AFOSR PROGRAM REVIEW JUNE 5-7, 2003 PRINCETON, NJ DATA HIDING IN TIME-FREQUENCY DISTRIBUTION OF IMAGES Bijan Mobasseri ECE Department Villanova University Villanova, PA 19085

2 Outline Data hiding definition and modalities Motivation for using TF distributions Wigner distribution Watermarking model Embedding and detection Capacity Future work

3 Data hiding requirements Data hiding must meet at least the following three conditions: –Transparency; no visible impact on the cover signal –Robustness; Survive “friendly fire”: filtering, compression, cropping but break under attacks –Security; hidden data should not be easily removed or replaced

4 Data hiding modalities Watermarking –Message itself is not secret: owner identification, copyright protection, fingerprinting –Transparency, robustness and security still apply. –Embedding capacity not a major issue –In authentication applications, watermark must be content- dependent, secure but somewhat brittle Steganography –Used as a covert channel, the message is secret and its very presence within the host data must not be detectable

5 Information hiding as a game Information hiding has been stated as a game between two cooperative players (embedder and decoder) and an opponent (attacker) The first party tries to maximize a payoff function and the opponent tries to minimize it (Moulin, O’Sullivan)

6 Data hiding paradigm embedder attackerdecoder P. Moulan, J, O’Sullivan, IEEE Trans IT, March 2003

7 New domain Digital watermarking has heretofore been applied in either spectral or temporal/spatial domains but not in both simultaneously. The ability to watermark joint time-frequency cells provides additional control, capacity and security DCT TFD t f distinct keys

8 Time-varying data hiding t f Watermark can be designed to follow a trajectory in time- frequency plane Attackers have a harder time targeting watermarked bins or have to flood the whole TF plane Attacks with known T-F signatures can be circumvented An N-point signal has N 2 TF distribution cells a substantial fraction of which is available for watermarking

9 Previous work S. Stankovic, I. Djurovic, I. Pitas, “Watermarking in the space/spatial-frequency domain using two-dimensional Radon-Wigner distribution, “IEEE Transaction on Image Processing, vol. 10, no. 4, pp , April They add a sinusoidal pattern to the image in a way that is only detectable in time-frequency domain. It is presented as a watermarking algorithm Our approach hides data in the transform domain instead

10 Generating TFD: Wigner Distribution WD of function x is Fourier transform of its local autocorrelation function. The discrete-time WD of a 1-D signal is given below

11 WD at work

12 Watermarking model We parallel DCT watermarking by additively modifying selected T-F cells of WD. This simple model will not work unless certain precautions are taken into account

13 The Inverse Wigner Not every two dimensional function is an allowed time-frequency representation It is possible that no signal may be found that has the given TFD This is a synthesis problem and can be stated as follows Given a target (watermarked) WD Y, find the corresponding signal x whose Wigner distribution is closest to Y in some sense

14 A time-frequency filtering problem C (1) R (2) f1 f2  1 =Mf 1 ’2’2 M **  * :inadmissible   :admissible M:mapping function H:transformation  2 =HM  1 ’2 2’2 2  1 =Mf 1

15 Solutions There are a number of solutions to this problem. For DTWD: V. Kumar et al, “Discrete Wigner synthesis,” Signal Processing, vol. 11, pp , For DWD: S. Nelatury, B. Mobasseri,” Synthesis of discrete-time discrete- frequency Wigner Distribution “ IEEE Signal Processing Letters, in press.

16 Example: time-frequency filtering

17 2D Wigner Formally, the 2D Wigner Distribution is a 4-D function, In this work, we avoid this by applying a 1D Wigner to each block of image

18 1D Wigner distribution of 2D block Let define an NxN image block Define an “equivalent” linear array then do a 1D Wigner on it Column-wisezigzagrandom

19 Picking the order Since WD reflects local autocorrelation of the signal, different pixel arrangements produce distinctly different TFDs However, we are only interested in the integrity of signal synthesis. In this sense, it makes no difference how is found from X

20 Evidence SNR>300 dB originalreconstructed

21 Compression effect on time- frequency signature If robustness to compression is desired, only compression-resistant TF cells must be watermarked. We evaluate a simple error measure and apply it across JPEG Q-factor

22 Error surfaces

23 Error surfaces Q=30Q=50

24 Which component to watermark? JPEG follows YUV(luma-hue-saturation) color model. We have found that the TF signature of saturation band is most robust to compression

25 Band energy

26 MSE analysis

27 Watermarking Geometry Tile the image: –Exhaustively –Randomly (keyed) Embed one bit, spread spectrum- wise, in the WD of each block Use a unique key per block. Image is then tiled by a reference template

28 Algorithm Summary

29 Watermark detection Watermark is detected based on the following hypothesis testing –Ho: –H1: Rejecting the null hypothesis, when it is true, amounts to the probability of false alarm(picture is incorrectly decided to carry watermark)

30 Test statistic For candidate TF cells, evaluate the following test statistic The null hypothesis will be rejected at  significance level if

31 Watermark strength vs. image PSNR WSR(dB)SNR(dB)  x4 blocks, each carrying one bit Q=50

32 Results

33 Data hiding in saturation band:16x16 blocks Q=5 Q=50 Virtually identical performance across all Q-factors

34 Capacity: are TF cells independent? [Richard’01] has shown that: For all, the number of linearly independent components of discrete WD of x is upper bounded by (N even) For 8x8 blocks, there are 4096 components of which1056 are independent 8x8 DCT produces a maximum of 64 coefficients

35 Payload numbers Capacity=N 2 /block_size Larger block size provides bigger PG and watermark survival at lower Q In lena(256 2 ), we can embed 4096 bits using 4x4 blocks at WSR= -13dB Reliable detection is possible down to Q=25

36 Conclusions and future work A new transform domain for sata hiding is introduced It features high capacity, low probability of intercept and low JPEG Q-factor operation Need work on blind detection Robustness to geometric transformations Capacity and Steganalysis benchmarking

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