# Vector Representations of Vessel Trees

arXiv: https://arxiv.org/abs/2506.11163 · HTML: https://mlsanity.com/paper/2506.11163/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 35 references that are in the map.
- First posted on arXiv 11 Jun 2025.

## Builds on (most cited first, 27 of 27)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Group Normalization](https://mlsanity.com/paper/1803.08494/) (2018)
- [Object-Centric Learning with Slot Attention](https://mlsanity.com/paper/2006.15055/) (2020)
- [Automatic chemical design using a data-driven continuous representation of molecules](https://mlsanity.com/paper/1610.02415/) (2016)
- [Junction Tree Variational Autoencoder for Molecular Graph Generation](https://mlsanity.com/paper/1802.04364/) (2018)
- [MolGAN: An implicit generative model for small molecular graphs](https://mlsanity.com/paper/1805.11973/) (2018)
- [GraphVAE: Towards Generation of Small Graphs Using Variational Autoencoders](https://mlsanity.com/paper/1802.03480/) (2018)
- [GraphAF: a Flow-based Autoregressive Model for Molecular Graph Generation](https://mlsanity.com/paper/2001.09382/) (2020)
- [MeshGPT: Generating Triangle Meshes with Decoder-Only Transformers](https://mlsanity.com/paper/2311.15475/) (2023)
- [MeshDiffusion: Score-based Generative 3D Mesh Modeling](https://mlsanity.com/paper/2303.08133/) (2023)
- [GraphiT: Encoding Graph Structure in Transformers](https://mlsanity.com/paper/2106.05667/) (2021)
- [Generative and Discriminative Voxel Modeling with Convolutional Neural Networks](https://mlsanity.com/paper/1608.04236/) (2016)
- [A Survey on Deep Graph Generation: Methods and Applications](https://mlsanity.com/paper/2203.06714/) (2022)
- [Self-Consistent Trajectory Autoencoder: Hierarchical Reinforcement Learning with Trajectory Embeddings](https://mlsanity.com/paper/1806.02813/) (2018)
- [Seeing Implicit Neural Representations as Fourier Series](https://mlsanity.com/paper/2109.00249/) (2021)
- [Traj-MAE: Masked Autoencoders for Trajectory Prediction](https://mlsanity.com/paper/2303.06697/) (2023)
- [IntrA: 3D Intracranial Aneurysm Dataset for Deep Learning](https://mlsanity.com/paper/2003.02920/) (2020)
- [Blood Vessel Geometry Synthesis using Generative Adversarial Networks](https://mlsanity.com/paper/1804.04381/) (2018)
- [VesselVAE: Recursive Variational Autoencoders for 3D Blood Vessel Synthesis](https://mlsanity.com/paper/2307.03592/) (2023)
- [Deep Structural Causal Shape Models](https://mlsanity.com/paper/2208.10950/) (2022)
- [Dominant motion identification of multi-particle system using deep learning from video](https://mlsanity.com/paper/2104.12722/) (2021)

## Built on by (most cited first, 3 of 3)

- [VesselTok: Tokenizing Vessel-like 3D Biomedical Graph Representations for Reconstruction and Generation](https://mlsanity.com/paper/2603.18797/) (2026)
- [Sparse Representation Learning for Vessels](https://mlsanity.com/paper/2605.01382/) (2026)
- [SynVA: A Modular Toolkit for Vessel Generation and Aneurysm Editing](https://mlsanity.com/paper/2605.17620/) (2026)

## Abstract (arXiv)

We introduce a novel framework for learning vector representations of tree-structured geometric data focusing on 3D vascular networks. Our approach employs two sequentially trained Transformer-based autoencoders. In the first stage, the Vessel Autoencoder captures continuous geometric details of individual vessel segments by learning embeddings from sampled points along each curve. In the second stage, the Vessel Tree Autoencoder encodes the topology of the vascular network as a single vector representation, leveraging the segment-level embeddings from the first model. A recursive decoding process ensures that the reconstructed topology is a valid tree structure. Compared to 3D convolutional models, this proposed approach substantially lowers GPU memory requirements, facilitating large-scale training. Experimental results on a 2D synthetic tree dataset and a 3D coronary artery dataset demonstrate superior reconstruction fidelity, accurate topology preservation, and realistic interpolations in latent space. Our scalable framework, named VeTTA, offers precise, flexible, and topologically consistent modeling of anatomical tree structures in medical imaging.