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Abstract

Due to structural anisotropy and complex anatomical boundaries, 3D medical image segmentation remains a challenging task. To address these issues, this paper proposes the Direction-Sensitive Equilibrium Mamba Network (DEM-Mamba). Through directional decoupling, balanced enhancement, and adaptive fusion, this network systematically enhances structure perception and boundary preservation capabilities in 3D space. Specifically, DEM-Mamba integrates three core designs: First, it employs an Orientation-Aware Module (OAM) based on learnable Riesz wavelets to decouple high-frequency directional features and mitigate information imbalance caused by anisotropic resolution. Second, it designs a Bidirectional Balanced Mamba (BBM), which effectively captures long-range anisotropic dependencies and maintains boundary clarity through complementary bidirectional scanning combined with adaptive normalization. Finally, it introduces an Orientation-Conflict Fusion (OCF) mechanism that dynamically aggregates multi-directional information based on correlation weights, enhancing the model’s adaptability to complex boundaries. Experiments across multiple 3D medical image datasets demonstrate that this method outperforms existing state-of-the-art approaches in both segmentation accuracy and boundary integrity, providing an effective new framework for 3D medical image segmentation.

Links to Paper and Supplementary Materials

Main Paper (Open Access Version): https://papers.miccai.org/miccai-2026/paper/1575_paper.pdf

SharedIt Link: Not yet available

SpringerLink (DOI): Not yet available

Supplementary Material: Not Submitted

Link to the Code Repository

https://github.com/pky888/DEM-Mamba

Link to the Dataset(s)

BraTS2023 dataset: https://www.med.upenn.edu/cbica/brats/ BraTS2024 dataset: https://www.med.upenn.edu/cbica/brats/ AIIB2023 dataset: https://codalab.lisn.upsaclay.fr/competitions/13238

BibTex

@InProceedings{ZhuZhi_Towards_MICCAI2026,
        author = { Zhu, Zhiqin AND Pu, Keyu AND Liu, Yu AND Qi, Guanqiu AND Ding, Yan AND Cong, Baisen},
        title = { { Towards Direction-Equilibrated Segmentation in 3D Medical Images } },
        booktitle = {Medical Image Computing and Computer Assisted Intervention -- MICCAI 2026},
        year = {2026},
        publisher = {Springer Nature Switzerland},
        volume = {LNCS 16884},
        month = {September},
        page = {pending}
}

Reviews

Review #1

  • Please describe the contribution of the paper

    This paper presents the Direction-Sensitive Equilibrium Mamba Network (DEM-Mamba). Specifically, it introduces a unified DEM-Mamba framework that integrates direction-adaptive perception with state space modeling, offering a novel approach for anisotropic boundary modeling. It also includes the OAM, BBM, and OCF modules, which enable direction-sensitive decoupling, long-range complementary balanced fusion, and adaptive conflict suppression. The method demonstrates superior performance compared to state-of-the-art approaches across four 3D medical datasets. This paper discusses about the Direction-Sensitive Equilib- rium Mamba Network (DEM-Mamba). Specifically, it includes the unified DEM-Mamba framework that deeply integrates direction-adaptive perception with state space modeling, introducing a novel paradigm for anisotropic boundary modeling; the OAM, BBM, and OCF modules that systematically enable direction-sensitive decoupling, long- range complementary balanced fusion, and adaptive conflict suppression; and superior performance over state-of-the-art methods on four 3D medical datasets.

  • 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 is well motivated and clearly written, with sufficient technical details. The results include multiple comparative evaluations.

  • 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.

    The manuscript does not provide any discussion of the computational complexity of the proposed method. Including details such as training and inference time, as well as memory requirements, would help readers better assess its efficiency, scalability, and practical applicability.

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

  • Based on your review and your understanding of the MICCAI Scientific Code of Ethics, do you believe this submission may involve a potential ethics concern or violation?

    N/A

  • 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/2026/en/REVIEWER-GUIDELINES.html

    I have two minor suggestions: it would be beneficial to include details on computational complexity, and the availability of code upon acceptance would further enhance the impact and reproducibility of the work.

  • 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?

    The problem is well-motivated, the formulation is good, and the paper is well-written.

  • 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.

    The rebuttal addressed my concerns.



Review #2

  • Please describe the contribution of the paper

    Authors developed DEM-Mamba to tackle structural anisotropy and complex anatomical boundaries in medical image segmentation. DEM-Mamb employes OAM to extract direction-aware features via learnable Riesz wavelet transform, BBM to enrich multi-directional feature fusion, and OCF for conflict-aware feature fusion based on feature correlation. BraTS2023, BraTS2024, AIIB2023, and a private Cardiac Calcified Plaque dataset were investigated.

  • 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. The anisotropic resolution issue in 3D medical images is a real practical concern, and framing the pipeline as “direction decoupling → equilibrium modeling → adaptive aggregation” offers a clear and coherent design logic

    2.Validation across four datasets covering brain tumor, CT lung airway tree, and cardiac plaque segmentation shows an effort toward generalizability, which is appreciated.

  • 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. Authors claimed “learnable Riesz wavelets” as a major contribution, but this implementation basically refers to multiplying the directional wavelets components by a learnable matrix U (Eq. 2), a minor point that was overly emphasized.

    2.For the top-K wavelets components, not sure why Mamba or bidirectional Mamba is needed to establish bidirectional state flows. How does Mamba enable “sufficient to capture key information”? What is the key information captured? The motivation of using Mamba is not justified.

    3.OCF calculates the overall correlations between adjacent wavelets components, which were used to scale the inputs. I highly doubt if this global, rather than component-specific, scaling is necessary.

    4.Why different methods were compared on different datasets? Authors should the same methods for each dataset.

    5.Please carefully check the label ID (WT, TC, ET ,RC) for Brats24.

    6.No computational cost analysis was provided.

    7.No differences between DEM-Mamba and VSMU-Net on BraTS2023 and AIIB2023, AAHN on BraTS2024, and VSMU-Net on Cardiac Calcified Plaque dataset, which weaken the creditability of the proposed method.

    8.Table 8 and comment 3 above show that M3 (or OCF) ineffective.

  • 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.

  • Based on your review and your understanding of the MICCAI Scientific Code of Ethics, do you believe this submission may involve a potential ethics concern or violation?

    N/A

  • 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/2026/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.

    (2) Reject — should be rejected, independent of rebuttal

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

    The contribution of “learnable Riesz wavelets” is quite minor. The use of Mamba or bidirectional Mamba is not justified and I am not sure if this is really needed. The OCF applies global scaling to the extracted wavelet components and this does not affect the training or optimization. In addition, the minimal differences between the proposed method and other baselines weaken the methodological creditability.

  • Reviewer confidence

    Confident but not absolutely certain (3)

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

    Reject

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

    I appreciate authors’ efforts in the rebuttal but major concerns remain:

    1.The Riesz basis R̂ⁿ(ω) and the log-Gabor filter G(ρ) remain mathematically fixed; the learnable components are confined to the pre-filter M(·) and the linear recombination matrix U in Eq. 2.Does the combination of Gabor filter, Riesz transform, and learnable weights to extract the Top-K directional features warrant a substantial contribution?

    2.Marginal differences between the proposed and other baselines. For the claimed advantage of boundary precision, I would use ASD (or ASSD) rather than HD95, which is sensitive to extremas of boundary distances. In addition, all metrics should be provided with a standard deviation. Superiority can not be claimed without statistical tests.

    3.Eq. (8) and (9). A critical typo, as per authors feedback, is methodologically problematic at any stage of review. Regardless of this reinterpretation, Eq. (10) applies the same spatially-varying weights to the aggregated directional components, so the output is not component-specific, which was the substantive part of my original concern.

    4.Please include the same baselines for comparison across all datasets to show the generalizability of each method.

    5.Didirectional Mamba vs multi-directional or multi-path scanning remains unsolved.

    While the “direction decoupling → equilibrium modeling → adaptive aggregation” framework is conceptually appealing, significant revisions are needed for the work to be published.



Review #3

  • Please describe the contribution of the paper

    This paper introduces the Direction-Sensitive Equilibrium Mamba Network (DEM-Mamba) to address structural anisotropy and boundary degradation in 3D medical image segmentation. The core contribution is a novel pipeline integrating an Orientation-Aware Module (OAM) using learnable Riesz wavelets for directional feature decoupling, a Bidirectional Balanced Mamba (BBM) for long-range dependency modeling, and an Orientation-Conflict Fusion (OCF) mechanism to dynamically aggregate multi-directional information. The authors demonstrate state-of-the-art performance across four diverse 3D medical imaging datasets.

  • 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.

    • Novel Formulation: Integrating a learnable 3D Riesz wavelet transform with a Mamba architecture is highly innovative. It explicitly addresses the problem of fixed wavelet bases failing to adapt to diverse anatomical patterns, allowing for a continuous, steerable directional representation that integrates deeply into modern deep learning frameworks.

    • Strong Methodological Design: The Orientation-Conflict Fusion (OCF) module elegantly tackles a persistent issue in multi-directional feature fusion: phase conflicts and destructive interference. By dynamically adjusting aggregation weights based on global conflict intensity and feature correlation, the model successfully maintains structural integrity without losing high-frequency details.

    • Comprehensive Evaluation Methodology: The evaluation is rigorous, leveraging four distinct 3D medical datasets (BraTS2023, BraTS2024, AIIB2023, and an internal Cardiac Calcified Plaque dataset), showcasing the model’s adaptability to brain tumors, complex airway structures, and cardiac plaques. Furthermore, detailed ablation studies effectively justify the inclusion of each proposed module and parameter setting.

  • 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.

    • Top-K Gradient Flow and Differentiability: The OAM employs an energy-based Top-K selection mechanism to emphasize dominant directional components. However, as a point of general deep learning knowledge outside of your provided sources, a standard “hard” Top-K selection is a discrete operation that is mathematically non-differentiable and would theoretically break the gradient flow. The paper completely omits any explanation of how this operation is made differentiable to allow for end-to-end backpropagation during training.

    • Lack of Intermediate Visual Validations: While the final segmentation outputs are visualized, the paper lacks visual evidence demonstrating the intermediate efficacy of the three proposed core modules, making it difficult to empirically verify their theoretical claims:
    • OAM: There are no visualizations of the decoupled directional feature maps or the specific Top-K directional feature responses. This is needed to verify that the module isolates anisotropic structural patterns.
    • BBM: The BBM uses a Dual-Equal Gate (DEG) mechanism to suppress out-of-phase destructive interference. The absence of feature map visualizations before and after DEG processing leaves this suppression effect empirically unsubstantiated.

    • OCF: The manuscript lacks spatial heatmaps representing the global conflict intensity parameter. Visualizing the spatial distribution of these “phase conflicts” (e.g., overlaid on airway trees or tumor edges) is critical to validate that OCF adaptively suppresses conflicts at degrading boundaries.

    • Mamba Scanning Path Justification: The BBM utilizes only forward and reverse scanning, arguing theoretically that multi-path effects introduce directional redundancy and high-frequency loss. However, the paper lacks empirical ablation comparisons against standard multi-directional sweep strategies commonly used in recent 3D Mamba architectures.

    • Limited Reproducibility of Proprietary Data: While three of the datasets are public benchmarks, the Cardiac Calcified Plaque dataset is sourced internally from an anonymized hospital. This limits the ability of the broader research community to benchmark against or reproduce these specific cardiac findings.
  • 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.

  • Based on your review and your understanding of the MICCAI Scientific Code of Ethics, do you believe this submission may involve a potential ethics concern or violation?

    N/A

  • 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/2026/en/REVIEWER-GUIDELINES.html
    • Major Comments:
    • Clarify Top-K Gradient Flow: Please detail the backpropagation mechanism through the Top-K selection step in Equation 3.Since a hard Top-K operation breaks gradient flow, if a straight-through estimator or a soft-Top-K approximation is used, it must be formally described in the methodology section.
    • Add Intermediate Visualizations: Please provide visual outputs in the manuscript or supplementary material for your core modules. Specifically: visualize the Top-K directional feature responses from the OAM, show feature maps before and after the DEG processing in the BBM, and provide spatial heatmaps of the conflict intensity from the OCF overlaid on complex boundaries.
    • Empirical Multipath Comparison: Provide an ablation study explicitly comparing the proposed Bidirectional Mamba scanning against existing multi-directional scanning techniques to empirically support the claim that multipath effects introduce detrimental energy averaging.

    • Code Availability: Explicitly state whether the source code and trained weights will be made publicly available upon acceptance. Providing code is highly recommended to meet MICCAI’s reproducibility standards.

    • Minor Comments:
    • Correct the spelling typo in the Section 2.1 heading, which is currently written as “Overiew”.
    • The formatting of the mathematical equations could be improved for readability. For example, Equation 1 contains nested parentheses that are slightly hard to parse, and Equation 4 has unusual bracket alignment.
    • Consider adding a brief discussion or a table detailing the computational complexity (FLOPs/Parameters) of DEM-Mamba compared to top-performing baselines. Demonstrating that the OAM and OCF modules do not introduce excessive overhead would strengthen the paper’s practical appeal.
  • 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.

    (4) Weak Accept — marginally above the acceptance threshold, but would not mind if rejected, dependent on rebuttal

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

    My recommendation is borderline leans toward acceptance, if the authors can comprehensively address the comments during the rebuttal phase. The paper presents a highly original integration of frequency-domain wavelet analysis (Riesz transforms) with modern state-space models (Mamba) to address structural anisotropy in 3D medical images. The extensive empirical validation demonstrates clear state-of-the-art performance across multiple domains and modalities. While there are presentation gaps—most notably the omission of how gradient flow is maintained through the Top-K selection, the lack of intermediate visualizations to empirically back up the theoretical claims of the modules, and clarity on code availability—the theoretical novelty, rigor of the evaluation, and clear performance gains strongly justify its place at MICCAI if these revisions are made.

  • 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.

    Gradient Flow: Clarifying Eq. 3 as a discrete routing operation resolves the immediate trainability issue. However, exploring a continuous relaxation or soft Top-K approximation for more robust gradient flow should be discussed as an architectural improvement in the manuscript.

    Scanning Path Design: The defense of the Bidirectional Balanced Mamba (BBM) is logical. Pre-filtering components via Top-K makes exhaustive 3D multipath scanning redundant and computationally wasteful.

    Efficiency & Reproducibility: The model’s footprint (72.68M parameters, ~1.64 TFLOPs) aligns with standard 3D networks. The commitment to open-sourcing the code, weights, and intermediate visualizations thoroughly satisfies my reproducibility concerns.

    Baselines: The combination of general architectures and domain-specific baselines is well-reasoned. The consistent gains across diverse modalities demonstrate robust boundary-oriented modeling.



Author Feedback

We thank the reviewers for their constructive comments. We focus on the main concerns: the necessity of BBM/Mamba and OCF, baseline selection, Top-K gradient flow, and efficiency/reproducibility/visualization.

(1) Necessity of BBM/Mamba (R2,R3): In DEM-Mamba, OAM provides local directional components but does not model long-range volumetric dependency or cross-slice continuity. BBM is therefore introduced to propagate information along the selected components via complementary forward/reverse state flows with linear complexity. Table 4 supports this role: after OAM improves Dice/HD95 from 90.23/3.62 to 90.82/3.43, adding BBM further improves them to 91.32/3.35.Thus, BBM contributes beyond local directional extraction within our pipeline.

(2) Scanning path design (R3): We agree that direct comparison with exhaustive 3D multi-path scanning would further strengthen the paper. Our intention is not to claim that all multi-path designs are inferior. Rather, since Top-K first selects dominant directional components, BBM scans only these selected components instead of repeatedly scanning the full 3D volume along many predefined paths. Table 5 indirectly supports this design choice: increasing Top-K from 2 to 3 does not improve performance. We will clarify bidirectional scanning as an efficiency-oriented design choice, not a theoretical rejection of all multi-path methods.

(3) Top-K gradient flow (R3): We will clarify Eq.3.Top-K is used as a discrete routing operation. The ranking indices are not differentiated, but the selected feature values are not detached. Therefore, gradients from the segmentation loss flow through the gathered components back to $F_dir$, the learnable matrix U, and preceding layers; non-selected paths receive zero gradient for that sample. Active paths remain end-to-end trainable without requiring a soft approximation.

(4) Necessity of OCF (R2): We clarify a critical typo in Eq. 8 that caused a misunderstanding: $u_i$ is not a spatial mean over $[D,H,W]$, but a channel-wise mean (see code: dim=1). Thus, $\gamma$ is not a fixed global scaling, but a dense, voxel-wise spatial attention map that dynamically penalizes phase conflicts at specific local regions. Because it specifically refines local boundary conflicts rather than global volumes, its necessity reflects in boundary metrics: Table 4 shows OCF meaningfully improves HD95 from 3.35mm to 3.23mm.

(5) Baselines and performance differences (R2): Different datasets include different additional baselines because some methods are domain-specialized. General baselines such as nnU-Net, TransUNet, SwinUNETR, and VSMU-Net are included where applicable, while task-specific SOTAs such as AAHN for BraTS2024 and plaque-focused methods are added for stricter comparison. We acknowledge that improvements over strong baselines are modest and not uniformly better on every metric. Our intended claim is not dominance on all sub-regions, but consistent boundary-oriented competitiveness across diverse 3D tasks.

(6) Efficiency & Reproducibility (R1, R2): Efficiency: Our 72.68M parameters and ~1.64 TFLOPs (1×4×128×128×128 input) align with standard 3D models. Since FLOPs understate Mamba’s hardware efficiency, we will clarify actual latency in the revision. Crucially, our efficiency stems from BBM processing only K=2 components, avoiding the massive overhead of exhaustive 3D sweeps. Reproducibility: Code, public weights, and private dataset protocols will be released.

(7) Visualization and presentation (R3): Per rebuttal policy, we do not introduce new figures here. To provide more comprehensive validation, we will release the organized experimental results, including intermediate visualizations on our GitHub repository. We will clarify Table 2 regions (WT/TC/ET are composite regions calculated per official guidelines; RC is resection-cavity) and fix the “Overview” typo and Eq.1/4 formatting.



Meta-Review

Meta-review #1

  • Your recommendation

    Invite for Rebuttal

  • Please justify your decision. In case you deviate from the reviewers’ recommendations, explain in detail the reasons why. In case of an invitation for rebuttal, clarify which points are important to address in the rebuttal.

    The rebuttal should clarify the necessity of Mamba/OCF, explain gradient flow through Top-K selection, and provide stronger efficiency, reproducibility, and ablation evidence.

  • 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.

    The proposed Direction-Sensitive Equilibrium Mamba Network (DEM-Mamba) is recognized as a technically rigorous and innovative paradigm for anisotropic boundary modeling in 3D medical image segmentation. While concerns were initially raised regarding the novelty of the learnable wavelets, differentiable gradient flow through Top-K routing, and lack of efficiency profiling, consensus post-rebuttal highlights that the authors have successfully resolved these queries through detailed mathematical justifications, computational footprints, and code-release commitments.



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.

    As noted by the reviewers, the overall design of the pipeline is reasonable. Experiments have been conducted on four datasets, and the writing is satisfactory. On the other hand, the reviewers have raised concerns regarding certain technical details and experimental results, some of which have been addressed in the rebuttal. Overall, this paper includes several interesting components, such as adaptive conflict suppression and learnable Riesz steerable wavelets, which may be valuable to the MICCAI audience. Therefore, I recommend acceptance.



Meta-review #3

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

    Reject

  • Please justify your recommendation.

    The paper shows relevant motivation of improving anisotropic boundary modelling in 3D Mamba-based segmentation. However, as R2 pointed out, the learnable Riesz wavelet is an incremental novelty.

    My main concern is that the evaluation is not strong enough. 1) The reported improvements over baselines are often marginal, and no std or statistical tests are provided. Also, additional boundary-sensitive metrics like ASD would be more appropriate.

    2) I’m not convinced by the rebuttal about the use of different baselines across datasets. While some methods may be task-specific, important baselines such as SwinUNETR, MedNeXt, and nnFormer are not task-specific and should have been evaluated consistently.

    3) The comparison misses widely used and highly relevant Mamba baselines, such as U-Mamba and SegMamba variants, as discussed in the paper “Taming Mambas for Voxel-Level 3D Medical Image Segmentation”.

    Overall, the current evaluation does not convincingly demonstrate an advance of the proposed method. I recommend rejection.



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