## 4 Experiments and Results
### Cornea Segmentation Results
The resolution of the HCT accumulator was 1600 \(\times\) 1200 pixels, the minimum distance for the center of each detected circle was set to 40 pixels, and the radius of the detected circles was set to 120-1600 pixels. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Model Name** & **Feature Maps** & **Kernel Size** & **Depth** & **Trainable Parameters** & **Memory Usage [GB]** & **Training Time per Epoch [s/Epochs]** \\ \hline SCED1 & 64 & 9 & 3 & 2,338,561 & 8.7 & 63 \\ SCED2 & 64 & 9 & 4 & 3,332,241 & 8.8 & 67 \\ SCED3 & 64 & 9 & 5 & 3,997,761 & 8.9 & 69 \\ SCED4 & 64 & 11 & 3 & 3,493,121 & 8.8 & 74 \\ SCED5 & 64 & 11, 11, 9, 9, 7 & 4 & 4,029,889 & 8.9 & 77 \\ U-Net & 64, 128, 256, 512, 1024 & 3 & 4 & 36,605,317 & 21.0 & 96 \\ U-Net-ResNet-50 & 64, 128, 256, 512, 1024, 2048 & 1, 3, 7 * & 5 ** & 73,378,625 & 11.3 & 110 \\ \hline \hline \end{tabular}  
* The kernel size of the initial convolutional layer was 7; for blocks 2 to 5, the convolutional layers used kernel sizes of 1-3-1 for each block. ** U-Net–ResNet-50 included 54 convolutional layers distributed across five depth levels.  
\end{table} 
Table 1: Cornea segmentation model architectures and resources required for training. All circles obtained from this process were evaluated using the objective function \(F_{\alpha}(C)\) mentioned in Equation (1). The circle that maximizes \(F_{\alpha}(C)\) was selected to represent the cornea area. In the experiment, we determined the best hyperparameter \(\alpha\) by varying the values of \(\alpha\) between 4.6 to 5.8 and calculating the IoU of the detected cornea areas for each \(\alpha\) value. We first identified the optimal value of \(\alpha\) using 120 additional ocular staining images that were not included in the SUSTech-SYSU dataset. An \(\alpha\) value of 5.2 achieved the highest IoU for cornea segmentation. These \(\alpha\) values were also verified with 712 images from the SUSTech-SYSU dataset, and provided the same results. The relation between the IoU and \(\alpha\) is shown in Figure 8. The optimal \(\alpha\) value of 5.2 was used for the entire experiment. To evaluate the performance of the objective function \(F_{\alpha}(C)\) for circle selection to represent the cornea regions, we calculated the percentage of the selected circles based on their IoU rankings among the candidates. From the graph in Figure 9, the circle which maximized \(F_{\alpha}(C)\) is 67.79% of the circles which obtained the highest IoU from all candidates; 84.53% of the selected circles were among the two highest-ranked candidates, and 92.27% were within the top three highest-ranked candidates. To assess the segmentation performance, the SCED and SCED-HT models were evaluated based on accuracy, IoU, and MAPE of cornea size. Table 2 displays the results from all models in this experiment. The values following MAPE represent the standard deviation of MAPE, indicating the variability of the error in predicted cornea area around the mean in percentage. From the results, the SCED3 model has the highest accuracy and IoU compared to other methods, with 96.97% and 90.21%, respectively. The SCED2 model has the lowest MAPE at 7.28%. Overall, SCED models perform slightly better than SCED-HT models with the same architecture. The samples of cornea segmentation results for our work are illustrated in Figure 10.  
Figure 7: Training and validation accuracy and loss curves for cornea segmentation models. Figure 8: Cornea segmentation IoU from \(\alpha\) values in the proposed objective function (Equation (1)).