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

2026-02-02

AI Summary

This work addresses the challenge of topological incompleteness in lung airway trees extracted from CT scans, where missing or disconnected branches hinder downstream anatomical analysis and modeling. To this end, the authors propose TopoField, a novel framework that explicitly treats topological repair as a core modeling objective. By constructing a topology-aware implicit field from sparse surface and skeleton point clouds, TopoField enables end-to-end learning of topological restoration, anatomical label prediction, and lobar segmentation without requiring explicit disconnection annotations. The model is trained solely on synthetically perturbed, incomplete tree structures. Evaluated on the Lung3D+ dataset, the method significantly improves both topological completeness and labeling accuracy, completing the entire pipeline in just over one second—demonstrating strong potential for clinical deployment.

Technology Category

• Computer Vision: 3D Computer Vision
• Machine Learning: Learning with Manifolds
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

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 or explicit graph reasoning, leading to limited efficiency 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 \textit{already} 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. 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. Code and data will be available at https://github.com/HINTLab/TopoField.

Problem

• pulmonary tree
• topological incompleteness
• branch disconnection
• anatomical analysis
• structural corruption

Innovation

• implicit field
• topology-aware modeling
• pulmonary tree reconstruction
• incomplete supervision
• unified multi-task inference