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Abstract

A fundamental tension underlies uncertainty estimation for clinical segmentation: Bayesian methods—MC Dropout, Deep Ensembles, TTA—demand repeated inference incompatible with real-time workflows, while single-pass alternatives either alter the training objective(EDL) or impose global architectural constraints that risk distorting learned representations (DUQ, SNGP, DDU). The core scientific question is whether prediction uncertainty can be read directly from the activation geometry of a learned function in a single forward pass, without auxiliary losses, repeated sampling, or global architectural change. We identify a principled answer in the local-support property of B-spline basis functions within Kolmogorov–Arnold Network (KAN) layers: because each basis function has compact support, activation concentration directly proxies training-data density—well-covered inputs produce winner-take-all activation while distribution boundaries and misclassified sites produce dispersed patterns. We verify this statistically (Mann Whitney p<0.001, Cohen’s d up to 1.61 across colonoscopy, ultrasound,and dermoscopy) and operationalize it via the Residual KAN Head, a plug-and-play classifier adding <0.01M parameters that preserves segmentation accuracy (Dice change <0.3%). On four medical imaging benchmarks, our single-pass method achieves the best selective prediction per formance in 4 of 12 backbone×dataset settings at 6.9× faster inference than multi-pass alternatives.

Links to Paper and Supplementary Materials

Main Paper (Open Access Version): https://papers.miccai.org/miccai-2026/paper/5070_paper.pdf

SharedIt Link: Not yet available

SpringerLink (DOI): Not yet available

Supplementary Material: Not Submitted

Link to the Code Repository

https://github.com/Wenju-Du/B-spline-uncertainty-segmentation.

Link to the Dataset(s)

CVC-ClinicDB (colonoscopy): https://polyp.grand-challenge.org/CVCClinicDB/ BUSI - Breast Ultrasound Images (ultrasound): https://scholar.cu.edu.eg/?q=afahmy/pages/dataset ISIC 2018 Task 1 - lesion segmentation (dermoscopy): https://challenge.isic-archive.com/data/ REFUGE (retinal fundus): https://refuge.grand-challenge.org/

BibTex

@InProceedings{DuWen_Bspline_MICCAI2026,
        author = { Du, Wenju AND Wu, Zhiwei AND Zeng, Bing AND Rao, Nini AND Liu, Wei},
        title = { { B-spline Activations as Intrinsic Uncertainty Estimators in Medical Image Segmentation } },
        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

    Authors propose to use a KAN residual network to estimate uncertainty in semantic segmentation. They show that learned B-spline functions activate in a way that reflects a deterministic coverage signal, and this signal can be uncovered in a single pass, in contrast to multi-pass uncertainty estimation methods. By designing a residual head around KAN they also estimate this uncertainty without changing the loss function and with minimum impact on performance (measured as DICE). Authors validate the method by first showing there’s no significant decrease in DICE on four medical imaging databases and compare to other uncertainty methods in a ranking task (using E-AURC), showing comparable performance to SOTA.

  • 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.

    Novelty - The application of KAN activations as a signal of support is novel, to the best of my knowledge. Applicable method - Authors claim the FPS supports real-time deployment.

  • 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.

    Statistical evaluation - the E-AURC table would benefit from std values and a statistical support for claims and comparisons should be added. Unclear scope - While the authors show that the uncertainty signal carried by B-spline activation reflects distributional coverage, they do not explain if there is a relation between distributional coverage and model confidence, and in particular whether pixel, segment, or boundary reliability capture the true confidence that can be useful in practice. For example, it is not clear if the per-pixel uncertainty represented by entropy in B-spline activations can be calibrated to inform decisions beyond the ranking task that is demoed in the paper.

  • 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

    My suggestion is, first, to clarify the relation between distributional coverage and model confidence. Some SOTA methods estimate only model confidence and do not explicitly account for distributional coverage or distribution shift, and it is not clear whether the present manuscript addresses both or only uncertainty related to distributional coverage. Second, the manuscript would benefit from a discussion of how the derived uncertainty signal can be used in practice; that is, whether the uncertainty can be calibrated and whether the model supports calibration. Although no existing approach provides universally reliable uncertainty estimates, some perform better than others in terms of calibration, and it would be helpful to give some intuition for where the presented model falls. Third, confidence intervals and statistical testing should be added to support the claims made in the paper.

  • 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 — marginally below the acceptance threshold, but would not mind if accepted, dependent on rebuttal

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

    Poor statistical evaluation. Unclear scope: The usefulness of uncertainty estimation is demonstrated through per-frame averaging, and it is not clear whether uncertainty at the pixel or region level also translates downstream. It is also unclear whether model uncertainty is captured, in addition to uncertainty arising from distributional coverage. The authors show that the uncertainty signal carried by the B-spline activation reflects distributional coverage, but the relation between distributional coverage and model confidence is not obvious. It is also not clear how the approach could be used in practice: the authors only demonstrate the use of averaged uncertainty to rank segmented frames, whereas broader practical use would likely benefit from some discussion of whether the uncertainty can be calibrated.

  • 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 authors will update the submission with statistical testing and a clearer explanation of the scope and applicability of their method. The promised additions answered my concerns.



Review #2

  • Please describe the contribution of the paper

    The paper addresses uncertainty estimation in clinical image segmentation, where existing approaches either rely on computationally expensive multi-pass inference (e.g., test-time augmentation, MC Dropout) or introduce modified training objectives and architectural constraints (e.g., evidential learning). The authors propose a single-pass uncertainty estimation method based on the activation geometry of Kolmogorov–Arnold Network (KAN) layers. Leveraging the local-support property of B-spline basis functions, they interpret activation dispersion as a proxy for prediction uncertainty, where concentrated activations indicate well-supported regions and dispersed activations indicate uncertain predictions.

    To operationalize this idea, a lightweight Residual KAN Head is introduced and integrated into existing segmentation architectures. The method derives pixel-wise uncertainty directly from activation patterns without requiring repeated inference, modified loss functions, or changes to the backbone.

    Experiments on four medical imaging datasets across multiple backbones show that the proposed approach achieves competitive or superior uncertainty estimation performance compared to both multi-pass and single-pass baselines, while maintaining segmentation accuracy and significantly reducing computational cost.

  • 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 proposes a novel perspective on uncertainty estimation by linking activation dispersion in KAN layers to prediction uncertainty. The interpretation of local B-spline support as a proxy for data density is intuitive and provides a clear conceptual foundation.
    • The proposed Residual KAN Head is lightweight and can be incorporated into existing segmentation architectures with minimal overhead, without requiring repeated inference or modifications to the training objective.
    • Efficient single-pass uncertainty estimation: The method enables uncertainty estimation in a single forward pass and is substantially faster than multi-pass approaches such as MC Dropout and test-time augmentation, making it attractive for real-time applications.
    • The approach achieves competitive or superior uncertainty estimation performance across multiple datasets and backbones, while preserving segmentation accuracy.
    • No degradation of primary task performance: In contrast to some alternative single-pass methods, the proposed approach maintains segmentation accuracy across all evaluated settings.
    • The method is validated on several medical imaging benchmarks and backbone models, supporting its general applicability.
    • Initial ablation analysis: The paper includes an ablation study investigating architectural components (e.g., the role of the KAN head and grid size), providing initial insight into the behavior of the method.
    • The figures are very well designed and help to illustrate the core ideas of the paper effectively.
  • 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.
    • While an ablation study is provided, it is relatively narrow in scope and does not sufficiently disentangle the contribution of key design choices (e.g., spline order). The current analysis (e.g., Table 4) remains limited and could be better structured to provide clearer insights.
    • While the method is significantly faster than multi-pass approaches, it is slightly slower than other single-pass methods. This trade-off is not clearly discussed, which somewhat weakens the efficiency argument.
    • Certain aspects of the training procedure and integration of the Residual KAN Head (e.g., whether training is fully end-to-end or partially frozen) are not explicitly described, which makes the method harder to fully assess.
    • Some sections lack sufficient explanation (e.g., the “Inference Efficiency” section contains little to no descriptive text), and certain tables or formatting choices (e.g., Table 4 structure) reduce clarity.
  • 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

    The paper presents an interesting and conceptually appealing approach to single-pass uncertainty estimation. In particular, the use of activation dispersion in KAN layers as a proxy for uncertainty is a novel and well-motivated idea, and the overall framework is simple and practical to integrate.

    For further improvement, a more detailed and structured ablation study (e.g., including additional hyperparameters such as spline order) and a clearer discussion of efficiency trade-offs compared to other single-pass methods would strengthen the paper.

    Minor comments:

    • Table 4: The “Factor” column contains only a single entry (“Head Design”) and could be simplified or removed to improve clarity.
    • Section 3.3: Minor formatting issue (“strongest” extends into the margin).
    • Section 3.4 (“Inference Efficiency”) lacks explanatory text and would benefit from additional discussion.
    • Some references point to arXiv preprints instead of final published versions (e.g., KAN paper).
  • 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?

    The paper presents a conceptually interesting and well-motivated approach to single-pass uncertainty estimation based on activation geometry in KAN layers. The proposed method is simple, practical, and demonstrates competitive performance across multiple datasets and backbones, while preserving segmentation accuracy and offering a clear efficiency advantage over multi-pass methods.

    However, the overall contribution is somewhat limited by a relatively narrow ablation study, minor inconsistencies in the reported results, and aspects of the presentation that could be improved for clarity.

    Overall, the paper provides a solid and relevant contribution with clear practical potential, although it would benefit from a more thorough experimental analysis and improved presentation.

  • 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 original submission already presented a conceptually interesting and practically relevant approach to single-pass uncertainty estimation with competitive empirical performance. In their rebuttal, the authors directly addressed several of my main concerns, particularly regarding computational efficiency, training details, ablation scope, and reproducibility.

    The clarification that the method is trained fully end-to-end, the more nuanced discussion of efficiency trade-offs relative to other single-pass approaches, and the planned release of code and experimental configurations significantly improved my confidence in the work. The authors also provided reasonable justification for the chosen ablation scope and acknowledged remaining limitations transparently.

    Overall, the rebuttal strengthened the paper considerably, and I believe the work constitutes a solid and practically relevant contribution suitable for acceptance.



Review #3

  • Please describe the contribution of the paper

    There are 3 Contributions in this paper: a statistical characterization of B-spline activation dispersion, the residual KAN Head, and an empirical that the resulting single-pass method achieves the best E-AURC.

  • 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.

    Major strengths:

    • the technique presented in the paper is tested on 4 data sets, which is a good approach (enough to be convincing)

    • this technique needs a very small number of additional parameters which shows that it is powerful

    • this method is shown to be around 7 times faster than well-known TTA, deep ensembles, and MC DropOut, which seems very promising for real time applications

    • the main ways to compute uncertainty are recalled in the state of the Art (MC Dropout, deep ensembles, and Test Time Augmentation for multiple pass algorithms and single pass algorithms), so it seems complete

    • the ablation study is correctly done in this context

  • 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.

    Major weaknesses :

    • This is not because an approach is in multiple passes that it is slower than a single pass one, so the motivation in the abstract of the paper is not correctly built or presented (since real-time seems important in this paper)

    • there is no explanation of which uncertainty is measured. Is it the epistemic one ? or the random one ? this should be recalled and detailed.

    • it seems hard to understand the way the uncertainty can be computed in only one pass, some diagrams or pictures might be be missing

    • I see no picture of spline activation function with a finite/Local support, so it is hard to understand exactly how they are utilized and why it is so important here to have a local support. Details are missing

  • Please rate the clarity and organization of this paper

    Poor

  • 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.

    (3) Weak Reject — marginally below the acceptance threshold, but would not mind if accepted, dependent on rebuttal

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

    This paper seems to provide a really important way to estimate uncertainty in a single pass, but the papers lacks of mathematical recall, pictures, and diagrams explaining the spline activation maps. Furthermore, it does not explain which uncertainty is measured (epistemic or random), which makes me not confident about the paper.

  • 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.

    I am convinced by Argument 5 which answers to my main question (computational requirements and efficiency).



Author Feedback

We thank the reviewers and AC for the feedback. We address the AC’s convergent themes below. 1.SCOPE OF UNCERTAINTY [R1, R3, AC]. Our signal captures an epistemic component of predictive reliability arising from limited training-data coverage, not a full Bayesian decomposition. Local-support B-spline bases concentrate activation where inputs are well-covered during training and disperse it where coverage is sparse. Fig. 3 supports this: misclassified pixels show significantly higher activation entropy than correct ones (Cohen’s d up to 1.61, all p<0.001), and boundary pixels exceed interior ones (d up to 1.43)—confirming coverage-to-reliability and pixel-level discriminability. We will clarify in Sec. 2.1.2.STATISTICAL EVALUATION [R1, AC]. Per-cell ±std (3 seeds) computed; std on best cells is small (e.g., ISIC/UNet 18.7±1.2). Wilcoxon signed-rank across 12 backbone×dataset settings: Ours significantly outperforms Softmax (11/12, p=0.0015) and achieves statistical parity with the strongest multi-pass baselines (TTA×8 p=0.42, MC Dropout×10 p=0.79) as well as EDL (p=0.79), while running 6.9–8.9× faster than multi-pass methods and preserving Dice unlike EDL. Full results will be added to Table 2.3.APPLIED FRAMING [R1, AC]. Our framework targets selective prediction (Sec. 2.3): uncertainty ranks images so unreliable cases can be deferred for clinician review. Ranking and calibration address distinct clinical needs—ranking supports triage prioritization (our focus); calibration supports threshold-based automation. Fig. 4 demonstrates the practical sufficiency of ranking: at 50% coverage, our curve approaches the oracle on ISIC/UNet and clearly outperforms TTA/MC Dropout, confirming frame-level uncertainty supports the “defer top-k uncertain cases” workflow without absolute confidence thresholds. Because activation entropy is a continuous scalar, it remains compatible with post-hoc calibration (e.g., temperature scaling) if threshold decisions are needed. 4.LOCAL SUPPORT VISUALIZATION [R3]. Fig. 2 shows per-basis activation intensity but not Bk(x) themselves. We will add a compact-support Bk(x) inset and a brief B-spline definition in Sec. 2.1.The one-pass mechanism: during a standard forward pass, the KAN layer evaluates B-spline bases for each input feature; we read the distribution of these already-computed values as uncertainty, no additional computation needed. 5.COMPUTATIONAL PERFORMANCE [R2, R3, AC]. Our claim concerns sequential repeated inference in latency-sensitive workflows (not all multi-pass methods). Table 3: TTA 100.69 ms; MC Dropout 129.48 ms; ours 14.60 ms. Among single-pass methods, our 1.1× overhead (14.60 vs. 12.79 ms) is slightly above Softmax (13.12) and EDL (13.5). However, Softmax ranks significantly worse (p=0.0015); EDL requires loss modification and degrades Dice up to 2.5%. Ours maintains Dice (<0.3%) without altering training, matching EDL in win count (6/12 each) while preserving accuracy across all settings. 6.ABLATION SCOPE AND TRAINING [R2]. Table 4 isolates grid size G and residual structure, the two largest empirical factors. We fix S=2 and acknowledge spline-order sensitivity is not experimentally disentangled. Mechanistically, G directly controls the resolution of the basis decomposition (K=G+S) and is the dominant factor, as the G=5→3 effect (E-AURC 82.1→50.8) confirms. Training is fully end-to-end with no frozen components. 7.REPRODUCIBILITY AND MINOR ISSUES [R1, R2, R3]. Upon acceptance we will release code, checkpoints, and config files with a reproducibility checklist; we will also expand Sec. 3.4, update arXiv refs, simplify Table 4, and fix Sec. 3.3 formatting. We hope these clarifications address the reviewers’ and AC’s concerns; all promised revisions will be incorporated in the camera-ready.



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.

    This submission proposes an uncertainty estimation method for image segmentation using b-spline activation functions. The reviews diverge in appreciation, note potential relevance to the field, but also converge on major concerns: unclear scope of uncertainty and motivation of application, limitations in the experimental evaluation, concerns on computational performance. A rebuttal should clarify these points with realistically minor changes to the manuscript. For these reasons, the recommendation is to request a rebuttal.

  • 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 rebuttal was helpful in addressing the reviewer concerns on a statistical validation, computational efficiency, and methodological scope. A consensus has been reached to recommended for acceptance due to the practical value and novelty of its single-pass uncertainty estimation approach.



Meta-review #2

  • 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.

    I recommend rejection. The paper studies an interesting direction—using B-spline/KAN activation patterns as a single-pass uncertainty signal for medical image segmentation—but the current evidence is not sufficiently convincing for acceptance. The central claim that B-spline activation dispersion serves as an intrinsic uncertainty estimator remains largely heuristic and empirically under-validated; the pixel-level statistics show correlation with errors/boundaries, but do not establish reliable uncertainty estimation, calibration, or density-awareness.

    Experimentally, the results are mixed. The proposed method achieves the best E-AURC in only 4 of 12 settings, while multi-pass baselines often outperform it despite higher cost. The advantage over single-pass alternatives is also not decisive, as EDL is competitive or better in several cases. Important uncertainty baselines discussed in the paper, such as DUQ, SNGP, DDU, or deep ensembles, are not evaluated. The validation sets are also small for some datasets, and the paper lacks stronger statistical testing, calibration analysis, OOD/domain-shift evaluation, and broader ablations.

    Overall, while the idea is potentially useful, the novelty and empirical support are currently insufficient. The claims about intrinsic uncertainty estimation and clinical real-time applicability are stronger than what the presented results justify.



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.

    The paper presents a useful single-pass uncertainty quantification method with competitive performance. The authors have properly addressed reviewers’ concerns, including outlying the scope and significance of their results.



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