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Abstract

Promoting the connectivity of curvilinear structures, such as neuronal processes in biomedical scans and blood vessels in CT images, remains a key challenge in semantic segmentation. Traditional pixel-wise loss functions, including cross-entropy and Dice losses, often fail to capture high-level topological connectivity, resulting in topological mistakes in graphs obtained from prediction maps. In this paper, we propose CAPE (Connectivity-Aware Path Enforcement), a novel loss function designed to enforce connectivity in graphs obtained from segmentation maps by optimizing a graph connectivity metric. CAPE uses the graph representation of the ground truth to select node pairs and determine their corresponding paths within the predicted segmentation through a shortest-path algorithm. Using this, we penalize both disconnections and false positive connections, effectively promoting the model to preserve topological correctness. Experiments on 2D and 3D datasets, including neuron and blood vessel tracing demonstrate that CAPE significantly improves topology-aware metrics and outperforms state-of-the-art methods.

Links to Paper and Supplementary Materials

Main Paper (Open Access Version): https://papers.miccai.org/miccai-2025/paper/4309_paper.pdf

SharedIt Link: Not yet available

SpringerLink (DOI): Not yet available

Supplementary Material: Not Submitted

Link to the Code Repository

https://github.com/NeuraVisionLab/CAPE

Link to the Dataset(s)

CREMI: https://cremi.org/data/ DRIVE: https://drive.grand-challenge.org

BibTex

@InProceedings{EsmEly_CAPE_MICCAI2025,
        author = { Esmaeilzadeh, Elyar AND Garaaghaji, Ehsan AND Hallaji Azad, Farzad AND Oner, Doruk},
        title = { { CAPE: Connectivity-Aware Path Enforcement Loss for Curvilinear Structure Delineation } },
        booktitle = {proceedings of Medical Image Computing and Computer Assisted Intervention -- MICCAI 2025},
        year = {2025},
        publisher = {Springer Nature Switzerland},
        volume = {LNCS 15971},
        month = {September},
        page = {183 -- 193}
}

Reviews

Review #1

Please describe the contribution of the paper

This paper proposes a differentiable loss computation method tailored for curve structures, enhancing the connectivity of curves by incorporating such a loss. The method relies on calculating the shortest topological path length between connected points on the skeleton of the ground truth, and applies Dijkstra’s algorithm to compute the cost of the predicted paths, thereby specifically strengthening the connectivity of the structures. The approach is designed for both 2D and 3D scenarios, with experiments conducted to demonstrate its effectiveness. It provides valuable insights into the optimization of curve structures.
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.
Focusing specifically on the challenges of curve structures, this work identifies their distinct characteristics compared to other types of structures and accordingly designs a specialized loss function, CAPE.
1. This loss optimizes topological correctness by comparing the shortest paths between ground truth and predictions using Dijkstra’s algorithm, penalizing disconnected predictions. 2.Experimental results demonstrate clear advantages in topology-aware performance. 3.Inspired by APLS, the authors further propose a differentiable implementation of this concept.
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 experimental results are unconvincing, showing no significant improvement compared to the listed baselines (with slight wins and losses, and the differences are marginal).
2. The degree of innovation is limited. The proposed loss is added on top of the standard MSE loss, and the actual improvement brought by this design is limited, despite being specifically targeted for the problem. (Refer to the following two papers for comparison: (1) Topology-Preserving Deep Image Segmentation (2019); (2) BuyTheDips: PathLoss for improved topology-preserving deep learning-based image segmentation (2022)).
3. The 2D visualization results fail to demonstrate the actual superiority of the method. In Figure 3, the second-row fundus image shows that the proposed method introduces more false signals compared to other methods (for example, a bifurcation appears at the left end of a vessel slightly below the center, which does not appear in the results of other methods).
4. The results on 3D data are not presented, and the method performs worse than others in pixel-wise metrics. In my view, post-processing approaches may be more effective and targeted than innovations purely at the loss function level.
5. The dataset size is limited. With a larger amount of data, conventional pixel-level losses might be sufficient to optimize these problems.
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.
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?

Innovation and experimentation are limited, and there is almost only one innovation, the loss design, and it does not show a clear advantage over the baseline. Although the author’s motivation is clear and justified.
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 loss presented in the article provide some degree of improvement in connectivity, but still do not achieve breakthrough segmentation performance improvements. While it is true that connectivity considerations are important in the field of curved structures, as stated by the authors, the contribution of the achieved enhancement is still insufficient for publication in MICCAI. However, it is worth recognizing that this is a meaningful direction, and the authors are very much looking forward to the article after conducting more refined as well as comprehensive experiments.

Review #2

Please describe the contribution of the paper

This paper focuses on preserving connectivity of curvilinear structures for medicinal applications. To achieve this, the authors proposes a loss that aims to optimize a graph connectivity metric. The experiment on 2D and 3D medical datasets shows the advantage of the proposed method.
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 integration of Average Path Length Similarity into Curvilinear Structure segmentation for preserving topology connectivity is reasonable.
2. The proposed method can serve as a plug-and-play component and can be used in other tasks.
3. Evalutation on both 2D and 3D tasks is compresnive.
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. It is unclear how to construct a graph for both the GT and the predicted mask. Suppose the predicted mask is the worst, and even with all the background, there might not be a graph. Considering this, how can we perform Connectivity-Aware Path Enforcement?
2. In metrology, more discussion on how to convert non-differentiable APLS into differentiable APLS is necessary. In the current version, it is hard to get this point.
3. The choice of different backbones will be more helpful, such as ViT, Mamba, etc.
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.
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.

(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?

Overall, this paper presents a new solution for preserving the connectivity of curvilinear structures for medicinal applications. However, the details and discussion on how to convert non-differentiable APLS into differentiable APLS are necessary.
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.

After reading other reviews and the authors’ rebuttal, I think this paper’s novelty can meet the high standard of MICCAI. The proposed loss optimizes topological correctness by comparing the shortest paths between ground truth and predictions using Dijkstra’s algorithm. This seems novel to me. Meanwhile, the high performance gain on topology-aware metrics shows the superiority of the proposed method. In this regard, I think this paper can be accepted. Nonetheless, I would not defend its rejection.

Review #3

Please describe the contribution of the paper

The main contribution of the paper is the introduction of a novel loss function, CAPE (Connectivity-Aware Path Enforcement), which improves the segmentation accuracy of curvilinear structures such as neuronal processes and blood vessels. Unlike conventional pixel-wise loss functions that often fail to preserve topological connectivity, CAPE is specifically designed to enforce path continuity—an essential factor in biomedical image analysis. The method is intuitive, well-motivated, and addresses a known limitation in the field. While similar goals have been pursued in prior work, this paper’s approach is distinguished by its simplicity and effectiveness, making it a timely and valuable contribution.
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 introduces a new loss function, Connectivity-Aware Path Enforcement (CAPE), which is specifically designed to address a well-known limitation in biomedical segmentation—preserving topological connectivity in curvilinear structures such as neuronal processes and blood vessels. This focus on connectivity, rather than pixel-level accuracy alone, represents a meaningful advancement.
Please list the major weaknesses of the paper. Please provide details: for instance, if you state that a formulation, way of using data, demonstration of clinical feasibility, or application is not novel, then you must provide specific references to prior work.
Major comments:
1. The network is trained to predict a distance map rather than a binary segmentation. This design choice is interesting but lacks references or discussions that justify its effectiveness. Please consider citing relevant prior work or including an explanation in the methodology section.
2. In Table 1, it is unclear whether the method labeled “CAPE” refers to using the CAPE loss alone or in combination with MSE loss, as defined in the total loss function. If MSE was used alongside all loss functions for training (as suggested in the Method section), this should be clearly stated either in the table caption or in the experimental setup description. Otherwise, the results may be misleading. In such a case, it may also be more appropriate to relabel the method as “Ours” instead of “CAPE,” since the comparison would not reflect a pure ablation of CAPE loss. Overall, clarification is needed to understand the setup under which each result in the table was obtained.
3. The paper focuses on evaluating segmentation performance, but the quality of the predicted distance map itself is not quantitatively assessed. Since the method relies on distance prediction, a statistical or visual analysis (e.g., MSE to ground truth, smoothness, histogram comparison) would strengthen the empirical validity.
4. Figure 3 only shows binary masks. A side-by-side comparison of predicted distance maps and ground-truth distance maps would offer insight into how accurately the network captures the shape and continuity of structures.
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 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
Minor comments:
1. Since the network predicts a distance map, it’s unclear how segmentation masks (as shown in Figure 3) were obtained from those predictions. Was thresholding applied? Or perhaps morphological filtering? A brief description of this post-processing step is important for clarity and reproducibility.
2. In Figure 3, red arrows indicate regions that are disconnected in other methods but successfully connected using CAPE. This is an important qualitative result and should be explicitly described in the figure caption or main text.
3. Since the datasets used are relatively small, it would be appropriate to include a comment in the discussion or future work section indicating that further validation on larger datasets is necessary.
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 gave this paper a score of 5 (Accept) because it presents a timely and technically sound contribution to the field of biomedical image segmentation, particularly in the context of curvilinear structures where topological connectivity is critical. The proposed CAPE loss introduces a novel way of directly enforcing path connectivity using a differentiable shortest-path formulation, which sets it apart from existing pixel-wise or heuristic connectivity-aware methods. The results are promising and demonstrate competitive improvements over state-of-the-art techniques on both 2D and 3D datasets.

While I have raised several concerns regarding clarity in the experimental setup (e.g., ambiguity in Table 1, post-processing explanation, and lack of distance map evaluation), these are largely addressable in a revision. Importantly, these issues do not undermine the fundamental soundness or originality of the proposed method.

In conclusion, the paper offers a compelling and well-motivated idea with strong practical relevance, and I believe it should be accepted. I look forward to seeing a clearer and more polished version of this work in the final publication.
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 authors have provided clear and reasonable responses to all of my concerns. Their justification for using distance maps instead of probability maps—specifically to penalize larger disconnections and emphasize topological continuity—was well-articulated and aligned with prior literature. The clarification that CAPE refers to the combined loss with MSE resolves the ambiguity in Table 1. While I originally suggested a more thorough evaluation of the predicted distance maps, I agree with the authors that assessing final graph representations is more meaningful for the task at hand. Their promise to add more visualizations in the final manuscript is appreciated. Additionally, their post-processing and dataset-related responses were satisfactory. Overall, the rebuttal demonstrates that the authors have thoughtfully addressed all major critiques, and I believe this work makes a valuable contribution to the field. I recommend Accept.

Author Feedback

We thank the Reviewers for their comments. R1

Graph Construction GT graphs are either provided by annotators or extracted from binary masks. For predictions, we treat the distance map as an 8-connected grid in 2D (26-connected in 3D) where pixels are nodes and edge costs depend on predicted distances. Selected GT nodes are projected onto this grid, and the shortest path between them is computed. Even if the network predicts all background, the grid still exists with high-cost edges.

Differentiable APLS In (non-differentiable) APLS, edges are binary—either present or absent. In our differentiable adaptation, we replace these binary affinities with continuous ones (distance values predicted by our network). This allows path lengths to be computed as sums of network predictions, enabling optimization.

Backbone We used U-Net for fair comparison, as all baselines are built and optimized on it. However, our loss is model-agnostic. Testing newer backbones is a promising direction for future work. R2

Distance vs. Probability Map We use distance maps to penalize larger disconnections more, as edge costs grow with gap size. This helps the network focus on harder connectivity errors, unlike probability maps. Prior work [18,20] also shows predicting distance maps is as effective as probability maps. We will include the explanation in final manuscript.

Clarification of Table 1 CAPE indeed refers to our total loss, which combines CAPE with MSE loss. We will clarify this explicitly in the final version.

Evaluation and Visualization of Predicted Distance Maps The distance map is an intermediate representation. In delineation task, the goal is to extract topologically correct structures as graphs or masks. Hence, evaluating the graph representation offers a more meaningful assessment than comparing distance maps. Nevertheless, we will also include additional visual results to further show the quality of the predicted distance maps.

Post-Processing We apply thresholding to convert predicted distance maps into segmentation masks.

Figure 3 We will incorporate the suggestions into the final manuscript.

Dataset Size We will discuss further validation on larger dataset in Conclusion. Please also refer to R3.5-6. R3

Performance Improvement We respectfully disagree that the gains are marginal. While pixel-wise metrics are similar to baselines, our method shows consistent and significant improvements on connectivity-aware metrics, with ~18% gain in TLTS and ~13% in APLS. Improving connectivity is the primary goal of our work, and these results confirm the effectiveness of our approach in achieving better connectivity.

Limited Innovation CAPE integrates a classical shortest-path algorithm into deep net training to optimize a differentiable relaxation of APLS, which to our knowledge is the first such attempt in the literature. Regarding the use of MSE loss, this is a common practice in the field. Majority of SOTA rely on pixel-wise losses [3,11,17,18] for dense supervision as discussed in Section 3.2 of our manuscript.

Visual Results Our figure clearly highlights areas with improved connectivity using arrows, demonstrating CAPE’s advantages. We will include additional qualitative results, including for 3D, in the final manuscript as it allows more space.

Post-Processing CAPE is complementary to post-processing methods and can be combined with them to further improve the final output, as they address the problem from different angles.

Dataset Size The datasets used, are well-established in the field, and the 3D dataset is substantial, approximately equivalent to 2,800 2D images of size 250×250.

Conventional Losses with More Data A key challenge is to achieve competitive performance within the common constraint of limited training data, a practical scenario in many clinical applications. This motivates the development of methods when pixel-wise losses perform poorly.

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’

This paper presents a novel and technically sound loss function aimed at improving topological connectivity in the segmentation of curvilinear structures. It directly aims to optimize the topology-aware metric (APLS) and find out the regions that need to be fixed through the Dijkstra’s algorithm.

While there were initial concerns regarding experimental clarity, particularly around the loss formulation and post-processing, the authors have provided thorough and convincing clarifications in the rebuttal. Their rationale for using distance maps, clarification of the combined loss, and commitment to enhancing visualizations in the final manuscript have addressed key reviewer concerns.

Meta-review #3

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. You may optionally write justifications for ‘accepts’, but are expected to write a justification for ‘rejects’

The paper introduces a clever concept to

Unfortunately, the authors do not compare their method to the de-facto state of the art which are 1) persistent homology based methods (E.g. the Betti Matching method which does not ignore spatial alignment as the authors claim persistent homology methods would in the introduction https://proceedings.mlr.press/v202/stucki23a/stucki23a.pdf ). and 2) skeleton based methods which go beyond the sub-optimal soft-clDice.

Furthermore the evaluation of the methods does not consider frequently used topology metrics such as Betti numbers.

Last, the experimentation is limited as mentioned by R3.

In my opinion, these are significant shortcomings and the paper does therefore not meet the standards of MICCAI in its current form.

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CAPE: Connectivity-Aware Path Enforcement Loss for Curvilinear Structure Delineation

Author(s):