## 4 Experiments and Evaluation
### Imperceptibility Assessment  
We evaluated the imperceptibility of the watermarked images to the human eye using two key metrics: the Peak Signal-to-Noise Ratio (PSNR) and the Structural Similarity Index (SSIM). Higher PSNR values indicate better quality, with minimal visual distortion caused by the watermark. The PSNR provides a more comprehensive assessment of visual fidelity, as the PSNR can be fooled by noise that appears similar to the image details. The results assessing the effect of different watermark sizes on imperceptibility are summarized in Table 1.  
From Table 1, it is evident that smaller watermark sizes tend to yield slightly higher PSNR values, indicating better imperceptibility. This aligns with the principle that smaller watermarks are less likely to introduce noticeable visual artifacts in the watermarked images. However, it is noteworthy that, even with larger watermark sizes, the imperceptibility remains high, underscoring the robustness of our watermarking technique. For instance, using a medium watermark size (\(10^{3}\) bytes) results in an image with almost imperceptible changes. Human eyes generally would not perceive any significant quality difference between the original and watermarked images if the PSNR value is above 50 dB. This demonstrates the effectiveness of our method in preserving the visual quality of the medical images while embedding the watermark. The findings from this analysis reinforce the practical applicability of our watermarking approach in medical imaging scenarios. The ability to embed watermarks with minimal impact on image quality, even with larger sizes, enhances the sensitive medical data without compromising the diagnostic integrity of the images.  
To further elucidate the impact of different sizes of watermarks on the imperceptibility of our watermarking technique, we provide a visual illustrations in Figure 3. As depicted in Figure 3, varying sizes of watermark images are embedded within the cover images, ranging from small to large. As it appears, the quality and structural similarity between the watermarked (b)-(c) and the cover image (a) does not degrade as the size of the watermark increases.  
To establish the superiority of imperceptibility, we compared various watermarking methods. The primary objective was to evaluate each technique's effectiveness in concealing watermarks within images while minimizing visual distortion. Notably, our method, as illustrated in Table 2, surpassed competing approaches by achieving the highest imperceptibility score. This outcome confirms our method's exceptional ability to seamlessly integrate watermarks into medical images while preserving their original visual quality.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Watermark Size (Bytes)** & **PSNR (dB)** & **SSIM** \\ \hline
96 & \(59.843\pm 1.738\) & \(0.91\pm 0.091\) \\
411 & \(59.835\pm 1.735\) & \(0.85\pm 0.057\) \\
10,779 & \(59.554\pm 1.549\) & \(0.81\pm 0.027\) \\
43,228 & \(58.867\pm 1.122\) & \(0.8\pm 0.026\) \\
97,493 & \(57.941\pm 0.698\) & \(0.79\pm 0.021\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Imperceptibility assessment results across different watermark sizes.