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VesselTok: Tokenizing Vessel-like 3D Biomedical Graph Representations for Reconstruction and Generation

Conference: ECCV2026
Paper: ECCV 2026
Code: https://github.com/chinmay5/vessel_tok
Area: Medical Imaging
Keywords: Vessel graph tokenization / Neural implicit representation / Graph generation / Topology preservation / Tubular structures

TL;DR

VesselTok dilates a 3D centerline graph of vessels or airways into a continuous "graph occupancy field" with a fixed pseudo-radius, then learns fixed-length compact tokens (512 × 4) with a VAE-style transformer over centerline points, so that a single latent space supports high-fidelity reconstruction, cross-anatomy generalization, vascular graph generation, and missing-link infilling.

Background & Motivation

Tubular networks — blood vessels, airways, neurons, lymphatics — pervade physiological systems and serve to connect anatomical regions and transport signals and substrates; their normal and abnormal morphology matters in cerebrovascular disease, pulmonary disorders, and diabetic peripheral neuropathy. A 3D spatial graph built from the centerlines of these structures is a natural representation: one graph already carries length, radius, branch topology, and the structural inputs computational flow modeling needs. The problem is resolution. At high spatial resolution such graphs routinely contain tens of thousands of nodes and edges, which is beyond what off-the-shelf graph algorithms and generative models can process, so prior work has been forced back to simplified structures (tree-only graphs), small components or subgraphs, or individual vessel segments, and scale has stayed low.

Shape tokenization already offers a mature recipe: 3DShape2VecSet and Hunyuan3D 2.0 compress a 3D shape into a compact set of latent vectors that plug directly into a diffusion model. But they all sample surface points, and vascular networks are exactly the sparse, thin, highly branched, high surface-to-volume case: one representative ATM case has roughly 64,000 surface points against only about 3,000 centerline points. A tokenizer with a fixed query budget spends much of it on redundant vessel walls, while small branches, endpoints, and bifurcations — the places that actually determine topology — are undersampled. The authors further argue that vessel radius, despite varying widely, is not the bottleneck for compact representations: in systems such as airways and cerebral vasculature, radii are anatomically constrained and vary smoothly along the centerline, and can be reliably regressed from centerline coordinates (verified in the supplementary Sec. B). Giving centerline points a fixed pseudo-radius and treating the true radius as an inferable attribute therefore concentrates model capacity on 3D geometry and topology and avoids the severe scale imbalance of wide radius distributions. Core idea: rather than tokenizing a graph as a set of nodes, dilate the centerline graph into a continuous occupancy field and tokenize only the centerline points with a VAE-style encoder — the saved capacity buys expressiveness for complex 3D topology, and this compact latent is itself the shared interface for reconstruction, generation, and infilling.

Method

Overall Architecture

The problem is formalized as follows: given a 3D spatial graph \(G=(V,E,\{P\})\) (vertices, edges, and node coordinates), learn a graph tokenizer \(\mathcal{T}\) that maps \(G\) to a token sequence of length \(l\) and channel size \(c\) (continuous latent \(Z\in\mathbb{R}^{l\times c}\) in the VAE case), together with a decoder \(\mathcal{D}\) such that \(\tilde{G}=\mathcal{D}(\mathcal{T}(G))\) preserves the topology and structure of the input graph \(G\). The pipeline has three stages: turn the discrete centerline graph into a continuous graph occupancy field, encode it into fixed-length compact tokens over the centerline points, then decode the tokens back into an occupancy field and recover a discrete graph through skeletonization and neighborhood connectivity. The detour through a "field" is needed because the positions and the number of centerline points can vary without changing the underlying vessel structure (the graph-to-point map is not injective), and a continuous field is invariant to such sampling choices. The detour back to a "graph" is needed because downstream topology analysis, link prediction, and flow modeling want a usable centerline graph, not a voxel field.

Encoder and decoder follow the transformer design of recent shape tokenizers in a VAE-style arrangement: the encoder compresses the centerline point cloud together with initializing queries into a latent, and the decoder reconstructs the occupancy field by cross-attending to query points sampled on a 3D grid. The figure below shows the end-to-end data flow; "generation / infilling" is a downstream use of the latent and does not change the tokenizer itself.

%%{init: {'flowchart': {'rankSpacing': 24, 'nodeSpacing': 28, 'padding': 6, 'wrappingWidth': 400}}}%%
flowchart TD
    A["Input: 3D centerline graph"] --> B["Centerline occupancy field<br/>pseudo-radius dilation"]
    B --> C["Tokenizing on centerline points<br/>FPS queries + attention"]
    C --> D["Fixed-length compact token space<br/>512 x 4, no codebook"]
    D --> E["Decoding back to a discrete graph<br/>threshold, skeleton, adjacency"]
    E --> F["Reconstructed graph"]
    D -->|EDM diffusion / conditional flow matching| G["Graph generation and link infilling"]

Key Designs

1. Centerline occupancy field: turning a discrete graph into a sampling-invariant continuous field

Feeding node coordinates to a network ties what the model learns to the sampling convention: re-sample the same vessel at a different density, or subdivide an edge differently, and it becomes "another graph." VesselTok instead treats every edge as a straight segment in \(\mathbb{R}^3\), thickens it by a fixed pseudo-radius \(r>0\), and obtains a continuous graph occupancy field \(\phi_r\): the value at any point \(p\) depends only on the distance to the closest edge, and the point counts as occupied when that distance does not exceed \(r\).

\[d_G(p,G)=\min\Big(\min_{(i,j)\in E}\big\|p-\big(p_i+\alpha_{ij}(p)(p_j-p_i)\big)\big\|,\ \min_{i\in V}\|p-p_i\|\Big),\qquad \phi_r(p,G)=\begin{cases}1, & d_G(p,G)\le r\\ 0, & \text{otherwise}\end{cases}\]

Here \(\alpha_{ij}(p)\) is the projection parameter of \(p\) onto edge \((i,j)\), clamped to \([0,1]\) so the closest point lies on the segment rather than its extension, and the second term covers isolated and boundary nodes. Supervision is thereby decoupled from how an edge is split or where points are sampled: the same vascular graph yields essentially the same occupancy field regardless of discretization.

The pseudo-radius \(r\) is the one quantity this design must trade off. Too small and the field is too sparse for the network to learn; too large and thin branches and short connections are smeared out, harming topology (see the ablation; \(r=0.016\) is chosen as the global operating point). The construction also removes a long-standing constraint: generation no longer requires knowing the node count in advance, whereas native graph generation methods such as MIDI and Prabhakar et al. must fix it a priori.

2. Tokenizing on centerline points: spending the query budget on topology, not on vessel walls

The occupancy field settles what the supervision is; the next question is where to place the queries. Surface-point tokenizers work well for generic 3D shapes but are wasteful on tubular networks: wall area grows linearly with radius, and a 3,000-centerline-point airway graph renders into 64,000 surface points, so a fixed cross-attention budget fills up with redundant surface samples while bifurcations, endpoints, and branch points remain in the minority. VesselTok therefore abandons surface sampling entirely and works directly on the centerline point cloud \(P\), without subsampling — all centerline points participate in encoding at once.

The encoder is built as follows: farthest point sampling (FPS) selects \(L\) points from \(P\) as the initial queries \(Q_{in}\), giving a uniformly covering initial skeleton of the structure; both \(P\) and \(Q_{in}\) go through Fourier positional encoding and a linear layer to the hidden dimension \(d\); the first encoder layer cross-attends from the queries to the point cloud to inject point-cloud context, a stack of self-attention layers then produces the hidden representation \(H\in\mathbb{R}^{l\times d}\), and two final linear layers output the mean and variance \(Z_\mu,Z_\sigma\in\mathbb{R}^{l\times c}\). The essential difference is not "using attention" — everyone does — but that the keys and values come from centerlines rather than surfaces: each of the \(l\) tokens corresponds to a semantic location on the structure rather than to a patch of wall that could be moved around arbitrarily.

3. Fixed-length compact token space: continuous VAE latents instead of a quantization codebook

For the tokens to serve as a generative interface, the latent must be both short and stable. VesselTok uses VAE-style continuous latents (reparameterized from \(\mathcal{N}(Z_\mu,\mathrm{diag}(Z_\sigma))\)) rather than a VQ-style discrete codebook — a direct contrast with VesselGPT, the vessel-specific tokenizer. Continuous latents let the decoder differentiate directly with respect to arbitrary real-valued tokens and let a diffusion model denoise in continuous space, avoiding codebook collapse and quantization error; the price is that there is no explicit vocabulary imposing a compression ceiling, so the token count and channel size must be designed explicitly.

Compression is quantified by the average compression ratio \(\kappa\): for \(M\) samples with \(N_i\) nodes each (three coordinates per node),

\[\kappa=\frac{1}{M}\sum_{i=1}^{M}\frac{3N_i}{K\cdot C}\]

where \(K\) is the number of tokens per graph and \(C\) the channel dimension of each token. The final configuration is \(K=512\), \(C=4\) — 2,048 floating-point numbers per graph, an average compression ratio of about 7 on ATM. The fixed-length sequence (512 tokens) is what makes the latent attachable to a generative model: graph tokenizers such as VQGraph and OpenGraph do tokenize graphs, but their latents retain the original node count and generation at this scale is computationally infeasible. The ablation shows that neither \(K\) nor \(C\) is "the larger the better", and that 512 × 4 is the balance point between fidelity and compression.

4. Decoding back to a discrete graph: threshold, skeletonization, adjacency

An occupancy field alone is not usable — downstream consumers need a centerline graph. The decoder first processes the latent with a series of self-attention layers, then samples query points \(Q_{out}\) on a 3D grid, embeds them with Fourier positional encoding and a linear projection, and finally cross-attends to predict the occupancy value \(\tilde{\phi}_\theta\) at those points. At inference the predicted field is evaluated on a regular grid and binarized with a threshold \(\tau\) between 0 and 1, a 3D skeletonization algorithm extracts the skeleton points \(\hat{V}\), and deterministic neighborhood-based connectivity yields the edges \(\hat{E}\), producing a topology-preserving discrete graph \(\hat{G}\).

This step is deliberately modular: the same graph-extraction procedure is applied to every compared method, so the comparison reflects the quality of the occupancy field rather than of the post-processing; a more robust graph extractor (for instance the Voreen segmentation-based tool) could be substituted without touching anything upstream. All model capacity therefore rests on how accurately the field is predicted — which is why the Betti-error analysis later deserves close reading.

A Worked Example

Take one ATM airway graph with about 3,000 centerline points: every edge is dilated with \(r=0.016\) into an occupancy field, and the centerline point cloud \(P\) (about 3,000 points) is kept in full; FPS selects 512 initial queries \(Q_{in}\) from it, and \(Q_{in}\) and \(P\) enter the encoder after Fourier encoding; the first cross-attention layer pulls point-cloud information onto the queries, several self-attention layers refine it, and two linear layers emit \(Z_\mu\) and \(Z_\sigma\) of size \(512\times 4\); reparameterized sampling yields the token \(Z\) (2,048 numbers, about 7× compression against the original \(3\times 3000\) coordinates). For decoding, query points are sampled on a 512³ grid, cross-attention predicts occupancy, and after thresholding, skeletonization produces centerline points that are connected by neighborhood adjacency into the reconstructed graph \(\hat{G}\) — which reaches clDice 96.61, Chamfer distance 0.005, and \(|\Delta\beta_1|\) 8.97 on ATM. For generation, the same 512 tokens are fed directly to an EDM diffusion model; for link prediction, a graph with about 40% of its edges removed is encoded into tokens, which serve as the conditioning signal for conditional flow matching toward the complete graph.

Loss & Training

The training objective combines a reconstruction loss with a latent regularizer: the reconstruction term is the binary cross-entropy between predicted and reference occupancy at the query points, and the regularizer is the KL divergence of the latent distribution from a standard normal.

\[\mathcal{L}_{\text{total}}=\mathbb{E}_{p\in\mathbb{R}^3}\big[\mathrm{BCE}\big(\tilde{\phi}_\theta(p),\phi(p,G)\big)\big]+\lambda\cdot\mathrm{KL}\big(\mathcal{N}(Z_\mu,\mathrm{diag}(Z_\sigma)),\,\mathcal{N}(\mathbf{0},\mathbf{I})\big)\]

Because the occupancy field is extremely sparse over the whole domain, uniformly random queries would be almost entirely background, so the imbalance-aware query selection strategy of 3DShape2VecSet is adopted, emphasizing points near the object boundary. Key hyper-parameters: pseudo-radius \(r=0.016\) (global, not tuned per dataset), token count \(K=512\), channel size \(C=4\). Generation is trained separately: an EDM backbone in token space, with a class-conditional variant conditioned on anatomical category and hyper-parameters matched to 3DShape2VecSet; link prediction instead uses a Diffusion Transformer with a conditional flow-matching objective.

Key Experimental Results

The datasets span three anatomies: airways (ATM, AIIB, AeroPath), cerebral vasculature (COSTA), and pulmonary vessels (HiPas, PARSE, Pulmonary-AV). All graphs are extracted from segmentation masks with the Voreen graph-extraction tool, keeping the original centerline geometry with no post-processing that could perturb the structure; out-of-distribution validation uses TopCoW (Circle of Willis) and renal vasculature (RV). Alongside clDice (centerline overlap, which emphasizes connectivity) and Chamfer distance (CD, geometric discrepancy), topology is measured by Betti-number differences \(|\Delta\beta_0|\) (connected components) and \(|\Delta\beta_1|\) (loops). All metrics are computed on 512³ grids after rendering graphs into an occupancy field with pseudo-radius \(r\).

Main Results

Reconstruction results on the six testing anatomies (higher clDice, lower CD is better):

Dataset Method clDice ↑ CD ↓
ATM Hunyuan3D 2.0 / 3DShape2VecSet / VesselTok 86.75 / 90.08 / 96.33 4.08 / 2.14 / 0.96
AIIB Hunyuan3D 2.0 / 3DShape2VecSet / VesselTok 85.13 / 87.22 / 94.85 2.90 / 2.74 / 0.66
COSTA Hunyuan3D 2.0 / 3DShape2VecSet / VesselTok 56.53 / 59.65 / 77.26 4.28 / 2.29 / 1.64
HiPas Hunyuan3D 2.0 / 3DShape2VecSet / VesselTok 52.58 / 55.58 / 67.59 3.95 / 2.92 / 1.82
PARSE Hunyuan3D 2.0 / 3DShape2VecSet / VesselTok 42.64 / 42.44 / 57.03 3.42 / 3.19 / 0.69
Pulmonary-AV Hunyuan3D 2.0 / 3DShape2VecSet / VesselTok 79.46 / 86.40 / 94.30 6.99 / 1.59 / 0.74

On topology errors the advantage is clearest for loop-rich structures: on COSTA, \(|\Delta\beta_0|\) drops from 70.85 / 79.15 to 26.81 and \(|\Delta\beta_1|\) from 54.35 / 56.19 to 26.83; \(|\Delta\beta_0|\) is also consistently lower on ATM (4.91 vs 7.28 / 7.46), AIIB (4.47 vs 8.40 / 8.60), and PARSE (128.06 vs 155.06 / 159.06). \(|\Delta\beta_1|\) is not uniformly best — on AIIB it ties Hunyuan (11.00, slightly behind 3DShape2VecSet's 10.85) and on HiPas (38.42) it is worse than both baselines, indicating that loop preservation on such dense pulmonary vasculature remains a weak point.

Vessel-specific baselines are only comparable on the airway tree ATM (VesselGPT is a tree-only method and requires removing the spurious cycles caused by segmentation noise before it can be trained; VesselTok needs no such cleanup):

| Method | clDice ↑ | CD ↓ | \(|\Delta\beta_0|\) ↓ | \(|\Delta\beta_1|\) ↓ | |--------|----------|------|------|------| | VesselGPT | 77.09 | 0.008 | 0.05 | 10.28 | | Hunyuan3D 2.0 | 87.31 | 0.007 | 0.11 | 9.31 | | 3DShape2VecSet | 90.11 | 0.007 | 0.09 | 9.48 | | VesselTok | 96.61 | 0.005 | 0.07 | 8.97 |

⚠️ The CD scale in this table (0.005–0.008) differs from the main table (0.66–6.99); the two tables are not directly comparable. VesselVAE failed to converge and was not included.

Out-of-distribution generalization (unseen anatomies and scales: renal graphs exceed 100,000 nodes, Circle of Willis graphs average under 1,000 nodes; large graphs were inferred with spatial chunking on a 150³ grid):

| Dataset | Method | clDice ↑ | CD ↓ | \(|\Delta\beta_0|\) ↓ | \(|\Delta\beta_1|\) ↓ | |---------|--------|----------|------|------|------| | TopCoW (Circle of Willis) | 3DShape2VecSet / VesselTok | 97.96 / 99.42 | 0.001 / 0.002 | 0.06 / 0.07 | 0.14 / 0.04 | | RV (renal vasculature) | 3DShape2VecSet / VesselTok | 79.66 / 88.86 | 0.019 / 0.017 | 11.91 / 13.09 | 6.45 / 6.25 | | ATM (sagittal cut) | 3DShape2VecSet / VesselTok | 96.26 / 99.16 | 0.097 / 0.001 | 0.049 / 0.049 | 5.34 / 5.29 | | COSTA (sagittal cut) | 3DShape2VecSet / VesselTok | 82.65 / 95.44 | 0.123 / 0.125 | 0.85 / 0.24 | 5.20 / 3.49 |

Entries marked * are a synthetic set in which vessels are partitioned along the sagittal plane to induce anatomically implausible edits, probing long-range consistency; VesselTok still holds 99.16 / 95.44 clDice there, suggesting it learns more than a local fit. Note that on RV, VesselTok's \(|\Delta\beta_0|\) (13.09) is slightly worse than 3DShape2VecSet's (11.91); the paper describes \(\beta_0\) as "competitive" rather than best.

For generation, an EDM diffusion model is trained in token space (512 fixed tokens per graph), with a class-conditional variant conditioned on anatomical category:

Setting Method FID ↓ MMD-CD ↓ MMD-EMD ↓ MMD-\(\beta_0\) ↓ MMD-\(\beta_1\) ↓ COV-CD ↑ COV-EMD ↑
Conditional 3DShape2VecSet / VesselTok 73.58 / 43.13 1.92 / 0.25 0.18 / 0.14 24.07 / 7.25 6.82 / 1.01 0.44 / 0.48 0.50 / 0.53
Unconditional 3DShape2VecSet / VesselTok 146.57 / 96.87 1.88 / 0.30 3.45 / 2.35 127.60 / 78.36 3.22 / 2.64 0.39 / 0.42 0.26 / 0.32

(MMD-CD and MMD-EMD are reported in units of \(10^{-2}\). FID is computed in a PointNet++ encoder space, where the encoder is trained to predict the anatomical labels of centerlines; the comparison is between training-set samples and 1,000 generated samples.)

Link prediction on ATM, with about 40% of edges removed and the model asked to infer the missing connections:

| Method | clDice ↑ | CD ↓ | \(|\Delta\beta_0|\) ↓ | \(|\Delta\beta_1|\) ↓ | |--------|----------|------|------|------| | Autodecoder | 83.49 | 0.066 | 4.32 | 8.68 | | VesselTok | 88.13 | 0.043 | 3.19 | 8.58 |

Ablation Study

The pseudo-radius \(r\) directly governs how faithfully the occupancy field captures topology. Three encoders trained on ATM with 0.008 / 0.016 / 0.032 show that larger \(r\) is easier to learn and reconstructs better (clDice loss ≈0.007) but erases fine topology (\(|\Delta\beta_1|\) error ≈16 per sample), while smaller \(r\) preserves topology better (\(|\Delta\beta_1|\) ≈4) at a clear reconstruction cost (clDice loss ≈0.28); \(r=0.016\) is chosen as a single global value.

The compression–fidelity trade-off over token count and channel size (VAEs trained from scratch on ATM):

| Config | clDice ↑ | CD ↓ | \(|\Delta\beta_0|\) ↓ | \(|\Delta\beta_1|\) ↓ | Compression ratio κ ↑ | |--------|----------|------|------|------|------| | \(K=768,\ C=4\) | 97.13 | 0.005 | 0.07 | 8.93 | 4.68 | | \(K=512,\ C=4\) | 96.61 | 0.005 | 0.07 | 8.97 | 7.03 | | \(K=256,\ C=4\) | 80.35 | 0.006 | 25.61 | 10.02 | 14.06 | | \(K=128,\ C=4\) | 12.29 | 0.114 | 1.90 | 10.39 | 28.12 | | \(K=64,\ C=4\) | 8.42 | 0.116 | 2.52 | 10.27 | 56.24 | | \(K=512,\ C=16\) | 96.32 | 0.004 | 0.06 | 8.52 | 1.76 | | \(K=512,\ C=8\) | 95.95 | 0.004 | 0.06 | 8.80 | 3.51 | | \(K=512,\ C=2\) | 7.08 | 0.058 | 1.68 | 10.36 | 14.06 |

Key Findings

  • Centerline tokenization yields broad, consistent reconstruction gains: clDice and CD beat both strong baselines on all six datasets, and on COSTA — the most loop-rich anatomy — \(|\Delta\beta_1|\) is roughly halved from 54–56 to 26.83. This matches the stated motivation about wasted query budget on high surface-to-volume structures: the denser the branching and looping, the larger the advantage of a centerline representation over a surface representation.
  • Token count falls off a cliff rather than degrading smoothly: going from \(K=768\) to 512 costs almost nothing (clDice 97.13 → 96.61), 256 drops to 80.35, and 128 or below collapses to around 12 (CD jumps from 0.005 to 0.114). Channel size behaves the same way: \(C=4\) and \(C=8\) differ by 0.6 points, while \(C=2\) fails outright (clDice 7.08). 512 × 4 sits just before the cliff, which is what justifies compressing a graph to 2,048 numbers.
  • The pseudo-radius makes "reconstructs well" and "topology is right" an explicitly tunable tension: as \(r\) grows, clDice loss falls from 0.28 to 0.007 while \(|\Delta\beta_1|\) error rises from 4 to 16. Topology errors are thus largely caused by an over-fat field merging thin connections, which suggests choosing \(r\) adaptively per scale instead of globally.
  • Generalization comes from the representation, not from scale: trained only on airways, whole-brain vessels, and pulmonary trees (2,500–10,000 nodes), the model reaches 99.42 clDice on sub-1,000-node Circle of Willis graphs and 88.86 on renal graphs exceeding 100,000 nodes, and still holds 95+ clDice under sagittal-cut edits that are anatomically implausible.
  • The bottleneck is topological complexity, not graph size: stratifying samples at 5.5K nodes, ATM clDice only falls from 98.90 to 91.43, while the more complex COSTA falls from 89.19 to 75.20. The same analysis explains the lower absolute numbers on dense pulmonary vasculature such as PARSE and HiPas (clDice 57.03 / 67.59).
  • The token space is genuinely semantic enough to generate from: conditional FID drops from 73.58 to 43.13 (nearly halved) and MMD-\(\beta_1\) from 6.82 to 1.01, indicating that generated samples match the real anatomical distribution in connected components and loops, not merely in point-cloud geometry.

Highlights & Insights

  • "Dilate into a field first, then tokenize only centerlines" is a pair of mutually supporting choices: the occupancy field decouples supervision from sampling density, and the centerline points put the query budget on topology. Neither is novel alone, but together they address both "representation should be sampling-invariant" and "budget should be spent where it matters" — a clean restatement of the problem.
  • Taking radius out of the modeling target: instead of fitting radii, the authors use a fixed pseudo-radius and argue (with supplementary evidence) that radius can be regressed from centerline coordinates. This removes the scale imbalance of wide radius distributions and, as a side effect, the "fix the node count before generating" constraint — at the explicit price that generated graphs carry no radius information.
  • Choosing continuous VAE latents over a VQ codebook is counterintuitive but justified: on the vascular tokenization line, VesselGPT uses a discrete codebook; VesselTok's continuous latent lets diffusion and flow matching operate directly on tokens with no codebook collapse, and replacing native node counts with 512 fixed tokens is what makes graph generation at this scale computationally feasible.
  • The metric design is worth borrowing: Betti numbers alone miss spatial coverage, while clDice and CD alone miss topology, so the paper reports both and additionally computes MMD and Coverage on Betti summaries for generation — a dual geometric/topological evaluation protocol that transfers directly to other curvilinear-structure generation settings.
  • Transferable recipe: any high surface-to-volume curvilinear structure — neuronal morphology, corneal nerve fibers, vascularized tumor organoids, road or river networks — can use the "centerline + pseudo-radius occupancy field" tokenization to compress a voxel-level, high-resolution problem into a few hundred tokens for generation or infilling.

Limitations & Future Work

  • The authors' stated limitation is intrinsic to fixed-capacity latents: performance degrades as input complexity grows. Their stratification shows the bottleneck is topological complexity (COSTA clDice 89.19 → 75.20) rather than node count alone (ATM 98.90 → 91.43), but no remedy for topological complexity is proposed.
  • The pseudo-radius is a single global hyper-parameter (\(r=0.016\)) while the ablation shows it simultaneously pulls reconstruction and topology in opposite directions; for datasets whose radius scales differ substantially (mouse brain microvasculature vs. the human aorta), a single \(r\) is unlikely to be optimal, and adaptive or multi-scale \(r\) is a direct improvement.
  • Radius information is discarded throughout the pipeline: training uses a pseudo-radius and evaluation renders with one too, so generated and infilled graphs carry no true caliber. Downstream tasks requiring radius — flow simulation, stenosis quantification — would need an extra regression, and the paper only argues the premise ("radius is regressible from the centerline") in the appendix without end-to-end validation.
  • Reconstruction topology errors remain substantial (COSTA \(|\Delta\beta_1|\) 26.83; PARSE \(|\Delta\beta_0|\) at the 128 level), and part of this comes from the deterministic skeletonization + neighborhood-adjacency post-processing; whether a more robust graph extractor would systematically reduce Betti errors is not ablated.
  • Generalization to large graphs relies on spatial chunking with a 150³ grid, and whether chunk boundaries introduce spurious connections or sever long-range branches is not discussed — precisely the weakest point for long-range consistency.
  • The generation FID rests on a PointNet++ encoder trained on anatomical labels, so the label taxonomy and its training coverage directly influence the scores; cross-method comparisons are fair but the absolute values are of limited interpretability.
  • vs 3DShape2VecSet / Hunyuan3D 2.0: both are surface-point tokenizers for generic 3D shapes (the former encodes surface points into a set of latent vectors for neural fields and diffusion, the latter improves shape encoding with query point sampling). VesselTok shares their transformer encoder-decoder backbone but moves the sampling domain from surfaces to centerlines, and compares under an identical graph-extraction procedure. It wins on reconstruction and generation for tubular structures; the cost is that the design requires a well-defined centerline.
  • vs VesselGPT: closest in spirit — a VQ-VAE that builds a discrete codebook for vessels and represents structure as a short token sequence — but it only supports vessel trees and requires removing spurious loops before training, and its ATM reconstruction (clDice 77.09) trails VesselTok (96.61). The difference is the discrete codebook plus the tree assumption, versus continuous latents over a continuous occupancy field that accommodates non-tree connectivity.
  • vs VesselVAE: a recursive VAE mapping vessel trees to a compact latent vector; under this setting it fails to converge and could not be compared.
  • vs native graph generation methods (Prabhakar et al.'s point-cloud diffusion, MIDI, and similar): these handle branches and loops but operate in uncompressed space and must fix the node count before generation; this paper's contribution is precisely to move such generation into a compressed token space, making it feasible at the ten-thousand-node scale.
  • vs generic graph tokenizers (VQGraph, graph quantized tokenizers, OpenGraph): they aim at semantically rich node- or subgraph-level tokens for downstream analysis and keep the original node count in the latent, which makes large-scale generation infeasible; VesselTok explicitly prioritizes compression, which is why it can train diffusion directly in token space.
  • vs hierarchical / part-based vessel generation (Batten et al., Chen et al.'s part-based model): those sample a tree topology first and then generate segment-level geometry, and remain limited to tree structures and smaller geometries; VesselTok targets large networks with arbitrary connectivity, including loops.

Rating

  • Novelty: ⭐⭐⭐⭐ Reframing tokenization around a "centerline + pseudo-radius occupancy field" is a well-motivated restatement of surface-point tokenizers rather than a wholly new mechanism, but the restatement is clean and evidence-backed.
  • Experimental Thoroughness: ⭐⭐⭐⭐⭐ Six datasets plus out-of-distribution, synthetic perturbation, generation, and inverse problems, with metrics covering both geometry and topology and with fair control of baselines and post-processing.
  • Writing Quality: ⭐⭐⭐⭐ The motivation chain (surface-to-volume ratio → query budget → centerlines) is clear and the ablations tie tightly to design choices, though some table scales are inconsistent and a few claims read as optimistic.
  • Value: ⭐⭐⭐⭐ It provides a reusable token interface for tubular networks such as vessels and airways that plugs cleanly into generation and infilling; the caveats are that radius is excluded and topology errors remain high on large graphs.