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Abstract
Thin vessel segmentation is challenging, where distinguishing between background artifacts and vessel-like structures is ambiguous. Recently, diffusion models have emerged as good candidates for vessel segmentation but they suffer from tens of iterations and stochastic noisy components. To overcome this, we formulate vascular segmentation as a binary iterative flow matching method named as Binary Flow Matching (BFM). BFM models segmentation updates as deterministic velocity fields in a Bernoulli parameter space, enabling stable refinement without iterative Gaussian noise injection. Through x1-parameterization, BFM directly predicts the final clean mask at each timestep, allowing supervision with segmentation-specific losses. In addition, we adopt straight-path regularization to enforce consistent update trajectories. Across three X-ray coronary angiography datasets, BFM achieves the best or highly competitive performance compared with single-pass discriminative models and diffusion-based approaches such as BerDiff in Dice, clDice, and Betti-0 error, while requiring only 5-10 iterative steps compared to 50-step diffusion sampling. These results demonstrate that BFM offers a more efficient and topology-preserving alternative to stochastic diffusion for vascular segmentation. Source code is available at https://github.com/YongjunKim98/BFM.
Links to Paper and Supplementary Materials
Main Paper (Open Access Version): https://papers.miccai.org/miccai-2026/paper/1869_paper.pdf
SharedIt Link: Not yet available
SpringerLink (DOI): Not yet available
Supplementary Material: Not Submitted
Link to the Code Repository
https://github.com/YongjunKim98/BFM
Link to the Dataset(s)
XACV dataset: https://kirito878.github.io/DeNVeR/
DCA1 dataset: https://www.kaggle.com/datasets/bard2024/database-x-ray-coronary-angiograms-dca1
SBCD dataset: https://huggingface.co/datasets/xinaloha/UniVG
BibTex
@InProceedings{KimYon_Improved_MICCAI2026,
author = { Kim, Yongjun AND Jin, Kyong Hwan AND Han, Yoseob AND Ryu, Kanghyun},
title = { { Improved Vascular Segmentation via Binary Flow Matching with Straight-Path Regularization } },
booktitle = {Medical Image Computing and Computer Assisted Intervention -- MICCAI 2026},
year = {2026},
publisher = {Springer Nature Switzerland},
volume = {LNCS 16883},
month = {September},
page = {pending}
}
Reviews
Review #1
- Please describe the contribution of the paper
The paper presents Binary Flow Matching (BFM), a segmentation framework that models capillary segmentation as a deterministic probability flow in Bernoulli space and predicts the clean segmentation mask through an x1-parameterized formulation. To improve stability in low-step inference, the method further introduces a straight-path regularization term to constrain the sampling trajectory. Experimental results on three X-ray coronary angiography datasets show that the method performs favorably against both discriminative segmentation models and Bernoulli diffusion baselines in terms of Dice, clDice, and Betti-0 error, while requiring substantially fewer sampling steps.
- Please list the major strengths of the paper: you should highlight a novel formulation, an original way to use data, demonstration of clinical feasibility, a novel application, a particularly strong evaluation, or anything else that is a strong aspect of this work. Please provide details, for instance, if a method is novel, explain what aspect is novel and why this is interesting.
1.The work tackles a practically important and technically difficult segmentation problem. Preserving the topology of thin vascular structures remains a nontrivial challenge, and the manuscript addresses this issue directly rather than focusing only on region overlap metrics. 2.Modeling segmentation as deterministic flow in Bernoulli space, together with direct x1-prediction, is a reasonable alternative to conventional diffusion-style noise prediction and appears better aligned with the target of binary segmentation. The straight-path regularization is a sensible design choice, and the reported performance under 5–10 sampling steps suggests that the method may offer a useful efficiency–accuracy tradeoff compared with iterative 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.
1.While the manuscript provides the high-level framework and update equations, several implementation details that are important for interpretation and reproduction are missing or insufficiently specified. These include the architecture of the core network, the design of the time encoding, the fusion mechanism between the input image and the binary state, the number of sampling steps used during training, and the inference protocol, including whether repeated sampling and averaging are used. The manuscript states that all competing methods were trained under the same optimization protocol using a Dice+BCE loss. While such a unified setting may simplify comparison for standard discriminative segmentation models, it is less clear that this is appropriate for methods such as SegDiff, MedSegDiff, BerDiff, and FlowSDF, whose original formulations rely on different objectives and training mechanisms. Replacing their native objectives with a segmentation loss may substantially alter their behavior, and therefore the current comparison may not fully reflect the actual strength of these baselines under their intended settings. 4.Statements such as outperforming all baselines or demonstrating strong generalization ability would be more convincing if phrased with greater caution, especially given the current experimental scope. 5.The manuscript defines pt as a continuous Bernoulli probability field and xt as a discrete binary sampled state. However, the initialization sets p0=x0, which appears to directly equate a continuous quantity with a discrete one. This point is likely fixable, but the current presentation is not sufficiently precise and may confuse readers.
- 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 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
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?
This manuscript studies an important and challenging task and presents a method with a reasonable degree of novelty. The reported empirical results are encouraging, particularly in the low-step inference setting. However, in its current form, the paper still has notable weaknesses in methodological transparency, baseline fairness, and the depth of analysis.
- Reviewer confidence
Very confident (4)
- [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 author’s rebuttal answers my question to some extent, hoping that the previous shortcomings will be corrected in the final revision.
Review #2
- Please describe the contribution of the paper
This paper proposes a multi-step refinement framework that iteratively updates the probability map. By adopting a flow-matching formulation under a straight-path trajectory assumption, the method derives an optimized loss function that enables the model to achieve accurate segmentation with fewer inference steps.
- Please list the major strengths of the paper: you should highlight a novel formulation, an original way to use data, demonstration of clinical feasibility, a novel application, a particularly strong evaluation, or anything else that is a strong aspect of this work. Please provide details, for instance, if a method is novel, explain what aspect is novel and why this is interesting.
1.The model does not explicitly learn a velocity field; instead, it derives it analytically under a straight-path assumption and uses it to regularize the training objective; 2.The method adopts a multi-step refinement strategy, progressively improving the segmentation probability map; 3.Compared to diffusion-based segmentation approaches, the proposed method is deterministic and achieves improved results through iterative refinement.
- 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 proposed method is not strictly a flow matching approach. In standard flow matching, the model explicitly learns a velocity field that governs the evolution of the probability distribution, enabling flexible and potentially complex trajectories. In contrast, BFM derives the velocity analytically under the straight-path assumption, thereby constraining the evolution to a predefined linear trajectory. This design may sacrifice the expressive power of flow matching in modeling complex refinement dynamics. The paper should explicitly discuss this limitation and clarify the associated trade-off between stability and expressiveness. 2.The proposed method is fundamentally different from diffusion-based segmentation approaches. While the paper draws comparisons to diffusion models and occasionally adopts similar terminology, the method itself does not follow a stochastic diffusion process. Instead, it performs deterministic multi-step refinement starting from an initial noisy mask. The current presentation may be confusing and could mislead readers into interpreting the method as a variant of diffusion. The authors should revise the description to more clearly distinguish their approach from diffusion frameworks. 3.The qualitative results shown in Figure 3 may be potentially misleading. While the highlighted regions demonstrate favorable performance, there are noticeable errors in finer vascular branches that are not discussed or visualized. The current visualization selectively emphasizes strong cases while overlooking failure regions, potentially biasing the interpretation of the results. A more balanced qualitative analysis, including representative failure cases, would improve the credibility of the evaluation. 4.Figure 1 is somewhat ambiguous and may lead to misinterpretation. In particular, the top-left illustration does not clearly convey the multi-step refinement of the probability map; instead, it resembles a diffusion-like process. This visualization could confuse readers regarding the underlying mechanism. The figure should be revised to more explicitly illustrate the iterative refinement process and to clearly differentiate it from diffusion-based pipelines.
- 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 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
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?
Overall, while the paper presents an efficient multi-step refinement framework for segmentation, its conceptual formulation is not entirely clear. The method deviates from standard flow matching by deriving, rather than learning, the velocity field under a straight-path assumption, which may limit its expressiveness but is not sufficiently discussed. In addition, the presentation blurs the distinction from diffusion-based methods, potentially causing confusion. Finally, the qualitative evaluation and figures are somewhat selective and unclear, which affects the credibility and interpretability of the results.
- Reviewer confidence
Very confident (4)
- [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 does not sufficiently address my core concerns. As mentioned in my original review, the overall presentation of the paper is highly misleading. Many descriptions strongly suggest that this is a diffusion-based method, while in fact the connection to diffusion is rather limited. The current framing and terminology are therefore inappropriate and may confuse readers regarding the actual technical contribution.
In addition, the paper still lacks comparisons with several important and relevant baselines. The authors themselves acknowledged in the rebuttal that additional baselines should be included, which would require substantial revisions to both the experimental section and the overall positioning of the work.
Another concern is the inconsistency regarding the role of the proposed “straight-path regularization.” In the paper, this component is emphasized as an important part of the method and motivation, whereas in the rebuttal the authors downplay its significance. This inconsistency further weakens the clarity and credibility of the presentation.
Overall, while the rebuttal clarifies some implementation details and wording issues, it does not fundamentally resolve the concerns about the paper’s framing, experimental completeness, and conceptual consistency. Therefore, I do not believe the paper is ready for publication in its current form.
Review #3
- Please describe the contribution of the paper
The paper proposes binary flow matching, which si a flow-based refinement framework that models segmentation as deterministic transport in Bernoulli space. The method predicts clean masks at each timesteop and enforce linear trajectories. It achieves superior topology preservation and efficiency compared to previous segmentation and 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.
(1) Harnessing flow matching and transferring it to binarized scenarios is both meaningful and straightforward. Previous diffusion-based segmentation methods are notorious for unstable and indirect refinement.
(2) The straight-path regularization effectively linearizes the probability flow, allowing the model to produce high-quality results in only 5–10 steps, compared to the 50 steps typically required by diffusion models like BerDiff.
(3) The performance gains are consistent across multiple imaging protocols and institutions, indicating strong generalization capabilities.
- 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) Betti-0 specifically counts connected components. The paper does not report Betti-1 error, which would measure the model’s ability to correctly preserve “loops” or “holes” in the vascular network.
(2) The paper does not demonstrate how BFM handles 3D volumes, which is the industry standard for many vascular interventions.
- 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
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?
A timely improvement and interesting finding for vessel segmentation.
- 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 okay with the response.
Author Feedback
We appreciate the positive assessments and address the remaining concerns below. To R1 – Implementation details, baseline fairness, claims, and notation. We appreciate the constructive comments on reproducibility and baseline fairness. BFM uses the U-Net backbone adopted from MedSegDiff. The input image and binary state are encoded separately, Fourier encoded, and fused at each encoder stage. For time conditioning, we sample t uniformly from [0,1], rescale it to the diffusion-style timestep range, encode it with sinusoidal positional embedding followed by a two-layer MLP, and inject it into ResNet blocks using scale-shift modulation. During training, timesteps are randomly sampled from [0,1]; inference uses fixed Euler steps. We did not replace all generative baselines with the same BCE+Dice loss. Diffusion/flow-based methods were trained with their intended objectives: SegDiff, MedSegDiff, and FlowSDF used their original MSE-based noise/velocity objectives, while BerDiff used binary cross-entropy as in its Bernoulli formulation. BCE+Dice was used for conventional discriminative segmentation baselines. We will revise overly strong claims such as “outperforming all baselines” and “strong generalization” to more cautious phrasing. Moreover, we acknowledge that notation for p₀=x₀ was imprecise. Initialization should be written as p₀=0.5 and x₀~Bernoulli(p₀). To R2 – Method identity, relation to diffusion, and figures. We thank the reviewer for recognizing the value of multi-step probability-map refinement and the efficiency of the proposed method. BFM does not derive the velocity field from a “straight-path assumption”. The velocity field is learned through the network, but we use an x₁-parameterized training objective rather than a velocity-MSE objective. Our method implies that directly supervising the predicted clean binary mask with BCE+Dice is better aligned with the discrete Bernoulli target than regressing a continuous velocity target from binary states. This is consistent with recent clean-target parameterizations in generative modeling [18] showing that predicting clean data can be a strong alternative to noise/velocity prediction. “Straight-path Regularization” is an additional term that encourages BFM to learn straighter trajectories. Diffusion models and flow matching share the general view of iterative generative refinement, but differ in their dynamics: diffusion typically relies on reverse SDE/denoising dynamics, whereas flow matching learns ODE-type transport dynamics, as formulated by Lipman et al. [13]. Thus, we compare with diffusion models as related iterative refinement methods, not as a diffusion variant. Also, BFM is not purely deterministic, since the binary state is re-sampled from the Bernoulli probability map at each step. Fig. 3 was intended to illustrate typical structural errors observed in competing methods rather than to claim that BFM resolves all fine-branch errors. The qualitative examples align with quantitative results (Dice: 0.86±0.04, clDice: 0.86±0.04, Betti-0: 3.3±2.4), while residual errors in distal or very thin vessels may still remain. Fig. 1 provides a high-level conceptual overview of BFM, showing iterative refinement from a random binary state to the final segmentation under image conditioning. The detailed probability-map update and Bernoulli re-sampling procedure are specified in the Method section and Algorithm. To R3 – Betti metrics and 3D extension We thank the reviewer for the positive and constructive assessment. We reported Betti-0 because disconnection and branch fragmentation dominate 2D coronary angiography. We agree that Betti-1 is also meaningful for evaluating loops or holes in vascular networks, and will discuss this as future work. Our current study focuses on 2D X-ray coronary angiography, where the proposed Bernoulli flow formulation was validated across multiple datasets. Extension to 3D is feasible but requires separate validation and is left as future work.
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.
Please try to address the pointed weaknesses during the rebuttal.
- After you have reviewed the rebuttal and updated reviews, please provide your recommendation based on all reviews and the authors’ rebuttal.
Reject
- Please justify your recommendation.
The initial reviews raise concerns regarding the implementation details and the experimental results. After reading the rebuttal, the reviewers are still concerned that the current framing and terminology are therefore inappropriate and may confuse readers regarding the actual technical contribution. Thus, I recommend rejecting this submission.
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.
Majority of reviewers agree that this work is a meaningful contribution. Experimental results seem convincing and the methodology and application scenario are novel and challenging. Concerns by one reviewer are noted and should be incorporated by attempting to tone down the description of the contribution in a final manuscript if accepted. Overall, I tend to accept this paper since it might be of interest to be discussed within the MICCAI community.
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 addresses an important problem in topology-preserving vascular segmentation and proposes a novel Binary Flow Matching (BFM) framework with straight-path regularization. Reviewers generally found the method technically sound, well motivated, and supported by strong empirical results, particularly in the low-step inference setting. One reviewer remained concerned about the paper’s framing and presentation. While these concerns are valid, they primarily relate to clarity and positioning rather than the core technical contribution. Therefore, I recommend to accept the paper.