The reference of Cho's method:
J.-W. Cho, R. Prost, and H.-Y. Jung, "An oblivious watermarking for 3D polygonal meshes using distribution of vertex norms," IEEE Trans. on Signal Process., vol. 55, no. 1, pp. 142–155, 2007.
The reference of Wang's method:
K. Wang, G. Lavoué, F. Denis, and A. Baskurt, "Robust and blind watermarking of polygonal meshes based on volume moments," Tech. Rep., LIRIS Laboratory - M2DisCo Team, 2009, available at http://liris.cnrs.fr/Documents/Liris-3713.pdf.
In the following tables, all the results are the averages of 5 trials with randomly selected watermark sequences and keys.
Table 1. Baseline evaluation results of the methods.
|
Protocol |
Perceptual |
Geometric |
||
|
Method |
Cho's |
Wang's |
Cho's |
Wang's |
|
WM capacity (bits) |
64 |
64 |
64 |
64 |
|
Embedding time (s) |
7.6 |
439.9 |
11.6 |
377.6 |
|
Extraction time (s) |
<1.0 |
3.3 |
<1.0 |
3.5 |
|
d_{MRMS} (w.r.t. l_{bbd}) |
0.0080% |
0.069% |
0.012% |
0.018% |
|
d_{MSDM} |
0.19 |
0.14 |
0.29 |
0.09 |
Table 2. Robustness comparison between the methods.
|
Protocol → |
Perceptual |
Geometric |
||
|
Attack ↓ |
Cho's BER |
Wang's BER |
Cho's BER |
Wang's BER |
|
File attack |
0 |
0 |
0 |
0 |
|
Similarity transformation |
0 |
0 |
0 |
0 |
|
Noise A=0.05% Noise A=0.10% Noise A=0.30% Noise A=0.50% |
0.01 0.03 0.13 0.28 |
0 0.01 0.08 0.16 |
0 0.01 0.10 0.24 |
0.02 0.15 0.29 0.40 |
|
Smoothing N_{itr}=5 Smoothing N_{itr}=10 Smoothing N_{itr}=30 Smoothing N_{itr}=50 |
0.10 0.23 0.38 0.45 |
0 0.01 0.07 0.14 |
0.06 0.16 0.34 0.42 |
0.06 0.18 0.39 0.51 |
|
Quantization R=11 Quantization R=10 Quantization R=9 Quantization R=8 Quantization R=7 |
0 0.04 0.14 0.26 0.46 |
0 0.01 0.01 0.05 0.17 |
0 0.02 0.06 0.18 0.41 |
0.01 0.17 0.27 0.39 0.53 |
|
Average geometry attacks |
0.18 |
0.05 |
0.14 |
0.24 |
|
Subdivision Midpoint Subdivision Sqrt3 Subdivision Loop |
0.04 0.14 0.16 |
0 0 0 |
0.02 0.09 0.09 |
0 0.01 0.01 |
|
Simplification E_{sim}=10% Simplification E_{sim}=30% Simplification E_{sim}=50% Simplification E_{sim}=70% Simplification E_{sim}=90% Simplification E_{sim}=95% Simplification E_{sim}=97.5% |
0.01 0.05 0.18 0.33 0.23 0.38 0.47 |
0 0 0 0 0.01 0.01 0.05 |
0 0.03 0.07 0.14 0.12 0.27 0.42 |
0 0 0.02 0.02 0.08 0.17 0.32 |
|
Cropping V_{cr}=10% Cropping V_{cr}=30% Cropping V_{cr}=50% |
0.50 0.53 0.51 |
0.51 0.49 0.49 |
0.50 0.51 0.52 |
0.51 0.48 0.49 |
|
Average connectivity attacks |
0.27 |
0.12 |
0.21 |
0.16 |
|
Average all attacks |
0.22 |
0.08 |
0.17 |
0.19 |
Last updated: Match 16, 2010