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

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, $\beta_{0}$ 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.

Shape-aware Sampling Matters in the Modeling of Multi-Class Tubular Structures

Accurate multi-class tubular modeling is critical for precise lesion localization and optimal treatment planning. Deep learning methods enable automated shape modeling by prioritizing volumetric overlap accuracy. However, the inherent complexity of fine-grained semantic tubular shapes is not fully emphasized by overlap accuracy, resulting in reduced topological preservation. To address this, we propose the Shapeaware Sampling (SAS), which optimizes patchsize allocation for online sampling and extracts a topology-preserved skeletal representation for the objective function. Fractal Dimension-based Patchsize (FDPS) is first introduced to quantify semantic tubular shape complexity through axis-specific fractal dimension analysis. Axes with higher fractal complexity are then sampled with smaller patchsizes to capture fine-grained features and resolve structural intricacies. In addition, Minimum Path-Cost Skeletonization (MPC-Skel) is employed to sample topologically consistent skeletal representations of semantic tubular shapes for skeleton-weighted objective functions. MPC-Skel reduces artifacts from conventional skeletonization methods and directs the focus to critical topological regions, enhancing tubular topology preservation. SAS is computationally efficient and easily integrable into optimization pipelines. Evaluation on two semantic tubular datasets showed consistent improvements in both volumetric overlap and topological integrity metrics.

A Digitalized Atlas for Pulmonary Airway

In this work, we proposed AirwayAtlas, which is an end-to-end pipeline for automatic extraction of airway anatomies with lobar, segmental and subsegmental labeling. A compact representation, AirwaySign, is generated based on diverse features of airway branches. Experiments on multi-center datasets validated the effectiveness of AirwayAtlas. We also demonstrated that AirwaySign is a powerful tool for correlation analysis on pulmonary diseases.