# Learning Topology-Aware Implicit Field for Unified Pulmonary Tree Modeling with Incomplete Topological Supervision

arXiv: https://arxiv.org/abs/2602.02186 · HTML: https://mlsanity.com/paper/2602.02186/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 67 references that are in the map.
- First posted on arXiv 2 Feb 2026.

## Builds on (most cited first, 19 of 19)

- [Convolutional Occupancy Networks](https://mlsanity.com/paper/2003.04618/) (2020)
- [Point-Voxel CNN for Efficient 3D Deep Learning](https://mlsanity.com/paper/1907.03739/) (2019)
- [clDice -- A Novel Topology-Preserving Loss Function for Tubular Structure Segmentation](https://mlsanity.com/paper/2003.07311/) (2020)
- [ImageCAS: A Large-Scale Dataset and Benchmark for Coronary Artery Segmentation based on Computed Tomography Angiography Images](https://mlsanity.com/paper/2211.01607/) (2022)
- [AirwayNet: A Voxel-Connectivity Aware Approach for Accurate Airway Segmentation Using Convolutional Neural Networks](https://mlsanity.com/paper/1907.06852/) (2019)
- [Learning Tubule-Sensitive CNNs for Pulmonary Airway and Artery-Vein Segmentation in CT](https://mlsanity.com/paper/2012.05767/) (2020)
- [Efficient automatic segmentation for multi-level pulmonary arteries: The PARSE challenge](https://mlsanity.com/paper/2304.03708/) (2023)
- [A joint 3D UNet-Graph Neural Network-based method for Airway Segmentation from chest CTs](https://mlsanity.com/paper/1908.08588/) (2019)
- [Fuzzy Attention Neural Network to Tackle Discontinuity in Airway Segmentation](https://mlsanity.com/paper/2209.02048/) (2022)
- [Multi-site, Multi-domain Airway Tree Modeling (ATM'22): A Public Benchmark for Pulmonary Airway Segmentation](https://mlsanity.com/paper/2303.05745/) (2023)
- [What Makes for Automatic Reconstruction of Pulmonary Segments](https://mlsanity.com/paper/2207.03078/) (2022)
- [Accurate Airway Tree Segmentation in CT Scans via Anatomy-aware Multi-class Segmentation and Topology-guided Iterative Learning](https://mlsanity.com/paper/2306.09116/) (2023)
- [Structure and position-aware graph neural network for airway labeling](https://mlsanity.com/paper/2201.04532/) (2022)
- [Topology Repairing of Disconnected Pulmonary Airways and Vessels: Baselines and a Dataset](https://mlsanity.com/paper/2306.07089/) (2023)
- [Efficient Anatomical Labeling of Pulmonary Tree Structures via Deep Point-Graph Representation-based Implicit Fields](https://mlsanity.com/paper/2309.17329/) (2023)
- [BCNet: Bronchus Classification via Structure Guided Representation Learning](https://mlsanity.com/paper/2205.06947/) (2022)
- [Restoring Connectivity in Vascular Segmentation using a Learned Post-Processing Model](https://mlsanity.com/paper/2404.10506/) (2024)
- [GDDS: Pulmonary Bronchioles Segmentation with Group Deep Dense Supervision](https://mlsanity.com/paper/2303.09212/) (2023)
- [HarmonySeg: Tubular Structure Segmentation with Deep-Shallow Feature Fusion and Growth-Suppression Balanced Loss](https://mlsanity.com/paper/2504.07827/) (2025)

## Abstract (arXiv)

Pulmonary trees extracted from CT images frequently exhibit topological incompleteness, such as missing or disconnected branches, which substantially degrades downstream anatomical analysis and limits the applicability of existing pulmonary tree modeling pipelines. Current approaches typically rely on dense volumetric processing, explicit graph reasoning, or generic point cloud completion priors, leading to limited efficiency, weak structural awareness, and reduced robustness under realistic structural corruption. We propose TopoField, a topology-aware implicit modeling framework that treats topology repair as a first-class modeling problem and enables unified multi-task inference for pulmonary tree analysis. TopoField represents pulmonary anatomy using sparse surface and skeleton point clouds and learns a continuous implicit field that supports topology repair without relying on complete or explicit disconnection annotations, by training on synthetically introduced structural disruptions over textitalready incomplete trees. Building upon the repaired implicit representation, anatomical labeling and lung segment reconstruction are jointly inferred through task-specific implicit functions within a single forward pass. Extensive experiments on the Lung3D+ dataset demonstrate that TopoField consistently improves topological completeness and achieves accurate anatomical labeling and lung segment reconstruction under challenging incomplete scenarios. We further validate TopoField on real incomplete outputs from an external segmentation model, demonstrating its applicability to realistic segmentation pipelines. Owing to its implicit formulation, TopoField attains high computational efficiency, completing all tasks in just over one second per case, highlighting its practicality for large-scale and time-sensitive clinical applications.