\section{Related Work}

\subsection{Pulmonary Artery-Vein Segmentation}

Early work on pulmonary artery-vein (A/V) segmentation primarily relied on CTPA and classical image-processing pipelines combining vesselness filtering, anatomical heuristics, or semi-automatic propagation \cite{wittram2007ct, mekada2006pulmonary, buelow2005automatic, payer2016automated}. Learning-based variants such as AdaBoost voxel classifiers \cite{ochs2007automated} and early graph-based methods \cite{charbonnier2015automatic} improved robustness but remained limited by handcrafted features.

Deep learning substantially advanced pulmonary vessel segmentation. CNN-based approaches \cite{nardelli2018pulmonary, tetteh2020deepvesselnet} improved voxel-level accuracy but often struggled with distal branches and global A/V distinction. Subsequent work emphasized better structural context via tubule-sensitive designs \cite{qin2021learning}, geometry-aware or multi-resolution architectures \cite{pu2023automated, pan2023learning}, and hierarchical prediction schemes such as HiPaS \cite{chu2025deep}. Transformers have also been explored for vessel modeling and A/V separation by leveraging long-range attention \cite{wu2023transformer, wu2023hepatic, lv2024tcddu}.

\subsection{Pulmonary Anatomical Vessel Labeling}

Anatomical labeling assigns each vessel branch to a semantic pulmonary region and has been studied more extensively for airways than for vasculature. Prior work includes structure-aware CNN-GNN hybrids \cite{tan2021sgnet}, topology-guided GNNs \cite{xie2024structure}, and hypergraph-based tree models \cite{yu2022tnn}. These approaches capture hierarchical structure but generally rely on voxel-based predictions or predefined templates, limiting applicability to complex vascular trees.

Point-based and graph-based learning provide more flexible representations. Earlier work explored geometric matching of bronchial trees \cite{bulow2006point}, while recent point-cloud pipelines such as RibSeg demonstrated strong anatomical labeling performance for bony structures \cite{jin2023ribseg}. Graph-based models further encode topological relationships but still require mechanisms for dense reconstruction.

Most relevant to our work is the Implicit Point-Graph Network (IPGN) \cite{xie2025efficient}, the first anatomical labeling framework developed specifically for pulmonary arteries and veins. IPGN integrates point-based and graph-based reasoning with an implicit field decoder to obtain dense, high-resolution anatomical labels for the full vascular tree.
