{"id":"bb7b72ae-884a-4571-899c-bf34365ff4f0","arxiv_id":"2506.12395","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"A new patch-size allocation rule and skeleton-weighting scheme improves volumetric overlap and topology preservation for multi-class tubular structure segmentation in CT images.","lead":"The paper proposes a training-time method for deep learning segmentation of thin tubular anatomy: it sizes the training patches according to the measured complexity of each axis and uses a path-cost skeleton to weight the loss. On two CT datasets, aorta branches and airway bronchi, the method improves Dice and topology metrics when added to three existing skeleton-aware loss functions.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Algorithm 1 cannot produce the reported axis-specific fractal dimensions, so FDPS's causal claim is unsubstantiated and the FDPS-only gains are confounded with patch-shape/volume changes.","rationale":"The reader's weakest_assumption already targets Algorithm 1; my read agrees and extends it to the ablation interpretation. The empirical tables are internally consistent and MPC-Skel is independently evaluated, so I would not escalate to REJECT on the available text. The paper should remain CONDITIONAL: authors must supply the exact axis-specific FD computation, code, and a volume-matched or randomized-axis control before the FDPS mechanism can be credited. No fraudulent intent is implied; the pseudocode and text are simply insufficient for the claimed mechanism.","tokens_in":9515,"tokens_out":14542,"duration_ms":179296,"concrete_test":"On AortaSeg24, fix total patch voxels to the FDPS budget and compare three configurations with the same backbone and seed: FDPS {176,176,112}, the stated baseline {288,112,112}, and a control {112,288,112} that swaps the two equal-FD axes. Also re-implement Algorithm 1 exactly on the real training labels and report the three regression slopes. If the control reproduces FDPS's gain, or if the three slopes are not distinct, the fractal-complexity mechanism is unsupported.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Eq. 1 and Fig. 1 claim axis-specific fractal dimensions FD_i, and Eq. 2 ranks patch sizes by them. In Algorithm 1, however, the inner box-counting loop never uses i except to set the upper r limit: `Split Y to separate boxes with size of r` and `Number of counted boxes that contains foreground` produce the same global N(r) for every i. The three linear regressions therefore cannot yield the reported distinct vectors {0.58,0.58,0.71} and {0.44,0.40,0.53}; values below 1 are also not a standard box-counting dimension for a connected 3D tubular object. If the intended computation was slab counting or a 1D projection per axis, it is not the algorithm given and Eq. 1 is not the formula. This matters because FDPS is only a permutation of patch sizes (Eq. 2): without verified axis-specific FDs, the F-only rows in Tables 1-2 may reflect the changed patch geometry or total patch volume rather than fractal complexity. The §3 implementation note compounds this: Aorta starts at {112,112,176}, maps to {176,176,112}, then 'the original patchsize was increased to 288,112,112,' so the F=0 comparison configuration is unclear. The central causal mechanism of the paper is thus not established as written.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":9791,"tokens_out":6239,"duration_ms":71484,"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":[{"comment":"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.","section":"Algorithm 1 and Eq. (1) in Section 2.1"},{"comment":"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.","section":"Section 3, Implementation Details, and Tables 1-2"},{"comment":"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.","section":"Section 2.1, Eq. (2)"}],"minor_comments":[{"comment":"The word 'descibed' should be 'described' near the box-counting definition.","section":"Section 2.1"},{"comment":"The word 'deterimined' in the description of Eq. (5) should be 'determined'.","section":"Section 2.2"},{"comment":"There are typos and spacing issues: 'loss funcition' should be 'loss function', and 'TheL generic' should have a space after 'The'.","section":"Section 3, Implementation Details"},{"comment":"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.","section":"Eq. (1)"},{"comment":"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.","section":"General / Figure 1"},{"comment":"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.","section":"Section 3, Tables 1-2"}],"recommendation":"major_revision","confidential_remarks":"The paper is a reasonable candidate for a medical image analysis venue if the FDPS computation can be corrected and the patch-size confound removed. As written, the FDPS contribution is not adequately supported; the MPC-Skel component is more clearly specified, though its gains are modest and parameter sensitivity is not studied. I would not reject the paper outright, but the revision must include a corrected definition/implementation of axis-specific fractal dimension and a re-analysis of the F-only comparisons with controlled patch volume and shape."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: the paper's empirical spine is plausible, but the central mechanism as written does not close. The stress-test note is right: Algorithm 1 computes a global box-counting curve, not axis-specific fractal dimensions. The `for i` loop only changes the upper limit of the box size, so the only way to get three distinct FD_i is by fitting the same N(r) curve over three different ranges of r. The reported values (0.44–0.71) are also suspicious—a connected 3D tubular structure should give a box-counting dimension at least around 1 at coarse scales, so values below 1 suggest either a different quantity or a bug. Equation 1 is not what Algorithm 1 implements.\n\nWhat is actually new: FDPS as a patch-size allocation rule based on shape complexity is a genuine idea, and MPC-Skel is a sensible TEASAR-style skeletonizer grafted onto a skeleton-weighted loss. The evaluation is broad—three backbones, two datasets, multiple topology metrics—and the gains are consistent across the board. That consistency is real evidence that *something* in the SAS recipe helps.\n\nThe soft spots are concentrated in FDPS. The ablation does not isolate fractal complexity from patch geometry and total patch volume. The aorta implementation note is confusing: the baseline patchsize is {112,112,176}, then you say 'the original patchsize was increased to 288,112,112.' That changes aspect ratio and volume, so the F-only rows could be explained by a bigger or differently shaped patch, not by any fractal-aware allocation. On the airway, the patchsize permutation preserves volume, so those rows are cleaner, but the FD computation issue still applies. There are also no significance tests on small test sets, and no code or data. None of this smells like circularity or fabrication—just under-specification.\n\nMPC-Skel looks like the more defensible half. The cost function and adaptive sphere are standard machinery, and the comparison to clDice skeletonization is a reasonable way to show fewer artifacts. If I were working on tubular segmentation, I'd re-use the MPC-Skel part and treat FDPS with caution until the algorithm is corrected.\n\nBottom line: the paper deserves a serious referee, but the referee should ask for a corrected fractal dimension algorithm, a volume-controlled ablation, and significance tests. I would not cite the FDPS claims yet, but I'd watch for a revision.","headline":"Consistent empirical gains, but the fractal-dimension patch-size mechanism is not established as written; the MPC-Skel half is more solid.","tokens_in":10329,"tokens_out":4121,"would_cite":false,"duration_ms":47687,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"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.","keywords":["shape-aware sampling","fractal dimension","patch size allocation","tubular structure segmentation","skeleton-weighted loss","topology preservation","multi-class segmentation","minimum path-cost skeletonization"],"falsifier":"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.","tokens_in":9280,"feed_emoji":"🩻","tokens_out":8370,"duration_ms":89041,"temperature":0.7,"pith_summary":"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.","feed_headline":"Axis-wise patch sizing lifts tubular segmentation Dice","feed_subtitle":"Per-axis fractal dimension picks patch sizes; a path-cost skeleton cleans the loss for aorta and airway.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Supplies the definition that higher fractal dimension reflects finer structural detail, which motivates the inverse patch-size rule.","marker":"[6]"},{"why":"Provides the AortaSeg24 dataset with 23 aortic branches and zones used for the aorta experiments.","marker":"[8]"},{"why":"Supplies the nnUNet framework whose default patch-size rule FDPS modifies and whose pipeline hosts the integrations.","marker":"[9]"},{"why":"Provides the Skeleton-Recall loss backbone that FDPS and MPC-Skel are integrated with.","marker":"[12]"},{"why":"Supplies the box-counting algorithm used to estimate fractal dimension.","marker":"[13]"},{"why":"The thinning-based skeletonization whose clump and spurious artifacts MPC-Skel aims to remove.","marker":"[14]"},{"why":"Supplies the path-cost and tree-extraction idea that MPC-Skel's shortest-path sampling is inspired by.","marker":"[19]"},{"why":"Defines clDice and its skeletonization procedure, used both as a backbone loss and as an evaluation metric for topological integrity.","marker":"[21]"},{"why":"Provides the Airway Anatomical Labeling dataset with segmental bronchus classes used for the airway experiments.","marker":"[22]"},{"why":"Provides the CAL connectivity-aware loss backbone used in experiments.","marker":"[24]"}],"fun_headline_variants":["Fractal axis patch sizes boost tubular topology","Shape-aware sampling improves tubular Dice and topology","Per-axis fractal sizing sharpens multi-class tubules","Skeleton-weighted loss with fractal patches lifts segmentation"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Fractal axis patch sizes boost tubular topology","Shape-aware sampling improves tubular Dice and topology","Per-axis fractal sizing sharpens multi-class tubules","Skeleton-weighted loss with fractal patches lifts segmentation"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000618,"raw_usage":{"total_tokens":2883,"prompt_tokens":975,"completion_tokens":1908,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":591,"completion_tokens_details":{"reasoning_tokens":1849}},"tokens_in":591,"tokens_out":1908,"duration_ms":16400,"temperature":1.0,"reasoning_tokens":1849,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T00:51:46.301641+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":"John Wiley & Sons (2013)","cited_arxiv_id":null,"evidence_quote":"Supplies the definition that higher fractal dimension reflects finer structural detail, which motivates the inverse patch-size rule."},{"cited_title":"In: European Conference on Computer Vision","cited_arxiv_id":null,"evidence_quote":"Provides the Skeleton-Recall loss backbone that FDPS and MPC-Skel are integrated with."},{"cited_title":"In: 2020 24th International Conference on Informa- tion Technology (IT)","cited_arxiv_id":null,"evidence_quote":"Supplies the box-counting algorithm used to estimate fractal dimension."},{"cited_title":"CVGIP: Graphical Models and Image Processing 56(6), 462–478 (1994)","cited_arxiv_id":null,"evidence_quote":"The thinning-based skeletonization whose clump and spurious artifacts MPC-Skel aims to remove."},{"cited_title":"In: Proceedings the Eighth Pacific Conference on Computer Graphics and Applications","cited_arxiv_id":null,"evidence_quote":"Supplies the path-cost and tree-extraction idea that MPC-Skel's shortest-path sampling is inspired by."},{"cited_title":"In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition","cited_arxiv_id":null,"evidence_quote":"Defines clDice and its skeletonization procedure, used both as a backbone loss and as an evaluation metric for topological integrity."},{"cited_title":"IEEE Transactions on Medical Imaging 42(1), 103–118 (2022)","cited_arxiv_id":null,"evidence_quote":"Provides the Airway Anatomical Labeling dataset with segmental bronchus classes used for the airway experiments."},{"cited_title":"IEEE Journal of Biomedical and Health Informatics (2023)","cited_arxiv_id":null,"evidence_quote":"Provides the CAL connectivity-aware loss backbone used in experiments."}],"review_version":1}