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.

翻译：从CT图像中提取的肺树结构常呈现拓扑不完整性，例如分支缺失或连接中断，这会显著降低下游解剖分析的可靠性，并限制现有肺树建模流程的适用性。现有方法通常依赖密集体素处理或显式图推理，导致效率受限且在真实结构破损情况下鲁棒性降低。我们提出TopoField——一种拓扑感知的隐式建模框架，将拓扑修复视为核心建模问题，并支持肺树分析的多任务统一推理。TopoField使用稀疏表面与骨架点云表示肺部解剖结构，通过在对\textit{已存在}不完整树结构上引入合成断裂进行训练，学习能够支持拓扑修复的连续隐式场，且无需依赖完整或显式的断连标注。基于修复后的隐式表示，解剖标记与肺段重建可通过任务专用隐式函数在单次前向传播中联合推断。在Lung3D+数据集上的大量实验表明，TopoField能持续提升拓扑完整性，并在具有挑战性的不完整场景下实现精确的解剖标记与肺段重建。得益于其隐式表示形式，TopoField具备高计算效率，每例病例可在略超一秒内完成全部任务，凸显了其在大规模及时间敏感临床场景中的实用性。代码与数据将在https://github.com/HINTLab/TopoField发布。