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

TL;DR

This work tackles the problem of topological incompleteness in CT-derived pulmonary trees, where missing or disconnected branches hinder downstream analysis. It introduces TopoField, a topology-aware implicit framework that represents pulmonary anatomy with sparse surface and skeleton point clouds and learns a unified implicit field to repair topology while simultaneously performing anatomical labeling and lung-segment reconstruction in a single forward pass. A weakly supervised topology repair strategy (TopoBreak) enables learning connectivity restoration without explicit disconnection annotations, improving robustness under realistic corruption. Across the Lung3D+ dataset, TopoField achieves state-of-the-art repair performance and competitive labeling and segment reconstruction with greatly improved efficiency (≈1s per case), making it practical for large-scale clinical use and time-sensitive workflows.

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.

Figures (7)

• Figure 1: Comparison between conventional task-specific pipelines and our unified multi-task implicit framework (TopoField). Compared to task-specific pipelines, TopoField enables topology repair under incomplete topological supervision, without disconnection annotations, and jointly performs repair, anatomical labeling, and lung segment reconstruction in a single forward pass, achieving a two-orders-of-magnitude reduction in inference time (Section \ref{['sec:experiment']}).
• Figure 2: Overview of the proposed TopoBreak strategy.. Starting from a complete pulmonary tree mask, the skeleton is extracted and two breakpoints (BP) are selected along a branch. Guided by the skeleton and branch radius, TopoBreak removes the segment between these points to create realistic topological disconnections, as shown in the close-up view.
• Figure 3: An overview of the Lung3D+ dataset. The dataset contains both complete and simulated disconnected pulmonary trees across the airways, arteries, and veins. For clarity, we illustrate the disconnected input trees alongside their corresponding complete labeled trees and lung segments. All three types of trees belong to the same subject and share identical segmental anatomy. In the corrupted binary trees, disconnection sites are highlighted and magnified with green boxes, indicating regions of structural disruption requiring repair.
• Figure 4: Overview of our TopoField framework. (a) The incomplete pulmonary tree is represented using both a surface point cloud ($\mathcal{S}$) and a skeleton point cloud ($\mathcal{K}$), which are respectively encoded by point-based networks. Surface features are further enriched by a super-point descriptor, while skeleton features capture the global topological structure. The two representations are fused via the proposed Surface-to-Skeleton Attention (SSA) module, where surface points act as queries and skeleton points as keys/values. The fused features are then projected onto three orthogonal planes to generate tri-plane feature maps, which are jointly processed by a shared 2D U-Net encoder to construct a unified multi-task implicit field. Task-specific implicit functions subsequently enable efficient inference on sampled query points during training and dense full-volume queries during inference, supporting pulmonary tree repair, anatomical labeling, and lung segment reconstruction simultaneously. (b)–(d) illustrate the detailed designs of the corresponding modules. (e) illustrates our Topological Repair without Disconnection Annotations, which implicitly restores missing connectivity without requiring explicit disconnection annotations.
• Figure 5: Visualization of Pulmonary Tree Topology Repair Results. Representative samples from the airway, artery, and vein datasets (top to bottom) are shown for comparison. From left to right, each row presents the ground truth, corrupted input, two 3D-UNet baselines (DS: down-sampled; SW: sliding-window), and different TopoField variants. Target structures are rendered in red, false positives in blue, and false negatives (disconnected segments) in green. Purple boxes indicate locally disconnected regions, with zoomed-in views highlighting repair details. DMF1 (%), GDice (%), and NCC are reported for each method on the corresponding sample. Overall, TopoField variants, particularly TopoField (Full), achieve more accurate reconnections and better structural consistency with the ground truth than the 3D-UNet baselines across all three pulmonary structures.