Spatial graphs provide a lightweight and elegant representation of curvilinear anatomical structures such as blood vessels, lung airways, and neuronal networks. Accurately modeling these graphs is crucial in clinical and (bio-)medical research. However, the high spatial resolution of large networks drastically increases their complexity, resulting in significant computational challenges. In this work, we aim to tackle these challenges by proposing VesselTok, a framework that approaches spatially dense graphs from a parametric shape perspective to learn latent representations (tokens). VesselTok leverages centerline points with a pseudo radius to effectively encode tubular geometry. Specifically, we learn a novel latent representation conditioned on centerline points to encode neural implicit representations of vessel-like, tubular structures. We demonstrate VesselTok's performance across diverse anatomies, including lung airways, lung vessels, and brain vessels, highlighting its ability to robustly encode complex topologies. To prove the effectiveness of VesselTok's learnt latent representations, we show that they (i) generalize to unseen anatomies, (ii) support generative modeling of plausible anatomical graphs, and (iii) transfer effectively to downstream inverse problems, such as link prediction.

翻译：空间图提供了一种轻量且优雅的方式来表征曲线解剖结构，如血管、肺气道和神经网络。准确建模这些图在临床和（生物）医学研究中至关重要。然而，大型网络的高空间分辨率会急剧增加其复杂度，带来显著的计算挑战。本研究旨在通过提出VesselTok框架来应对这些挑战，该框架从参数化形状角度处理空间密集图，以学习潜在表示（令牌）。VesselTok利用带有伪半径的中心线点有效编码管状几何结构。具体而言，我们学习了一种以中心线点为条件的新型潜在表示，以编码血管样管状结构的神经隐式表征。我们在多种解剖结构（包括肺气道、肺血管和脑血管）上展示了VesselTok的性能，突显了其鲁棒编码复杂拓扑结构的能力。为证明VesselTok所学潜在表示的有效性，我们表明它们：(i) 可泛化至未见过的解剖结构，(ii) 支持对合理解剖图进行生成建模，以及 (iii) 有效迁移至下游逆问题（如链接预测）。