respect to the percentages of false negatives, the only exception is low pass filtering even though the percentages for high and low frequency bands are close to each other.
•
If the smaller percentage is taken for a given attack, we obtain the following table. Note that for a majority of the attacks, the percentages are either zero or close to zero. False negatives
Attacks\Frequency Bands
•
False positives
T
%
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
Histogram equalization
0.275
0.00
0.275
0.00 0.00
Intensity adjustment
0.279
0.00
0.279
0.00
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 is definitely not visible, and the highest percentage computed in the experiments is 25%.
9
In the proposed semi-blind image watermarking scheme, the watermark detector correlates the magnitudes of the of DFT coefficients of the watermarked (and possibly attacked) image with the components of the watermark. It is important 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 the detector based on this modification.
REFERENCES [1]
A. M. Eskicioglu and E. J. Delp, “Overview of Multimedia Content Protection in Consumer Electronics Devices,” Signal Processing: Image Communication, 16(7), pp. 681-699, April 2001.
[2]
A. M. Eskicioglu, J. Town and E. J. Delp, “Security of Digital Entertainment Content from Creation to Consumption,” Signal Processing: Image Communication, Special Issue on Image Security, 18(4), pp. 237262, April 2003.
[3]
E. T. Lin, A. M. Eskicioglu, R. L. Lagendijk, and E. J. Delp, “Advances in Digital Video Content Protection,” Proceedings of the IEEE, Special Issue on Advances in Video Coding and Delivery, 2004.
[4]
I. J. Cox, M. L. Miller, and J. A. Bloom, Digital Watermarking, Morgan Kaufmann Publishers, 2002.
[5]
Content Protection Status Report III, http://judiciary.senate.gov/special/mpaa110702.pdf.
[6]
M. Barni, F. Bartolini, V. Cappellini, and A. Piva, “DCT-Domain System for Robust Image Watermarking,” Signal Processing, Special Issue on Copyright Protection and Control, 66(3), 1998, pp. 357-372.
[7]
R. Dugad, K. Ratakonda, and N. Ahuja, “A New Wavelet-Based Scheme for Watermarking Images,” Proceedings of 1998 International Conference on Image Processing (ICIP 1998), Vol. 2, Chicago, IL, October 4-7, 1998, pp. 419-423.
[8]
R. Caldelli, M. Barni, F. Bartolini, A. Piva, “Geometric-Invariant Robust Watermarking through Constellation Matching in the Frequency Domain,” Proceedings of the 2000 International Conference on Image Processing (ICIP 2000), Vancouver, BC, Canada, September 10-13, 2000, Vol. II, Vancouver, Canada, September 10-13, 2000, pp. 65-68.
[9]
S. Pereira and T. Pun, “Robust Template Matching for Affine Resistant Image Watermarks,” IEEE Transactions on Image Processing, 9(6), June 2000, pp. 1123-1129.
[10]
C.-Y. Lin, M. Wu, J. A. Bloom, I. J. Cox, M. L. Miller, Y. M. Lui, “Rotation, Scale, and Translation Resilient Watermarking for Images,” IEEE Transactions on Image Processing, 10(5), May 2001.
[11]
V. Solachidis and I. Pitas, “Circularly Symmetric Watermark Embedding in 2-D DFT Domain,” Proceedings of the 1999 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 1999), Vol. 6, Phoenix, AZ, March 15-19, 1999, pp. 3469-3472.
[12]
V. Licks and R. Jordan, “On Digital Image Watermarking Robust to Geometric Transformations,” Proceedings of 2000 International Conference Image Processing (ICIP 2000), Vol. 3, Vancouver, BC, Canada, September 10-13, 2000, pp. 690-693.
[13]
R. Mehul and R. Priti, “Discrete Wavelet Transform Based Multiple Watermarking Scheme,” Proceedings of IEEE Region 10 Technical Conference on Convergent Technologies for the Asia-Pacific, Bangalore, India, October 14-17, 2003.
[14]
P. Tao and A. M. Eskicioglu, “A Robust Multiple Watermarking Scheme in the Discrete Wavelet Transform Domain,” Optics East 2004 Symposium, Internet Multimedia Management Systems V Conference, Philadelphia, PA, October 25-28, 2004.
[15]
E. Ganic and A. M. Eskicioglu, “A DFT-Based Semi-Blind Multiple Watermarking Scheme for Images,” 4th New York Metro Area Networking Workshop, The Graduate Center, The City University of New York, September 10, 2004. Available at http://www.nyman-workshop.org/2004.
November
7,
2002,
available
at
10
