TopoMatch: Topology-Constrained Semi-Balanced Transport for Open-World 3D Vascular Graph Parsing

Anatomical vessel labeling is more structured than closed-set branch classification: expected vessels may be absent, one vessel may be fragmented into multiple observations, and unseen anatomy may coexist with extraction artifacts. We introduce TopoMatch, an open-world framework that formulates 3D vascular parsing as structured correspondence between observed branches and an anatomical label space. A reversal-invariant curve tokenizer and an incidence-aware encoder retain ordered geometry and physical branch–junction structure. Topology-aware semi-balanced matching preserves branch-wise assignment, softly constrains the mass of known classes, and leaves separate unknown-anatomy and artifact slots unconstrained in total mass. A learned gate combines local and structured predictions before conditional topology-aware decoding. On CoW-VTP, TopoMatch achieves 94.72% Macro-F1 and 42.0% exact-graph accuracy. Capacity-matched controls remain close on clean recognition, whereas controlled experiments locate the clearest benefit of relaxed target mass in missing-anatomy regimes. Strict open-set evaluation further shows that separate free slots improve the distinction between unknown anatomy and extraction artifacts. Corruption-aware training improves robustness with little change in clean performance. Task-specific retraining yields consistent branch-level gains across graph-construction pipelines, larger vascular graphs, and coronary anatomy, though whole-graph recovery remains challenging on TopBrain. These results support open-world structured matching without a fixed one-to-one anatomical template.