# Causal Inference-Based Self-Supervised Cross-Domain Fundus Image Segmentation
## 4 Experiments
### Loss Ablation Study  
To further validate the effectiveness of our approach, we conducted an ablation study on the loss functions. We progressively incorporated the loss components used in the overall loss function and recorded the corresponding performance on three datasets, as shown in Table 6. The contributions of each loss term are analyzed as follows:  
* Baseline Segmentation Loss (\(L_{seg}^{s}\)): The results obtained using only \(L_{seg}^{s}\), which relies solely on the labeled source data, establish the baseline segmentation performance.
* Adversarial Loss (\(L_{adv}\)): By incorporating \(L_{adv}\), we observed significant performance gains--especially on the RIM-one-R3 dataset, which exhibits a larger domain shift.
* Target Segmentation Loss (\(L_{seg}^{t}\)): Next, we incorporated the target segmentation loss \(L_{seg}^{t}\), which is based on the pseudo-labels generated by our causal inference-based pseudo-label fusion module. The addition of \(L_{seg}^{t}\) resulted in substantial improvements across all three datasets, thereby demonstrating the reliability of the predicted pseudo-labels.
* Maximum Square Loss (\(L_{m}\)): Incorporating the maximum square loss \(L_{m}\) further improved segmentation performance by regularizing pseudo-label predictions and balancing high-confidence outputs.
* Cross-domain Contrastive Loss (\(L_{c}\)): Finally, the cross-domain contrastive loss \(L_{c}\) was introduced to constrain the features extracted from the original images and their style-transferred counterparts, ensuring consistency between the dual-path outputs.  
\begin{table}
\begin{tabular}{l l c c c} \hline \hline
**Dataset** & **Method** & \(\mathbf{DI_{cap}}\) & \(\mathbf{DI_{disc}}\) & \(\delta\) \\ \hline \multirow{8}{*}{Drishti-GS} & \(L_{seg}^{s}\) & 0.822 & 0.941 & 0.097 \\  & \(L_{seg}^{s}+L_{adv}\) & 0.829 & 0.939 & 0.093 \\ \cline{1-1}  & \(L_{seg}^{s}+L_{adv}+L_{seg}^{t}\) & 0.867 & 0.958 & 0.084 \\ \cline{1-1}  & \(L_{seg}^{s}+L_{adv}+L_{seg}^{t}+L_{m}\) & 0.869 & 0.961 & 0.084 \\ \cline{1-1}  & \(L_{seg}^{s}+L_{adv}+L_{seg}^{t}+L_{m}+L_{c}\) & **0.876** & **0.971** & **0.081** \\ \hline \multirow{8}{*}{RIM-ONE-R3} & \(L_{seg}^{s}\) & 0.757 & 0.873 & 0.103 \\  & \(L_{seg}^{s}+L_{adv}\) & 0.781 & 0.883 & 0.097 \\ \cline{1-1}  & \(L_{seg}^{s}+L_{adv}+L_{seg}^{t}\) & 0.805 & 0.897 & 0.090 \\ \cline{1-1}  & \(L_{seg}^{s}+L_{adv}+L_{seg}^{t}+L_{m}\) & 0.814 & 0.913 & 0.085 \\ \cline{1-1}  & \(L_{seg}^{s}+L_{adv}+L_{seg}^{t}+L_{m}+L_{c}\) & **0.818** & **0.922** & **0.083** \\ \hline \multirow{8}{*}{REFUGE Val} & \(L_{seg}^{s}\) & 0.831 & 0.941 & 0.056 \\ \cline{1-1}  & \(L_{seg}^{s}+L_{adv}\) & 0.849 & 0.951 & 0.055 \\ \cline{1-1}  & \(L_{seg}^{s}+L_{adv}+L_{seg}^{t}\) & 0.871 & 0.953 & 0.054 \\ \cline{1-1}  & \(L_{seg}^{s}+L_{adv}+L_{seg}^{t}+L_{m}\) & 0.873 & **0.959** & 0.049 \\ \cline{1-1}  & \(L_{seg}^{s}+L_{adv}+L_{seg}^{t}+L_{m}+L_{c}\) & **0.885** & 0.958 & **0.049** \\ \hline \hline \end{tabular}
\end{table}
Table 6: Ablation study of various loss functions. The best results are highlighted in bold.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Dataset** & **Method** & \(\mathbf{DI_{cap}}\) & \(\mathbf{DI_{disc}}\) & \(\delta\) \\ \hline \multirow{2}{*}{Drishti-GS} & CycleGAN & 0.853 & 0.942 & 0.089 \\  & Fourier & **0.876** & **0.971** & **0.081** \\ \multirow{2}{*}{RIM-ONE-r3} & CycleGAN & 0.793 & 0.911 & 0.094 \\  & Fourier & **0.818** & **0.922** & **0.083** \\ \multirow{2}{*}{REFUGE Val} & CycleGAN & 0.861 & 0.923 & 0.056 \\  & Fourier & **0.885** & **0.958** & **0.049** \\ \hline \hline \end{tabular}
\end{table}
Table 5: Performance of different domain transformation methods. The best results are highlighted in bold.