# An Adaptive and Secure Holographic Image Watermarking Scheme
## 5 Experiments and Results
### Test for the Effectiveness of Our Watermarking Scheme
#### 5.2.2 Robustness to Attacks  
Different kinds of attacks were conducted to verify the robustness of the proposed method. They are Gaussian low-pass filtering (\(\text{hsize}=5\), \(\text{sigma}=9\)), Average filtering (\(5\times 5\)) Median filtering (\(7\times 7\)), Occlusion (\(25\%\)), Unsharp (\(\text{alpha}=1\)), Blurring (Circular average, radius = 3), JPEG compression (Q = 30), Gaussian noise (0.0005), Salt and pepper noise (0.005), Brighten (adds 50 to each pixel of the images), Darken (subtracts 50 from each pixel of the images), Rescaling (1024\(\rightarrow\)512\(\rightarrow\)1024), Rotation (30\({}^{\circ}\)\(\rightarrow\)\(-\)30\({}^{\circ}\)) and Painting, respectively. For all attack cases, a comparison of NCs between our method and the schemes from the literature [2,4,7] is listed in Tables 2 and 3. In Tables 4 and 5, a comparison of BERs is made between our method and the three schemes. Figure 5 displays some distorted watermarked images of the proposed method together with PSNRs. The corresponding reconstructed images of the mark CGH, which are extracted from the attacked images in Figure 5, are exhibited in Figure 6. As can be seen from Tables 2-5 and Figure 6, our method has good robustness against various kinds of attack. It can be observed from Tables 2 and 3 and Figure 6 that most of the NCs of the proposed method are above 0.9 and the corresponding reconstructions are clear enough to be recognized. Almost of all BERs of the reconstructed images in Figure 6 are zero, or close to zero. In addition,  
the watermarked image under this attack is highly corrupted. Experimental results indicate that the reconstruction of the extracted CGH cannot be distinguished when the noise density of salt and pepper noise is bigger than 0.01. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Eline**} & \multicolumn{4}{c}{**Goldhill**} \\ \cline{2-10}  & \multicolumn{2}{c}{**Our**} & \multicolumn{2}{c}{**Scheme**} & \multicolumn{2}{c}{**Scheme**} & \multicolumn{2}{c}{**Scheme**} & \multicolumn{2}{c}{**Our**} & \multicolumn{2}{c}{**Scheme**} & \multicolumn{2}{c}{**Scheme**} \\
**Attacks** & **Method** & **in[7]** & **in[2]** & **in[4]** & **Method** & **in[7]** & **in[2]** & **in[4]** \\ \hline Gaussian low-pass filtering & 0 & 0.007 & 0.387 & 0.724 & 0.005 & 0.013 & 0.364 & 0.407 \\ Average filtering & 0 & 0.008 & 0.395 & 0.725 & 0.005 & 0.015 & 0.409 & 0.405 \\ Median filtering & 0.002 & 0.013 & 0.412 & 0.751 & 0.118 & 0.33 & 0.423 & 0.403 \\ Occlusion & 0.023 & 0.162 & 0.027 & 0.026 & 0.068 & 0.132 & 0.042 & 0.022 \\ JPEG & 0.038 & 0.008 & 0.395 & 0.007 & 0.052 & 0.01 & 0.316 & 0.421 \\ Unsharp & 0 & 0.009 & 0.12 & 0 & 0.003 & 0.012 & 0.073 & 0 \\ Blurring & 0 & 0.006 & 0.407 & 0.318 & 0.008 & 0.015 & 0.389 & 0.391 \\ Gaussian noise & 0.001 & 0.001 & 0.162 & 0 & 0.003 & 0.003 & 0.249 & 0.008 \\ Salt and pepper noise & 0.107 & 0.24 & 0.078 & 0.009 & 0.105 & 0.208 & 0.071 & 0.009 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The \(BERs\) of the reconstructions of the mark CGHs which were extracted from the attacked watermarked Elaine and Goldhill comparing between our method and the schemes in [2,4,7].