TopoSculpt: Betti-Steered Topological Sculpting of 3D Fine-grained Tubular Shapes

Abstract

Medical tubular anatomical structures are inherently three-dimensional conduits with lumens, enclosing walls, and complex branching topologies. Accurate reconstruction of their geometry and topology is crucial for applications such as bronchoscopic navigation and cerebral arterial connectivity assessment. Existing methods often rely on voxel-wise overlap measures, which fail to capture topological correctness and completeness. Although topology-aware losses and persistent homology constraints have shown promise, they are usually applied patch-wise and cannot guarantee global preservation or correct geometric errors at inference. To address these limitations, we propose a novel TopoSculpt, a framework for topological refinement of 3D fine-grained tubular structures. TopoSculpt (i) adopts a holistic whole-region modeling strategy to capture full spatial context, (ii) first introduces a Topological Integrity Betti (TIB) constraint that jointly enforces Betti number priors and global integrity, and (iii) employs a curriculum refinement scheme with persistent homology to progressively correct errors from coarse to fine scales. Extensive experiments on challenging pulmonary airway and Circle of Willis datasets demonstrate substantial improvements in both geometry and topology. For instance, $β_{0}$ errors are reduced from 69.00 to 3.40 on the airway dataset and from 1.65 to 0.30 on the CoW dataset, with Tree length detected and branch detected rates improving by nearly 10\%. These results highlight the effectiveness of TopoSculpt in correcting critical topological errors and advancing the high-fidelity modeling of complex 3D tubular anatomy. The project homepage is available at: https://github.com/Puzzled-Hui/TopoSculpt.

Figures (11)

• Figure 1: Existing methods often yield fragmented or disconnected structures (arrows) when modeling fine-grained three-dimensional tubular anatomy, whereas the proposed TopoSculpt improves structural continuity and preserves global topological integrity (from left to right: pulmonary airway, Circle of Willis, and coronary artery).
• Figure 2: Pipeline of the proposed TopoSculpt. a.1) Existing topological refinement methods typically rely on patch-wise training and sliding-window testing, which cannot guarantee the topological integrity of the whole structure, as a single patch fails to capture global geometric attributes. a.2) In contrast, our method adopts a holistic modeling strategy by feeding the entire image region covering the complete target structure into the network, ensuring that the full spatial context is preserved. Betti-guided refinement alone can improve certain topological characteristics but often compromises global integrity. a.3) By jointly incorporating Betti guidance and topological integrity constraints, our method preserves global topology while enhancing local topological correctness. b) We further design a curriculum learning strategy to progressively refine segmentation results: initially correcting large-scale errors through dense persistent homology (PH) calculations, and gradually focusing on finer-scale errors with sparser PH sampling. This enables efficient learning of topological corrections across multiple scales. c) The refinement process is supervised by both Betti numbers and topological integrity metrics, ensuring optimization consistently improves both local correctness and global fidelity.
• Figure 3: Detailed framework of the proposed TopoSculpt. (a) Training paradigm. TopoSculpt is optimized via a holistic-view modeling strategy, where entire anatomical regions encompassing the complete target structure are fed into the network to capture full spatial and topological context. Voxel-wise supervision is applied in the training stage. (b) TopoSculpt refinement on unseen test cases. For a given test scan, the initial prediction is generated by the trained encode-decoder network and iteratively refined under the supervision of a topological integrity prior. This refinement progressively corrects connectivity errors, thereby improving the topological accuracy. (c) Details of the topological integrity prior supervision. During refinement, the persistent homology (PH) barcodes of the likelihood maps are analyzed to identify critical topological features. The Betti-guided correction term encourages the removal of spurious PH components (enhancing topological correctness), while the topological integrity constraint penalizes deviations from the original global topology, preserving topological completeness. Through iterative refinement, TopoSculpt achieves consistent suppression of erroneous components and convergence toward topologically faithful 3D reconstructions.
• Figure 4: Qualitative comparison of TopoSculpt with competing methods, including clDice, CAL, SkeletonRecall (SR), cbDice, BoundaryLoss (BL), TopoLoss (TL) and DMT, on three representative fine-grained tubular datasets. The green boxes highlight local regions where TopoSculpt better preserves fine structural details and achieves higher topological fidelity.
• Figure 5: The visualization of TopoSculpt illustrates the refinement process from the initial airway structure to the final result, exhibiting substantial enhancement in topological fidelity. In each case, the first row depicts the holistic view of the airway structures, demonstrating progressive improvements in overall topology. The second row offers a zoomed-in perspective, emphasizing localized refinements and enhanced topological consistency in the detailed airway branches.