PDE-Refined Local Fractal Dimension Prior Conditioning and Topology-Aware Refinement for Retinal Vessel Segmentation with a Swin-UNet-Style Backbone

Retinal vessel segmentation remains challenging for thin vessels and low-contrast bifurcations. We evaluate a Swin-UNet-style model family that conditions decoder features with a single-channel local fractal dimension prior refined by a short learnable anisotropic diffusion model and injected through Spatially-Adaptive Normalization (SPADE). On Fundus Image Vessel Segmentations (FIVES), the strongest no-test-time-augmentation result was obtained by OPT-I v2 at 200 epochs, reaching Dice 0.8899, clDice 0.8517, and Area Under the ROC Curve (AUC) 0.9904, compared with 0.8643, 0.8125, and 0.9856 for the matched 200-epoch baseline. In a matched Neural Cellular Automata (NCA)/no-NCA ablation using the same seed, data, 200-epoch budget, and evaluation pipeline, enabling NCA improved the test Dice from 0.8813 to 0.8907 and the test clDice from 0.8325 to 0.8518, with NCA winning on all 80 paired test images for both metrics. The results support PDE (partial differential equation)-SPADE fractal prior conditioning and NCA topology refinement as ablation-grounded improvements over the tested baseline family, while broader matched external validation requires future work.