Frequency-enhanced Multi-granularity Context Network for Efficient Vertebrae Segmentation

Haojie Li; Hongli Zhang; Jian Shi; Pingping Zhang; Rui Xu; Tianqi You

REVIEW 3 major objections 5 minor 22 references

Frequency-enhanced Multi-granularity Context Network for Efficient Vertebrae Segmentation

T0 review · 3 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read A wavelet-based segmentation network achieves state-of-the-art vertebrae segmentation on CT and MRI by processing high- and low-frequency signal components separately, restoring blurred detail and distinguishing look-alike vertebrae.

desk verdict Solid incremental architecture paper, but the SOTA claim is undercut by a numerical slip and single-run margins of about 1 DSC point. read the letter →

arxiv 2506.23086 v1 pith:KX63ONND submitted 2025-06-29 cs.CV

Jian Shi , Tianqi You , Pingping Zhang , Hongli Zhang , Rui Xu , Haojie Li This is my paper · ORCID

classification cs.CV

keywords vertebraesegmentationwavelettransformstatespacemodelmulti-granularitycontexthigh-frequencyfeaturerefinementcomputedtomographymagneticresonanceimagingmedicalimage

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

FMC-Net is designed to solve two specific failures in vertebrae segmentation: blur and noise that smudge fine detail in CT and MRI, and the near-identical appearance of adjacent vertebrae that makes them hard to tell apart. The paper's central claim is that replacing ordinary downsampling with a wavelet transform, then treating the high- and low-frequency components differently, fixes both problems. For high frequencies it restores edges and texture while filtering noise; for low frequencies it builds multi-scale context models that capture long-range spatial dependencies cheaply. On the VERSE2019 CT benchmark the method reports a mean Dice score of 79.92% (HD95 of 3.04 mm), and on the LUMBAR MRI benchmark 79.13% DSC (HD95 17.13 mm), both above the prior methods compared. If the reported gains hold up, the practical payoff is more reliable automated labeling of individual vertebrae for surgical planning and diagnosis.

What carries the argument

The engine of the argument is the discrete wavelet transform used as a lossless downsampling step (WTD): it splits each 3D feature map into one low-frequency band and seven high-frequency sub-bands instead of pooling away information. The high-frequency bands go through a High-frequency Feature Refinement (HFR) module with two attention paths, one amplifying salient structures (max-pooling plus softmax weighting) and one smoothing noise (average pooling); the low-frequency band goes through a Multi-granularity State Space Model (MG-SSM) that runs three parallel dilated depthwise convolutions into three state-space modules and merges their outputs, capturing long-range dependencies at linear complexity. A Wavelet Transform Upsampling (WTU) step reuses encoder wavelet coefficients during decoding. Each named component does specific work: WTD avoids information loss, HFR restores fine detail, and MG-SSM supplies the spatially-varying multi-scale context the paper argues is needed to tell similar vertebrae apart.

What would settle it

Run the released code on both benchmarks under the stated settings with at least five random seeds; the central claim would be undermined if the seed-to-seed variation in FMC-Net's mean DSC overlaps the reported scores of the best prior method in Table 1 (a 1.64-point margin on VERSE2019 and a 0.96-point margin on LUMBAR), or if the DWT-Sample component changes the DSC by less than the 0.66 points reported in the ablation.

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Extended reading notes

Core claim

The discovery this paper puts forward is a segmentation architecture whose performance gains come from where information is lost, not from a bigger model. FMC-Net replaces max-pooling and interpolation with a discrete wavelet transform, which splits each feature map into one low-frequency band (the bulk of the image content) and seven high-frequency bands (edges, texture, noise) without discarding information. High-frequency bands pass through a High-frequency Feature Refinement (HFR) module with two spatial-attention paths — one that amplifies salient structure via max-pooling, one that smooths noise via average pooling. Low-frequency bands pass through a Multi-granularity State Space Model (MG-SSM): three dilated depthwise convolutions feed three state-space modules whose outputs are merged, capturing contexts at multiple receptive fields with linear complexity in sequence length. The wavelet-based sampling is also used in the decoder (Wavelet Transform Upsampling), so encoder detail is reused during upsampling. The author's claim is that this combination specifically targets the two failure modes — blur and vertebra similarity — and that it outperforms previous convolutional, transformer, and state-space-model methods on both CT and MRI vertebrae benchmarks.

Load-bearing premise

The load-bearing premise is that the reported performance gaps over the prior methods are genuine effects of the architecture and not artifacts of a single training run: the paper reports no error bars, repeated trials, or significance tests, so the observed 1–2 point DSC advantages are assumed to be stable.

Editorial extensions

If this is right

Because the ablation isolates each piece, the wavelet sampling, the high-frequency refinement, and the multi-granularity state-space module each can be added to an existing U-shaped baseline independently and raise the Dice score.
The same network, with only patch size and epoch count changed, produces the reported results on both CT and MRI, so the design is not tied to one imaging modality.
The underlying state-space formulation keeps long-range context capture at linear complexity, avoiding the quadratic cost of self-attention that limits transformer-based segmentation of large 3D volumes.
Public release of the code means the reported numbers on both benchmarks can be checked directly against the paper's tables.

Reading between the lines

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

My inference: if the failure-mode analysis is right, the accuracy gains should concentrate on blurry slices and on the boundaries between adjacent vertebrae; a stratified error analysis by sharpness and inter-vertebral border distance would confirm where the method actually helps.
My inference: the component-wise ablation numbers come from single runs, so the exact size of each module's contribution is not yet established; multi-seed ablations would turn the observed ordering of gains into a quantitative claim.
My inference: the frequency-split recipe (wavelet downsampling plus separate high/low treatment) is a general remedy for repetitive-anatomy segmentation with blur, and could be tested on ribs, teeth, or finger bones where the same two failure modes dominate.
My inference: the method's reported improvements over the closest prior model are in the 1–2 DSC point range; whether that margin is clinically meaningful for vertebrae labeling is a separate question the paper does not address, since DSC gains of that size may or may not change surgical planning decisions.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Quick take: this is a decent incremental architecture paper for vertebrae segmentation, but the SOTA claim is not yet established because the reported margins over the strongest baselines are about one DSC point and come from a single run. There is also a numerical mismatch in the text that needs fixing.

What's new: the paper adapts wavelet transform downsampling from semantic segmentation (Xu et al.) to 3D vertebrae segmentation and combines it with a high-frequency refinement module and a multi-granularity state space model. The specific combination is new, and the ablation on LUMBAR shows each component adds something: baseline 71.09 DSC, adding DWT gives 71.75, HFR 75.30, MG-SSM 76.56, full 79.13. That internal evidence is the strongest part of the paper. The code is public, baselines include nnU-Net, Swin-UNetR, CoTR, and three Mamba variants, and the evaluation covers both CT and MRI.

Soft spots: the biggest is a concrete error in Section 3. The text claims improvement of 1.64% over 'the best-performing Mamba-based method, SegMamba' on VERSE2019, but Table 1 has SegMamba at 72.22 mean DSC and FMC-Net at 79.92; the 1.64 gap actually matches UMamba (78.28). Either the table is wrong or the text names the wrong baseline. Second, no error bars, repeated seeds, or significance tests anywhere. Given that the true margins over UMamba (CT) and SegMamba (MRI) are 1.64 and 0.96 DSC points, the SOTA claim is within typical seed noise for 3D medical segmentation. Third, the data split for both datasets is not stated, so protocol comparability with published baselines is unclear. Fourth, MRI evaluation is limited to T1-weighted LUMBAR, with no T2 or contrast-enhanced T1, so the generalization to MRI is narrow.

The paper is coherent and the thinking is clear; the flaws are missing statistics rather than bad logic. A serious referee should see this, but the authors need to correct the SegMamba/UMamba discrepancy, report variance over multiple runs, and specify the split before the SOTA claim can be taken at face value.

Referee Report

3 major / 5 minor

Summary. The paper proposes FMC-Net, a 3D encoder-decoder for vertebrae segmentation that replaces standard downsampling with discrete wavelet transform, splits features into high- and low-frequency components, enhances them with a High-frequency Feature Refinement (HFR) module and a Multi-granularity State Space Model (MG-SSM), and reconstructs features via inverse wavelet transform. The method is evaluated on VERSE2019 (CT) and LUMBAR (MRI) datasets, reporting DSC and HD95 against CNN-, Transformer-, and Mamba-based baselines, together with an ablation study on LUMBAR. The central claim is that FMC-Net achieves state-of-the-art performance on both datasets.

Significance. If the reported results are reliable, the paper would make a modest but useful contribution to vertebrae segmentation: it combines two established ideas (wavelet-domain downsampling and state-space modeling) in a new way, addresses the clinically relevant problem of blurred and morphologically similar vertebrae, and provides a public codebase. The ablation study on LUMBAR shows large gains from the proposed components (DSC from 71.09 to 79.13), and the design is plausible and well-motivated. However, the significance as stated depends on the SOTA claim, which currently rests on a single training run and on a numerical mismatch between the text and Table 1. The gains over the strongest baselines are small (1.64 DSC over UMamba on VERSE2019 and 0.96 DSC over SegMamba on LUMBAR), and no evidence rules out seed or protocol variation. The manuscript is therefore of interest to the community, but the SOTA claim is not yet established at the level of certainty the paper asserts.

major comments (3)

[Section 3, Table 1 and text] There is a direct numerical contradiction in the SOTA claim. The text states that compared with the best-performing Mamba-based method, SegMamba, the approach improves the mean DSC per class by 1.64% on VERSE2019. Table 1, however, lists SegMamba at 72.22 DSC and FMC-Net at 79.92 DSC on VERSE2019, a difference of 7.70 percentage points, not 1.64. The 1.64-point gap corresponds to UMamba (78.28 vs. 79.92), not SegMamba. Either the text identifies the wrong baseline or the table reports different numbers. This is load-bearing because the paper's central claim is state-of-the-art performance, and the reader cannot tell which baseline is actually the strongest. The authors must correct the text/table inconsistency and clearly state which baseline is the best prior method on each dataset.
[Section 3, Tables 1 and 2] No error bars, confidence intervals, repeated runs, or significance tests are reported for any of the quantitative results. The margins over the strongest baselines are approximately 1.64 DSC points on VERSE2019 and 0.96 DSC points on LUMBAR; in 3D medical segmentation, single-seed differences of this size are typically within random seed variation and hyperparameter sensitivity. Without at least three independent runs with mean and standard deviation, or a paired statistical test, the claim that FMC-Net outperforms state-of-the-art methods is not established. The same issue affects the ablation study in Table 2: for example, adding HFR improves DSC by 3.55 points (71.75 to 75.30) but worsens HD95 from 22.12 to 24.52, and adding MG-SSM improves DSC by 1.79 points (76.56 to 78.35?) while worsening HD95 from 16.72 to 17.13 in the final row. Without variance information, the claim that each component 'significantly enhances' performance is unsupported.
[Section 3, Datasets and Implementation Details] The experimental protocol is incompletely specified. The paper does not state how the VERSE2019 (160 scans) and LUMBAR (156 scans) datasets were split into training, validation, and test sets, nor whether the baseline numbers in Table 1 were obtained under the same split and preprocessing as the proposed method. If baseline results are quoted from their original papers and those papers use different splits or evaluation protocols, the cross-method comparison in Table 1 is not valid. The authors should state the exact split, the number of folds if cross-validation is used, and either re-evaluate all baselines under the identical protocol or justify that the cited numbers are protocol-comparable.

minor comments (5)

[Section 2.3, Eq. (8)] Equation (8) appears to have a missing closing parenthesis: X2 = phi(Conv([Fd1, Fd2, Fd3])) is presumably intended. Please fix the typo.
[Section 3, Table 2] The checkmark pattern in Table 2 is ambiguous. The rows with the same number of checkmarks ('✓ ✓') cannot be reliably mapped to components without carefully cross-referencing the text; for example, the row at 76.56 could be Baseline+DWT+MG-SSM or Baseline+HFR+MG-SSM. Please label each row explicitly or use separate columns with Y/N entries.
[Title and Section 2] The title claims 'Efficient' segmentation, but no efficiency metrics (parameters, FLOPs, inference time, GPU memory) are reported, and the only efficiency evidence is the linear-complexity statement about SSMs. Please add quantitative efficiency comparisons with the baselines, or soften the efficiency claim.
[Section 2.2 and Table 1] The dilation rates d1, d2, d3 in MG-SSM and the group counts 2^i in HFR are fixed hyperparameters, but no sensitivity analysis or ablation is provided for them. Since the multi-granularity argument depends on these choices, a short ablation or at least a statement of how they were chosen would strengthen the paper.
[Throughout] There are several typographical errors: 'he evaluation results' should be 'The evaluation results' in Section 3; 'are in illustrated Fig. 1 (a)' should be 'are illustrated in Fig. 1 (a)' in Section 1; and Eq. (1) lists eight sub-bands but uses a notation where F_i_{llh,...,hhh} is written with only one representative subscript. These should be cleaned up.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: FMC-Net is an empirical architecture paper whose claims are measured against external public benchmarks, not derived from fitted parameters or self-citation.

full rationale

The paper makes no parameter-free predictions or first-principles derivations; its central contribution is an architectural design (wavelet-based downsampling/upsampling, HFR, and MG-SSM) evaluated by measured DSC and HD95 on two public datasets, VERSE2019 and LUMBAR. The components are defined by explicit equations (Eqs. 1-9) but none of these equations is fitted to the reported metrics, and the benchmark numbers in Tables 1 and 2 are external measurements, not consequences of the method's mathematical definitions. Citations such as [12] and [13] for wavelet transforms are external prior work and are not load-bearing self-citations. The reported text/table mismatch about SegMamba's DSC (1.64% vs 7.70%) is an internal consistency or correctness issue, not a circularity issue, because the claimed comparison does not reduce to the paper's own assumptions. No fitted parameter is renamed as a prediction, no uniqueness theorem is imported from the authors' prior work, and no ansatz is smuggled in via citation. The derivation chain is therefore self-contained with respect to circularity, and the appropriate score is 0.

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

The central claim rests on standard DWT mathematics, dataset representativeness, and the architectural hypothesis that separate high/low frequency processing with the proposed HFR and MG-SSM modules improves segmentation. The only hand-chosen numbers are the disclosed training hyperparameters and undisclosed dilation rates and group schedules. No new physical entities are introduced.

free parameters (3)

dilation rates (d1, d2, d3) of MG-SSM branches = not disclosed
Three parallel 3D depth-wise conv layers with different dilation rates are used (Sec. 2.3), but the concrete values are not reported. These hand-chosen hyperparameters define the receptive field granularity and are central to the multi-granularity claim.
Group counts 2^i in HFR GroupMax = 2^i groups, i is encoder stage
Eq. 4 and Sec. 2.2 specify that each high-frequency component is divided into 2^i groups for max and average pooling. The grouping schedule is a hand-designed choice that affects the spatial attention granularity.
Training hyperparameters = patch sizes (128,160,96) and (32,256,160); 1000/600 epochs; lr 0.01
These settings (Sec. 3) are standard but manually chosen and directly affect the reported DSC/HD95 values; different settings could change the comparison.

assumptions (4)

standard math The Haar Discrete Wavelet Transform is invertible and information-preserving, so downsampling via DWT does not lose details.
Invoked in Sec. 2.1 for WTD and WTU. The mathematics is correct for unchanged coefficients, though the network modifies coefficients before inverse transform.
domain assumption VERSE2019 and LUMBAR are representative benchmarks for vertebrae segmentation in CT and MRI.
The paper generalizes from these two datasets to vertebrae segmentation broadly (Sec. 3).
domain assumption DSC and HD95 are sufficient metrics for comparing vertebrae segmentation methods.
Used in Sec. 3 without justification; a standard choice in the field.
ad hoc to paper Splitting features into high- and low-frequency components and enhancing them separately improves segmentation over joint feature processing.
This is the core design hypothesis of FMC-Net. It is supported only by the ablation on LUMBAR (Table 2), not by a derivation or external evidence.

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Cite this review

Pith. "Pith review of Frequency-enhanced Multi-granularity Context Network for Efficient Vertebrae Segmentation." pith.science (2026). https://pith.science/paper/KX63ONND

@misc{pith2026250623086,
  author       = {Pith},
  title        = {Pith review of: Frequency-enhanced Multi-granularity Context Network for Efficient Vertebrae Segmentation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KX63ONND}},
  note         = {Machine review of arXiv:2506.23086}
}

read the original abstract

Automated and accurate segmentation of individual vertebra in 3D CT and MRI images is essential for various clinical applications. Due to the limitations of current imaging techniques and the complexity of spinal structures, existing methods still struggle with reducing the impact of image blurring and distinguishing similar vertebrae. To alleviate these issues, we introduce a Frequency-enhanced Multi-granularity Context Network (FMC-Net) to improve the accuracy of vertebrae segmentation. Specifically, we first apply wavelet transform for lossless downsampling to reduce the feature distortion in blurred images. The decomposed high and low-frequency components are then processed separately. For the high-frequency components, we apply a High-frequency Feature Refinement (HFR) to amplify the prominence of key features and filter out noises, restoring fine-grained details in blurred images. For the low-frequency components, we use a Multi-granularity State Space Model (MG-SSM) to aggregate feature representations with different receptive fields, extracting spatially-varying contexts while capturing long-range dependencies with linear complexity. The utilization of multi-granularity contexts is essential for distinguishing similar vertebrae and improving segmentation accuracy. Extensive experiments demonstrate that our method outperforms state-of-the-art approaches on both CT and MRI vertebrae segmentation datasets. The source code is publicly available at https://github.com/anaanaa/FMCNet.

Figures

Figures reproduced from arXiv: 2506.23086 by the authors.

**Figure 1.** Challenging examples in vertebrae segmentation. (a) and (b) present examples of image blurring caused by current imaging techniques in CT and MRI modalities, respectively. (c) presents examples of the challenges in distinguishing similar vertebrae. (d) highlights the importance of multi-granularity contextual information contained in the features of different receptive fields for distinguishing similar vertebrae. an… view at source ↗

**Figure 2.** (a) is the overall architecture of the proposed FMC-Net. (b) and (c) are HFR and MG-SSM, which enhance the high-frequency and low-frequency components, respectively. (d) is WTU, which utilizes features from different scales of the encoder while performing upsampling in the decoder. 2.1 Wavelet Transform-based Sampling Wavelet Transform Downsampling. Inspired by Guo et al. [12], we implement Wavelet Transform Downs… view at source ↗

**Figure 3.** Qualitative results with different methods. The top three rows display segmentation results from the VERSE2019 dataset, covering cervical, thoracic, and lumbar regions with various regions and views, whereas the bottom row shows results from the LUMBAR dataset. (a) nn-UNet, (b) UMamba, (c) MambaClnix, (d) Segmamba, (e) FMC-Net (Ours), (f) Ground Truth. to the lumbar regions. The LUMBAR dataset [16] contains 156 MRI… view at source ↗

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Reference graph

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Pith tools

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

[1] [1]

In: Proceedings of the AAAI Conference on Artificial Intelligence, Vol

Wang,H.,Song,Q.,Yin,R.,Ma,R.:B-spine:LearningB-splinecurverepresentation for robust and interpretable spinal curvature estimation. In: Proceedings of the AAAI Conference on Artificial Intelligence, Vol. 38, No. 6, pp. 5381-5389 (2024)

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[2] [2]

IEEE Transactions on Medical Imaging, 40(1), 262-273 (2020)

Pang, S., Pang, C., Zhao, L., Chen, Y., Su, Z., Zhou, Y., Feng, Q.: SpineParseNet: spine parsing for volumetric MR image by a two-stage segmentation framework with semantic image representation. IEEE Transactions on Medical Imaging, 40(1), 262-273 (2020)

work page 2020

[3] [3]

A., Išgum, I.: Iterative fully con- volutional neural networks for automatic vertebra segmentation and identification

Lessmann, N., Van Ginneken, B., De Jong, P. A., Išgum, I.: Iterative fully con- volutional neural networks for automatic vertebra segmentation and identification. Medical Image Analysis, 53, 142-155 (2019)

work page 2019

[4] [4]

In: Medical Image Computing and Computer Assisted Intervention, pp

Wu, H., Zhang, J., Fang, Y., Liu, Z., Wang, N., Cui, Z., Shen, D.: Multi-view ver- tebra localization and identification from ct images. In: Medical Image Computing and Computer Assisted Intervention, pp. 136-145 (2023)

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Medical Image Analysis, 75, 102258 (2022)

Tao,R.,Liu,W.,Zheng,G.:Spine-transformers:Vertebralabelingandsegmentation in arbitrary field-of-view spine CTs via 3D transformers. Medical Image Analysis, 75, 102258 (2022)

work page 2022

[6] [6]

IEEE Journal of Biomedical and Health Informatics, 26(8), 3976-3987 (2022)

Shi, W., Xu, T., Yang, H., Xi, Y., Du, Y., Li, J., Li, J.: Attention gate based dual- pathway network for vertebra segmentation of X-ray spine images. IEEE Journal of Biomedical and Health Informatics, 26(8), 3976-3987 (2022). 10 Jian Shi et al

work page 2022

[7] [7]

In: Medical Image Computing and Com- puter Assisted Intervention, pp

Masuzawa, N., Kitamura, Y., Nakamura, K., Iizuka, S., Simo-Serra, E.: Automatic segmentation, localization, and identification of vertebrae in 3D CT images using cascaded convolutional neural networks. In: Medical Image Computing and Com- puter Assisted Intervention, pp. 681-690 (2020)

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[8] [8]

In: International Symposium on Biomedical Imaging, pp

You, X., Gu, Y., Liu, Y., Lu, S., Tang, X., Yang, J.: EG-Trans3DUNet: a single- staged transformer-based model for accurate vertebrae segmentation from spinal CT images. In: International Symposium on Biomedical Imaging, pp. 1-5 (2022)

work page 2022