4.2 Proposed System
4.2.4 Oracle Design
In Section 4.2.2, it is shown that there is a statistical difference in the local variance histograms of the PEFs corresponding to a sequence carrying an MC watermark and that carrying an MIC watermark.
Based on this difference in the local variance histograms, an oracle for the sequences carrying an MIC watermark is now designed. The first step in the design process is to study how the difference in the histograms are reflected in the distribution parameters of the corresponding Gamma approximations.
The study is performed with three test video sequences: Antibes, Foreman and Mobile. The Antibes is a synthetic sequence made from a panoramic image with a simple horizontal translation of 2 pix- els/frame from left to right. The other two sequences are standard MPEG test sequences with complex motion. The sequences are marked using the SS scheme, which always embeds MIC watermarks. The embedding strength of the watermark is chosen such that a PSNR value of38dB is maintained for the watermarked sequences.
First, the PEFs of the uncompressed sequences are analyzed. By using the hierarchical variable size block-matching algorithm [CW99], the P-PEF and B-PEF are computed for both the host video sequences and the watermarked ones. Subsequently, the local variance is estimated in each point by using a3×3sliding window. Finally, the distribution parameters of their Gamma approximations are calculated using Equations 4.2.18 and 4.2.19. The estimated scale and shape parameters corresponding to the P-PEFs are plotted in Figure 4.3 for different values of the upper-threshold τ. It is observed that the scale-shape parameters are clustered into two regions: one corresponding to MC watermark
4.2. PROPOSED SYSTEM 80
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scale
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Figure 4.3: Scale-Shape plots corresponding to the P-PEFs from the Antibes, Foreman and the Mobile sequences for different thresholds of the estimated local variance data. Each gray circles (resp. black squares) correspond to one PEF from videos carrying no watermark (resp. a SS watermark).
and the other corresponding to MIC watermark. The clusters are separable even without discarding the outliers in the estimated local variances. However, by setting an upper threshold on the estimated local variance, the clusters become easily separable. The better discriminative power of the shape parameter as compared to the scale parameter is also evident from the plots.
A similar study is conducted for the sequences in the compressed format. The only difference between the PEFs corresponding to the uncompressed and compressed sequences is that the latter is quantized. The quantization step sizes are different for the P-PEFs and the B-PEFs. In a given compressed sequence, the B-PEFs are coarsely quantized compared to the P-PEFs. Due to the non- linear nature of the quantization process, deriving a statistical model for the PEFs of the compressed sequences is not straightforward as we did for the PEFs of uncompressed sequences. Instead, we study whether the statistical model derived for the PEFs of the uncompressed sequences is valid for that of
4.2. PROPOSED SYSTEM 81
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shape = 0.79
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shape = 2.01
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shape = 0.81
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shape =1.71
(c)No watermark (3 Mbps) (d) SS watermark (3 Mbps)
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shape = 0.76
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shape = 1.36
(e)No watermark (2 Mbps) (f) SS watermark (2 Mbps)
Figure 4.4: Local variance histogram (τ = 100) of a P-PEF from the Foreman sequence, coded at different bit-rates and their Gamma approximations.
4.2. PROPOSED SYSTEM 82
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shape = 0.77
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shape = 1.87
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shape = 0.74
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shape = 1.33
(c)No watermark (3 Mbps) (d) SS watermark (3 Mbps)
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shape = 0.66
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shape = 0.94
(e)No watermark (2 Mbps) (f) SS watermark (2 Mbps)
Figure 4.5: Local variance histogram (τ = 100) of a B-PEF from the Foreman sequence, coded at different bit-rates and their Gamma approximations.
4.2. PROPOSED SYSTEM 83 the compressed sequences. It should be noted that our objective is to quantify the difference in the PEFs corresponding to the sequences carrying an MC watermark and those carrying MIC watermark. This may be achieved with an approximate statistical model for the PEFs.
The local variance histograms of the PEFs are studied for the sequences coded using the MPEG-2 standard. The host and the SS watermarked sequences are MPEG-2 coded using the VCDemo soft- ware [vcd]. Each sequence is coded at three different bit rates of5Mbps,3Mbps and2Mbps and with a frame rate of25frames/second. Note that depending on the bit-rate, a number of8×8blocks in the PEFs are quantized to zero-blocks. These blocks are excluded from the analysis. Figures 4.4 and 4.5 plot the normalized histograms of the local variance estimates from a P-PEF and B-PEF respectively and the corresponding Gamma approximations for the Foreman sequence. From these plots and similar plots for other sequences, it is observed that:
1. The Gamma distribution is a reasonably good approximation to the histograms of the local vari- ance estimated from the PEFs of a compressed sequence.
2. The change in the bit rate has little effect on the histograms corresponding to the host sequence, whereas the histograms corresponding to the sequence carrying an MIC watermark change sig- nificantly.
3. For the sequences carrying an MIC watermark, an increase in the compression ratio decreases the shape parameter of the Gamma approximation of the histogram. Due to the coarser quantization as compared to P-PEFs, the decrease in the shape value is more in the case of the B-PEFs.
We now formulate the design of the oracle as a pattern classification problem. The block diagram of the proposed oracle is shown in Figure 4.6. The shape parameter of the Gamma approximation of the local variances estimated from the PEF is used as a feature vector of a pattern classifier which makes the decision that the watermark carried by the test sequence is MC or MIC. The main steps of the oracle can be summarized as:
1 Compute the PEF with a given motion model
2 Compute the local variances and discard values exceeding a predecided thresholdτ
3 Compute the shape parameter of the Gamma distribution which best fits the observed local vari- ances
4 Train a pattern classifier with the estimated shape parameter as the feature vector.