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 \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. 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.

翻译：从CT图像中提取的肺树常存在拓扑不完全性（如分支缺失或断开），这严重降低了下游解剖分析的质量，并限制了现有肺树建模流程的适用性。当前方法通常依赖密集体素处理、显式图推理或通用点云补全先验，导致效率有限、结构感知能力弱，且在真实结构损坏场景下鲁棒性不足。我们提出TopoField框架——一种拓扑感知隐式建模方法，将拓扑修复作为优先建模问题，并支持肺树分析中的统一多任务推理。TopoField利用稀疏表面和骨架点云表征肺解剖结构，通过在不完全树上引入合成结构破坏进行训练，学习无需完整或显式断开标注即可支持拓扑修复的连续隐式场。基于修复后的隐式表示，通过单次前向传播中特定任务的隐式函数联合推断解剖标注和肺段重建。在Lung3D+数据集上的大量实验表明，TopoField持续提升拓扑完整性，并在具有挑战性的不完全场景下实现精确的解剖标注与肺段重建。我们进一步在外部分割模型输出的真实不完全结果上验证TopoField，证明其对实际分割流程的适用性。得益于隐式建模特性，TopoField实现高计算效率，每例病例全部任务耗时仅一秒余，凸显其在大规模及时间敏感型临床应用中的实用性。