# Causal Inference-Based Self-Supervised Cross-Domain Fundus Image Segmentation
## 1 Introduction  
Glaucoma is the world's second leading cause of blindness [1], with its primary pathologic mechanism attributed to the degeneration of retinal ganglion cells. Without timely intervention, the progressive damage to the optic nerve can result in irreversible vision loss. However, early screening and prompt treatment can significantly reduce these risks. The cup-to-disc ratio (CDR)--defined as the ratio of the vertical cup diameter (VCD) to the vertical disc diameter (VDD)--is a widely used diagnostic indicator for glaucoma, as a higher CDR often signals an increased risk of the disease. Given that manually delineating the optic disc (OD) and optic cup (OC) and computing the CDR is both time-consuming and labor-intensive, there is an urgent need for research into automated segmentation methods to improve the efficiency and accuracy of glaucoma diagnosis. In traditional methods for automatic segmentation of the OD and OC, a variety of approaches have been proposed, including active contour models [2; 3], Hough-transform-based detection [2; 4; 5], morphological operations [6; 7], weakly supervised techniques [8], among others. For example, [PERSON] et al. [2] proposed a cascaded pipeline in which the red channel is first enhanced by adaptive histogram equalization and subjected to morphological vessel removal and binarization; a circular Hough transform then generates initial disc contours, which are iteratively evolved under the gradient vector flow (GVF) energy functional to accurately delineate the disc boundary. [PERSON] et al. [5] described a similar pipeline that converts fundus images to a luminance representation for artifact removal, extracts edges via Sobel or Canny operators, detects circular candidates via the Hough transform, and refines them by intensity thresholding to precisely locate the disc. [PERSON] et al. [6] designed a two-stage adaptive morphological framework: in Stage 1, vessel skeletonization--using reconstruction, top-hat filtering and skeletonization--localizes the disc region; in Stage 2, a marker-controlled watershed transform adaptively segments the exact boundary. [PERSON] et al. [9] converted color retina images to grayscale with histogram equalization, performed multilevel thresholding followed by morphological erosion and dilation to extract boundary candidates, and then fitted a circle to the resulting points to determine the disc center and radius. However, these traditional approaches typically depend on handcrafted feature extraction, heuristic processing pipelines, and domain-specific parameter tuning, which render them sensitive to image artifacts, inter-patient variability, and inconsistent acquisition conditions. With the advent of deep learning, convolutional neural networks and related architectures have been widely adopted for OD and OC segmentation, learning hierarchical feature representations directly from data and demonstrating superior robustness and accuracy. Although numerous deep learning-based automated segmentation models have achieved excellent performance in segmenting OD and OC, most rely on training with labeled source-domain images. In practical applications, target-domain images are typically unlabeled, and variations in imaging equipment and acquisition conditions introduce a significant distribution discrepancy between source and target domains, resulting in a marked decline in conventional models' target-domain performance. While assembling a fundus-image dataset that encompasses all domain styles could enable the model to adapt to diverse styles and thereby mitigate the effects of domain shift, such an undertaking is extremely time-consuming, labor-intensive, and demands substantial additional computational resources. Consequently, recent studies have explored domain adaptation techniques to enhance the generalization ability of cross-domain segmentation.