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Abstract

Accurate 3D bone defect completion is critical for personalized implant design and surgical planning, where both boundary alignment and surface quality are essential. Existing voxel-, point-, or implicit-based generative models often struggle to simultaneously preserve topology, surface fidelity, and conditional consistency near defect regions. We propose FDMMBone, a flow-based conditional mesh completion framework operating in a deformable tetrahedral mesh (DMTet) parameter space. By representing shapes on a unified, geometry-aware tetrahedral grid, FDMMBone enables stable conditional generation of mesh parameters via probability flow ODE integration. A subsequent subdivision-based deformation refinement further enhances surface smoothness and boundary continuity. Experiments on multiple public datasets demonstrate consistent improvements over state-of-the-art methods in shape accuracy, boundary fidelity, and generalization, highlighting the robustness and clinical potential of the proposed approach.

Links to Paper and Supplementary Materials

Main Paper (Open Access Version): https://papers.miccai.org/miccai-2026/paper/1918_paper.pdf

SharedIt Link: Not yet available

SpringerLink (DOI): Not yet available

Supplementary Material: Not Submitted

Link to the Code Repository

N/A

Link to the Dataset(s)

N/A

BibTex

@InProceedings{LiuZhe_FDMMBone_MICCAI2026,
        author = { Liu, Zhenhong AND Wang, Xingce AND Wu, Zhongke AND Ju, Xiaodong AND Liu, Jingyi AND Zhu, Yicheng AND Shui, Wuyang},
        title = { { FDMMBone: Flow-Based Conditional Deformable Mesh Modeling for Accurate 3D Bone Defect Completion } },
        booktitle = {Medical Image Computing and Computer Assisted Intervention -- MICCAI 2026},
        year = {2026},
        publisher = {Springer Nature Switzerland},
        volume = {LNCS 16889},
        month = {September},
        page = {pending}
}

Reviews

Review #1

  • Please describe the contribution of the paper

    The authors propose FDMMBone, a bone defect completion pipeline aiming at generating implants for defective bones. The pipeline is composed of two stages: in the first stage a generator is trained using Flow Matching learning objective to synthesize bone implants; the second stage is a refinement one, where the generated implant is upsampled and improved. The generative model trained in the first stage operates on the meshes parameterized in the DMTet parameter space: the input defective mesh is fitted to the DMTet representation, and used to condition a U-Net like generative model that synthesizes the DMTet parameters of the bone implant. The mesh of the generated implant is obtained from its DMTet representation via Marching Tetrahedra algorithm. In the second stage, an higher resolution mesh is obtained applying face subdivision. The high-resolution mesh is fed to a U-Net like refinement network, which predicts vertex displacements that are used to refine the implant mesh. The authors’ contributions consist in the usage of a Flow Matching generative model in the DMTet parameter space, and in the implementation of a two-stage pipeline which allows to locally refine the generated implants. Additionally, the authors modify the denoising process applying a projection correction strategy: the result of each intermediate step of the denoising process is optimized with two gradient descent steps to enforce consistency with the defective bone and to smooth high-frequency details. Quantitative and qualitative evaluations show the strength of the proposed pipeline compared to SOTA methods on standard benchmarks like MedShapeNet and SkullBreak.

  • 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.The main strength of the work lies in the quantitative and qualitative results, which show that the proposed pipeline outperforms significantly all the competing methods. S2.The idea of applying flow matching to the DMTet parameterization is original S3.The experimental evaluation is extensive, as it includes four different datasets spanning over two different anatomical regions, and seven competing methods. These are evaluated with the most prominent metrics used in the relevant literature. S4.The ablation studies are satisfactory and highlight that the proposed changes, i. e. the projection-correction strategy and the refinement network, are effective and contribute to the improvement of the performance of the model.

  • 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.The presentation of the method is unclear in many parts and important hyperparameters are not specified in implementation details. This severely limits the clarity and reproducibility of the work. Here is a non-exhaustive list of unclear aspects or missing data:

    • The integration of DMTet in the pipeline is confusing. It is not clear how the DMTet representations are obtained. In Sec 2.1, where the parameterization is described, it is missing if a network or classical optimization is used to predict it. In case of a network, which network is used to predict it and how is this network optimized?
    • I was not able to find in reference [1] the geometric consistency loss cited in Sec. 2.2 and used to fit the meshes to the DMTet representation.

    • The cardinality of the DMTet representations, N, is not defined in the Implementation details in Sec. 3.

    • The projection correction strategy is clear, but the definition of the optimization problem is not. More specifically, it is not clear what the L_cond is. Being this one of the main contributions of the work, the optimization losses should be more thoroughly described. Moreover, the parameter lambda_i is not specified in Sec. 3 with the other implementation details.

    • The description of the architecture of the geometric refinement network is confusing. In Section 2.3, where the module is introduced, the architecture is not described. In Section 3, under implementation details, it is written that the refinement network adopts a U-Net architecture. In Figure 1 the architecture is depicted as an MLP (with unclear connections between the nodes). I’d suggest to clarify the description of the architecture, move it in Sec. 2.3 and modify Figure 1 to make it coherent with the description. W2.The manuscript does not clarify if all the competing methods have been retrained on the datasets, and if all are using the same training protocol. Therefore, the reader cannot be sure if the comparisons are fair. W3.The considered baselines are mainly generic shape completion methods. At least for the skull completion problem, i. e. the SkullBreak and the Mandibular datasets, stronger, problem-specific baselines exists [A,B]. Since the authors already used a method proposed only for skull completion (PCDiff) also on the MedShapeNet, they could add these stronger baselines in all datasets. Was there a good reason to exclude these baselines? [A]. Wodzinski, M. , Daniol, M. , Hemmerling, D. : Automatic skull reconstruction by deep learnable symmetry enforcement. Computer Methods and Programs in Biomedicine 263, 108670 (2025) [B]. 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
  • 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

    C1.Citations to Flow Matching (Lipman et al. , 2022) are missing. C2.In Sec. 3 it is written that vertices not contributing to the surface generation are assigned fixed distances +-1.As I understand, this is a difference w. r. t the original DMTet representation. If this is the case, I’d suggest to better motivate it. C3.Table 2, which shows the results of the ablation experiments, would be more easily interpretable if the ablation on K and the ablation on (wn, wl) are separated. Specifically, (A7) could cover only the variation of K and an additional (A8) could cover the changes of (wn, wl) C4.Finally, reproducibility and method understanding could be eased by providing the code in the review phase using resources such as https://anonymous. 4open. science/

  • 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?

    Despite the good performance obtained by the proposed pipeline (S1), I am inclined toward rejection as the description of the method is not clear (W1) and the experimental protocol presents issues (W2-W3). These weaknesses severely limit the understanding of the pipeline in all its parts and make the method not reproducible. Since the issues related to clarity affect the whole pipeline, I feel that the paper at this stage is not ready for publication. While some of the issues related to the experimental protocol (W2) could be addressed in the rebuttal, clarifying the method (W1) would require a heavy revision of the paper, not suitable for a rebuttal phase as per the reviewer guidelines. Therefore, my reject recommendation. However, the experimental results are strong, and an extensive revision of the presentation of the method and an improvement of the experimental settings would make for a strong future submission.

  • 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.

    The rebuttal clarifies some of the issues raised in the reviews, including missing hyperparameters, experimental setup and results, and runtime considerations. Nevertheless, even after considering the rebuttal, I feel that the work lacks clarity in important aspects and presents several inconsistences:

    • The rebuttal specifies that the DMTet representation is optimized using a Chamfer distance combined with SDF regularization and Laplacian terms, whereas the manuscript refers to a generic “geometric consistency loss [1]”. However, in [1] I could not find any reference either to the geometric consistency loss nor to the optimization strategy described in the rebuttal.
    • Explicitly defining the losses used in the projection-correction step, rather than describing them only qualitatively, would have helped the reviewers to better understand the proposed method. In its current form, the definition remains unclear, and the reference to [3] does not help. Moreover, the rebuttal introduces key information regarding how these losses are computed, namely that they are evaluated only within a narrow band around the defect boundary. This raises two concerns: first, it is a significant implementation detail that is not present in the manuscript, negatively affecting clarity and reproducibility; second, it appears that information about the defect boundary is explicitly provided during inference, which raises concerns regarding the fairness of the experimental setting and whether the method benefits from additional prior information unavailable to competing approaches.
    • The ablation inconsistency highlighted by R2.2 is not resolved in the rebuttal, since the issue is not a typo in the ablation numbering, but rather a description of the results inconsistent with Table 2.Similarly, other claims regarding the ablation study do not seem to be supported by the reported evidence (e.g. A6 degrades across all metrics, not only across the boundary-related ones).
    • While the authors state that the code will be released upon acceptance, the current manuscript omits several implementation details that are necessary to reproduce the method. Given these omissions, the absence of publicly available code greatly limits reproducibility.

    As also acknowledged by all the reviewers, the empirical results are strong. However, the inconsistencies in the method’s description, the concerns related to fairness, the lack of code and implementation details, and the issues in the interpretation of the ablation studies let me confirm my opinion that the work is not yet ready for publication without substantial revision. I would encourage the authors to revise the paper according to the reviews and resubmit it.



Review #2

  • Please describe the contribution of the paper

    The paper proposes to apply conditional flow matching to a deformable tetrahedral mesh representation, solving anatomical shape completion. The authors make use of a two-stage pipeline that first applies conditional flow matching for coarse reconstruction and second refines this coarse mesh through deformation-based adjustments. The method is evaluated across multiple publicly available datasets and performs well across all of them. Core decisions are well ablated.

  • 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 generally well-written and easy to follow. The method is explained clearly, with a consistent mathematical notation, and all relevant hyperparameters are reported.

    • The application of flow-matching to shapes parameterized with Deep Marching Tetrahedra (DMT) is interesting and I’m not aware of similar work for a medical problem.

    • The projection correction strategy, as well as the second-stage geometric refinement network seem to offer lightweight improvements. All components, as well as core design choices (losses, network components, …) are ablated.

    • Evaluation is performed over a broad range of four publicly available datasets and the presented method seems to perform well across all of them. The experiment which evaluates the models performance (trained on SkullBreak) on MUG500 demonstrates good generalizability.

  • 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 this is a generally interesting paper, I have some minor concerns:

    • The authors report no training/ inference times. I think comparing this (also across the comparing methods) would help to further contextualize the performance. I believe that they are quite different for the shown methods, which can have practical implications.

    • The claim, that ablation (A1) results in the most significant performance drop is wrong, as (A6) leads to much lower scores.

  • 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

    There is a link to a repository at the end of the abstract (currently leading nowhere). I hope this means that the authors plan to publish their code, which would really strengthen 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?

    I think this is a strong paper that mostly lives from the good empirical performance on a really relevant task (anatomical shape completion). While the presented work is mostly a combination of existing concepts, I’m not aware of any other work that applies them for anatomical shape reconstruction. The novelty of this paper is limited to some extent, but the experiments compare to recent SOTA methods and on a wide range of datasets, with good performance across all of them. I think this paper is between “Weak Accept” and “Accept”, leaning towards “Accept”.

  • 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 still think that the merits of this paper outweigh its weaknesses. The presented method demonstrates strong performance on a relevant problem, cleverly combining an underexplored data representation with an efficient processing framework. While I agree with some of R1s concerns (e.g. the one regarding more problem specific baselines), I still find the evaluation convincing. More problem specific baselines would have been nice to see, but a comparison to 7 relatively recent methods (including a problem specific baseline: pcdiff) + a well conducted ablation are in my opinion above average for a conference paper with 8 pages. From my perspective this paper is interesting for the community and warrants discussion at MICCAI. I recommend to accept this paper, but encourage the authors to add the additional clarifications (e.g. on their training setup, that comparing methods were retrained, the DMTet resolution, etc.).



Review #3

  • Please describe the contribution of the paper

    The paper presents FDMMBone, for 3D bone defect completion using conditional flow matching within a deformable tetrahedral mesh space. The approach uses a two phase setup: the first stage employing probability flow ODE integration for coarse shape generation, and a second stage involving subdivision-based refinement to capture high-frequency surface details. The method is evaluated on three distinct datasets with a focus on boundary accuracy.

  • 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.A strong evidence of the methodology in this paper is the consistent reduction in HD95 across all three datasets. While many generative models prioritize volume overlap, FDMMBone demonstrates a measurable ability to align the reconstructed surface with the GT boundaries. 2.The cross-dataset evaluation on the MUG500 is highly rigorous. Achieving a DSC of 91.8 and HD95 of 1.72 on an unseen dataset proves that the model has captured underlying anatomical priors rather than merely overfitting on the training dataset.

  • 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.The paper would benefit from a breakdown of the inference latency introduced by the 200-step ODE solver vs the refinement stage. 2.The results are geometrically excellent, but the authors haven’t described how these meshes integrate into a standard CAD manufacturing pipeline. This would strengthen the clinical impact claim.

  • 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

    The authors should consider adding a brief discussion on how the model performs when presented with noisy input segmentations to further demonstrate the robustness of the method.

  • 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 provides quantitative and qualitative evidence that FDMMBone outperforms current SOTA methods in the most critical metric for bone reconstruction. The technical combination of applying flow matching to a deformable tetrahedral mesh is mathematically sound and demonstrates high generalization capability on unseen datasets.

  • 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 (Rn) for their comments and for recognizing the strengths of our work, including its strong quantitative and qualitative performance across multiple datasets (R1,R2,R3), the original formulation combining flow matching with DMTet (R1,R2,R3), and its excellent generalization capability (R2,R3). The reviewers (Rn) raised a few questions and sought clarifications(Rn.m) , which we address below. 【Unclear presentation (R1.1)】. The missing details were unfortunately omitted due to page limits and narrative compression, but they do not reflect fundamental methodological flaws. The resolution of DMTet is 128^3, and N = 277410 tetrahedral vertices. Each vertex stores a 4D attribute consisting of a 3D displacement vector and one SDF value. 【DMTet Parameterization (R1.2)】.We clarify that the DMTet representation is not predicted by a preprocessing network. Instead, each training mesh is converted into a fixed DMTet parameter space through a deterministic fitting procedure. The fitting minimizes the Chamfer distance between the DMTet-extracted mesh and the target, combined with SDF regularization and Laplacian terms. 【Projection-Correction (R1.4)】. L_cond measures the SDF consistency exclusively within a narrow band around the defect boundary, preventing the generated implant from drifting away from the observed conditional defect. L_lap is a local Laplacian smoothing term in Eq. (3). We will explicitly define L_cond, L_lap, the complete optimization objective, and add the omitted hyperparameters as $lambda_i=0.1$ for all ODE steps and step size $\eta = 1 \times 10^{-3} $ in Sec. 3.【CAD Integration (R3.2)】. Since FDMMBone outputs an explicit continuous triangular mesh, it circumvents complex post-processing. The result can be directly exported as an STL/OBJ file and imported into standard medical CAD software (e.g., 3D Slicer, 3-matic) for non-manifold checking, Boolean validation, and rapid manufacturing preparation. 【Network Architecture (R1.3)】. We apologize for the misleading schematic in Fig. 1.The refinement network is indeed a U-Net architecture, not an MLP. We will update Fig. 1.【Baseline (R1.4,R2.1,R3.1,R2.2)】.We guarantee that all competing baselines were strictly retrained on our datasets using the identical train/test splits, preprocessing pipeline, and evaluation metrics. Regarding the suggested skull-specific baselines, they were not presented in the submitted manuscript due to the page limit. Since our evaluation covers multiple anatomical structures, in the previous version, we prioritized generally applicable 3D completion methods. We highly respect the suggested strong skull-specific baselines ([A] Wodzinski 25, [B] Wodzinski 24). In our preliminary comparison, [A] achieved DSC/bDSC/HD95/MMD of 0.916/0.924/1.80/0.201 on MedShapeNet, 0.919/0.922/1.77/0.207 on Mandibular, and 0.923/0.927/1.72/0.191 on SkullBreak. [B] achieved 0.922/0.920/1.74/0.193 on MedShapeNet, 0.918/0.924/1.79/0.210 on Mandibular, and 0.926/0.931/1.68/0.169 on SkullBreak. We will cite and compare these two methods in the revised (R1.4). Our model was trained for 33 hours on two NVIDIA A800 GPUs. During inference, generating a single implant takes approximately 2.9 seconds in total (R2.1). Among this runtime, the 200-step ODE solver takes the majority of the computation (approx. 2.1s), while the projection-correction and the subdivision-based refinement stage add a very lightweight overhead (approx. 0.8s combined) (R3.1). There is the ablation typo. Removing the conditional injection (A6) leads to the most significant performance drop (Table 2) (R2.2). We will incorporate the above clarifications and fix minor errors in the final version. We will add the missing citation (Lipman, 22), clarify assigning fixed $±1$ SDF values to avoid numerical artifacts. The ablations and robustness to noisy input will be discussed in the final version. We will provide a GitHub repository containing all our code.



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.

    Given the strong performance, broad multi-dataset evaluation, and novelty of applying flow matching in a DMTet/deformable mesh spac but issues on method clarity, reproducibility, fairness of baseline comparisons, and missing stronger skull-specific baselines, this submission requires a rebuttal. Please respond to the unclear DMTet fitting/parameterization details, projection-correction loss definition, refinement network architecture, missing implementation hyperparameters, whether all baselines were retrained under the same protocol, why stronger anatomy-specific baselines were omitted, and the practical issues of inference time and CAD/manufacturing integration

  • 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 work addresses an important anatomical shape completion problem and proposes a technically interesting framework that applies conditional flow matching in a deformable tetrahedral mesh representation, followed by a refinement stage for improved surface detail. The empirical results are strong across multiple datasets, and the evaluation includes comparisons to several recent methods as well as ablation studies supporting the main components. The remaining concerns about method clarity, implementation details, projection-correction losses, DMTet fitting, and ablation interpretation should be addressed carefully in the final version to improve reproducibility and presentation.



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.

    Although some concerns remain regarding methodological clarity, implementation details, ablation interpretation, the paper presents a technically sound and interesting approach that combines flow matching with deformable tetrahedral meshes, demonstrates strong quantitative and qualitative performance against multiple recent baselines, and addresses a relevant bone reconstruction problem. Therefore, the AC recommends 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.

    Accept

  • Please justify your recommendation.

    This paper presents a technically interesting and clinically relevant approach to 3D bone defect completion, with strong empirical performance across multiple datasets. Although Reviewer #1 raised substantial concerns about clarity and reproducibility, the rebuttal addresses many of the major issues, including the DMTet parameterization, loss definitions, refinement architecture, baseline retraining, and runtime. The authors also promised that they will provide a GitHub repository containing all the code after acceptance. Overall, I believe the paper’s motivation, method design, and experimental evidence are sufficiently sound, and I am inclined to accept it.



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