## 4 Experiments and Results
### Comparisons with the State of the Art  
We compared Polarformer with other methods, including U-Net variant methods, which utilize skip connections, and transformer-based methods, which introduce global contextual information. The methods with U-Net and variants include U-Net [39], U-Net++ [40], U-Net3+ [41] and Attention-based U-Nets [42]. The transformer-based methods include SETR [33] and TransU-Net [34]. We compared with BGA-Net [43], NENet [44], PraNet [45], M-Net [6], nnU-Net [46], which were proposed for OD and OC segmentation tasks. We compared DeepLabV3+ [47] as well. We compared them using RIM-ONE v3, REFUGE and DRISHTI-GS with their released source codes. Table 1 tabulates the Dice scores of Polarformer compared with the state-of-the-art methods. From the table, it can be seen that our Polarformer achieved better results. SETR [33] and TransU-Net [34] are transformer-based methods. In terms of accuracy, we can see that these methods are slightly inferior to our method, indicating that more detailed features are learned under polar representation. The shape of the OC and OD are non-rotated ellipses, and their features contain structural information. Our model can learn more discriminative features of the OD and OC by learning long-range dependencies. Furthermore, our proposed LPTM automatically globally optimizes the spatial relationship between the OD and OC and can be explicitly modeled in a prior way. In addition, our model has a greater advantage compared with M-Net [6]. The reason is that the polar transformation in [6] is a hyper-parameter that may fall into local optima. Clearly,we observe that our Polarformer demonstrates the competitive performance of the OC segmentation compared with DeepLabV3+ [47] and U-Net [34], even if there is difficulty distinguishing and there is noise in the images. Figures 6-8 show the comparison between our method and other methods on REFUGE dataset, DRISHTI-GS dataset and RIM-ONE v3 dataset of the same image. The figures' black parts represent the OC, and the gray parts represent the OD. By comparing the ground truth and our visualization results in the figures, we can see that the segmentation results of different models have differences, particularly in the edge of the OD and OC. From the visualization of the experimental results, DeepLabV3+ had a better effect on the boundary segmentation of the OC. AttU-Net showed results that were not ideal. The U-Net methods were inaccurate, and the boundaries were chaotic. Compared with our method, this is because the method in this paper adopts the transformer module to take advantage of its unlimited effective receptive fields to introduce global contextual information, which makes the boundary segmentation more accurate. \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{2}{c}{**RIM-ONE v3**} & \multicolumn{2}{c}{**DRISHTI-GS**} & \multicolumn{2}{c}{**REFUGE**} \\  & \(\mathbf{Dice_{up}}\) & \(\mathbf{Dice_{disc}}\) & \(\mathbf{Dice_{up}}\) & \(\mathbf{Dice_{disc}}\) & \(\mathbf{Dice_{up}}\) & \(\mathbf{Dice_{disc}}\) \\ \hline U-Net & 0.837 & 0.948 & 0.830 & 0.945 & 0.835 & 0.951 \\ U-Net3+ & 0.843 & 0.955 & 0.833 & 0.952 & 0.837 & 0.959 \\ DeepLabV3+ & 0.857 & 0.961 & 0.842 & 0.951 & 0.855 & 0.943 \\ AttU-Net & 0.852 & 0.965 & 0.845 & 0.950 & 0.857 & 0.964 \\ M-Net & 0.862 & 0.952 & 0.859 & 0.948 & 0.864 & 0.952 \\ PraNet & 0.856 & 0.961 & 0.841 & 0.953 & 0.857 & 0.966 \\ nnU-Net & 0.865 & 0.966 & 0.862 & 0.960 & 0.876 & 0.965 \\ SETR & 0.877 & 0.965 & 0.880 & 0.954 & 0.878 & 0.955 \\ TransU-Net & 0.874 & 0.954 & 0.883 & 0.944 & 0.877 & 0.964 \\ BGA-Net & 0.872 & 0.967 & 0.898 & 0.975 & ✗ & ✗ \\ NENet & ✗ & ✗ & ✗ & 0.963 & ✗ & ✗ \\ Polarformer(R101) & 0.888 & 0.968 & 0.893 & 0.974 & 0.890 & 0.975 \\ Polarformer(eff-B4) & 0.895 & 0.972 & 0.901 & 0.977 & 0.892 & 0.974 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparisons of our approach compared with different state-of-the-art methods on the DRISHTI-GS dataset, RIM-ONE v3 dataset and REFUGE dataset.