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VesselTok turns large vessel graphs into compact tokens that reconstruct, generate, and repair tubular anatomy.

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2026-07-13 22:23 UTC pith:YSNA3B7E

load-bearing objection Solid, usable tokenizer for large tubular biomedical graphs; the fixed-pseudo-radius bet is load-bearing but already ablated and the multi-task evidence holds. the 2 major comments →

arxiv 2603.18797 v2 pith:YSNA3B7E submitted 2026-03-19 cs.CV

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

Chinmay Prabhakar , Bastian Wittmann , Tamaz Amiranashvili , Paul B\"uschl , Ezequiel de la Rosa , Julian McGinnis , Benedikt Wiestler , Bjoern Menze
show 1 more author
Suprosanna Shit
This is my paper
classification cs.CV
keywords vessel graphs3D tokenizationneural implicit representationstubular structuresgraph generationlink predictioncenterline occupancy
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Large 3D graphs of blood vessels, airways, and similar tubular networks are too dense for ordinary graph algorithms once node counts climb into the thousands. VesselTok reframes each graph as a tubular surface around its centerlines, thickens those centerlines with a single fixed pseudo-radius, and learns a short sequence of continuous latent tokens that encode the resulting occupancy field. The tokens reconstruct the original topology more faithfully than surface-based shape tokenizers, still work on anatomies and scales never seen in training, and serve as the latent space for both generative sampling of new plausible graphs and inverse tasks such as filling missing vessel links. The practical payoff is a reusable, compressed representation that makes high-resolution biomedical networks tractable for reconstruction, synthesis, and repair.

Core claim

A VAE-style encoder that attends over centerline points (not surface samples) can compress topologically complex 3D vessel graphs into fixed-length continuous tokens; decoding those tokens back to an occupancy field and skeletonizing it recovers graphs whose connectivity and geometry outperform surface-based baselines, and the same tokens support generation and link prediction.

What carries the argument

VesselTok: a transformer VAE that maps centerline points plus a fixed pseudo-radius occupancy field into a compact latent token sequence Z, then reconstructs the field by cross-attention to query points.

Load-bearing premise

A single fixed pseudo-radius around every centerline is enough to capture real vessel topology, so that skeletonization of the decoded occupancy field recovers a faithful discrete graph and true radius variation can be left as a later regression step.

What would settle it

Train and decode the same model on graphs whose true radii vary sharply or that contain loops thinner than the chosen pseudo-radius; if the recovered Betti numbers and centerline Dice collapse relative to surface-based baselines, the fixed-radius premise fails.

Watch this falsifier — get emailed when new claim-graph text bears on it.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 5 minor

Summary. VesselTok is a VAE-style tokenizer that maps large 3D spatial graphs of tubular biomedical structures (airways, pulmonary vessels, cerebral vessels) to compact continuous latent tokens. It represents each graph as a continuous occupancy field obtained by dilating centerline segments with a fixed pseudo-radius, encodes the centerline point cloud with a transformer VAE, and decodes an occupancy field from which a discrete graph is recovered by skeletonization. The paper reports improved reconstruction (clDice, Chamfer, Betti errors) relative to 3DShape2VecSet and Hunyuan3D 2.0 across multiple anatomies, generalization to unseen scales and topologies (TopCoW, renal vasculature, sagittal cuts), unconditional/conditional generation via EDM diffusion in token space, and transfer to a link-prediction inverse problem. Ablations cover token count K, channel dimension C, and pseudo-radius r; a post-hoc radius regressor is shown in the supplement.

Significance. If the empirical claims hold, VesselTok supplies a practical, domain-adapted latent interface for topologically complex vessel-like graphs that prior graph or surface tokenizers struggle to scale. The multi-anatomy training set, OOD tests (including order-of-magnitude larger renal graphs via chunking), generative metrics (FID/MMD/Betti/Coverage), link-prediction comparison, and explicit ablations on the free parameters constitute a solid experimental package. The centerline-plus-pseudo-radius design is a clear, falsifiable modeling bet that concentrates capacity on topology and large-scale geometry; the promised code release further raises the work’s utility for the community. These strengths make the contribution relevant for biomedical shape analysis and generative modeling of curvilinear networks.

major comments (2)
  1. Table 1 (and the corresponding average row): while VesselTok improves clDice and Chamfer Distance on every dataset, |Δβ1| is higher than at least one baseline on AIIB, PARSE, HiPas and Pulmonary-AV. The abstract and introduction claim that the tokens “robustly encode complex topologies.” The mixed loop-error results indicate a geometry–topology trade-off that is not discussed; a short analysis of when and why loops are lost or hallucinated would make the topology claim precise rather than overstated.
  2. Section 3.1 Eq. (1) and Section 4.6: the entire pipeline rests on a single fixed pseudo-radius r = 0.016. The ablation on ATM is useful, yet the main multi-anatomy tables, OOD experiments and generative models all use this one value. Because true radius variation is deferred to a post-hoc regressor (Supp. B), it remains unclear whether the latent itself is invariant to realistic radius changes (e.g., stenoses or aneurysms). A controlled experiment that re-renders the same centerlines at several radii and measures latent/reconstruction stability would directly test the load-bearing modeling assumption.
minor comments (5)
  1. Table and figure captions occasionally contain spacing artifacts (“T able 1”, “Fig. 1:VesselTok”). Clean these for production.
  2. Section 4.4 / Table 4: MMD-CD and MMD-EMD are reported ×10^{-2}; state the scaling factor explicitly in the table header for readability.
  3. Inference (Section 3.2): the occupancy threshold τ = 0.5 and the skeletonization algorithm are fixed; a one-sentence sensitivity note (or reference to the modular claim) would help readers who wish to substitute other extractors.
  4. Supplementary Sec. B reports R² and sMAPE for radius regression; adding the same metrics on the held-out OOD sets (TopCoW, renal) would strengthen the claim that radius can safely be treated as post-hoc.
  5. Figure 3 and Figure 5 would benefit from a small inset or color legend that distinguishes true-positive, false-positive and false-negative branches, making qualitative topology differences easier to judge.

Circularity Check

0 steps flagged

No significant circularity: empirical tokenizer trained by reconstruction+KL and evaluated on held-out multi-anatomy, OOD, generative, and inverse-task metrics against external baselines.

full rationale

VesselTok is a standard VAE-style shape tokenizer (centerline points + fixed pseudo-radius occupancy field, transformer encoder/decoder, BCE+KL loss) whose latents are then used for EDM diffusion and conditional flow-matching. All quantitative claims (clDice/CD/Betti, FID/MMD/COV, link-prediction) are measured on held-out or OOD data against independently reimplemented external baselines (3DShape2VecSet, Hunyuan3D 2.0, VesselGPT, autodecoder). The pseudo-radius r=0.016 is an explicit hyper-parameter chosen by ablation (Sec. 4.6, Fig. 6), not a fitted constant later re-labeled as a prediction; true radius is deferred to a separate post-hoc regressor whose R^{2}/sMAPE are reported only as supporting evidence (Supp. B). Self-citations to the authors’ prior vessel-generation papers appear only as related-work baselines that the present method is claimed to improve upon, never as uniqueness theorems or load-bearing premises. No equation reduces a claimed first-principles result to its own inputs by construction. The derivation chain is therefore self-contained and non-circular.

Axiom & Free-Parameter Ledger

5 free parameters · 3 axioms · 2 invented entities

The central claim rests on a small set of modeling choices (fixed pseudo-radius, centerline-only input, continuous occupancy) and standard VAE/diffusion machinery. No new physical entities are postulated; free parameters are ordinary architectural and loss hyperparameters selected by ablation on ATM.

free parameters (5)
  • pseudo-radius r = 0.016
    Fixed dilation radius used to turn centerline edges into an occupancy field; ablated on {0.008, 0.016, 0.032} and set to 0.016.
  • token count K = 512
    Number of latent tokens per graph; ablated and set to 512 for the main experiments.
  • latent channel dimension C = 4
    Channel size of each token; ablated and set to 4.
  • KL weight λ = 1e-3
    Weight of the KL term in the VAE loss.
  • occupancy threshold τ = 0.5
    Threshold applied to the decoded field before skeletonization.
axioms (3)
  • ad hoc to paper A fixed pseudo-radius occupancy field around centerline segments is a topology-preserving representation of real vessel graphs whose true radii vary.
    Stated in Section 3.1 and justified by the claim that radii are smoothly varying and can be regressed post-hoc (Supp. B).
  • domain assumption Skeletonization of a thresholded occupancy field followed by neighborhood connectivity recovers a discrete graph whose Betti numbers and geometry can be fairly compared across methods.
    Inference procedure in Section 3.2; same post-processing applied to all baselines.
  • standard math Standard transformer VAE + EDM diffusion machinery is a valid generative model once a continuous latent of fixed length is obtained.
    Architecture follows Zhao et al. (Hunyuan3D) and Karras et al. (EDM); no novel theoretical claim.
invented entities (2)
  • graph occupancy field ϕ_r with fixed pseudo-radius no independent evidence
    purpose: Provides a continuous, sampling-invariant target for the VAE decoder that encodes tubular topology from centerlines alone.
    Defined in Eq. (1); the paper’s central representational device.
  • VesselTok continuous token sequence Z ∈ R^{l×c} no independent evidence
    purpose: Compact latent interface for reconstruction, diffusion-based generation, and conditional link prediction.
    Output of the encoder T; evaluated empirically but not independently measured outside the paper’s tasks.

pith-pipeline@v1.1.0-grok45 · 26163 in / 2794 out tokens · 30549 ms · 2026-07-13T22:23:43.581547+00:00 · methodology

0 comments
read the original abstract

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.

Figures

Figures reproduced from arXiv: 2603.18797 by Bastian Wittmann, Benedikt Wiestler, Bjoern Menze, Chinmay Prabhakar, Ezequiel de la Rosa, Julian McGinnis, Paul B\"uschl, Suprosanna Shit, Tamaz Amiranashvili.

Figure 1
Figure 1. Figure 1: VesselTok provides expressive latent representations Z which can be effectively leveraged to several downstream tasks, including generalization to unseen anatomies, generative modeling (i.e., sample additional graphs), and inverse problems (e.g., repair of incomplete structures). the purpose of connecting different anatomical regions, facilitating the trans￾portation of signals and substrates. Studying the… view at source ↗
Figure 2
Figure 2. Figure 2: Architectural overview of VesselTok. VesselTok consists of an encoder T , which extracts features from a pre-processed centerline point cloud P to generate a continu￾ous, expressive, and compressed latent token Z. A decoder D subsequently reconstructs the graph occupancy field ϕ˜θ from Z via cross-attention to output query points Qout. The final graph is subsequently reconstructed from ϕ˜θ. structures, and… view at source ↗
Figure 3
Figure 3. Figure 3: Qualitative results for the graph reconstruction task. We find that VesselTok demonstrates superior reconstruction capabilities. D, respectively. Tab. 1 shows that VesselTok attains higher clDice, lower Cham￾fer Distance, and smaller |∆β0| and |∆β1| errors. A per-dataset breakdown on [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Qualitative results for the graph reconstruction task of previously unseen do￾mains. This demonstrates VesselTok’s strong prior, resulting in robust reconstructions. VesselGPT performs best on |∆β0|, likely benefiting from the simplication step in its preprocessing pipeline. 4.3 Generalization to Unseen Anatomies To assess VesselTok’s generalization, we evaluate it on anatomies and graph scales outside the… view at source ↗
Figure 5
Figure 5. Figure 5: Qualitative results for conditional generation. VesselTok consistently generates more realistic vessels than previous methods. 4.4 Generative Modeling We generate anatomical graphs by training a diffusion model in the token space. Using a fixed-length sequence of 512 tokens per graph keeps training and sam￾pling tractable compared to native graph generation [35]. We train both uncondi￾tional and class-cond… view at source ↗
Figure 6
Figure 6. Figure 6: Comparison of reconstruction fi￾delity vs. topological characteristics re￾tained as we change the pseudo radius r. Lower values of r improve topological characteristics but degrade reconstruction performance (|∆β1|). We find r = 0.016 strikes a good balance [PITH_FULL_IMAGE:figures/full_fig_p014_6.png] view at source ↗
Figure 8
Figure 8. Figure 8: Left: Representative samples from the training distribution. We cover a range of anatomies in our training samples, such as airways, cerebral vasculature, and pul￾monary vessels. Right: Representative samples from the renal vasculature and the Circle of Willis dataset used to evaluate the performance of the model on samples not seen during training. A Additional Details on Datasets We extract spatial graph… view at source ↗
Figure 9
Figure 9. Figure 9: We summarize the structural variability of our datasets by reporting the dis￾tributions of node and edge counts across the training set. In addition, we include the number of connected components (β0) and loop count (β1) for each dataset. The sam￾ples exhibit substantial variation in both graph size and topology, with wide ranges in node/edge counts and β1. For number of connected components (β0), COSTA ex… view at source ↗
Figure 10
Figure 10. Figure 10: Quantile-binned reliability diagram for edge-radius regression across anatom￾ical categories. Edges are grouped into quantile bins by ground-truth radius (x-axis). For each bin we plot the mean predicted radius (y-axis) with the interquartile range (shaded). The identity line (rˆ = r) indicates perfect agreement between predictions and ground truth. tures. Edge radii are predicted by concatenating the fea… view at source ↗
Figure 11
Figure 11. Figure 11: Additional qualitative results for the graph reconstruction task. We find that VesselTok demonstrates superior reconstruction capabilities. D.2 Training Details We train the VAE for 24,000 epochs using 2,048 query points per sample to com￾pute the occupancy loss. To bias supervision toward the vessel surface, 50% of query points are sampled near the centerlines by adding Gaussian perturbations with σ ∈ [0… view at source ↗
Figure 12
Figure 12. Figure 12: Additional qualitative results for the graph reconstruction task of previously unseen domains. Our results demonstrate VesselTok’s strong prior, resulting in robust reconstructions. F Additional Results on Unseen Anatomies We evaluate VesselTok’s generalization beyond the training distribution. Specif￾ically, we test renal vasculature as an extreme scalability case and sagittal-plane clipped half-lung and… view at source ↗
Figure 13
Figure 13. Figure 13: Additional qualitative results for conditional generation. VesselTok consis￾tently generates more realistic vessels in comparison to previous methods. only the incomplete point cloud is available, and the model infills the missing regions based on the learned prior. We train the infill model exclusively on the training split. For evaluation, we fix a random seed, generate partial observations \protect \ti… view at source ↗
Figure 14
Figure 14. Figure 14: Qualitative examples from our generative model based link prediction on airway dataset. on these held-out incomplete graphs. Training details. We perform the link prediction task on the ATM split only, using 198 training samples. The conditional flow-matching model is trained for \x@protect \,\protect \, 10{,}000 epochs with an \x@protect \,\protect \, 800-epoch warm-up. The learning rate is linearly in￾c… view at source ↗

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Cited by 1 Pith paper

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    SynVA toolkit generates realistic vascular meshes and anatomically plausible aneurysms, releasing 50,000 labeled samples for medical vision tasks.

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