On the Topological Sculpting for Vessel-like Structure Segmentation

Thin 3D structures such as vessels, airways, and other branching tubular anatomies demand not only voxel-level accuracy but also correct global connectivity. Standard overlap-driven objectives often tolerate small breaks or spurious connections that severely damage topology, while many topology-aware losses are local, patch-based, or only influence training and thus cannot reliably repair errors at inference time. We present TopoSculpt, a generic refinement framework that improves the topology of predicted 3D tubular segmentations by explicitly enforcing global topological priors. TopoSculpt introduces a Topological Integrity Betti (TIB) loss that combines (i) Betti-number guidance toward a desired topology and (ii) an integrity regularizer that discourages destructive deviations from the initial prediction. To make persistent-homology computations tractable, we propose a curriculum refinement strategy that progressively transitions from coarse to fine corrections with adaptive sampling. Experiments on three challenging 3D benchmarks (pulmonary airway, Circle of Willis, and coronary artery) show consistent gains in both geometric accuracy and topology fidelity, reducing large connectivity errors by an order of magnitude and improving tree/branch detection rates. These results indicate that TopoSculpt is an effective, broadly applicable mechanism for topology-preserving refinement of 3D thin-structure segmentation.