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Abstract

Accurate segmentation of vascular networks from sparse CT scan slices remains a significant challenge in medical imaging, particularly due to the thin, branching nature of vessels and the inherent sparsity between imaging planes. Existing deep learning approaches, based on binary voxel classification, often struggle with structural continuity and geometric fidelity. To address this challenge, we present VesselSDF, a novel framework that leverages signed distance fields (SDFs) for robust vessel reconstruction. Our method reformulates vessel segmentation as a continuous SDF regression problem, where each point in the volume is represented by its signed distance to the nearest vessel surface. This continuous representation inherently captures the smooth, tubular geometry of blood vessels and their branching patterns. We obtain accurate vessel reconstructions while eliminating common SDF artifacts such as floating segments thanks to our adaptive Gaussian regularizer which ensures smoothness in regions far from vessel surfaces while producing precise geometry near the surface boundaries. Our experimental results demonstrate that VesselSDF significantly outperforms existing methods and preserves vessel geometry and connectivity, enabling more reliable vascular analysis in clinical settings.



Links to Paper and Supplementary Materials

Main Paper (Open Access Version): https://papers.miccai.org/miccai-2025/paper/2121_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)

IRCADb1: https://www.ircad.fr/research/data-sets/ Medical Segmentation Decathlon (MSD): http://medicaldecathlon.com/

BibTex

@InProceedings{EspSal_VesselSDF_MICCAI2025,
        author = { Esposito, Salvatore AND Rebain, Daniel AND Onken, Arno AND Li, Changjian AND Mac Aodha, Oisin},
        title = { { VesselSDF: Distance Field Priors for Vascular Network Reconstruction } },
        booktitle = {proceedings of Medical Image Computing and Computer Assisted Intervention -- MICCAI 2025},
        year = {2025},
        publisher = {Springer Nature Switzerland},
        volume = {LNCS 15961},
        month = {September},
        page = {674 -- 683}
}

Reviews

Review #1

  • Please describe the contribution of the paper

    This paper presents a signed distance field (SDF) refiner as a second-stage module to mitigate floating artifacts in hepatic vessel modeling. Gaussian regularization is incorporated into the SDF refinement to enforce geometric smoothness. Experiments on two hepatic vessel datasets demonstrate the effectiveness of the SDF module in improving reconstruction quality.

  • 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.

    This paper improves upon the original SDF loss function [7] for implicit shape modeling and adapts it for vessel shape reconstruction in CT scans, thereby enhancing the generalization ability of this smooth representation framework.

    The paper is well organized and easy to follow, the representation is clear to illustrate the core method or experiments.

  • 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.

    My major concern lies in:

    1. The proposed Gaussian regularization in Eq. (8) appears functionally similar to the surface regularization in Eq. (9), which has been previously defined in [7] and widely adopted as part of standard SDF constraints. However, Eq. (9) is defined over the entire domain $\Omega$, potentially including true boundary regions. Should this term instead exclude regions near the true surface, where suppression might erroneously penalize valid structures?
    2. A more critical concern lies in the design of the Gaussian regularization, which does not incorporate any ground-truth constraint. How can the method ensure that all floating components it suppresses are indeed false positives, rather than disconnected true positives? This is particularly relevant in vessel segmentation tasks, where discontinuities are common from the binary occupancy network. Some floating structures may actually correspond to anatomically valid but disconnected vessel segments. How does the proposed regularization avoid erroneously removing such true positives?
    3. The SDF refiner does not share gradients with the occupancy network, effectively decoupling the two stages. This design suggests that the proposed SDF refinement could function as a plug-and-play module applicable to other segmentation backbones, such as nnU-Net [9] or 3D SA-UNet [8]. This is particularly relevant in light of the experimental results, where nnU-Net achieves comparable volumetric performance to VesselSDF. Whether VesselSDF offers consistent improvement when used as a post-processing module for these baselines?
    4. Furthermore, the current experimental section lacks explicit evidence demonstrating which artifacts or floating segments are suppressed by the SDF refiner. Are the removed components predominantly false positives, or do they also include disconnected true positives introduced by the binary occupancy stage? A visual or statistical analysis of the specific corrections made by the SDF stage would greatly strengthen the claims.

    Minor concern: The paper exclusively evaluates VesselSDF on hepatic vessels. Given this focus, the title “VesselSDF” may overstate the generalizability of the proposed approach to other vascular structures. The paper claims to reconstruct vascular structures from sparse CT scans, which is an important and clinically relevant objective. However, the current experimental results do not explicitly simulate or evaluate performance under varying degrees of sparsity.

  • Please rate the clarity and organization of this paper

    Satisfactory

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

    The submission does not provide sufficient information for reproducibility.

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

    N/A

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

    (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 lack of clear methodological descriptions, along with the absence of direct experimental evidence supporting key claims, limits the ability to fully assess the effectiveness of the proposed approach. These concerns have impacted the overall evaluation score.

  • 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 regularizer (Eq. 8 & Eq. 9) has been widely adopted in SDF-based implicit representations to penalize off-surface points and encourage near-zero SDF values, as demonstrated in prior work such as [S1]. However, the authors do not provide sufficient clarification regarding the specific types of artifacts or floating segments that are mitigated by the SDF refiner. It remains unclear whether the removed components are primarily false positives, or if they also include disconnected true positives introduced during the binary occupancy stage. Moreover, the rebuttal fails to clarify these methodological aspects. The lack of direct experimental evidence supporting the key claims further limits the ability to rigorously evaluate the effectiveness of the proposed approach.

    [S1]Sitzmann V, Martel J, Bergman A, et al. Implicit neural representations with periodic activation functions[J]. Advances in neural information processing systems, 2020, 33: 7462-7473.



Review #2

  • Please describe the contribution of the paper

    The paper presents a method for vessel segmentation from few-slice CT images using a combination of a binary occupancy segmentation and a signed distance field based refinement stage. The paper further presents an adaptive Gaussian regularizer, aiming to enforce smoothness and reduce the number of disconnected components, while maintaining fine vessel geometry.

  • 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.

    a. The problem is well motivated and prior art well documented - the paper is in general well written.

    b. The ablation study demonstrates the effectiveness of using a two-stage approach with separate binary occupancy segmentation and SDF refinement.

    c. The method is evaluated both quantitatively and qualitatively and demonstrates improvement in comparison to state of the art.

  • 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.

    a. The gaussian loss is presented as one of the major contributions of the proposed method. The ablation study in Table 2 however shows none (or very limited) improvement in segmentation accuracy by incorporating this loss.

    b. The SDF-refinement network is not described. It is unclear to me if it is a continuous MLP/SIREN type of decoder or a voxel-based CNN-like network. Similarly the construction of the training data is limited. This also goes for the loss-functions are they calculated based on continuous points or on the input image grid?

    c. What resolution is used for evaluating the proposed method and the baselines? The proposed method inputs a 512x512x16 image and extracts the output meshes from a SDF with a resolution of 512^3. How is this resolution achieved and is this comparable to what is done for the baselines?

    d. The two networks are trained jointly, but the gradient is detached. There is no motivation given for why this is preferred over a two-step approach training first the occupancy and then the refinement.

    e. How are the hyperparameters (i.e. Weightings of the loss functions) decided? The used weights for lambda_s, lambda_o og lambda_r are not given, which makes it difficult to judge which parts of the loss function that drives the learning.

  • Please rate the clarity and organization of this paper

    Satisfactory

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

    The submission does not provide sufficient information for reproducibility.

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

    a. Some parameters are not introduced (i.e. Theta_o, L_eik, L_occ, etc.). While some of them are easy to guess, it is good practice to introduce all parameters and abbreviations.

    b. The authors could for future work consider including the number of connected components as an evaluation metric - maybe this can show the benefit of the gaussian regularization.

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

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

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

    The presented work aims to solve an important problem and demonstrates that the method can achieve good results. There are however some questions regarding the implementation and evaluation that makes it difficult to fully asses the work.

  • 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 methodological novelty of the paper is limited, but I recognize the need for specialized methods for segmenting thin vessels from sparse-slice images. The method is sound and evaluated reasonably and I therefore think we can consider accepting the paper.



Review #3

  • Please describe the contribution of the paper

    This paper proposes a supervised learning method for vessel segmentation and reconstruction. Unlike previous approaches that regress binary occupancies, the proposed method predicts continuous SDF values, offering a more accurate representation of thin vascular structures. Additionally, the authors introduce novel regularization techniques to enhance smoothness and reduce artifacts. Experimental results demonstrate that the proposed approach outperforms existing methods both quantitatively and qualitatively.

  • 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. This paper proposes an interesting idea: predicting signed distance functions (SDFs) instead of binary labels for vessel segmentation. By leveraging the smoother geometric representation of SDFs, the method enables more accurate modeling of thin vascular structures. Additionally, the paper introduces innovations such as a two-stage network and Gaussian regularization to further enhance performance.
    2. Experimental results show that the proposed VesselSDF method outperforms previous approaches.
    3. The paper is well-structured, featuring a solid literature review, clear writing, and effective visualizations.
  • 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 idea of predicting signed distance functions (SDFs) instead of occupancy is not new in RGB-based surface reconstruction (e.g., NeuS, NeurIPS 2021), which somewhat diminishes the originality of the method. Nevertheless, I acknowledge the meaningful methodological contribution in the medical imaging domain.
    2. The two-stage pipeline lacks sufficient clarification. Based on Eq 3 (detach…), it appears that the occupancy network is first trained, and then the SDF refiner. However, Figure 1 and Section 3.4(Eq.4) suggest that both networks are jointly trained, leading to some confusion.
    3. Although the authors mention downsampling and upsampling operations in Section 3.2, these components are not clearly reflected in the method design.
    4. Given that the method includes two large 3D U-Nets, a discussion of the hardware requirements and computational cost is expected but currently missing from the paper.
  • 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.

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

    The term BCE loss in Figure 1 is not mentioned or explained in the main text. I assume it refers to the occupancy loss?

  • 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 — could be 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 proposes an SDF-based method for vessel segmentation and reconstruction. While the overall design may not be entirely novel, the authors clearly articulate the motivation behind their approach, which I find to be a meaningful contribution. The experimental results demonstrate the effectiveness of the proposed method. [–] Some important details are missing, particularly regarding the training procedure and hardware requirements.

  • 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 have adequately addressed my concerns. I therefore recommend acceptance.



Author Feedback

We thank the reviewers for their feedback.

[R1-a/R2] Gaussian regularisation and disconnected vessel segments. Our approach differs significantly from [7] in both form and function: (1) The Gaussian regularizer (Eq. 8) is distance-weighted (scales with |f_SDF(x)|), while [7] applies uniform Eikonal constraints; (2) Our surface regularization (Eq. 9) specifically prevents spurious surfaces between sparse CT slices where no supervision exists, addressing a different problem than [7]; (3) Our two-stage pipeline ensures vessel regions are identified first under supervision, before regularization refinement. These regularizers serve complementary purposes: Eq. 9 prevents false surfaces in gaps, while Eq. 8 ensures smooth level sets with distance-adaptive strength. With the Gaussian regularizer, surface metrics improve (Chamfer: -2.9%, Hausdorff: -4.7%) while maintaining Dice score (0.72). Component analysis shows it eliminates 41 floating artifacts per volume while preserving all ground truth vessel segments, demonstrating it correctly distinguishes between artifacts and true disconnected vessels.

[R2-4] Evidence of artifact suppression.
We have extensive qualitative comparisons showing the Gaussian regularizer’s effect, which have been omitted due to space in the original draft. We will include examples in the revised text. In addition, connected-component analysis, quantifying the specific floating artifacts removed, will also be included.

[R1-b/R3] SDF refiner architecture.
Sec. 3.3 describes the SDF refiner as “a 3-level encoder-decoder 3D U-Net with attention gates”. All loss terms in Eq. 4 are computed on the full 3D grid (including axial dimension), ensuring proper volumetric supervision rather than slice-wise processing. The network is regressing the signed distance to the surface. We will update this description in the paper to make this clear.

[R1-c] Evaluation resolution comparison.
VesselSDF takes as input full volume slices of 512×512×16. At inference, we query the learned SDF on an isotropic 512^3 grid via trilinear interpolation and extract meshes using Marching Cubes. Baselines extract meshes at the same 512^3 resolution for fair comparison.

[R1-d/R2] Gradient detaching vs joint training.
Eq. 3 prevents SDF constraints from destabilising the occupancy decoder. Our ablations show that gradient detachment improves all metrics (Dice: +0.03, CD: -20%, HD: -21%). This occurs because the networks optimise different objectives: binary classification vs. continuous distance fields with geometric constraints. The refiner could potentially be a plug-and-play module as R2 suggests - we agree this is promising for future work.

[R1-e] Hyperparameter selection.
We will include all hyperparameters in the camera-ready version: λ_g=0.1, λ_s=0.1, λ_e=0.01, λ_o=0.01, and λ_r=0.1.

[R2-minor] Generalisability & title.
Our two public datasets have a range from 3 to 5 mm slice spacing, precisely the “sparse slice” scenario that the paper targets. We agree that the current scope is hepatic vessels, however, we also have qualitative and quantitative results on different organs, such as the liver (IRCADb in Table 1), that show our superior reconstruction performance and were omitted due to space constraints. We will update the text to reflect these comments.

[R3-1] Novelty wrt RGB SDF work.
NeuS/VolSDF overfit single scenes via a volume-rendering ray tracing approach. In contrast, our VesselSDF approach is the first multi-scene continuous SDF regressor for sparse medical data and introduces a distance-adaptive Gaussian prior that directly tackles floating artifacts - neither appears in prior vision work.

[R3-4] Hardware & runtime. We train on a single NVIDIA RTX 4090 GPU (24GB) in approximately 9 hrs. Inference requires 5 mins per volume, including all processing steps and Marching Cubes mesh extraction. For comparison, nnU-Net inference takes 8 mins per volume on the same hardware.



Meta-Review

Meta-review #1

  • Your recommendation

    Invite for Rebuttal

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

    N/A

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

    Accept

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

    N/A



Meta-review #2

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

    Accept

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

    N/A



Meta-review #3

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

    Accept

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

    I find the formulation of vessel segmentation as a continuous SDF regression problem to be novel and interesting and therefore recommend acceptance overall.



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