# A Hybrid Watermarking Approach for DICOM Images Security
## 4 Experiment Results
### Evaluation Metrics
#### 4.1.2 Robustness Analysis  
To evaluate the robustness of the embedded watermark against different attacks, Bit Error Rate (BER) and Normalized Correlation (NC) are used. Bit Error Rate (BER) measures the percentage of erroneous bits between the extracted watermark and the original watermark. Lower BER values indicate higher robustness of the watermark against different attacks. The BER is given by Equation (6)  
\[\text{BER}=\frac{1}{\text{M}\times\text{N}}\left[\sum\
olimits_{i=1}^{\text{M} }\sum\
olimits_{j=1}^{\text{N}}(\text{w}(\text{i},\text{j})\oplus\text{w}^{ \prime}(\text{i},\text{j})\right] \tag{6}\]where \(\rm w(i,j)\) represents the pixel \(\rm(i,j)\) in the original watermark \(\rm w\), \(\rm w^{\prime}(i,j)\) represents the pixel \(\rm(i,j)\) in the watermarked image \(\rm w^{\prime}\), and \(\rm M\times N\) is the watermark's size. Normalized Coefficient (NC) is a coefficient used to indicate the similarity between the original and the extracted watermark. Its value is between [-1, 1]. When the NC is 1 the original and extracted watermarks are absolutely identical. When NC = 0 the original and extracted watermarks are divergent. When NC = \(-\)1 the original and extracted watermarks are completely anti-similar. NC is defined as follows:  
\[\rm NC\big{(}w,\ w^{\prime}\big{)}=\frac{\sum_{i=1}^{M}\sum_{j=1}^{N}\big{[} \big{(}w_{ij-}\mu_{w}\big{)}\times\big{(}\ w^{\prime}{}_{ij}-\mu_{w^{\prime}} \big{)}\big{]}}{\sqrt{\sum_{i=1}^{M}\sum_{j=1}^{N}\big{(}w_{ij}-\mu_{w}\big{)}^ {2}}\sqrt{\sum_{i=1}^{M}\sum_{j=1}^{N}\big{(}\ w^{\prime}{}_{ij}-\mu_{w^{\prime}} \big{)}^{2}}} \tag{7}\] \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Attacks**} & \multicolumn{4}{c}{**PSNR Values**} & \multicolumn{2}{c}{**Average Values**} \\ \hline  & **Image 1** & **Image 2** & **Image 3** & **Image 4** & \\ \hline Median filtering 3 \(\times\) 3 & 65.80 & 68.78 & 74.66 & 77.52 & 71.69 \\ Median filtering 5 \(\times\) 5 & 68.76 & 70.82 & 71.75 & 78.36 & 72.42 \\ Salt and pepper noise (0.01) & 83.27 & 80.21 & 79.26 & 78.99 & 80.43 \\ Salt and pepper noise (0.03) & 75.12 & 77.87 & 77.89 & 75.63 & 76.62 \\ Average filtering (3 \(\times\) 3) & 69.46 & 70.66 & 71.63 & 78.45 & 72.55 \\ Cropping left top corner (25\%) & 76.25 & 80.78 & 75.63 & 71.86 & 76.13 \\ Gaussian filtering (3 \(\times\) 3) & 68.76 & 78.36 & 83.25 & 80.36 & 77.68 \\ Histogram equalization & 65.32 & 77.32 & 77.46 & 80.15 & 75.06 \\ Gaussian noise (0.05) & 70.63 & 72.96 & 75.12 & 78.99 & 74.42 \\ Gaussian noise (0.01) & 72.46 & 80.16 & 80.47 & 80.96 & 76.23 \\ Gaussian Noise (20) & 69.89 & 70.35 & 82.79 & 81.89 & 76.23 \\ Rotation 45\({}^{\circ}\) & 73.78 & 73.88 & 83.19 & 80.78 & 77.90 \\ Rotation 10\({}^{\circ}\) & 70.77 & 80.36 & 80.96 & 80.98 & 78.26 \\ Rotation 5\({}^{\circ}\) & 78.36 & 80.78 & 80.23 & 82.93 & 80.75 \\ Sharpening & 72.63 & 80.12 & 80.38 & 80.18 & 78.32 \\ Translate (10) & 71.89 & 80.98 & 80.63 & 80.42 & 78.48 \\ Scaling & 72.38 & 75.22 & 80.69 & 80.38 & 77.16 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Values of PSNR between the original and attacked watermarked images.