Vessel-RW: Weakly Supervised Subcutaneous Vessel Segmentation via Learned Random-Walk Propagation

Accurate segmentation of subcutaneous vessels from clinical images is hampered by scarce, expensive ground truth and by low-contrast, noisy appearance of vessels across patients and modalities. We present a novel weakly supervised training framework tailored for subcutaneous vessel segmentation that leverages inexpensive sparse annotations (e.g., centerline traces, dot markers, or short scribbles). Sparse labels are expanded into dense, probabilistic supervision via a differentiable random-walk label-propagation model whose transition weights incorporate image-driven vesselness cues and tubular continuity priors. The propagation yields per-pixel hitting probabilities together with calibrated uncertainty estimates; these are incorporated into an uncertainty-weighted loss to avoid over-fitting to ambiguous regions. Crucially, the label-propagator is learned jointly with a CNN-based segmentation predictor, enabling the system to discover vessel edges and continuity constraints without explicit edge supervision. We further introduce a topology-aware regularizer that encourages centerline connectivity and penalizes spurious branches, improving clinical usability. In experiments on clinical subcutaneous imaging datasets, our method consistently outperforms naive training on sparse labels and conventional dense pseudo-labeling, producing more complete vascular maps and better-calibrated uncertainty for downstream decision-making. The approach substantially reduces annotation burden while preserving clinically relevant vessel topology.