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REVIEW 5 major objections 7 minor 49 references

PASC-Net:Plug-and-play Shape Self-learning Convolutions Network with Hierarchical Topology Constraints for Vessel Segmentation

T0 review · 5 major / 7 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read PASC-Net claims that replacing standard square convolutions with four self-learning strip kernels and adding hierarchical topology losses consistently improves vessel segmentation on four backbones, reaching state-of-the-art Dice of…

desk verdict Plausible empirical gains on two solid datasets, but the SSL module cannot be reconstructed from the paper and the derivation in Eqs. (1)-(4) is mathematically invalid; worth refereeing as a major-revision candidate. read the letter →

arxiv 2507.04008 v1 pith:S3SEAF7I submitted 2025-07-05 eess.IV cs.CV

Xiao Zhang , Zhuo Jin , Shaoxuan Wu , Fengyu Wang , Guansheng Peng , Xiang Zhang , Ying Huang , JingKun Chen
show 1 more author
Jun Feng
This is my paper · ORCID
classification eess.IVcs.CV
keywords vesselsegmentationshapeself-learningconvolutionstriphierarchicaltopologyconstraintscenterlinelossneighborconnectivitycoronaryangiographyfundusimage
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

The paper tries to show that two plug-in components can fix the two things that most often go wrong in blood-vessel segmentation: tiny branches being missed and the vessel tree breaking at bifurcations. The first component, Shape Self-Learning (SSL) convolution, replaces ordinary square kernels with four elongated strip kernels (horizontal, vertical, and the two diagonals) whose points shift perpendicularly while sliding, so the receptive field bends with the vessel. The second, Hierarchical Topology Constraints (HTC), adds losses on centerlines, masks, and eight-neighbour connectivity to push predictions toward connected trees. On two public datasets, coronary angiography and retinal fundus photos, the authors report consistent gains across four segmentation backbones, with the strongest variant exceeding all compared methods. A sympathetic reader would take the claim as: a compact, architecture-agnostic module plus three loss terms raises overlap and topology metrics by roughly one to two Dice points and reduces average surface distance.

What carries the argument

The central object is the SSL convolution: four length-9 strip kernels (directions $x$, $y$, $z$, $w$) whose points are shifted perpendicularly by offsets $\Delta x_m$, $\Delta y_m$ around a fixed midpoint, then applied as ordinary convolutions and summed. The paper invokes a 'convolutional invariance theorem' to claim that shifting the kernel is equivalent to shifting the feature map, so the learnable shape can be implemented as a sum of standard convolutions. The second mechanism is the HTC loss, which combines centerline Dice (line level), mask Dice (surface level), and a BCE on an 8-neighbor connectivity matrix (the neighborhood level). Together these carry the argument: the SSL kernel adapts the receptive field to tubular geometry, and HTC regularizes the output so connectivity is penalized at every scale.

What would settle it

Run the ARCADE experiment with an SSL module implemented exactly as the text specifies: because Section 3.1.1 does not say how $\Delta x_m$ and $\Delta y_m$ are predicted, no independent implementation can be built, and if a DSCNet-style offset branch is supplied instead, the reported 1.29-point Dice gain over nnU-Net is no longer a test of the paper's stated mechanism. A faster check: substitute any random feature map and kernel into Eq. (1); the two sides are not equal, so the kernel-shift/feature-map-shift equivalence the derivation relies on is not the identity the paper claims.

Watch

Extended reading notes

Core claim

The authors claim that standard convolutions are a poor inductive bias for tree-like tubular structures, and that making kernels shape-adaptive at inference time is enough to recover lost branches and broken topology. Concretely, they replace every convolutional layer's square kernel with the sum of four strip convolutions oriented horizontally, vertically, diagonally, and anti-diagonally; each strip's non-center points acquire learned perpendicular offsets, and the four outputs are added to form the SSL convolution. Around this they add the HTC loss: centerline Dice to keep the line skeleton aligned, mask Dice to keep the surface overlap, and a binary cross-entropy term on an 8-neighbour connectivity matrix to keep adjacent vessel pixels linked. Integrated into nnU-Net, the method reports Dice 82.39% versus 81.10% for nnU-Net on ARCADE and 91.83% versus 89.40% on FIVES, with IoU, clDice, and ASD improving as well. Ablation tables on U-Net, FCN, U-Mamba, and nnU-Net show every added component improving most metrics on both datasets.

Load-bearing premise

The load-bearing premise is that the SSL module's per-point perpendicular offsets are produced by a defined learned mechanism; the paper never specifies how $\Delta x_m$ and $\Delta y_m$ are generated, and the convolution-invariance identity used to justify the kernel shifts has sign and index errors as written.

Editorial extensions

If this is right

  • Replacing square kernels with the four-direction SSL strip convolution is reported to raise Dice, IoU, and clDice on both datasets for every backbone tested, so the module transfers without architectural redesign.
  • Adding the HTC losses (centerline, mask, and 8-neighbour connectivity) is reported to reduce topological breakpoints and lower average surface distance compared with the same networks without them.
  • The full PASC-Net on nnU-Net is reported to outperform all compared methods on ARCADE and FIVES, with Dice gains of 1.29 points and 2.43 points over nnU-Net, respectively.
  • Because the SSL module is described as plug-and-play, the same gain pattern is what the authors predict if the module is dropped into any convolutional segmentation backbone.
  • The HTC module's centerline and connectivity losses directly target the bifurcation breakpoints that overlap-only losses miss, so the framework's benefit is largest exactly where topology, not just pixel overlap, matters for clinical use.

Reading between the lines

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

  • Because the offset-generation mechanism is unspecified, the module's novelty may reduce to a four-direction variant of DSCNet-style learned offsets; if so, the distinctive contribution would be the HTC losses, not the shape learning itself.
  • The precision/recall pattern on FIVES suggests the gains come from detecting more small branches at the cost of a small precision drop; a clinical deployment would need to decide whether the extra positives are acceptable.
  • The HTC loss has a direct 3D analogue: replace the 8-neighbour connectivity matrix with a 26-neighbour one and apply the same centerline/mask/connectivity triple to CTA or MRA volumes, which the authors name as future work.
  • On datasets whose annotations are only coarse masks without skeletonized ground truth, the centerline and connectivity losses would have to be computed from the masks themselves, so the reported benefit may depend on annotation quality.
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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

5 major / 7 minor

Summary. The paper proposes PASC-Net, a vessel segmentation framework combining a shape self-learning (SSL) convolution module, intended to adapt strip-shaped convolutional kernels to tubular structures, and a hierarchical topology constraint (HTC) module with centerline, mask, and neighbor-connectivity losses. The authors report consistent improvements over U-Net, FCN, U-Mamba, and nnU-Net on the ARCADE and FIVES datasets, achieving state-of-the-art Dice scores of 82.39% and 91.83%, respectively, with claimed gains of about 1–2 Dice points over the strongest baselines.

Significance. If the method is exactly as claimed and reproducible, the plug-and-play nature of the SSL module and the multi-level topology constraints would be a practical contribution to vessel segmentation, and the cross-architecture ablations on two public datasets are a strength. The paper also reports standard deviations and provides a code link, which aids reproducibility. However, the significance is currently weakened by the incomplete formal description of the core SSL convolution and by internal inconsistencies in the connectivity loss and ablation mapping, so the central claims are not yet verifiable from the manuscript alone.

major comments (5)
  1. [3.1.1 and 3.1.2, Eqs. (1)–(4)] The SSL convolution is not defined precisely enough to be implemented. The offset process (Section 3.1.1) is purely qualitative: no network branch, equation, or parameterization is given for predicting the per-point shifts Δx_m and Δy_m, so it is unclear how the kernel shape is learned. The 'convolutional invariance theorem' in Section 3.1.2 then asserts equalities that are not algebraic identities. For example, Eq. (1) claims Σ_m X(i+Δx, j+m) W(i, j+m) = Σ_m X(i, j+m) W(i+Δx, j+m), which holds only under very special assumptions about X and W, and the m-dependence of the offsets is omitted. Because this is the load-bearing definition of the proposed module, the central claim that replacing standard convolutions with SSL convolutions yields the reported gains is not substantiated by the written description.
  2. [3.2.3, Eq. (10)] The neighbor connectivity matrix is defined as C_{i,j,k} = 1 if P_{i,j} = N_k, where N_k includes P_{i,j} itself as the 5th element. As written, this makes C_{i,j,5} always 1 and C_{i,j,k} always 0 for k ≠ 5, so it does not encode any meaningful 8-neighbor connectivity. Consequently the ground-truth connectivity matrix used in L_con (Eq. 11) is degenerate, and the claimed topological constraint from the NC unit is not well defined.
  3. [3.2.1 and Tables 1–2] The centerline loss L_cl in Eq. (7) is essentially the clDice objective (Dice between predicted and ground-truth centerlines), while clDice is also a headline reported metric in Table 1 and in the ablation Table 2. Therefore the reported clDice improvements are partly a training echo: optimizing L_cl is expected to raise the clDice metric by construction. The paper should either report clDice from models trained without the centerline loss, or discuss this circularity explicitly and justify why the clDice comparison is still informative.
  4. [4.5, Table 2] The ablation table is not aligned with the text. The text describes 'xy-based', 'zw-based', and 'xyzw-based' SSL configurations, while the table has separate checkmarks for x, y, z, w; it is unclear which rows correspond to which configuration. The text also says the fourth row for each backbone shows 'only the mask constraint', but the table rows include checkmarks for SSL components before the NC and CL columns, so the claimed isolation of the HTC components is not actually demonstrated. This makes the central ablation claim—that every added component improves metrics—unverifiable from the reported table.
  5. [3.2 and Eq. (12)] The total loss in Eq. (12) is given as L = L_dice + L_cl + L_con, but L_dice is never defined, while the mask constraint defined in Eq. (8) is called L_mask and is not included in the total loss. This leaves the actual training objective ambiguous: it is unclear whether the mask Dice loss is part of the optimization, whether L_dice refers to L_mask, or whether an additional unstated Dice loss is used.
minor comments (7)
  1. [3.1.2, Eqs. (5)–(6)] Equations (5) and (6) are identical and appear to be a duplication artifact; one should be removed.
  2. [Figure 2 caption] The caption refers to the 'SSH module', which appears to be a typo for 'SSL module'.
  3. [2.2] The phrase 'topological conherence' should be 'topological coherence'.
  4. [4.5.1] The text says 'zy-base convolutions' where 'zw-base' is clearly intended, and the description of the three SSL configurations does not match the column structure of Table 2.
  5. [Figure 4 caption] The caption states that red indicates 'true negative (over-segmentation)' and blue indicates 'false positive (mis-segmentation)', but over-segmentation is a false positive and under-segmentation is a false negative; the color-to-error mapping appears mislabeled.
  6. [Table 2] Several entries in Table 2 are malformed, e.g., '68.260.96±' in the U-Mamba ARCADE row and '64.87±0.8 5' in the UNet ARCADE row; these should be corrected.
  7. [4.2] The experimental setup does not report training epochs, loss-weight hyperparameters, or whether the reported runs use a fixed random seed; these details are needed to assess the stability of the reported standard deviations.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the central Dice/IoU gains are empirical and held-out; the clDice metric is closely tied to the L_cl loss but is measured on test data and corroborated by ASD; self-citations are not load-bearing. The paper's serious defects are reproducibility errors, not circular reasoning.

full rationale

The paper's load-bearing claims are empirical: replacing standard convolutions with the described SSL block and adding the HTC losses yields higher Dice/IoU on held-out ARCADE and FIVES test sets. These results do not reduce by construction to any fitted parameter or to the loss definitions. The reported Dice and IoU are computed on test predictions after training, and even the clDice metric, although closely related to the L_cl loss in Eq. (7), is measured on held-out data and additionally corroborated by ASD improvements. The self-citations to the authors' prior hierarchical-topology works [44,45] provide inspiration and naming, but the losses are explicitly defined in Eqs. (7)-(11), so the argument does not rest on unverified prior claims. The serious defects — the unspecified offset-prediction mechanism in Sec. 3.1.1, the algebraically invalid 'convolutional invariance' equalities in Eqs. (1)-(4), and the degenerate self-referential connectivity matrix in Eq. (10) — are correctness/reproducibility problems, not circular reasoning. Accordingly, the circularity score is low (2), reflecting only minor non-load-bearing self-citation.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central claim rests on three hand-chosen hyperparameters (kernel length 9, equal loss weights, learning rate 0.01), a standard convolution property that is misapplied in the printed equations, and two unverified domain assumptions: that learned offsets track vessel shape and that local connectivity supervision yields global topological correctness. No new entities are introduced. The modest ledger is typical for an empirical segmentation paper; the main deficit is that the offset-learning assumption is load-bearing but unspecified.

free parameters (3)
  • strip convolution length = 9
    Section 3.1: 'the length of the strip convolution was set to 9', chosen by hand to match a 3x3 receptive field; no ablation over lengths is reported.
  • loss weights (L_dice, L_cl, L_con) = 1.0, 1.0, 1.0 (implicit)
    Eq. (12) sums the three losses with equal weight; no tuning or sensitivity analysis is reported, and Eq. (12) omits the separately named L_mask.
  • initial learning rate = 0.01
    Section 4.2 states Adam with initial learning rate 0.01; a standard but hand-chosen hyperparameter not ablated.
assumptions (4)
  • standard math Convolutional invariance: shifting a convolution kernel is equivalent to shifting the feature map (translation equivariance).
    Invoked in Section 3.1.2 to equate kernel-shifted and feature-shifted forms; the property is standard but is misapplied in Eqs. (1)-(4) as printed, with the shift sign inverted.
  • domain assumption Per-point kernel offsets are learnable and remain smooth (relative shift between neighbors <= 1), producing kernels that track vessel shape.
    Section 3.1.1 asserts the shifts are learned and bounded without specifying the predictor; DSCNet-style offset branches are assumed by the reader.
  • domain assumption Local 8-neighbor connectivity supervision improves global vessel topology.
    Section 3.2.3 claims the connectivity loss preserves topology; no theory or experiment isolates global topology correctness (for example Betti numbers) from the local loss.
  • domain assumption Centerline Dice is a valid topology objective.
    Section 3.2.1 adopts the centerline Dice loss from prior work [45]/clDice; the paper provides no new justification and the objective is nearly identical to the reported clDice metric.

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Cite this review

Pith. "Pith review of PASC-Net:Plug-and-play Shape Self-learning Convolutions Network with Hierarchical Topology Constraints for Vessel Segmentation." pith.science (2026). https://pith.science/paper/S3SEAF7I

@misc{pith2026250704008,
  author       = {Pith},
  title        = {Pith review of: PASC-Net:Plug-and-play Shape Self-learning Convolutions Network with Hierarchical Topology Constraints for Vessel Segmentation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/S3SEAF7I}},
  note         = {Machine review of arXiv:2507.04008}
}
read the original abstract

Accurate vessel segmentation is crucial to assist in clinical diagnosis by medical experts. However, the intricate tree-like tubular structure of blood vessels poses significant challenges for existing segmentation algorithms. Small vascular branches are often overlooked due to their low contrast compared to surrounding tissues, leading to incomplete vessel segmentation. Furthermore, the complex vascular topology prevents the model from accurately capturing and reconstructing vascular structure, resulting in incorrect topology, such as breakpoints at the bifurcation of the vascular tree. To overcome these challenges, we propose a novel vessel segmentation framework called PASC Net. It includes two key modules: a plug-and-play shape self-learning convolutional (SSL) module that optimizes convolution kernel design, and a hierarchical topological constraint (HTC) module that ensures vascular connectivity through topological constraints. Specifically, the SSL module enhances adaptability to vascular structures by optimizing conventional convolutions into learnable strip convolutions, which improves the network's ability to perceive fine-grained features of tubular anatomies. Furthermore, to better preserve the coherence and integrity of vascular topology, the HTC module incorporates hierarchical topological constraints-spanning linear, planar, and volumetric levels-which serve to regularize the network's representation of vascular continuity and structural consistency. We replaced the standard convolutional layers in U-Net, FCN, U-Mamba, and nnUNet with SSL convolutions, leading to consistent performance improvements across all architectures. Furthermore, when integrated into the nnUNet framework, our method outperformed other methods on multiple metrics, achieving state-of-the-art vascular segmentation performance.

Figures

Figures reproduced from arXiv: 2507.04008 by the authors.

Figure 1
Figure 1. The challenges of vessels segmentation: 1) Lost small branches (green box): Small branches at the end of the vascular tree are lost due to low contrast; 2) Incorrect topological structures (red box): The appearance of breakpoints disrupts the vascular topology. The left side shows the original image, the middle displays the prediction results of nnUNet, and the right side shows the ground truth. and exhibits diverse… view at source ↗
Figure 2
Figure 2. The proposed PASC-Net framework, including overall network architecture, SSH module, HTC module (Neighbor Connectivity Constraint Unit and Center Line Constraint Unit). improving performance without manual tuning. Another no￾table model is U-Mamba [25], which combines the strengths of U-Net and Mamba networks. U-Mamba is designed to handle the challenge of long-range dependency loss, which is particularly significan… view at source ↗
Figure 3
Figure 3. The detail process of SSL Module. SSL Convolution slides over the input feature map to calculate the output, and automatically changes shape according to the shape of the blood vessel during the sliding process. designed a convolutional kernel that can automatically learn the tubular structure of vessels, as shown in Fig.3. The learning of SSL convolution kernel occurs in two aspects: on one hand, the convolutional … view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Qualitative comparison of our PASC-Net with other state-of-the-art methods on two public datasets. The red part of the prediction results indicates true negative (over-segmentation), and the blue part indicates false positive (mis-segmentation). superior performance co…

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Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.