## 4 Experiments and Evaluation
### Robustness Evaluation  
In addition to assessing imperceptibility, we also evaluated the robustness of our watermarking technique against common image processing operations and attacks. Robustness testing is crucial to ensure that the embedded watermark remains intact and detectable even after various modifications to the watermarked image. Random noise or intentional tampering could heavily affect the extracted watermark, making it essential to evaluate how well the watermark withstands such conditions. In Figure 4, we show the watermark extracted before and after applying image attacks using Gaussian and salt and pepper (S & P) noises. These results illustrate the robustness of our watermarking method under different types of noise, demonstrating its ability to maintain watermark integrity even in challenging conditions.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Method** & **PSNR** & **SSIM** \\ \hline [PERSON] et al. [13] & 44.19 & 0.85 \\ [PERSON] et al. [25] & 41.67 & 0.82 \\ [PERSON] et al. [26] & 42.34 & 0.84 \\ [PERSON] et al. [27] & 45.22 & 0.87 \\ [PERSON] et al. [6] & 46.64 & 0.89 \\ [PERSON] et al. [28] & 42.97 & 0.83 \\ [PERSON] et al. [29] & 47 & 0.91 \\ Our method (Avg) & 59.84 & 0.91 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Comparison of PSNR and SSIM scores.  
Figure 4: The effect of noise on the watermark-extraction process. (**a-c**) Watermarks extracted without image tampering. (**d–f**) Extracted watermarks after applying Gaussian noise. (**g–i**) Extracted watermarks under salt and pepper noise.  
Figure 3: Illustration of watermark embedding and extraction process. (**a**) Cover image where the information will be hidden. (**f**) Watermark. (**b–e**) are watermarked images with increasingly larger watermark sizes. (**g-i**) are the corresponding extracted watermarks from the watermarked images.  
We subjected the watermarked images to a series of attacks, including noise, scaling, filtering, and intensity enhancement, among others. The goal was to determine the resilience of the embedded watermark under different scenarios.  
Table 3 summarizes the results of our robustness testing, showing the performance of the watermark under each operation or attack.  
From Table 3, it is evident that the proposed method demonstrates robustness across various attacks, achieving high NC values. Specifically, it exhibits strong resilience against both Gaussian and salt and pepper noises (NC: 0.97), outperforming most of the comparison methods. Despite the challenges posed by histogram equalization, the proposed method maintains a respectable NC value (0.8). Additionally, its robustness against the median filter (NC: 0.86) and scaling (NC: 0.78) underscores its applicability in medical imaging scenarios where image orientation and cropping are common. The Normalized Correlation (NC) metric is not sufficient for evaluating the performance of watermarking techniques, as it only reflects the true positives. A more important metric is the Bit Error Rate (BER), which considers the matching of both positive and negative bits, providing a more comprehensive assessment of the watermark's performance. Our method outperforms all other methods in this task, demonstrating superior accuracy and reliability in watermark detection and integrity. Overall, while the proposed method exhibits promising robustness against a wide range of attacks, further exploration and refinement in certain areas could enhance its effectiveness in robust medical image watermarking applications.  
These results demonstrate the effectiveness of our watermarking method in preserving the integrity and authenticity of medical images, even in the face of potential alterations and attacks. The high detection rates across various tests underscore the reliability and robustness of our approach, making it suitable for real-world applications where image security is paramount. The scaling and sharpening attacks highlight potential limitations of our method, requiring further investigation.