Discussion

Chapter 4

An Oracle for Motion-Incoherent Watermarking

Inter-frame collusion attacks have been studied extensively and many watermarking schemes have been proposed in recent years to resist such attacks. However, for a given watermarking scheme, there is no tool available to assess whether the produced watermark is resistant to the inter-frame collusion attacks or not. Today, this assessment relies on a computationally expensive procedure: (1) a sequence is wa- termarked, (2) the watermarked sequence is subjected to different inter-frame collusion attacks and (3) the detector checks the presence of the watermark in the attacked sequences. Inter-frame collusion re- sistance can be guaranteed only if the watermark survives all the attacks. Similarly, in the attacker-side, it may be of interest to know whether the inter-frame collusion will be effective on a given watermarked sequence or more importantly, whether an attacked sequence still carries the watermark. This assess- ment is more challenging since in many applications of watermarking like fingerprinting and copyright protection, the attacker may not have access to the watermark detector. If a tool which can predict the presence of watermark is available to the attacker, the attack efficiency can be improved by changing the attack parameters. For example, the attacker may increase the temporal window width of the FTF attack until the watermark becomes undetectable.

This chapter presents a novel technique to evaluate the inter-frame collusion resistance without going through the expensive attack-detect procedure. As shown in the previous chapter, the motion- coherency in the watermark is a sufficient condition to guarantee the resistance to inter-frame collusion.

So, assessing the motion-coherency in the watermark is a sufficiency test for inter-frame collusion resis- tance. We propose a simple oracle which reports the presence/absence of motion-incoherent watermark in a given sequence. In other words, the oracle reports whether a given sequence carries a watermark

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4.1. RELATED WORK 69 which is susceptible to inter-frame collusion or not. The oracle does not make use of any watermark detection algorithm, thereby making it useful to the attacker as well. The proposed oracle exploits the motion-compensated prediction module present in the state-of-the-art video coding techniques. It will be shown that it is possible to extract some statistical features, which can distinguish between the presence of motion-coherent (MC) and that of motion-incoherent (MIC) watermarks, from the motion- compensated prediction error frames. These features are then used to train a pattern classifier which discriminates between the prediction error frames corresponding to a sequence carrying the MC water- mark and that carrying the MIC watermark. The proposed system is presented in Section 4.2, after a review of related work in Section 4.1. Experimental results are then reported in Section 4.3 to validate the accuracy of the proposed system.

4.1 Related Work

In a previous work [BK04], a steganalysis technique has been introduced to distinguish watermarked video contents from the non-watermarked video material. The underlying idea is to exploit the sen- sitivity of some watermarking systems against a certain class of collusion attacks. For example, the temporal frame averaging (TFA) can be introduced to detect the presence of uncorrelated watermarks embedded in successive frames.

Many video watermarking algorithms can be reduced to a frame-by-frame additive procedure as written below [DD03a]

y_k =x_k+w_k, w_k∼ N(0, σ_w²) (4.1.1) wherex_kis the frame at instantkin the host video sequence,y_kthe corresponding watermarked frame andw_kthe watermark signal embedded at instantk, assumed to be normally distributed with zero mean and a variance ofσ²_w. If the watermarked sequence is temporally averaged with an odd window length ofT + 1, the resulting attacked framesy¯_kare given by

¯

y_k= 1 T + 1

X

i∈W_k

y_i (4.1.2)

where W_k = {k −T /2, k−T /2 + 1,· · · , k+T /2}is the set of temporal indices in the averaging window. When y_k is substituted by Equation (4.1.1) in Equation (4.1.2), the following equation is obtained

¯

y_k= 1 T + 1

X

i∈W_k

x_i + 1 T + 1

X

i∈W_k

w_i = ¯x_k+ ¯w_k (4.1.3)

4.1. RELATED WORK 70 Assuming that the host frames in the temporal window are perceptually similar, the difference framez_k =y_k−y¯_kbetween watermarked and attacked contents can be approximated as follows:

z_k = (xk−x¯_k) + (wk−w¯_k)≈w_k−w¯_k . (4.1.4) Depending on the sensitivity of considered watermarking algorithm to the TFA, the difference frame z_k will exhibit different statistics. In particular, if the watermarks embedded in successive frames are uncorrelated, averagingT + 1watermarks leads to a normally distributed signal with zero mean and a variance of _T^σ₊₁^2w , and the difference framez_kcan be modelled as

z_k≈w_k−w¯_k ∼ N

0, T T + 1σ²_w

. (4.1.5)

Therefore, if the tested sequence is carrying a watermark,z_k will be Gaussian. On the other hand, if the video is not watermarked, the difference will not be Gaussian. Based on the Gaussianity ofz_k, one can thus decide whether a watermark is present or not. A classifier can be trained using some features extracted fromz_k to make this decision. In [BK04], the authors proposed to use the kurtosis, the entropy and the25^thpercentile.

The kurtosis [RS00] of a random variableXis the forth central moment defined as:

Kurtosis = 1

σ_x⁴NE(x_i−µ_x)⁴

whereµ_xandσ_xare respectively the mean and the standard deviation andEis the expectation operator.

The kurtosis is the degree of peakedness of the corresponding distribution. The kurtosis for a normal distribution is3and varies for most of the other distributions.

The entropy is a measure of randomness in a given distribution. The entropy estimate is given by Entropy = −X

PX(i) logPX(i) (4.1.6)

where PX(i)is an estimate for probability and the summation is over all the estimated probabilities.

The entropy estimate from a watermarked sequence is expected to have a higher value as compared to that estimated from the host sequence. Finally, the25^th percentile of a distribution is the value above which25%of points in the histogram reside.

This steganalysis scheme accurately detects the presence (or absence) of uncorrelated watermarks within static video contents. However, its performance is likely to be severely degraded as soon as some dynamic components, e.g. moving objects and/or camera motion, are present in the video. Indeed, the energy of (xk −x¯_k) in Equation (4.1.4) will no longer be negligible, thus interfering with the

4.2. PROPOSED SYSTEM 71