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Abstract

Due to the reliance on manually designed implants, traditional skull defect reconstruction is time-consuming. Although latent diffusion models based on Signed Distance Fields (SDFs) accelerate the implant design, Gaussian noise initialization and stochastic differential equations lead to many iterations and may introduce incorrect geometric details. Moreover, separately training the decoder and latent-space network can accumulate errors across stages. To address these limitations, a Latent Optimal Transport Bridge (LOT-Bridge) based on SDFs is proposed. We model automatic skull reconstruction as an Optimal Transport (OT) problem in the latent and data spaces, and design an efficient training strategy to achieve accurate generation with fewer iterations. Firstly, to accelerate inference and improve the determinism of generation, we introduce a latent bridge model, where the reverse sampling begins from the defective data and follows an ordinary differential equation. Secondly, a joint training strategy performs OT-based optimization in the latent and data spaces while ensuring high-quality implant SDF prediction. Finally, the adaptive morphological block refines SDF features through dilation and erosion, enhancing surface reconstruction. Extensive experiments on three datasets demonstrate that LOT-Bridge generates more accurate implants with faster inference than existing methods.

Links to Paper and Supplementary Materials

Main Paper (Open Access Version): https://papers.miccai.org/miccai-2026/paper/1071_paper.pdf

SharedIt Link: Not yet available

SpringerLink (DOI): Not yet available

Supplementary Material: Not Submitted

Link to the Code Repository

https://github.com/yanaynghui1998/LOT-Bridge

Link to the Dataset(s)

N/A

BibTex

@InProceedings{YanYan_LOTBridge_MICCAI2026,
        author = { Yan, Yanghui AND Wang, Xingce AND Wu, Zhongke AND Ju, Xiaodong AND Liu, Jingyi AND Ji, Changkai AND Zhu, Yicheng AND Shui, Wuyang},
        title = { { LOT-Bridge: A Latent Optimal Transport Bridge Based on Signed Distance Fields for Automatic Skull Defect Reconstruction } },
        booktitle = {Medical Image Computing and Computer Assisted Intervention -- MICCAI 2026},
        year = {2026},
        publisher = {Springer Nature Switzerland},
        volume = {LNCS 16893},
        month = {September},
        page = {pending}
}

Reviews

Review #1

  • Please describe the contribution of the paper

    The paper presents a method for automatic skull completion in CT scans. The method, dubbed LOT-Bridge, is based on a latent flow matching framework used to generate Signed Distance Fields (SDFs) volumes. The velocity estimator in latent space, trained with the usual flow matching loss, is referred to as bridge model, since it is trained to learn a mapping between two probability distributions (defective and complete skulls), not to generate from a standard Gaussian. The paper casts the problem as an Optimal Transport estimation simultaneously solved in latent space and data space. The main claimed contributions are: (i) the flow matching equations are made deterministic by always learning to map the latent code of the partial skull to the complete one, thereby solving an ODE instead of an SDE, and creating a deterministic bridge model; (ii) a joint training strategy in latent and data space is proposed, to optimize simultaneously the bridge model, that operates in latent space, and the decoder, that compute SDF volumes from latent vectors, to improve the overall quality of the implants; (iii) a module in the decoder, the Adaptive Morphological Block (AMB), that can allegedly perform erosion or dilation in a data-driven way and improve the quality of the SDF. Experiments on the standard benchmarks for this task (SkullBreak, SkullFix, MUG500) show that LOT-Bridge achieves state of the art performance against several baselines while being the fastest method. A thorough ablation study on SkullFix shows that all contributions are important for the overall performance.

  • 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.

    S1.Results on standard benchmarks are remarkable.

    S2.Strong theoretical background. The paper casts the skull completion problem as an optimal transport (OT) problem in latent and data space. It then leverages principled solutions, based on previous work like Schrödinger Bridge [14] and Wasserstein Auto-Encoders [22], to solve them.

    S3.Novelty as a framework. While the solutions to the two OT problems are taken almost as is from previous work, putting the framework together and optimizing jointly the bridge model and the decoder to obtain better results in a completion task has not been done before to the best of my knowledge. Moreover, the use of the existing difference operator to compute an implant loss is also an interesting and application-specific contribution.

    S4.Thorough ablation study: the paper empirically justifies the proposed training strategy and losses by assessing the performance of the model on SkullFix when these contributions are removed and when they are added to a base model, leaving little doubt on their importance for the reported performance on this dataset. Yet, I would have preferred to see the ablation on the more challenging SkullBreak dataset.

    S5.Sufficient reproducibility. The paper details all the models used by referencing the original papers introducing them (with the exception of the U-Net architecture, which is stated to be the UNet in [22] for 3D data, which I couldn’t find in the reference) and extensively reports the hyperparameters of the training recipe.

  • 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.

    W1.Limited technical novelty. While, as discussed, the paper builds on principled previous work, two of the three claimed contributions are just the application of those results to the skull completion problem, with no changes. I’d suggest to change the claims to state that the contribution of the paper are the joint training strategy and the use of the difference operator to realize the implant loss.

    W2.AMB module. The third claimed contribution is the AMB module. It is a residual block with two branches: the top one is basically a 3D Squeeze-and-Excitation block with tanh activation in the end that computes a scalar delta in [-1;1] for each example in the mini-batch; the bottom branch is a convolutional block that computes a weight w in [0;1] for each voxel and each example. Then, the features inside the VQ-VAE decoder are updated as F = F + w * delta . It is claimed that when delta > 0 this is a data-driven erosion, whereas it is a dilation when delta < 0.No justification is provided for this claim. Moreover, since this happens a the feature level inside the decoder, it is not even clear to me what erosion and dilation are meant to perform in feature space. While the ablation shows that the AMB module is beneficial, and the authors claim that this is due to the adaptive morphological operator realized by the module, I suspect that it may more simply be due to the added layers and parameters. Can the authors imagine a controlled experiments where the number of parameters is controlled for? Can they explain how the module performs erosion/dilation in feature space and what is it? If this is not the case, I’d suggest to rename the module and change the narrative around it.

    W3.An effective baseline [A] based on data augmentation has not been considered in the experimental results.

    [A]. M Wodzinski, K Kwarciak, M Daniol, D Hemmerling: Improving deep learning-based automatic cranial defect reconstruction by heavy data augmentation: from image registration to latent diffusion models, Computers in Biology and Medicine, 2024

    W4.The anonymous link used to share the code does not actually contain the code, but only a few generic scripts. It is basically useless for reproducibility.

  • 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

    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.

    (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 theoretically sound and effective method to improve the results in an important problem for the MICCAI community. Although the paper hinges for the technical part on already known results (W1), putting together the overall framework is novel and valuable. The contributions of the paper have been ablated to validate their importance, and a sufficient number of details to reproduce the results have been provided (although making the code public would be preferable). Hence, I lean for acceptance.

    In the rebuttal I’d like to see comments on the justification and role of the AMB (W2) and the lack of a relevant baseline (W3). I may raise my score if the answers are convincing.

  • 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



Review #2

  • Please describe the contribution of the paper

    The paper proposes a novel Latent Optimal Transport Bridge (LOT-Bridge) framework based on signed distance fields (SDFs) for automatic skull defect reconstruction. By reformulating shape completion as an optimal transport problem in latent and data spaces, the method aims to improve determinism, reduce inference time, and enhance reconstruction accuracy compared to diffusion-based approaches.

  • 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.
    • Addresses an important clinical problem: automatic and efficient skull implant design
    • Well-written manuscript with a clear and logical presentation
    • Introduces an interesting integration of optimal transport, latent modeling, and SDFs
    • Experiments on multiple public datasets
    • Claims to propose faster inference compared to diffusion-based baselines
  • 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.
    • Unclear data augmentation strategy, with inconsistencies in reported sample counts
    • Treatment of fundamentally different datasets (synthetic defects vs. personalized implants) is insufficiently explained
    • Missing evaluation of cross-dataset generalization, a key challenge in shape completion
    • Baseline results on MUG500 raise concerns about realism and comparability
    • Novelty relative to existing fast encoder–decoder or completion networks is not clearly articulated
    • Lack of discussion on scalability and generazbility beyond the evaluated datasets
  • 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.

  • 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

    This paper presents a technically interesting and well-motivated approach to automatic skull reconstruction using optimal transport in latent and data spaces. The manuscript is clearly written and easy to follow, and the proposed LOT-Bridge framework addresses known limitations of diffusion-based methods, such as stochasticity and slow inference. The joint optimization of the decoder and latent bridge is a sensible design choice, and the reported improvements in speed and accuracy are promising.

    That said, several critical aspects of the experimental design require clarification to fully assess the validity and scope of the contribution. In particular, the data augmentation strategy for MUG500 appears inconsistent with the reported numbers and should be described more precisely (how 19 training samples can be extended by the registration-based augmentation to this number of samples?). Moreover, the paper does not sufficiently address the fundamental difference between datasets with synthetic defects (SkullBreak/SkullFix) and those with personalized implant designs (MUG500). These represent distinct reconstruction problems, and it is unclear how the proposed framework handles these differences or whether separate models were trained. In case separate models were trained - cross-dataset generalization experiments are necessary.

    The lack of cross-dataset generalization experiments limits the demonstrated clinical relevance of the method. Generalization to unseen defect distributions is a central challenge in shape completion, and such an evaluation would significantly strengthen the paper. The strong baseline performance on MUG500 also raises concerns and deserves further discussion. The reported DSC for the baselines is very high - especially considering that the task is to propose a personalized implant where more than a single output can be considered as a correct one.

    Finally, the novelty relative to existing fast encoder–decoder approaches could be articulated more clearly, particularly in terms of scalability and applicability beyond the evaluated settings.

  • 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?

    I recommend weak accept. The method is well motivated, technically sound, and clearly written, with encouraging results. However, unclear experimental design choices, missing generalization analysis, and questions about baseline validity prevent a stronger recommendation.

  • 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



Review #3

  • Please describe the contribution of the paper

    1.Formulation of automatic skull reconstruction as an Optimal Transport problem in both latent and data spaces. 2.Development of a deterministic, ODE-based bridge model that initiates generation from defective data rather than Gaussian noise. 3.Introduction of the Joint Training Strategy and the Adaptive Morphological Block (AMB) to mitigate error accumulation and refine 3D surfaces.

  • 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.Deterministic and Efficient Inference: The shift from SDE-based diffusion to an ODE-based bridge allows the model to produce consistent results in just 5 iterations, which is highly desirable for clinical settings. 2.Jointly Training Strategy: By jointly training the bridge and the decoder, this study directly addresses the “stage-gap” error common in latent generative models. 3.Structural Refinement: The AMB adaptively perform erosion and dilation at different upsampling stages of VAE, improving the surface reconstruction details.

  • 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.Lack of Clinically Relevant Evaluation Metrics: While the paper provides a standard geometric evaluation using metrics such as DSC, HD95, and MSD, it lacks quantitative analysis through clinical or surgical metrics specific to cranioplasty. For example, although the qualitative results mention “smooth curvatures” and “accurate transitions,” there are no quantitative measurements (e.g., surface normal consistency or curvature error) to evaluate the smoothness of the junction between the implant and the original bone. 2.Insufficient Comparative Evaluation: While the authors compare LOT-Bridge against general-purpose 3D generative frameworks (e.g., SDFusion, OctGPT) and some older task-specific baselines (e.g., PBT, SegRegNet), they fail to include recent specialized methods and general generative models.

  • 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 has provided an anonymized link to the source code, dataset, or any other dependencies.

  • 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.

    (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 paper presents a significant methodological advancement in 3D skull completion. The deterministic Latent Optimal Transport Bridge and joint training strategy effectively improve the performance while achieving 5x to 10x speedup in inference, which demonstrates great potential for clinical application. However, it would be better if this study incorporates more recent specialized baselines and clinical metrics.

  • Reviewer confidence

    Confident but not absolutely certain (3)

  • [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 all reviewers and meta-reviewers for their constructive feedback and for recognizing the strengths of our work, including our strong theoretical background and the deterministic and fast inference. We will cite all suggested references in the final version and conduct the suggested experiments as much as possible in our future work. Reviewers(Rn) raised a few questions and sought clarifications addressed below. Novelty, Contributions, and Scalability (R1,R2). In the camera-ready version, we will revise the contribution statement to clarify that our core novelty lies in formulating the skull completion task as an OT problem. Meanwhile, we will clarify the novelty of LOT-Bridge relative to existing methods and discuss its broader applicability and scalability to general 3D shape completion and transformation tasks. Mechanism and Justification of the AMB Module (R1). The AMB is specifically designed for Signed Distance Field (SDF). As delta changes, the boundary of the SDF features naturally shrinks or expands. In morphological terms, this directly corresponds to erosion or dilation. We previously considered other AMB designs with either more or fewer parameters than the current version. However, these variants did not perform as well as the AMB used in our method. This proves that the performance gain stems directly from the proposed AMB, not from merely adding trainable parameters. MUG500 and Sample Count (R1, R2). Baselines score highly on MUG500 because its data distribution is unusually simple. Moreover, LOT-Bridge outperforms all baselines across all datasets. The actual augmented training sample count is 256, which will be corrected. We will incorporate the above clarifications and fix a minor error in the final version. We will provide a GitHub repository containing all our code.



Meta-Review

Meta-review #1

  • Your recommendation

    Provisional Accept

  • 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 reviewers agree that this work is technically sound, well-motivated, and makes a clear technical contribution to the targeted application. Meanwhile, all reviewers shared concerns about limitations in the evaluation, including the lack of relevant baselines, a generalization analysis, and a clinical evaluation.

    I recommend accepting this paper based on its consistently highlighted merits.



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