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

2025-09-04

AI Summary

Existing methods rely on voxel-overlap metrics, failing to guarantee global topological correctness and geometric integrity in 3D reconstruction of tubular anatomical structures (e.g., pulmonary airways, cerebral vasculature). To address this, we propose the first global topology optimization framework, introducing Topological Integrity Betti-number (TIB) constraints. Our method jointly leverages persistent homology analysis, whole-volume contextual modeling, and progressive curriculum learning to co-optimize geometric fidelity and β₀ topological errors. Crucially, it actively rectifies topological defects during inference—surpassing conventional local topology-aware approaches. Experiments on pulmonary airway and Circle of Willis datasets demonstrate substantial improvements: β₀ error rates decrease from 69.00 to 3.40 and from 1.65 to 0.30, respectively; tree length and branch detection accuracy increase by nearly 10%, significantly enhancing fine-grained tubular structure reconstruction fidelity.

Technology Category

• Constraint Satisfaction and Optimization: Constraint Optimization
• Computer Vision: 3D Computer Vision
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

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.

Problem

• Reconstructing 3D tubular anatomy geometry and topology accurately
• Addressing voxel-based methods' failure in topological correctness
• Ensuring global topological preservation and geometric error correction

Innovation

• Holistic whole-region modeling for full spatial context
• Topological Integrity Betti constraint enforces global integrity
• Curriculum refinement with persistent homology corrects errors