# Blind Watermarking of Color Medical Images Using Hadamard Transform and Fractional-Order Moments
## 5 Experimental Results
### Robustness Evaluation  
The robustness of our method was evaluated over the bit error rate (\(BER\)) and normalized correlation (\(NC\)), which are formulated as  
\[BER=\frac{1}{P\times Q}\Bigg{(}\sum_{x=1}^{P}\sum_{y=1}^{Q}\left[W(x,y)-W^{*}(x,y)\right]^{2}\Bigg{)} \tag{30}\]  
\[NC=\frac{\sum_{x=1}^{P}\sum_{y=1}^{Q}\left[W(x,y)\times W^{*}(x,y)\right]}{ \sum_{x=1}^{P}\sum_{y=1}^{Q}\left[W(x,y)\right]^{2}} \tag{31}\]  
The robustness was evaluated over several categories of attacks, the first category comprised geometric attacks such as rotation, scaling, cropping, magnification, and shearing attacks, with different parameter factors. The second category included signal processing attacks such as jpeg, jpeg 2000, noising, salt and peppers, Gaussian, Gaussian low-pass, speckle noise attack, median filter attack, average filter attack, sharpen attack, histogram equalization, and motion blur attack. The third category included many common combination attacks. The watermark logo was first resized to 10 \(\times\) 10 and then embedded in the host color image by using and applying various geometric attacks on the watermarked image. Results for geometric attacks are shown in Table 2; several image processing attacks are also shown in Table 3, respectively. Figure 8: The PSNR values for selected color medical images at \(\Delta=0.2\). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Attacks** & **BER** & **NC** & **Extracted** \\  & & **Watermark** \\ \hline No Attack & 0 & 1 & **C** \\ \hline Rotation Attack & \(5^{\circ}\) & 0 & 1 & **C** \\  & \(15^{\circ}\) & 0 & 1 & **C** \\  & \(25^{\circ}\) & 0 & 1 & **C** \\  & \(65^{\circ}\) & 0 & 1 & **C** \\ \hline  & 0.5 & 0.0023 & 0.9962 & **C** \\  & 0.75 & 0 & 1 & **C** \\ Scaling Attack & 1.25 & 0 & 1 & **C** \\  & 1.5 & 0 & 1 & **C** \\  & 2 & 0 & 1 & **C** \\ \hline  & (15,2) & 0 & 1 & **C** \\  & (20,20) & 0 & 1 & **C** \\ Translation Attack & (2,15) & 0 & 1 & **C** \\  & (0,50) & 0.0001 & 0.9998 & **C** \\  & (50,0) & 0.0001 & 0.9998 & **C** \\ \hline Shearing Attack & (0–1\%) & 0.0075 & 0.9932 & **C** \\ \hline Magnification & (1.75) & 0 & 1 & **C** \\ \hline Cropping, Right & (25\%) & 0.0146 & 0.9820 & **C** \\ Cropping, Top & (25\%) & 0.0068 & 0.9916 & **C** \\ Cropping, Middle & (25\%) & 0 & 1 & **C** \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Robustness results of the extracted watermark from the attacked image “Lena” using geometric attacks, \(\Delta=0.2\). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Attacks** & BER & NC & **Extracted** \\  & 30 & 0 & 1 \\  & 40 & 0 & 1 \\ JPEG & 50 & 0 & 1 \\ Compression & 60 & 0 & 1 \\  & 70 & 0 & 1 \\  & 90 & 0 & 1 \\ \hline Motion Blur & (3,3) & 0 & 1 \\  & (4,8) & 0 & 1 \\ \hline Lossy Compression (80) & 0 & 1 & \\ \hline Salt and Pepper (0.03) & 0 & 1 & \\ \hline Gaussian (0.03) & 0 & 1 & \\ \hline Gaussian Low-Pass (3,3) & 0 & 1 & \\ \hline Poisson Noise & 0 & 1 & \\ \hline Speckle Noise Attack & 0 & 1 & \\ \hline Median Filter Attack & 0.0002 & 0.9972 & \\ \hline Average Filter Attack (3,3) & 0.0003 & 0.9961 & \\ \hline Sharpen Attack & 0.0001 & 0.9998 & \\ \hline Histogram Equalization & 0 & 1 & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Robustness results of the extracted watermark from the attacked image “Lena” using processing attacks \(\Delta=0.2\). The proposed method attained the highest robustness level against various geometrical and signal processing attacks. To assess the robustness of the proposed method and other mentioned methods, the average BER and NC values are represented in Figures 9 and 10 for easy comparison. From these simulation results, (in the referred Figures 9 and 10), we note that our method successfully scored the minimum average value (BER = 0.0032) among the compared methods. Moreover, our method scored the maximum average value of NC = 0.9974. From these compared values, we deduce that our method surpassed other existing methods.