Improving Retinal Artery-Vein Segmentation via Geometric Energy Fields

We propose a Geometric Energy Field (GEF) supervision framework to enhance the robustness and structural consistency of retinal artery/vein (A/V) segmentation. We introduce two geometrically complementary energy fields: the Distance Energy Field (DEF), which encodes soft, vessel-type-specific spatial territories by modeling pixel-wise proximity to arteries and veins, thereby explicitly capturing their spatial coupling, and the Orientation Energy Field (OEF), which models vessel elongation and directional continuity to enforce label consistency along entire vascular trajectories and suppress spurious artery/vein label flipping. These geometry-aware energy fields provide explicit supervisory signals that guide A/V segmentation beyond local appearance cues. Extensive experiments on six retinal datasets demonstrate that the proposed method outperforms state-of-the-art approaches, achieving A/V segmentation accuracies of 97.9%, 97.1%, 98.7%, 98.5%, 97.7% and 99.1%, respectively. The results indicate that the proposed GEF-enhanced architecture produces more coherent, stable, and clinically plausible artery/vein segmentation results.