Implicit Representation Embraces Challenging Attributes of Pulmonary Airway Tree Structures

High-fidelity modeling of the pulmonary airway tree from CT scans is critical to preoperative planning. However, the granularity of CT scan resolutions and the intricate topologies limit the accuracy of manual or deep-learning-based delineation of airway structures, resulting in coarse representation accompanied by spike-like noises and disconnectivity issues. To address these challenges, we introduce a Deep Geometric Correspondence Implicit (DGCI) network that implicitly models airway tree structures in the continuous space rather than discrete voxel grids. DGCI first explores the intrinsic topological features shared within different airway cases on top of implicit neural representation (INR). Specifically, we establish a reversible correspondence flow to constrain the feature space of training shapes. Moreover, implicit geometric regularization is utilized to promote a smooth and high-fidelity representation of fine-scaled airway structures. By transcending voxel-based representation, DGCI acquires topological insights and integrates geometric regularization into INR, generating airway tree structures with state-of-the-art topological fidelity. Detailed evaluation results on the public dataset demonstrated the superiority of the DGCI in the scalable delineation of airways and downstream applications. Source codes can be found at: https://github.com/EndoluminalSurgicalVision-IMR/DGCI .