Pulmonary diseases rank prominently among the principal causes of death
worldwide. Curing them will require, among other things, a better understanding
of the complex 3D tree-shaped structures within the pulmonary system, such as
airways, arteries, and veins. Traditional approaches using high-resolution
image stacks and standard CNNs on dense voxel grids face challenges in
computational efficiency, limited resolution, local context, and inadequate
preservation of shape topology. Our method addresses these issues by shifting
from dense voxel to sparse point representation, offering better memory
efficiency and global context utilization. However, the inherent sparsity in
point representation can lead to a loss of crucial connectivity in tree-shaped
structures. To mitigate this, we introduce graph learning on skeletonized
structures, incorporating differentiable feature fusion for improved topology
and long-distance context capture. Furthermore, we employ an implicit function
for efficient conversion of sparse representations into dense reconstructions
end-to-end. The proposed method not only delivers state-of-the-art performance
in labeling accuracy, both overall and at key locations, but also enables
efficient inference and the generation of closed surface shapes. Addressing
data scarcity in this field, we have also curated a comprehensive dataset to
validate our approach. Data and code are available at
\url{this https URL}.