## 4 Experimental Results and Analysis
### Robustness  
Robustness is a critical feature of digital watermarking technology. We assess ZWNet's robustness by comparing the zero-watermark of the original image with the zero-watermark \begin{table}
\begin{tabular}{c c} \hline \hline
**Methods** & **Method Description** \\ \hline Noise & Includes white noise and salt-and-pepper noise \\ Filter & Includes Average filter, median filter and Gaussian filter \\ Rotation & Rotates the image around the center with different angles \\ Crop & Crop out part of the image with different sizes \\ Mirror & Horizontal mirror and vertical mirror \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Methods of data augmentation. Figure 10: Loss changes in the training stage. Figure 9: Four test images. (**a**) Lena. (**b**) Mandrill. (**c**) Tree. (**d**) Girl. of the attacked image. The evaluation index employed is NC, as explained in Section 3.6, with a threshold set to 0.8. The attack methods used are consistent with those applied in data augmentation. Using the image Lena (Figure 9a) as an example, the visuals of the original image and the attacked image are displayed in Figure 11.  
The NC results of the images in Figure 9 under different attacks are listed in Table 2.  
The NC results of four test images under different attacks. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Attack Description** & **Lena** & **Mandril** & **Tree** & **Girl** \\ \hline Rotation (15\({}^{\circ}\)) & 0.9688 & 0.9609 & 0.9765 & 0.9688 \\ Rotation (30\({}^{\circ}\)) & 0.9258 & 0.9297 & 0.9258 & 0.9375 \\ Rotation (45\({}^{\circ}\)) & 0.8555 & 0.9063 & 0.8320 & 0.8203 \\ Pepper and salt noise (intensity = 0.01) & 0.9922 & 0.9961 & 0.9727 & 0.9805 \\ Pepper and salt noise (intensity = 0.05) & 0.9531 & 0.9609 & 0.9531 & 0.9375 \\ Pepper and salt noise (intensity = 0.1) & 0.9219 & 0.9336 & 0.9609 & 0.8750 \\ Gaussian noise & 1 & 0.9843 & 0.8828 & 0.9570 \\ (mean = 0, variance = 0.005) & 0.9063 & 1 & 1 & 0.9336 \\ Random crop (1/8) & 1 & 0.8945 & 0.8164 & 0.8984 \\ Random crop (1/4) & 0.8633 & 0.8984 & 0.8203 & 0.8710 \\ Crop upper-left corner (1/4) & 0.9414 & 0.8750 & 0.9570 & 0.8086 \\ Crop lower-left corner (1/4) & 0.9922 & 0.9258 & 0.9531 & 0.8867 \\ Crop upper-right corner (1/4) & 0.8945 & 0.9531 & 0.9375 & 0.8789 \\ Crop lower-right corner (1/4) & 0.9883 & 0.9609 & 0.9414 & 0.8086 \\ Crop upper-left corner (1/8) & 0.9961 & 0.9219 & 0.9805 & 0.9297 \\ Crop lower-left corner (1/8) & 1 & 0.9766 & 1 & 0.9922 \\ Crop upper-right corner (1/8) & 0.9882 & 0.9922 & 0.9883 & 0.9453 \\ Crop lower-right corner (1/8) & 1 & 0.9727 & 1 & 0.9453 \\ Blur (3 \(\times\) 3) & 1 & 0.9883 & 0.9922 & 0.9882 \\ Blur (5 \(\times\) 5) & 1 & 0.9883 & 0.9922 & 0.9922 \\ Blur (9 \(\times\) 9) & 1 & 0.9766 & 0.9922 & 0.9883 \\ Blur (11 \(\times\) 11) & 0.9961 & 0.9805 & 0.9609 & 0.9883 \\ Gaussian Blur (3 \(\times\) 3) & 1 & 0.9883 & 0.9922 & 0.9883 \\ Gaussian Blur (5 \(\times\) 5) & 0.9961 & 0.9727 & 0.9609 & 0.9844 \\ Gaussian Blur (9 \(\times\) 9) & 0.9844 & 0.9766 & 0.9492 & 0.9766 \\ Gaussian Blur (11 \(\times\) 11) & 0.9922 & 0.9844 & 0.9609 & 0.9766 \\ Median Blur (5 \(\times\) 3) & 0.9922 & 0.9688 & 0.9063 & 0.9688 \\ Median Blur (5 \(\times\) 5) & 0.9688 & 0.9648 & 0.9258 & 0.9688 \\ Median Blur (9 \(\times\) 9) & 0.9883 & 0.9805 & 0.9570 & 0.9805 \\ Median Blur (11 \(\times\) 11) & 0.9766 & 0.9648 & 0.8984 & 0.9688 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: NC results of four test images under different attacks. Figure 11: Examples of images under different attacks. (**a**) Original image. (**b**) Salt and pepper noise. (**c**) Horizontal mirror. (**d**) Rotation. (**e**) Gaussian filter. (**f**) Median filter. (**g**) Average filter. (**h**) Crop. The results in Table 2 clearly indicate that the test images, even when subjected to different types and intensities of attacks, all exhibit NC values above the 0.8 threshold. These results demonstrate the robustness of the proposed scheme.