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Abstract

MR imaging techniques are of great benefit to disease diagnosis. However, due to the limitation of MR devices, significant intensity inhomogeneity often exists in imaging results, which impedes both qualitative and quantitative medical analysis. Recently, several unsupervised deep learning-based models have been proposed for MR image improvement. However, these models merely concentrate on global appearance learning, and neglect constraints from image structures and smoothness of bias field, leading to distorted corrected results. In this paper, novel structure and smoothness constrained dual networks, named S2DNets, are proposed aiming to self-supervised bias field correction. S2DNets introduce piece-wise structural constraints and smoothness of bias field for network training to effectively remove non-uniform intensity and retain much more structural details. Extensive experiments executed on both clinical and simulated MR datasets show that the proposed model outperforms other conventional and deep learning-based models. In addition to comparison on visual metrics, downstream MR image segmentation tasks are also used to evaluate the impact of the proposed model. The source code is available at: https://github.com/LeongDong/S2DNets.

Links to Paper and Supplementary Materials

Main Paper (Open Access Version): https://papers.miccai.org/miccai-2025/paper/1472_paper.pdf

SharedIt Link: Not yet available

SpringerLink (DOI): Not yet available

Supplementary Material: Not Submitted

Link to the Code Repository

https://github.com/LeongDong/S2DNets

Link to the Dataset(s)

HCP dataset: https://db.humanconnectome.org/ BrainWeb dataset: https://brainweb.bic.mni.mcgill.ca/brainweb/

BibTex

@InProceedings{LiaDon_Structure_MICCAI2025,
        author = { Liang, Dong and Qiu, Xingyu and Li, Yuzhen and Wang, Wei and Wang, Kuanquan and Dong, Suyu and Luo, Gongning},
        title = { { Structure and Smoothness Constrained Dual Networks for MR Bias Field Correction } },
        booktitle = {proceedings of Medical Image Computing and Computer Assisted Intervention -- MICCAI 2025},
        year = {2025},
        publisher = {Springer Nature Switzerland},
        volume = {LNCS 15972},
        month = {September},
        page = {562 -- 572}
}

Reviews

Review #1

  • Please describe the contribution of the paper

    The authors propose a method for bias field correction based on joint bias field estimation and image clustering. Specifically, they assume that there is a discrete number of pixel intensities in the image and look to (non-locally) cluster the voxels into these bins. Local smoothness in the bias field is promoted by both kernel smoothing and a derivative based penalty. This information is encoded in an energy function, and the first order gradient conditions are derived, which are used to define a system of equations to minimize for the bias field, cluster centers and probability of cluster membership. The latter two are used to supervise the training of two deep networks for approximate the clustering and bias field. Experiments are reported improvement over existing methods.

  • Please list the major strengths of the paper: you should highlight a novel formulation, an original way to use data, demonstration of clinical feasibility, a novel application, a particularly strong evaluation, or anything else that is a strong aspect of this work. Please provide details, for instance, if a method is novel, explain what aspect is novel and why this is interesting.

    The experimental results include comparisons to a variety of existing methods on several relevant datasets, and so can be considered as exhaustive.

  • Please list the major weaknesses of the paper. Please provide details: for instance, if you state that a formulation, way of using data, demonstration of clinical feasibility, or application is not novel, then you must provide specific references to prior work.

    • On selecting N: In 3.4, it seems that the authors calculated metrics, e.g. PSNR, with reference to the clean image. When selecting N (as the authors admit is a critical hyperparameter for the performance of their method), they then select the value of N by looking at the same metrics (as in Fig. 2), presumably calculated using the clean image. This is problematic, as these clean images won’t be available in practice. The authors need to propose a method for reliably selecting N just using corrupted data. The authors should address this point specifically, as this would constitute a major limitation.

    • The exact training protocol of the network is unclear to this reviewer. Specifically, when optimizing the losses (8) and (9), the u’_i depends on the true b, and the b’ depends on the true u_i, both of which are of course unknown. Are these values just initialized as output of the networks, and then trained in an alternating fashion? It seems this way from the pseudo-code in the supplement. If so, it seems that ensuring convergence of this scheme may be difficult. The authors should provide clarity on these details

  • Please rate the clarity and organization of this paper

    Satisfactory

  • Please comment on the reproducibility of the paper. Please be aware that providing code and data is a plus, but not a requirement for acceptance.

    The submission does not provide sufficient information for reproducibility.

  • Optional: If you have any additional comments to share with the authors, please provide them here. Please also refer to our Reviewer’s guide on what makes a good review and pay specific attention to the different assessment criteria for the different paper categories: https://conferences.miccai.org/2025/en/REVIEWER-GUIDELINES.html

    N/A

  • Rate the paper on a scale of 1-6, 6 being the strongest (6-4: accept; 3-1: reject). Please use the entire range of the distribution. Spreading the score helps create a distribution for decision-making.

    (3) Weak Reject — could be rejected, dependent on rebuttal

  • Please justify your recommendation. What were the major factors that led you to your overall score for this paper?

    Concern over the selection of N and the lack of clear details on the training procedure, namely, how the updates are made using the derived coupled system of equations.

  • Reviewer confidence

    Somewhat confident (2)

  • [Post rebuttal] After reading the authors’ rebuttal, please state your final opinion of the paper.

    Accept

  • [Post rebuttal] Please justify your final decision from above.

    Authors responded to raised criticisms. The method to select N is still concerning, as it requires preprocessing with a standard method and using this as ground truth. Surely this has limitations, and the authors should indicate this and mention failure cases. However, it seems as though it is a standard approach in the field, as the authors cited several references which use this heuristic.



Review #2

  • Please describe the contribution of the paper

    In this study, the authors proposed a structural-and smoothness constrained dual network named S2DNets that aims at self-supervised bias field correction. The proposed method trains the network by introducing piecewise structure constraints and smoothness constraints to effectively remove nonuniform intensities and retain more structural details, which demonstrated superior results over other traditional and deep learning-based methods.

  • Please list the major strengths of the paper: you should highlight a novel formulation, an original way to use data, demonstration of clinical feasibility, a novel application, a particularly strong evaluation, or anything else that is a strong aspect of this work. Please provide details, for instance, if a method is novel, explain what aspect is novel and why this is interesting.

    The paper presents a novel S2DNets framework for MRI bias field correction, combining fuzzy clustering and spatial smoothness regularization in a dual-network architecture. It derives closed-form solutions for network training, ensuring physically plausible corrections. The method shows good performance on both synthetic and clinical datasets, improving quantitative metrics and segmentation tasks without needing paired training data.

  • Please list the major weaknesses of the paper. Please provide details: for instance, if you state that a formulation, way of using data, demonstration of clinical feasibility, or application is not novel, then you must provide specific references to prior work.
    1. When introducing the existing methods, the core advantages of deep learning (DL) technology in bias field correction are not adequately explained, especially the advantages of DL compared with traditional methods (such as N3/N4, fuzzy clustering, etc.). It is suggested to add in the introduction.
    2. Only “based on U-Net” is mentioned, but the key design is not stated. Do the two subnetworks share the encoder? If independent, how to ensure the consistency of features? Supplementary network structure diagram.
    3. Why does the ambiguity factor p choose 2? Why choose 4 and 17 for the Gaussian kernel parameters σ and d? Add experimental evidence in the “Parameter Setting” section, such as: “We tested p∈{1.5,2,3} and σ∈{2,4,8}, and found that p=2 and σ=4 provide the best balance between preserving tissue structure and removing bias fields.
    4. The manuscript presents a detailed comparison of the proposed method with existing approaches using four key metrics: Structural Similarity Index Measure (SSIM), Peak Signal-to-Noise Ratio (PSNR), Coefficient of Variation in Gray Matter (CVGM), and Coefficient of Variation in White Matter (GVWM). The results should be visualized in four subplots. Different indicators are not clearly expressed in the same figure.
  • Please rate the clarity and organization of this paper

    Satisfactory

  • Please comment on the reproducibility of the paper. Please be aware that providing code and data is a plus, but not a requirement for acceptance.

    The submission does not mention open access to source code or data but provides a clear and detailed description of the algorithm to ensure reproducibility.

  • Optional: If you have any additional comments to share with the authors, please provide them here. Please also refer to our Reviewer’s guide on what makes a good review and pay specific attention to the different assessment criteria for the different paper categories: https://conferences.miccai.org/2025/en/REVIEWER-GUIDELINES.html

    N/A

  • Rate the paper on a scale of 1-6, 6 being the strongest (6-4: accept; 3-1: reject). Please use the entire range of the distribution. Spreading the score helps create a distribution for decision-making.

    (3) Weak Reject — could be rejected, dependent on rebuttal

  • Please justify your recommendation. What were the major factors that led you to your overall score for this paper?

    The manuscript lacks sufficient explanation of DL’s advantages over traditional bias field correction methods and omits critical details on network design and parameter selection. Additionally, the comparison results are not clearly visualized. These deficiencies limit the paper’s clarity and impact。

  • Reviewer confidence

    Confident but not absolutely certain (3)

  • [Post rebuttal] After reading the authors’ rebuttal, please state your final opinion of the paper.

    Accept

  • [Post rebuttal] Please justify your final decision from above.

    The authors have addressed most of my previous concerns. While I remain worried about the clinical utility of the paper, I am willing to accept it.



Review #3

  • Please describe the contribution of the paper

    The paper introduces Structure and Smoothness Constrained Dual Networks (S2DNets), a novel self‑supervised framework for MR bias field correction that: Integrates structure constraints (via fuzzy clustering) and smoothness constraints (local Gaussian kernel and global total‐variation) into a unified objective. Derives closed‐form solutions for both cluster probability and bias‑field estimation and embeds them as loss functions. Employs a dual‑learning scheme—alternating between a clustering U‑Net and a bias‑estimation U‑Net—to iteratively refine both tasks without any clean reference images.

  • Please list the major strengths of the paper: you should highlight a novel formulation, an original way to use data, demonstration of clinical feasibility, a novel application, a particularly strong evaluation, or anything else that is a strong aspect of this work. Please provide details, for instance, if a method is novel, explain what aspect is novel and why this is interesting.

    1.Unified Self‑Supervised Formulation Rather than relying on paired or unpaired clean images, the authors craft a single objective that balances structural fidelity and bias‐field smoothness, with analytically derived losses guiding both sub‑networks in a dual‑learning loop 2.No Requirement for Clean Reference Data By leveraging the interplay between clustering and bias estimation tasks, S2DNets train purely on corrupted images—addressing the clinical reality that “clean” MR data is scarce or unavailable 3.Comprehensive Quantitative & Downstream Evaluation On 30,000 HCP T1‑weighted slices and simulated BrainWeb T1/T2 sets, S2DNets achieve up to 31.78 dB PSNR and 0.979 SSIM, outperforming top baselines like IRNet. Downstream segmentation with a pre‑trained 2D U‑Net and FSL shows the highest Dice scores (e.g., 85.03 % WM, 84.16 % GM) compared to other correction methods 4.Ablation & Statistical Significance An ablation study on the TV loss demonstrates PSNR boosts of 9.8 %–17.6 %, and Wilcoxon tests (p < 0.01) confirm S2DNets’ superiority over competitors, underscoring the robustness of the proposed smoothness regularization

  • Please list the major weaknesses of the paper. Please provide details: for instance, if you state that a formulation, way of using data, demonstration of clinical feasibility, or application is not novel, then you must provide specific references to prior work.

    1.Limited Architectural Novelty Both sub‑networks are based on standard 2D U‑Nets, offering minimal innovation in network design itself—novelty resides primarily in the loss formulation rather than architecture 2.Manual Cluster‑Number Tuning Selection of the number of fuzzy clusters (N) is conducted by brute‑force (incrementing N from 2 to 4 based on empirical performance), without an adaptive or data‑driven strategy, which may impede generalization to new datasets 3.Dataset & Modality Scope Evaluation is restricted to HCP T1‑w clinical slices and BrainWeb simulations. Absent are evaluations on other common MR contrasts (e.g., FLAIR, diffusion images), 3D volumetric correction, or images exhibiting pathology—leaving real‑world applicability partly unverified 4.Foreground Mask Dependence The method uses multi‑threshold Otsu (MOTSU) to isolate foreground regions. In cases of poor contrast or lesions, this binary masking may misclassify relevant tissue, biasing both clustering and bias estimation

  • Please rate the clarity and organization of this paper

    Good

  • Please comment on the reproducibility of the paper. Please be aware that providing code and data is a plus, but not a requirement for acceptance.

    The authors claimed to release the source code and/or dataset upon acceptance of the submission.

  • Optional: If you have any additional comments to share with the authors, please provide them here. Please also refer to our Reviewer’s guide on what makes a good review and pay specific attention to the different assessment criteria for the different paper categories: https://conferences.miccai.org/2025/en/REVIEWER-GUIDELINES.html

    N/A

  • Rate the paper on a scale of 1-6, 6 being the strongest (6-4: accept; 3-1: reject). Please use the entire range of the distribution. Spreading the score helps create a distribution for decision-making.

    (5) Accept — should be accepted, independent of rebuttal

  • Please justify your recommendation. What were the major factors that led you to your overall score for this paper?

    I recommend acceptance of this paper. The major factors driving this decision are: Novel, Well‑Motivated Formulation The authors address a clinically critical issue—MR intensity inhomogeneity—without relying on scarce “clean” data. By integrating piece‑wise structural constraints (via fuzzy clustering) and both local (Gaussian) and global (TV) smoothness priors into a single self‑supervised objective, they offer a conceptually elegant solution that stands apart from prior supervised or GAN‑based approaches Analytically‑Grounded, Closed‑Form Losses Deriving closed‑form updates for cluster centers, memberships, and the bias field (Eqs. 5–7) and converting them directly into self‑supervised loss functions (Eqs. 8–10) is both technically rigorous and practically powerful. This dual‑network scheme ensures stable training and clear interpretability. Downstream Impact: Improvement in segmentation Dice scores (e.g., 85.03 % WM with a pre‑trained U‑Net) demonstrates that their corrected images translate directly into better clinical outcomes Ablation & Significance Testing: The inclusion of TV loss yields 9.8 %–17.6 % PSNR boosts, with clear statistical support, underscoring the robustness of each component Clarity and Reproducibility The manuscript is well‑organized: the unified objective and its derivations are laid out clearly; network details (2D U‑Net backbones, training regimen) are fully specified; and the authors pledge to release code, promoting transparency and reuse

    While the architectural novelty is modest and cluster‑number tuning remains manual, these are minor against the paper’s strong theoretical grounding, impressive empirical gains, and clear path toward clinical utility. Overall, the work makes a significant contribution to MR bias correction and merits acceptance.

  • Reviewer confidence

    Very confident (4)

  • [Post rebuttal] After reading the authors’ rebuttal, please state your final opinion of the paper.

    N/A

  • [Post rebuttal] Please justify your final decision from above.

    N/A



Author Feedback

We sincerely thank reviewers for recognizing our work as “novel, well-motivated”, “technically rigorous and practically powerful”; “physically plausible” and “exhaustive” experimental results, and having a “clear path toward clinical utility”. Below are responses to weakness (W) and comments (C).

1.(R1.W1/C) N-selection without Clean Data When clean data are absent, non-parametric N4-correted results [4] are widely adopted as pseudo-GT for parameter selection[11][17]. We rigorously validated it: 1)Highly Pearson correlations between N4 corrected and clean data: r=0.989 (HCP), 0.979 (BrainWeb T1), 0.982 (BrainWeb T2) imply their linear alignment on intensity distribution, ensuring performance trends (e.g., PSNR, SSIM) computed by N4 closely mirror those from clean images. 2)Identical Optimal N: For all datasets, N=4 maximizes both N4-based metrics and clean-image-based metrics as HCP (26.0/0.96); BrainWeb T1 (27.4/0.97), T2 (28.5/0.98). Plots on data distribution and performance will be added to Suppl.

2.(R1.W2/C) Training Protocol Variables u (clustering map) and b (bias field) are network predictions, NOT Ground Truth. Procedure: 1 Networks predict u and b; 2 Calculate class centers c via Eq.5 by u and b; 3 Clustering Sub-network Update: Reconstruct u’ (by b and c via Eq.6); Optimize with Loss_clus(u,u’); 4 Bias Sub-network Update: Reconstruct b’ (by u and c via Eq.7); Optimize with Loss_bias(b,b’)+λLoss_TV(b); Alternate Training: Repeat steps 1-4 until convergence. Suppl. Fig.1 shows stable convergence within 1500 iterations.

3.(R2.W1) Architecture U-Net has been verified its stability in bias field correction tasks [11]. Our dual U-Nets inventively promote mutual optimization (Table 1). Future work will explore advanced architectures.

4.(R2.W2) Manual N Tuning Simple manual tuning is validated its effectiveness on datasets. Future: Adaptive strategies (e.g. Gap value).

5.(R2.W3) Dataset Scope HCP&BrainWeb are ONLY public benchmarks with standardized bias field labels for quantitative validation. Our model achieves SOTA on benchmarks, supporting its applicability. Code supports volumetric input; future extensions include 3D/FLAIR/pathological validation via clinical collaboration.

6.(R2.W4) MOTSU robustness MOTSU achieves nearly 100% foreground accuracy in tested datasets. For low-contrast, pre-processing by CLAHE or deep methods enhance accuracy [a]. [a]Zhang, et al. IEEE TIP, 2024.

7.(R3.W1/C) DL Advantages DL outperforms traditional methods via: 1)End-to-end optimization DL models learn bias field distributions by data-driven, surpassing traditional methods; 2)Efficiency: 0.1s/inference (ours) vs. N4 (2.3s), MICO (2.9s), fuzzy clustering (32.3s) 3)Generalization: Robust to intensity variations (Table1/2).

8.(R3.W2/C) Encoder/Feature Consistency Two sub-networks DO Not share the encoder and are independent U-Net (Fig.1). For task-specific normalization, sub-networks adopts Sigmoid (bias) and Softmax (clustering) as output layer, respectively. Feature consistency is NOT needed for that it risks entangling estimated bias fields with structural features, leading to distorted results (Fig 1).

9.(R3.W3/C) Parameter Selection 1)Fuzziness Factor p: Optimal p=2 (as [5][27]) balances clustering/correction accuracy. p=1.5, No significant performance difference with p=2 (p-value>0.1) but caused training instability with loss fluctuations. p=3, Degraded performance due to blurred clustering boundaries: HCP: PSNR↓6.5%, SSIM↓1.3% BrainWeb T1: PSNR↓4.8%, SSIM↓1.7% BrainWeb T2: PSNR↓4.9%, SSIM↓1%.

2)Gaussian Kernel σ: Optimal σ=4, d=4*σ+1=17 (as [9]) maximizes PSNR/SSIM: HCP: 28.43/0.979 vs 28.24/0.975 at σ=2; 25.58/0.95 at σ=8 BrainWeb T1: 31.80/0.980 vs 29.97/0.978 at σ=2; 27.58/0.962 at σ=8 BrainWeb T2: 30.53/0.97 vs 29.53/0.966 at σ=2; 24.60/0.96 at σ=8.

10.(R3.W4/C) Visualization Four-subplot figures (SSIM/PSNR/CVGM/CVWM) will be added to Github.

11.(All) Reproducibility Code/tutorial will be open-sourced upon acceptance.



Meta-Review

Meta-review #1

  • Your recommendation

    Invite for Rebuttal

  • If your recommendation is “Provisional Reject”, then summarize the factors that went into this decision. In case you deviate from the reviewers’ recommendations, explain in detail the reasons why. You do not need to provide a justification for a recommendation of “Provisional Accept” or “Invite for Rebuttal”.

    N/A

  • After you have reviewed the rebuttal and updated reviews, please provide your recommendation based on all reviews and the authors’ rebuttal.

    Accept

  • Please justify your recommendation. You may optionally write justifications for ‘accepts’, but are expected to write a justification for ‘rejects’

    N/A



Meta-review #2

  • After you have reviewed the rebuttal and updated reviews, please provide your recommendation based on all reviews and the authors’ rebuttal.

    Accept

  • Please justify your recommendation. You may optionally write justifications for ‘accepts’, but are expected to write a justification for ‘rejects’

    N/A



Meta-review #3

  • After you have reviewed the rebuttal and updated reviews, please provide your recommendation based on all reviews and the authors’ rebuttal.

    Accept

  • Please justify your recommendation. You may optionally write justifications for ‘accepts’, but are expected to write a justification for ‘rejects’

    For L1 norm in space there is prior work at: An L₁-Based Variational Model for Retinex Theory and Its Application to Medical Images” by Wenye Ma, Jean-Michel Morel, Stanley Osher, and Aichi Chien, presented at IEEE CVPR 2011 This study could have been cited.

    The part of the paper that is related to what is known as “bias field correction” is conservative. The argument that statistical entropy removes contrast but not piecewise constancy is weak. Also, the selection of say four clusters for the statistics compromises the unsupervised claim for the approach.

    An entire network is used to impose smoothness of the field. Is that necessary? Couldn’t that have been incorporated into the loss? Is the nonuniformity field assumption for smoothness representative? There exist studies removing non-smooth bias fields without a smoothness requirement.

    In any case, incorporating modern deep learning and gradient descent with a loss function for “unsupervised” learning into the problem is interesting and can improve efficiency. But there are also limitations in using deep learning networks in that they may not generalize to novel MRI contrasts with different parameters. I recommend acceptance but as a poster.



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