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REVIEW 4 major objections 5 minor 44 references

DeformCL: Learning Deformable Centerline Representation for Vessel Extraction in 3D Medical Image

T0 review · 4 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Deformable centerline graphs outperform per-pixel masks for 3D vessel extraction.

desk verdict DeformCL is a well-specified method-level advance in deformable centerline representation, but its topology claims are overstated because the graph cannot add or remove branches; still worth a serious referee. read the letter →

arxiv 2506.05820 v1 pith:HQAI5JCA submitted 2025-06-06 cs.CV

Ziwei Zhao , Zhixing Zhang , Yuhang Liu , Zhao Zhang , Haojun Yu , Dong Wang , Liwei Wang This is my paper
classification cs.CV
keywords deformablecenterlinevesselextraction3Dmedicalimagegraphrepresentationtubularstructuresegmentationtemplatetopologypreservation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper argues that the standard approach to vessel extraction in 3D medical images—classifying every voxel into a mask—is the root cause of fragmented, noisy, and topologically wrong vessel predictions. It introduces DeformCL, a continuous representation in which vessel centerlines are stored as a graph of points connected by edges, and trains a cascaded network that deforms a rough initial template to fit the true vessels. The authors report consistent gains over strong mask-based baselines on four datasets, with the largest improvements in connectivity-sensitive metrics such as clDice and Betti number errors. Because the network outputs structured centerlines directly, the result can be used for curved planar reformation without a separate skeletonization post-processing step. The paper is trying to establish that a connected, deformable representation is inherently better matched to curvilinear anatomy than discrete mask prediction.

What carries the argument

The machinery is the deformable centerline graph: a set of 3D points connected by edges, initialized per image from the coarse segmentation, and refined by a cascade of deformation stages. Each stage combines trilinear feature sampling, a Transformer over the graph for global context, an MLP with tanh activation for bounded point movement, and unpooling that inserts midpoints between connected points. Three auxiliary losses shape the deformation: a local Chamfer loss restricted to patches around ground-truth points, a signed-distance-function loss that pulls points toward the vessel center, and a regularization loss penalizing long edges. The segmentation head then converts the deformed centerlines into a mask through a distance map fused with the coarse prediction.

What would settle it

Compute per-branch centerline recall of the coarse segmentation and of DeformCL on a dataset with partially occluded vessels; if a branch entirely absent from the coarse mask appears in the final prediction, the deformation can create branches, whereas if none ever appear, the method's recall is capped by the coarse mask's completeness.

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Extended reading notes

Core claim

The central claim is that vessel extraction should be posed as deforming a connected centerline graph rather than classifying voxels. The paper introduces DeformCL, where a graph G = {V, ε} has 3D centerline points as nodes and edges that encode adjacency. An adaptive template, built by skeletonizing a coarse segmentation, reconstructing a graph via minimum spanning tree, and subsampling to a few control points, is refined through L cascaded stages. Each stage samples hierarchical feature maps at the point locations, aggregates features along the graph with a Transformer, predicts a bounded offset, and unpooling doubles the point density. The final centerlines are converted to a segmentation by computing a voxel-to-centerline distance map and fusing it with the coarse mask. The paper reports that this continuous representation with natural connectivity reduces fractures, filters local false positives, and improves topological metrics across HaN-Seg, HNCTA, ASOCA, and ImageCAS datasets.

Load-bearing premise

Every vessel branch that matters must already be present in the coarse segmentation, because the deformation and unpooling layers move points along existing edges and never create new branches.

Editorial extensions

If this is right

  • Adding DeformCL as an extra head improves Dice, clDice, and Betti number errors of softDice, clDice, and DSCNet baselines on all four datasets.
  • The predicted centerlines are structurally complete and smooth enough to be used directly for curved planar reformation, without the usual mask-to-skeleton conversion.
  • Because the representation is continuous, noise robustness follows from the top-down deformation, reducing scattered false positives compared with bottom-up per-pixel classification.
  • The added computational cost is modest: about 0.12M extra parameters and 0.06 seconds per image over the 3D UNet backbone.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A direct consequence not tested in the paper: since deformation never adds branches, centerline recall cannot exceed the recall of the coarse segmentation; a version that grows new edges during deformation would be needed for fully occluded vessels.
  • The same deformable-centerline principle could be applied to other curvilinear structures—neuronal arbors, airways, or road networks—where connectivity, centrality, and noise tolerance matter more than voxel-wise accuracy.
  • The paper's preference for rough initial templates (four control points) suggests the deformation is an active-contour-like process; measuring sensitivity to random template perturbations would reveal how much of the performance comes from the template prior versus the learned deformation.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. The paper introduces DeformCL, a continuous representation of 3D vessels as graphs of deformable centerline points. Starting from a coarse segmentation produced by the backbone, the method skeletonizes the coarse mask, builds a minimum-spanning-tree graph, selects k control points, and interpolates an initial centerline template. A cascade of Transformer feature aggregation, deformation, and unpooling layers then refines the point positions. The final centerline points are converted into a distance map that is fused with the coarse segmentation to produce a refined mask. The method is evaluated on HaN-Seg, HNCTA, ASOCA, and ImageCAS, with three base segmentors (softDice, clDice, DSCNet), reporting segmentation Dice/clDice, topological errors, HD95, and centerline F1/HD/Chamfer/beta0, plus qualitative CPR visualizations.

Significance. If its central claims are validated, DeformCL would be a practically useful representation: it outputs centerlines directly, supports feature aggregation along tubular curves, and improves segmentation connectivity. The manuscript has clear strengths: the code is released; the pipeline is specified in enough detail to reimplement; experiments cover four datasets and multiple backbones; ablations test template control-point count, loss components, interpolation, and interaction mechanism; and a Swin UNETR backbone is included. The clinical CPR visualization is a relevant and informative qualitative contribution. The main weakness is that the topology of the final centerline is fixed by the coarse-segmentation skeleton, which limits the claimed noise robustness and natural connectivity and makes the topological improvements in the main tables hard to attribute to the deformable representation.

major comments (4)
  1. [Sec. 3.2, Eqs. (4)-(5), Supplementary Fig. 13] The deformation and unpooling operations only move existing points and insert midpoints on existing edges; no operation adds or removes branches. Because the initial template is derived from the coarse segmentation skeleton, the final centerline topology is predetermined by the coarse segmentation. Therefore the method cannot recover a vessel branch that is absent from the coarse segmentation, nor can it prune a spurious branch that the coarse segmentation contains. This directly weakens the claims of 'noise robustness' and 'natural connectivity' and is consistent with the fragmented predictions on occluded vessels shown in Supplementary Fig. 13. To support the central claim, the authors should quantify, on the test sets, how often ground-truth branches are missing from the coarse segmentation and report branch-level recall/precision of the final centerlines relative to the coarse skeleton. Without such analysis, the topological gains in Table 1 cannot be separated from the quality of the initial skeleton.
  2. [Table 2] The centerline comparison is not apples-to-apples because the baseline methods are segmentation models that were not trained for centerline extraction, and the procedure used to derive their centerlines from the predicted masks is not described. A common protocol (same skeletonization algorithm, same tolerance, same matching criterion) is essential for F1, HD95, and Chamfer comparisons. Moreover, the claim of consistent centerline improvement is contradicted by the HaN-Seg row: Ours(DSCNet) reports HD95=8.222, which is worse than DSCNet's 7.462. The authors should specify the centerline generation procedure for all methods, release the evaluation script, and either train the baselines with a centerline-aware head or restrict the centerline claims to comparisons among methods that produce centerlines natively.
  3. [Tables 1 and 2] No standard deviations, confidence intervals, or significance tests are reported. This is particularly important because the test sets are small (11 images for HaN-Seg and 7 for ASOCA), and several reported improvements are around 1 Dice point or less (e.g., Ours(clDice) on ImageCAS improves Dice by only 0.07). Without variance estimates, the claim of 'effectiveness and superiority' is not statistically supported. The authors should report per-subject variability or fold-based intervals and apply paired tests to the Dice, clDice, Betti, and centerline metrics where small numbers of branches can drive the average.
  4. [Sec. 4.5, Table 4] The ablation of loss functions reports only segmentation Dice and clDice, yet the text argues that SDF loss and regularization loss improve centerline centrality and smoothness. These claims are qualitative and based on Fig. 7. The ablation should report the centerline metrics (F1, HD95, Chamfer, beta0) for each loss configuration, because the paper's central contribution is the centerline representation and its downstream effect on segmentation. Without these numbers, the contribution of L_sdf and L_reg to centerline quality is not quantitatively established.
minor comments (5)
  1. [Throughout] There are several typos: 'strcutures' in the SDF Loss paragraph, 'neightbour' in Eq. (8), 'analusis' in the caption of Table 5, and 'planner' should be 'planar' in Sec. 3.1.
  2. [Eq. (6)] The domain of the distance map is declared as R^{H*D*W}, but the input volume is described as R^{H*W*D}; please make the dimension order consistent.
  3. [Figure 3] The overview figure is dense and hard to read at print size; the stage weights and loss labels should be enlarged or split into a separate figure.
  4. [Sec. 4.4] The sentence 'We have not included PointScatter [31] and Topoloss [9] in the comparison as it is designed for 2D images' has an ambiguous pronoun; clarify that both methods are designed for 2D and are not applicable to 3D volumes under the reported GPU memory constraints.
  5. [Sec. 3.2, Eq. (2)-(4)] The Transformer architecture is not fully specified in the main text; please state the number of layers, heads, and hidden dimensions, or refer the reader to a precise supplementary section.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: DeformCL is an empirically trained pipeline evaluated on held-out test sets; the centerline template is an architectural initialization, not a fitted parameter renamed as a prediction.

full rationale

The derivation chain is supervised end-to-end by ground-truth masks and centerlines: coarse segmentation, centerline deformation (Eqs. 1-5), and distance-map-based refined segmentation (Eq. 6) are trained with Dice, local Chamfer, SDF, and regularization losses (Eqs. 7-13), and evaluated on held-out test splits of four datasets. The initial template is generated from the coarse segmentation skeleton, but deformation and unpooling are learned and tested against GT centerlines; this is an architectural initialization, not a fitted parameter renamed as a prediction. The paper's own Supplementary Fig. 13 documents a failure mode for occluded vessels where fragmented coarse segmentation cannot be recovered; this is a limitation of the fixed-topology deformation, not evidence that a claimed result reduces to its input by construction. Self-citations ([31], [39], [40]) are present, but [39] is only used as a graph-reconstruction recipe in template generation and [31]/[40] are related work; none is invoked as an unverified uniqueness theorem or as the answer to the central claim. Therefore no circular step is exhibited.

Assumptions & free parameters 5 free parameters · 4 assumptions · 0 invented entities

The central claim rests on domain assumptions about centerline validity, coarse-segmentation completeness, and fixed graph topology during deformation. No new physical entities are introduced. The main free parameters are empirical hyperparameters with limited sensitivity analysis.

free parameters (5)
  • Number of template control points k = 4
    Selected from ablation on HaN-Seg (Table 3) and used across datasets; k=0 also performs well (Dice 78.87 vs 79.58).
  • Centerline loss weights (lambda_cha, lambda_sdf, lambda_reg) = 30, 0.5, 60
    Chosen by hand in Sec 4.3 with no sensitivity analysis shown in the main text.
  • Stage balance weights w_l = 0.05, 0.60, 0.95, 1.00
    Chosen by hand for the four deformation stages; no ablation reported.
  • Initial centerline point count N_c = 100 per category
    Default setting in Sec 4.3; no ablation reported in the main text.
  • Local patch size M and patch count |Omega| = M unspecified; |Omega| sampled from U(60,80)
    The patch size M is not given in the main text, despite being required for the local chamfer loss in Eq. 7.
assumptions (4)
  • domain assumption Ground-truth centerlines obtained by 3D thinning of GT masks are valid supervision targets for vessel centerlines.
    Used for local chamfer and SDF losses in Sec 3.3; thinning-based centerlines may not be anatomically ideal for diseased or occluded vessels.
  • domain assumption The coarse segmentation from the 3D UNet backbone contains the correct vessel topology, so the initial template can capture all relevant branches.
    Adaptive Template Generation (Sec 3.2) skeletonizes the coarse segmentation; branches absent there cannot be created by deformation, as the failure case in Supplementary Fig. 13 shows.
  • domain assumption Deformation and unpooling never change graph topology; they only move points and insert points along existing edges.
    Eqs. (3)-(5) update positions and unpool along edges but do not add or remove edges; this is the mechanism behind the claimed natural connectivity.
  • domain assumption Minimum spanning tree reconstruction of the thinning output preserves vessel branching topology.
    Invoked in Sec 3.2 following the strategy in [39]; if the MST merges or drops branches, the template topology is wrong.

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Cite this review

Pith. "Pith review of DeformCL: Learning Deformable Centerline Representation for Vessel Extraction in 3D Medical Image." pith.science (2026). https://pith.science/paper/HQAI5JCA

@misc{pith2026250605820,
  author       = {Pith},
  title        = {Pith review of: DeformCL: Learning Deformable Centerline Representation for Vessel Extraction in 3D Medical Image},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HQAI5JCA}},
  note         = {Machine review of arXiv:2506.05820}
}
read the original abstract

In the field of 3D medical imaging, accurately extracting and representing the blood vessels with curvilinear structures holds paramount importance for clinical diagnosis. Previous methods have commonly relied on discrete representation like mask, often resulting in local fractures or scattered fragments due to the inherent limitations of the per-pixel classification paradigm. In this work, we introduce DeformCL, a new continuous representation based on Deformable Centerlines, where centerline points act as nodes connected by edges that capture spatial relationships. Compared with previous representations, DeformCL offers three key advantages: natural connectivity, noise robustness, and interaction facility. We present a comprehensive training pipeline structured in a cascaded manner to fully exploit these favorable properties of DeformCL. Extensive experiments on four 3D vessel segmentation datasets demonstrate the effectiveness and superiority of our method. Furthermore, the visualization of curved planar reformation images validates the clinical significance of the proposed framework. We release the code in https://github.com/barry664/DeformCL

Figures

Figures reproduced from arXiv: 2506.05820 by the authors.

Figure 1
Figure 1. Previous methods [1, 23, 28, 31, 33] primarily rely on the discrete mask representation, adopting a per-pixel classification paradigm for vessel segmentation. Common techniques in these approaches include incorporating tubular priors and applying topology￾preserving loss functions. In contrast, we introduce a new continuous representation, DeformCL, which employs centerline points con￾nected by edges to gradually fi… view at source ↗
Figure 2
Figure 2. Three significant properties of DeformCL compared [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Overview of the training process. Given a 3D medical image, the segmentation network first outputs a coarse prediction and [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (9 more)
Figure 4
Figure 4. Figure 4: Adaptive Template Generation. apply an unpooling strategy after deformation to increase point density. Specifically, a new point is inserted between each pair of connected points. We reuse the symbol {v l+1 i } for clarity. This process is iterated L times for accurate…
Figure 5
Figure 5. Figure 5: SDF Loss. As illustrated in [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]
Figure 6
Figure 6. Figure 6: Visualizations of the predictions from different methods [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]
Figure 8
Figure 8. Figure 8: Visual comparison of SCPR images reconstructed from [PITH_FULL_IMAGE:figures/full_fig_p008_8.png]
Figure 9
Figure 9. Figure 9: Visualizations of the centerline deformation process on [PITH_FULL_IMAGE:figures/full_fig_p011_9.png]
Figure 10
Figure 10. Figure 10: Visualization of centerline templates obtained through [PITH_FULL_IMAGE:figures/full_fig_p011_10.png]
Figure 11
Figure 11. Figure 11: Additional visualizations of the predictions from dif [PITH_FULL_IMAGE:figures/full_fig_p012_11.png]
Figure 12
Figure 12. Figure 12: Additional visual comparison of SCPR images recon [PITH_FULL_IMAGE:figures/full_fig_p012_12.png]
Figure 13
Figure 13. Figure 13: Performance of centerlines on occluded vessels. [PITH_FULL_IMAGE:figures/full_fig_p012_13.png]

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.