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REVIEW 3 major objections 6 minor 24 references

Shape-aware Sampling Matters in the Modeling of Multi-Class Tubular Structures

T0 review · 3 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read The paper claims that per-axis fractal dimension should set patch sizes, and a minimum path-cost skeleton should weight the loss, to preserve topology in multi-class tubular segmentation.

desk verdict Consistent empirical gains, but the fractal-dimension patch-size mechanism is not established as written; the MPC-Skel half is more solid. read the letter →

arxiv 2506.12395 v1 pith:WZBU3BHF submitted 2025-06-14 eess.IV cs.CV

Minghui Zhang , Yaoyu Liu , Xin You , Hanxiao Zhang , Yun Gu This is my paper · ORCID
classification eess.IVcs.CV
keywords shape-awaresamplingfractaldimensionpatchsizeallocationtubularstructuresegmentationskeleton-weightedlosstopologypreservationmulti-classminimumpath-costskeletonization
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 targets a blind spot in deep-learning segmentation of multi-class tubular structures: overlap metrics such as Dice do not penalize broken or clumped branches, and default patch sizes ignore that a tube's complexity differs along the x, y, and z axes. To fix this, the authors propose Shape-aware Sampling (SAS), a two-part plug-in for training pipelines. The first part, FDPS, measures an axis-specific fractal dimension of the label and reassigns patch sizes inversely proportional to it, so the most intricate axis is sampled at higher resolution. The second part, MPC-Skel, replaces standard skeletonization with a minimum path-cost tracing that yields a cleaner skeleton-weighted map for the loss. On AortaSeg24 and an airway labeling dataset, adding SAS to three skeleton-aware backbones consistently improves Dice, Hausdorff distance, and beta0 error, for example raising Dice from 74.78 to 77.20 and cutting Hd95 from 15.17 mm to 6.05 mm on the aorta benchmark with the Skeleton-Recall backbone.

What carries the argument

The central objects are FDPS (Fractal Dimension-based Patchsize) and MPC-Skel (Minimum Path-Cost Skeletonization). FDPS computes a box-counting fractal dimension for each axis of the label and reassigns the three initial patch sizes inversely proportional to those dimensions (Eq. 2), so the axis with the highest fractal complexity gets the smallest patch, capturing finer local details. MPC-Skel samples shortest paths through the shape using a cost function derived from the distance transform (Eqs. 3-4), expands each path with an adaptive sphere whose radius scales with the local distance (Eq. 5), and returns a skeleton-weighted map that is used in the training loss. Together these two mechanisms form SAS, a training-time plug-in that is computationally cheap and can be added to existing segmentation pipelines.

What would settle it

Run Algorithm 1's box-counting loop on a synthetic straight cylinder aligned with the z-axis: since every threshold r uses full 3D boxes over the entire volume, the counts are identical for all three axis labels, so the reported per-axis dimensions (e.g., 0.58, 0.58, 0.71) cannot come from the stated procedure. Alternatively, compute genuine axis-specific counts by slicing the volume along each axis; if those values fall outside the reported range or do not order as claimed, the FDPS mechanism fails.

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Extended reading notes

Core claim

The central claim is that the two components of SAS directly improve both volumetric overlap and topological integrity of multi-class tubular segmentation, as instantiated on aorta CT angiography and airway CT. FDPS first estimates a fractal dimension for each axis of the ground-truth shape; because a higher dimension indicates finer structural detail, FDPS swaps the initial patch sizes so that the highest-dimension axis receives the smallest patch. MPC-Skel then builds a skeleton-weighted map by tracing minimum-cost paths through a distance transform and expanding each path with an adaptive sphere, avoiding the clump-like and spurious artifacts of conventional thinning. The evidence is a set of controlled integrations: with FDPS alone, with MPC-Skel alone, and with both, over three backbone losses (Skeleton-Recall, cbDice, and CAL), on two datasets. The best configurations move Dice from 74.78 to 77.20 and Hd95 from 15.17 mm to 6.05 mm on the aorta, and from 83.63 to 84.38 Dice with Hd95 from 5.82 mm to 5.11 mm on the airway, while adding no meaningful training cost.

Load-bearing premise

The load-bearing premise is that Algorithm 1 actually measures a distinct fractal dimension for each axis, but its box-counting loop as written counts full 3D boxes over the whole volume at each scale, producing one global curve rather than three axis-specific values; if that is wrong, the inverse-proportional patch-size rule is not complexity-driven.

Editorial extensions

If this is right

  • If FDPS works as claimed, any segmentation pipeline can reallocate an existing patch-size budget toward the geometrically hardest axis without spending more GPU memory or training time.
  • If MPC-Skel's cleaner skeleton map is the cause, then skeleton-weighted losses become more reliable on classes with close, tangled branches such as aortic Zone 6 and the celiac artery.
  • The consistent gains across two datasets and three backbones suggest the method is a general add-on for multi-class tubular modeling, not a fix tuned to one architecture.
  • Better topological integrity in aorta and airway modeling would translate directly to downstream tasks such as dissection extent assessment and bronchoscopic navigation planning.
  • The reported improvements in Hd95 (15.17 to 6.05 mm) and beta0 error (0.50 to 0.21) indicate the main benefit is in recovering thin, easily missed branches rather than in bulk overlap.

Reading between the lines

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

  • A natural extension is to check whether the same patch-size permutation arises from simpler anisotropy statistics such as bounding-box extent or branch density; if it does, the fractal-dimension measurement may be a proxy rather than the causal driver.
  • The paper reports no sensitivity analysis for MPC-Skel's parameters (alpha1, gamma, alpha2, beta); a reader might test whether gains persist over a range of these settings, especially on datasets with different voxel spacings.
  • Because FDPS only permutes the three patch sizes, its benefit is capped by the initial configuration; testing it with more than three candidate patch sizes per axis could reveal whether the inverse-proportional rule generalizes.
  • One could also test the method on non-medical tubular data such as road networks or plant roots to see if the shape-aware sampling principle transfers beyond clinical imaging.
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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

3 major / 6 minor

Summary. The manuscript proposes Shape-aware Sampling (SAS), a training-time augmentation for multi-class tubular segmentation. SAS has two components: Fractal Dimension-based Patchsize (FDPS), which reassigns per-axis patch sizes according to axis-specific fractal dimensions (Eqs. 1-2), and Minimum Path-Cost Skeletonization (MPC-Skel), which builds a skeleton-weighted loss via cost-based shortest paths (Eqs. 3-5). The method is evaluated on AortaSeg24 and Airway Anatomical Labeling datasets using nnU-Net with three skeleton-weighted backbones. The reported results show consistent improvements in Dice, clDice, Hd95, and beta0 error when FDPS and/or MPC-Skel are added.

Significance. If the claims hold, SAS would be a practical, plug-in augmentation for tubular segmentation: it does not change the network architecture, is easy to integrate into nnU-Net-style pipelines, and reports consistent gains across two multi-class datasets and three backbones. The paper supplies algorithmic pseudocode, explicit parameter settings, and mean +/- std metrics in Tables 1-2, which is helpful for reproduction. However, the core causal mechanism of FDPS rests on an axis-specific fractal dimension computation that, as written, is undefined. Because the FDPS-only rows in Tables 1-2 may be confounded with changed patch geometry and total patch volume, the significance of the paper is contingent on correcting and re-testing the fractal dimension analysis.

major comments (3)
  1. [Algorithm 1 and Eq. (1) in Section 2.1] The algorithm as written cannot produce axis-specific fractal dimensions. The outer loop over i only changes the upper limit Size_i(Y)/2; the inner loop always splits the full volume Y into 3D boxes of the same size r and counts foreground voxels, so N(r) is a single global box-counting curve. The three linear regressions in Line 8 are therefore not per-axis measurements. The reported values {0.58,0.58,0.71} for the aorta and {0.44,0.40,0.53} for the airway are not derivable from the specified procedure, and values below 1 are not the standard box-counting dimension of a connected 3D tubular set. This is load-bearing because Eq. (2) ranks patch sizes by these FDi values; if the FDi values are not well defined, FDPS reduces to an arbitrary permutation of patch sizes and the complexity-driven mechanism is unsubstantiated. Please define precisely how per-axis box counts are computed (e.g., 1D projections, slab/brick counting, or axis-stratified boxes), state the exact regression range, and show the fitted curves or slopes.
  2. [Section 3, Implementation Details, and Tables 1-2] The comparison conditions for FDPS are not fully specified. The text states that the initial AortaSeg24 patchsize is {112,112,176}, FDPS gives {176,176,112}, and then 'the original patchsize was increased to 288,112,112' for fair comparison. It is unclear which patchsize was used in the F=0 rows of Table 1, which was used in the F=1 rows, and in what sense the 'original patchsize' was increased. Since FDPS changes both patch shape and total patch volume, the F-only improvements in Tables 1-2 may reflect the changed patch geometry or total patch volume rather than fractal complexity. Please report the exact patchsize used in every condition and, ideally, include an ablation that keeps the total patch volume fixed while permuting axis lengths.
  3. [Section 2.1, Eq. (2)] The rank-based reassignment in Eq. (2) is ambiguous when fractal dimensions are tied. AortaSeg24 reports {0.58,0.58,0.71}, yet Eq. (2) requires a strict max/median/min ordering. The reported output {176,176,112} implicitly breaks the x/y tie by giving both axes the larger patchsize, but this tie-breaking rule is not stated. Please specify how ties are handled, or replace the rank rule with a continuous mapping from FDi to patch size that can be applied deterministically.
minor comments (6)
  1. [Section 2.1] The word 'descibed' should be 'described' near the box-counting definition.
  2. [Section 2.2] The word 'deterimined' in the description of Eq. (5) should be 'determined'.
  3. [Section 3, Implementation Details] There are typos and spacing issues: 'loss funcition' should be 'loss function', and 'TheL generic' should have a space after 'The'.
  4. [Eq. (1)] The limit notation in Eq. (1) is informal; since the algorithm uses finite box sizes and linear regression, please state explicitly that FDi is the negative slope of the log-log regression over the specified finite range.
  5. [General / Figure 1] Figure 1 is very dense, especially the repeated box-counting panels; annotating the axis-specific step in the figure would help readers connect Fig. 1(a) to Algorithm 1.
  6. [Section 3, Tables 1-2] Please report the number of independent runs or cross-validation folds that produce the stated standard deviations, and indicate whether any differences between configurations are statistically significant.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: SAS components are empirical heuristics evaluated on held-out splits, not fitted predictions.

full rationale

I examined the derivation chain for circular reductions. FDPS computes axis-specific fractal dimensions from the label volume (Eq. 1, Algorithm 1) and then reallocates patch sizes by rank using Eq. 2. The paper explicitly frames this as a hypothesis ('We hypothesize that the patchsize for each axis during training should consider not only the size of the shape but also the heterogeneous complexity'), not as a result derived from the target metric. No test metric enters Eqs. 1-5, and the empirical Dice/Hd95/beta0 gains are measured on held-out splits against external backbones (SR [12], cbDice [20], CAL [24]). The CAL backbone is by one of the present authors, but it is one of three independent baselines and is not used to justify the correctness of SAS; the improvements are reported against it, not derived from it. MPC-Skel is a distance-transform-based skeletonization method inspired by cited prior work [2,19], and its hyperparameters are dataset-dependent heuristics, not fitted predictions of the test metrics. The concern that Algorithm 1 as printed may not produce genuinely axis-specific fractal dimensions is a correctness/reproducibility issue, not a circularity: even if the algorithm is flawed, the reported gains do not reduce to the inputs by construction. Therefore, no significant circularity is present.

Assumptions & free parameters 5 free parameters · 3 assumptions · 0 invented entities

The central claim rests on two domain assumptions: that axis-specific fractal dimension is meaningful as computed, and that smaller patches on higher-complexity axes improve segmentation. Both are plausible but unproven. The method also uses several hand-set constants (alpha1, gamma, alpha2, beta) and a fixed initial patch size, which are free parameters. No invented entities are introduced.

free parameters (5)
  • alpha1 (path-cost strength) = 1e5
    Set manually for all experiments; no sensitivity analysis. Appears in Eq. 4.
  • gamma (cost exponent) = 4
    Set manually for all experiments; no sensitivity analysis. Appears in Eq. 4.
  • alpha2 (radius scaling) = aorta: 1.8 x spacing_max; airway: 2.4 x spacing_max
    Per-dataset hand setting for adaptive sphere radius in Eq. 5; chosen by authors, not derived.
  • beta (radius offset) = aorta: 4 x spacing_max; airway: 2 x spacing_max
    Per-dataset hand setting in Eq. 5; affects which branches are retained in the skeleton.
  • initial patchsize configuration = aorta: 112,112,176; airway: 128,96,192
    Base configuration from which FDPS permutes; determined by median resampled shape and GPU memory, not swept in the paper.
assumptions (3)
  • ad hoc to paper The box-counting procedure in Algorithm 1 yields a per-axis fractal dimension FDi for each axis.
    The algorithm as written counts boxes in 3D and would produce a single global dimension; no projection or axis-specific box shape is described. This is needed for Eq. 1 and Eq. 2.
  • domain assumption Higher axis-specific fractal dimension implies finer detail that is better captured by smaller patch size.
    Used to justify inverse rank allocation in Eq. 2; not validated independently.
  • domain assumption A skeleton-weighting loss computed from MPC-Skel improves topology preservation over existing skeletonization.
    The paper assumes the cost-based path tracing captures topology better than thinning-based methods without a direct quantitative comparison of skeleton quality.

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Cite this review

Pith. "Pith review of Shape-aware Sampling Matters in the Modeling of Multi-Class Tubular Structures." pith.science (2026). https://pith.science/paper/WZBU3BHF

@misc{pith2026250612395,
  author       = {Pith},
  title        = {Pith review of: Shape-aware Sampling Matters in the Modeling of Multi-Class Tubular Structures},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WZBU3BHF}},
  note         = {Machine review of arXiv:2506.12395}
}
read the original abstract

Accurate multi-class tubular modeling is critical for precise lesion localization and optimal treatment planning. Deep learning methods enable automated shape modeling by prioritizing volumetric overlap accuracy. However, the inherent complexity of fine-grained semantic tubular shapes is not fully emphasized by overlap accuracy, resulting in reduced topological preservation. To address this, we propose the Shapeaware Sampling (SAS), which optimizes patchsize allocation for online sampling and extracts a topology-preserved skeletal representation for the objective function. Fractal Dimension-based Patchsize (FDPS) is first introduced to quantify semantic tubular shape complexity through axis-specific fractal dimension analysis. Axes with higher fractal complexity are then sampled with smaller patchsizes to capture fine-grained features and resolve structural intricacies. In addition, Minimum Path-Cost Skeletonization (MPC-Skel) is employed to sample topologically consistent skeletal representations of semantic tubular shapes for skeleton-weighted objective functions. MPC-Skel reduces artifacts from conventional skeletonization methods and directs the focus to critical topological regions, enhancing tubular topology preservation. SAS is computationally efficient and easily integrable into optimization pipelines. Evaluation on two semantic tubular datasets showed consistent improvements in both volumetric overlap and topological integrity metrics.

Figures

Figures reproduced from arXiv: 2506.12395 by the authors.

Figure 1
Figure 1. The framework of the Shape-aware Sampling (SAS). a) FDPS quantifies the axis-specific fractal dimension and subsequently reassigns the patchsize based on axis￾wise shape complexity. b) MPC-Skel samples the topology-preserved skeletal represen￾tation for precise skeleton-based weighting. c) SAS is computationally efficient and can be seamlessly integrated into training pipelines. optimal stent placement [3, 18]. Anat… view at source ↗
Figure 2
Figure 2. Visualization of the results on the modeling of multi-class aorta and airway. The Lgeneric denotes the combination of Cross-Entropy and Soft Dice loss. In the Lskel−weight term, the skeletonization techniques [14,21] were replaced with the MPC-Skel. Inspired by [2, 19], The calculation of MPC-Skel is based on accumulated path distance, which ensures computational efficiency. In all ex￾periments, α1 = 1e5 and γ = 4 w… view at source ↗
Figure 3
Figure 3. Comparative results with baselines for multi-class aorta and airway modeling. three backbones, it consistently improve the performance across both datasets. As detailed in Tab.1 and Tab.2, SAS improves the average Dice score by over 2% on the AortaSeg24 dataset on all three backbones. It achieves approximately 84% Dice on the multi-class airway, representing an increase of around 4.5% com￾pared to the baseline. Furt… view at source ↗

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