# A Hybrid Watermarking Approach for DICOM Images Security
## 4 Experiment Results
### Evaluation Metrics
#### 4.1.2 Robustness Analysis
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Attacks**} & \multicolumn{4}{c}{**SSIM Values**} & \multicolumn{2}{c}{**Average Values**} \\ \hline  & **Image 1** & **Image 2** & **Image 3** & **Image 4** & \\ \hline Median filtering 3 \(\times\) 3 & 0.9898 & 0.9875 & 0.9889 & 0.9981 & 0.9685 \\ Median filtering 5 \(\times\) 5 & 0.9880 & 0.9863 & 0.9896 & 0.9953 & 0.9898 \\ Salt and pepper noise (0.01) & 0.9820 & 0.9845 & 0.9863 & 0.9889 & 0.9854 \\ Salt and pepper noise (0.03) & 0.9930 & 0.9920 & 0.9776 & 0.9864 & 0.9872 \\ Average filtering (3 \(\times\) 3) & 0.9878 & 0.9886 & 0.9989 & 0.9982 & 0.9933 \\ Cropping left top corner (25\%) & 0.9880 & 0.9989 & 0.9992 & 0.9970 & 0.9957 \\ Gaussian filtering (3 \(\times\) 3) & 0.9884 & 0.9978 & 0.9964 & 0.9988 & 0.9953 \\ Histogram equalization & 0.9047 & 0.9470 & 0.9289 & 0.9089 & 0.9223 \\ Gaussian noise (0.05) & 0.9992 & 0.9845 & 0.9890 & 0.9995 & 0.9930 \\ Gaussian noise (0.01) & 0.9899 & 0.9898 & 0.9836 & 0.9975 & 0.9902 \\ Gaussian Noise (20) & 0.9976 & 0.9986 & 0.9893 & 0.9967 & 0.9955 \\ Rotation 45\({}^{\circ}\) & 0.9988 & 0.9988 & 0.9872 & 0.9880 & 0.9932 \\ Rotation 10\({}^{\circ}\) & 0.9887 & 0.9834 & 0.9873 & 0.9888 & 0.9870 \\ Rotation 5\({}^{\circ}\) & 0.9889 & 0.9877 & 0.9878 & 0.9899 & 0.9885 \\ Sharpening & 0.9998 & 0.9989 & 0.9888 & 0.9895 & 0.9942 \\ Translate (10) & 0.9922 & 0.9888 & 0.9978 & 0.9969 & 0.9939 \\ Scaling & 0.9982 & 0.9978 & 0.9988 & 0.9991 & 0.9984 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Values of SSIM between the original image and the attacked watermarked image. where w and w\({}^{\prime}\) are the original and extracted watermark, w\({}_{\rm ij}\) is the (i, j) pixel in the original watermark w\({}_{\rm r}\), w\({}^{\prime}\)\({}_{\rm ij}\) is the (i, j) pixel in the extracted watermark w\({}^{\prime}\), \(\mu_{\rm w}\) is the mean of the original watermark w, and \(\mu_{\rm w}\) is the mean of the extracted watermark w\({}^{\prime}\), and M \(\times\) N is the dimension of the watermark. Table 5 presents the values of NC and BER to prove the robustness of the watermark under different attacks. As mentioned in the previous section, two copies of the same watermark were embedded in the black background region of the original medical image. BER and NC values between the original and corresponding extracted watermarks were the same for the two copies of the watermark except in the case of the cropping left top corner attack. So, the values of BER and NC indicated in the table are common values for the two copies of the watermark, except for the Cropping left top corner attack where the values obtained for each copy of the watermark are mentioned. The values of BER presented in Table 5 show the high robustness of the embedded watermark against various attacks. Indeed, on average, the BER values are equal to 0.5%. Furthermore, the NC values in Table 5 show that the embedded watermark withstood the different attacks. The NC values between the extracted attacked watermark and the original one are, on average, equal to 0.98.