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

arXiv: https://arxiv.org/abs/2509.03938 · HTML: https://mlsanity.com/paper/2509.03938/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 45 references that are in the map.
- First posted on arXiv 4 Sep 2025.

## Builds on (most cited first, 28 of 28)

- [V-Net: Fully Convolutional Neural Networks for Volumetric Medical Image Segmentation](https://mlsanity.com/paper/1606.04797/) (2016)
- [3D U-Net: Learning Dense Volumetric Segmentation from Sparse Annotation](https://mlsanity.com/paper/1606.06650/) (2016)
- [TotalSegmentator: robust segmentation of 104 anatomical structures in CT images](https://mlsanity.com/paper/2208.05868/) (2022)
- [clDice -- A Novel Topology-Preserving Loss Function for Tubular Structure Segmentation](https://mlsanity.com/paper/2003.07311/) (2020)
- [DeepGlobe 2018: A Challenge to Parse the Earth through Satellite Images](https://mlsanity.com/paper/1805.06561/) (2018)
- [Topology-Preserving Deep Image Segmentation](https://mlsanity.com/paper/1906.05404/) (2019)
- [Metrics reloaded: Recommendations for image analysis validation](https://mlsanity.com/paper/2206.01653/) (2022)
- [Boundary loss for highly unbalanced segmentation](https://mlsanity.com/paper/1812.07032/) (2018)
- [A Topological Loss Function for Deep-Learning based Image Segmentation using Persistent Homology](https://mlsanity.com/paper/1910.01877/) (2019)
- [A roadmap for the computation of persistent homology](https://mlsanity.com/paper/1506.08903/) (2015)
- [Ripser: efficient computation of Vietoris-Rips persistence barcodes](https://mlsanity.com/paper/1908.02518/) (2019)
- [ROSE: A Retinal OCT-Angiography Vessel Segmentation Dataset and New Model](https://mlsanity.com/paper/2007.05201/) (2020)
- [Deep learning to achieve clinically applicable segmentation of head and neck anatomy for radiotherapy](https://mlsanity.com/paper/1809.04430/) (2018)
- [Topology-Aware Segmentation Using Discrete Morse Theory](https://mlsanity.com/paper/2103.09992/) (2021)
- [Common Limitations of Image Processing Metrics: A Picture Story](https://mlsanity.com/paper/2104.05642/) (2021)
- [OCTA-500: A Retinal Dataset for Optical Coherence Tomography Angiography Study](https://mlsanity.com/paper/2012.07261/) (2020)
- [The TopCoW Challenge -- Topology-Aware Circle of Willis Segmentation for CT and MR Angiography](https://mlsanity.com/paper/2312.17670/) (2023)
- [Topologically faithful image segmentation via induced matching of persistence barcodes](https://mlsanity.com/paper/2211.15272/) (2022)
- [Skeleton Recall Loss for Connectivity Conserving and Resource Efficient Segmentation of Thin Tubular Structures](https://mlsanity.com/paper/2404.03010/) (2024)
- [nnInteractive: Redefining 3D Promptable Segmentation](https://mlsanity.com/paper/2503.08373/) (2025)
- [Alleviating Class-wise Gradient Imbalance for Pulmonary Airway Segmentation](https://mlsanity.com/paper/2011.11952/) (2020)
- [AirwayNet: A Voxel-Connectivity Aware Approach for Accurate Airway Segmentation Using Convolutional Neural Networks](https://mlsanity.com/paper/1907.06852/) (2019)
- [Centerline Boundary Dice Loss for Vascular Segmentation](https://mlsanity.com/paper/2407.01517/) (2024)
- [Learning Probabilistic Topological Representations Using Discrete Morse Theory](https://mlsanity.com/paper/2206.01742/) (2022)
- [Topologically Faithful Multi-class Segmentation in Medical Images](https://mlsanity.com/paper/2403.11001/) (2024)
- [Topology Optimization in Medical Image Segmentation with Fast Euler Characteristic](https://mlsanity.com/paper/2507.23763/) (2025)
- [Reflecting Topology Consistency and Abnormality via Learnable Attentions for Airway Labeling](https://mlsanity.com/paper/2410.23854/) (2024)
- [AirMorph: Topology-Preserving Deep Learning for Pulmonary Airway Analysis](https://mlsanity.com/paper/2412.11039/) (2024)

## Built on by (most cited first, 1 of 1)

- [Towards High-Quality Image Segmentation: Improving Topology Accuracy by Penalizing Neighbor Pixels](https://mlsanity.com/paper/2603.18671/) (2026)

## Abstract (arXiv)

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, β0 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.