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REVIEW 5 major objections 6 minor 26 references

FAN-Unet: Enhancing Unet with vision Fourier Analysis Block for Biomedical Image Segmentation

T0 review · 5 major / 6 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read FAN-UNet adds Fourier-analysis blocks to U-Net and reports top segmentation scores on two skin-lesion benchmarks.

desk verdict A U-Net plus Fourier layer combo that is clearly described but undermined by a headline numbers mismatch and no reproducibility. read the letter →

arxiv 2411.18975 v1 pith:7JXIOKU6 submitted 2024-11-28 eess.IV cs.CV

Jiashu Xu This is my paper · ORCID
classification eess.IVcs.CV
keywords FourierAnalysisNetworkU-Netmedicalimagesegmentationself-attentionperiodicitymodelingskinlesionISIC2017ISIC2018
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 proposes FAN-UNet, a U-Net variant whose encoder blocks replace plain convolutions with Vision-FAN blocks: window-based self-attention for global context plus FANLayer2D, a layer that applies cosine and sine activations to learnable linear projections so the network can explicitly represent periodic structure. The stated goal is to fix two weaknesses at once—CNNs' poor long-range dependency modeling and standard networks' difficulty modeling periodic patterns—while keeping the model practical. On the ISIC17 and ISIC18 skin-lesion segmentation benchmarks, FAN-UNet reports the best mIoU and Dice among the compared models, including 78.99% mIoU, 88.25% Dice, and 96.30% accuracy on ISIC17. A sympathetic reader would care because the paper offers a concrete recipe for adding Fourier-style inductive biases to a standard segmentation backbone, and it suggests that explicit periodicity modeling can matter for biomedical images.

What carries the argument

The Vision-FAN Block is the core mechanism. It applies positional encoding to the downsampled feature map, runs window-based self-attention to capture long-range dependencies, and passes the result to FANLayer2D. FANLayer2D computes $\mathbf{P} = \mathbf{W}_p \ast \mathbf{X} + \mathbf{b}_p$ and $\mathbf{G} = \mathbf{W}_g \ast \mathbf{X} + \mathbf{b}_g$, applies sine and cosine activations to $\mathbf{P}$ and a nonlinear activation to $\mathbf{G}$, concatenates the periodic and nonlinear features along the channel dimension, and returns them as the output. Residual connections and layer normalization preserve input information and stabilize training. The block is inserted into the U-Net downsampling path, and the training loss is a batch-level combination of cross-entropy and Dice loss with mixing weight $\alpha = 0.5$.

What would settle it

Retrain FAN-UNet on ISIC17 with the FANLayer2D activation replaced by an equal-capacity nonlinearity; if mIoU and Dice do not drop, the Fourier component is not the source of the gain. Also, compute dominant-frequency or autocorrelation statistics on lesion crops: if periodic content is no stronger than natural images, the periodic-pattern premise fails.

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Extended reading notes

Core claim

The paper's central claim is that integrating FANLayer2D—a layer built from the Fourier-series expansion $f_S(\mathbf{x}) = B + \mathbf{W}^c \cos(\mathbf{W}^{in}\mathbf{x}) + \mathbf{W}^s \sin(\mathbf{W}^{in}\mathbf{x})$—into a U-Net, together with window-based self-attention, yields segmentation accuracy that surpasses recent CNN, Transformer, and Mamba-based models on ISIC17 and ISIC18. The paper attributes the gain to two complementary mechanisms: self-attention models long-range spatial dependencies, while the sine/cosine activations explicitly encode the regular, repetitive texture of tissue and lesion regions. In the paper's numbers, FAN-UNet reaches 78.99% mIoU and 88.25% Dice on ISIC17 and 78.74% mIoU and 88.11% Dice on ISIC18, and the ablation shows that removing the Vision-FAN Block lowers mIoU from 78.74% to 77.86%.

Load-bearing premise

The load-bearing premise is that skin-lesion images contain consistent periodic patterns, so that explicitly encoding sine and cosine features helps segmentation; if that premise is false, the reported improvements could come from added parameters rather than from Fourier analysis.

Editorial extensions

If this is right

  • If the claim holds, adding explicit frequency-domain activations to a U-Net is a low-cost way to improve segmentation on structured, repetitive textures.
  • The hybrid attention-plus-Fourier block is a recipe that could transfer to other biomedical segmentation tasks where anatomy or pathology appears with regular spatial repetition.
  • The reported margins over recent models—1.11% mIoU over HC-Mamba and 2.01% over U-Net on ISIC17—place Fourier feature modeling in the same range as recent Mamba-based global modeling.
  • The ablation numbers support the block's contribution: removing the Vision-FAN Block drops ISIC17 mIoU from 78.74% to 77.86%, and removing positional encoding drops it to 78.42%.

Reading between the lines

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

  • A direct test of the periodic-pattern premise would be to replace only the sine/cosine branch in FANLayer2D with an equivalently sized random nonlinearity; if mIoU and Dice stay flat, the gain comes from added capacity, not from Fourier structure.
  • The paper cites quasi-periodic brain fMRI patterns [15] as evidence that medical features are periodic, but never measures periodicity in dermatoscopic images; computing dominant frequencies or autocorrelation over lesion crops would settle whether the premise holds.
  • If the premise does hold, the same block may reduce the amount of training data needed for segmentation in modalities with repetitive texture, and may extend naturally to 3D volumes (CT/MRI) by replacing 2D convolutions with 3D Fourier layers.
  • A per-class or boundary-focused evaluation would show whether the Fourier block specifically improves edges and textured regions, which the aggregate metrics in the paper do not reveal.
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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 / 6 minor

Summary. The manuscript proposes FAN-UNet, a U-Net variant in which the standard encoder blocks are replaced by Vision-FAN blocks combining window-based self-attention with a 2D Fourier Analysis layer (FANLayer2D). The method is evaluated on the ISIC 2017 and ISIC 2018 skin lesion segmentation benchmarks and compared with CNN-, Transformer-, and Mamba-based baselines. The paper claims state-of-the-art results on ISIC17 with 78.99% mIoU, 88.25% Dice, and 96.30% accuracy, and reports an ablation study on ISIC18. The central claim is that explicitly modeling periodicity via Fourier features improves segmentation performance.

Significance. If the reported results were reproducible and the Fourier component were shown to be responsible for the improvement, the contribution would be a modest but useful addition to medical image segmentation: integrating FAN into U-Net is a simple and potentially principled way to capture periodic structures. However, the experimental evidence as presented is internally inconsistent and lacks reproducibility information. The abstract reports metrics identical to the Med-TTT baseline rather than the FAN-UNet row in Table 1, one ablation row is numerically identical to a Table 1 baseline, and no training configuration or code is provided. Until these issues are resolved, the paper cannot support its central claim of state-of-the-art performance.

major comments (5)
  1. [Abstract and §1] The abstract and the contribution bullet in §1 report FAN-UNet's ISIC17 results as accuracy 96.07%, mIoU 78.83%, and DSC 88.16%. These are exactly the Med-TTT row in Table 1 (reference [23]), whereas FAN-UNet's own row in Table 1 is 96.30%, 78.99%, and 88.25%. The paper's headline numbers are therefore not the proposed model's numbers, contradicting Table 1 and undermining the credibility of the reported experimental results.
  2. [§4.2, Table 1] The claimed state-of-the-art advantage over Med-TTT and HC-Mamba is tiny (e.g., +0.16 mIoU over Med-TTT on ISIC17), and the paper provides no error bars, confidence intervals, or significance tests. With only single-point comparisons and no information about the number of runs or variance, the claimed superiority is not statistically supported.
  3. [§4.1–§4.2] Section 4 gives no training details: no optimizer, learning rate, batch size, number of epochs, input size, data augmentation, normalization, hardware, random seed, or train/validation protocol for ISIC17/ISIC18. No code is released. This makes every number in Tables 1 and 2 impossible to reproduce or verify, leaving the central empirical claim unsupported.
  4. [§4.3, Table 2] The row 'Proposed w/o Vision-FAN Block' in Table 2 is numerically identical to the UNet row for ISIC18 in Table 1 (77.86/87.55/94.05/96.69/85.86). If the ablation was conducted by replacing the block with a convolution, exact equality with the pre-existing UNet baseline is implausible without additional explanation; the result suggests the ablation numbers may have been copied from the baseline table rather than produced by an actual experiment.
  5. [§3.1 and §1] The periodicity premise—that skin lesion images exhibit consistent periodic patterns—is asserted without evidence. The only citation is [15], which concerns quasi-periodic patterns in resting-state fMRI, a different imaging modality. No spectral analysis of ISIC images, frequency-domain diagnostics, or controlled experiment isolating the contribution of the Fourier terms is provided, so the architectural motivation is not validated empirically.
minor comments (6)
  1. [Abstract] The phrase 'we presents' is ungrammatical and should be corrected to 'we present'.
  2. [Title and running head] The title uses inconsistent spacing ('FAN-U NET' in the running head versus 'FAN-UNet' in the text); please unify.
  3. [§3.2, Eqs. (7)–(9)] Mathematical notation is inconsistent (e.g., Wp in Eq. (7) vs. W'_p in Eq. (6), and the capitalized 'Compute' mid-sentence). Please standardize notation and proofread the equations.
  4. [§3.3, Eq. (10)] Equation (10) is not clearly typeset and does not define Input_b, Target_b, epsilon, or B; these should be specified for the formula to be meaningful.
  5. [§4.1] The paper states 'Extensive experiments on various medical imaging datasets' but evaluates on only two ISIC datasets, both dermoscopic skin lesion datasets; this overstates the scope.
  6. [§4.2] The abstract and conclusion mention a 'favorable balance between model complexity and performance,' but no model complexity metrics (parameters, FLOPs, inference time) are reported.

Circularity Check

0 steps flagged · score 2.0 of 10

No circular derivation in the core claim; minor author self-citations in baselines and an abstract/table metric mismatch affect verifiability, not the derivation chain.

full rationale

The paper does not contain a derivation chain that reduces to its own inputs. FAN-UNet is defined by an explicit architectural recipe (Fourier-series parameterization in Eqs. 3-5, FANLayer2D with cos/sin activations in Eqs. 6-9, residual connections, layer normalization, and window-based self-attention), and its claimed contribution is an empirical segmentation benchmark on ISIC17/ISIC18. The reported metrics are measurements, not quantities derived from the architecture equations; no parameter is fitted to a data subset and then renamed a prediction. The periodicity motivation citing fMRI quasi-periodic patterns [15] is an unsupported analogy across modalities, but it is not circular because the cited work does not define or derive FAN-UNet's results. The strongest SOTA baselines, HC-Mamba [22] and Med-TTT [23], are prior papers by the same author, which is a minor self-citation that weakens independent comparison; however, those citations are not load-bearing for the architecture's internal derivation. The abstract and contribution bullet report 96.07% accuracy, 78.83% mIoU, and 88.16% DSC, which exactly match the Med-TTT row in Table 1 rather than the FAN-UNet row (96.30/78.99/88.25); this is an internal-consistency and reproducibility concern, not a circularity of the claimed derivation. Overall, there is no significant circularity, though the self-cited baselines and the metric mismatch justify a minor score above zero.

Assumptions & free parameters 1 free parameters · 3 assumptions · 0 invented entities

All learned weights (Wp, Wg, etc.) are trained from data, not free parameters of a derivation. The only hand-set constant is alpha=0.5. The central claim rests on unverified domain assumptions about periodicity in skin-lesion images and on standard assumptions about U-Net and self-attention. No invented physical entities are introduced; Vision-FAN Block is a designed architecture component, not an unexplained postulate.

free parameters (1)
  • loss weight alpha = 0.5
    Set by hand in eq. (10) to balance Dice and cross-entropy losses; the paper states 'set to 0.5 by default' with no tuning analysis.
assumptions (3)
  • domain assumption Medical image features, particularly skin lesions, exhibit consistent periodic patterns that Fourier activation functions can exploit.
    Motivates FANLayer2D in Sections 1 and 3.1, citing only an fMRI quasi-periodic patterns reference [15]; no evidence is given that ISIC skin lesions have exploitable periodicity.
  • domain assumption Window-based self-attention captures global long-range dependencies efficiently in medical images.
    Assumed in Section 3.1 based on prior transformer segmentation literature; not validated for the specific datasets.
  • domain assumption U-Net's encoder-decoder with skip connections provides a robust feature extraction backbone.
    Standard result from prior literature [5]; used as the framework for FAN-UNet.

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Cite this review

Pith. "Pith review of FAN-Unet: Enhancing Unet with vision Fourier Analysis Block for Biomedical Image Segmentation." pith.science (2026). https://pith.science/paper/7JXIOKU6

@misc{pith2026241118975,
  author       = {Pith},
  title        = {Pith review of: FAN-Unet: Enhancing Unet with vision Fourier Analysis Block for Biomedical Image Segmentation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7JXIOKU6}},
  note         = {Machine review of arXiv:2411.18975}
}
read the original abstract

Medical image segmentation is a critical aspect of modern medical research and clinical practice. Despite the remarkable performance of Convolutional Neural Networks (CNNs) in this domain, they inherently struggle to capture long-range dependencies within images. Transformers, on the other hand, are naturally adept at modeling global context but often face challenges in capturing local features effectively. Therefore, we presents FAN-UNet, a novel architecture that combines the strengths of Fourier Analysis Network (FAN)-based vision backbones and the U-Net architecture, effectively addressing the challenges of long-range dependency and periodicity modeling in biomedical image segmentation tasks. The proposed Vision-FAN layer integrates the FAN layer and self-attention mechanisms, leveraging Fourier analysis to enable the model to effectively capture both long-range dependencies and periodic relationships. Extensive experiments on various medical imaging datasets demonstrate that FAN-UNet achieves a favorable balance between model complexity and performance, validating its effectiveness and practicality for medical image segmentation tasks.

Figures

Figures reproduced from arXiv: 2411.18975 by the authors.

Figure 1
Figure 1. (A) Overall structure of FAN-Unet. (B) Overall structure of Vision-FAN Block foundation, Fourier Analysis Layers aim to embed periodic features directly into network architectures, enhancing generalization and performance across various tasks, especially in scenarios requiring the recognition of patterns and regularities. 3 Method The structure of FAN-Unet is shown in [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Schematic diagram of FANLayer2D Finally, concatenate the periodic features and activated nonlinear features along the channel dimension to form the output features. Building on this structure, FANLayer2D effectively captures both the periodic and nonlinear characteristics of input data in the 2D space. Its design enables the network to directly learn and represent repetitive patterns and intricate textures present i… view at source ↗

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Reference graph

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