# A Hybrid Watermarking Approach for DICOM Images Security
## 4 Experiment Results
### Evaluation Metrics  
#### 4.1.1 Perceptual Quality Analysis  
The peak signal-to-noise ratio (PSNR) and the structural similarity index measurement (SSIM) are used to evaluate the perceptual quality of the DICOM images after embedding the watermark.  
The peak signal-to-noise ratio (PSNR) measures the distortion between the original and the watermarked images. Higher values of PSNR indicate a lower distortion.  
For grayscale images with 8-bit pixels, the PSNR is given by:  
\[\text{PSNR}=10\log_{10}\left(\frac{255^{2}}{\text{MSE}}\right) \tag{3}\]  
where MSE is the Mean Squared Error between the original and the watermarked images (Equation (4))  
\[\text{MSE}=\frac{1}{\text{M}\times\text{N}}\sum\
olimits_{i=0}^{\text{N}-1} \sum\
olimits_{j=0}^{\text{M}-1}\left(\text{I}_{\text{o}}(\text{i},\text{j})- \text{I}_{\text{w}}(\text{i},\text{j})\right)^{2}\ \dots. \tag{4}\]  
where M \(\times\) N is the size of the images, I\({}_{\text{o}}\) is the original image, and I\({}_{\text{w}}\) is the watermarked image.  
The Structural Similarity Index (SSIM) quantifies the similarity between the original and watermarked images. It compares the similarity of three parameters: luminance, contrast, and structure. The SSIM takes a value between \(-1\) and \(1\). Higher values of SSIM (close to 1) indicate good imperceptibility.  
\[\text{SSIM}(\text{I}_{\text{o}},\text{I}_{\text{w}})=\frac{\left(2\mu_{\text{ I}_{\text{o}}}\mu_{\text{I}_{\text{w}}}+\text{c1}\right)\left(2\text{cov}+ \text{c2}\right)}{\left({\mu_{\text{I}_{\text{w}}}}^{2}+\text{t}_{\text{w}} \right.^{2}+\text{c1}\right)\left({\sigma_{\text{I}_{\text{w}}}}^{2}+{\sigma_ {\text{I}_{\text{w}}}}^{2}+{\sigma_{\text{I}_{\text{w}}}}^{2}+{\sigma_{\text{I }_{\text{w}}}}^{2}+{\sigma_{\text{I}_{\text{w}}}}^{2}+{\sigma_{\text{I}_{\text {w}}}}^{2}+{\sigma_{\text{I}_{\text{w}}}}^{2}+{\sigma_{\text{I}_{\text{w}}}}^{ 2}+{\sigma_{\text{I}_{\text{w}}}}^{2}+{\sigma_{\text{I}}}^{2}}\dots \tag{5}\]  
where \(\mu_{\text{I}_{\text{o}}}\) is the average of the original image I\({}_{\text{o}}\), \(\mu_{\text{I}_{\text{w}}}\) is the average of watermarked image I\({}_{\text{w}}\), \({\sigma_{\text{I}_{\text{o}}}}^{2}\) and \({\sigma_{\text{I}_{\text{w}}}}^{2}\) are respectively the variance of I\({}_{\text{o}}\) and I\({}_{\text{w}}\), cov is the covariance between I\({}_{\text{o}}\) and I\({}_{\text{w}}\), c1 and c2 are variables to stabilize the division with weak denominator, and L is the dynamic range of pixel values (L = 2\({}^{\text{(number of bits per pixels)}}-1\)). c1 and c2 are defined as follows:  
\[\begin{cases}c1=\left(\text{k}_{1}\text{L}\right)^{2},\text{ }\text{k}_{1}=0.01\\ c2=\left(\text{k}_{2}\text{L}\right)^{2},\text{ }\text{k}_{2}=0.03\end{cases}\]  
Table 3 presents the values of the SSIM between the original image and the watermarked image under different attacks. The results in this table show that the proposed approach ensures a good level of imperceptibility. The SSIM values are over 0.9, which means good similarity between the original and watermarked images.  
Table 4 presents the values of the PSNR between the original and the watermarked medical image under different attacks. In this table, the PSNR values between the original and the watermarked images are greater than 71 dB. So, there is a very low distortion between the original image and the attacked watermarked images.