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Abstract
Coronary Artery Calcification (CAC) is a key predictor of atherosclerotic cardiovascular risk and is typically quantified by the Agatston score, a non-differentiable metric derived by segmenting CAC from a patient’s ECG-gated CT scan. Automated segmentations of coronary calcifications can enable streamlining of clinical workflows. However, real-world cardiac CT databases typically only store the volume-level Agatston score without also storing the underlying coronary calcium segmentations. To enable automated CAC segmentation and Agatston score computation, we propose Proxy-CAC, an end-to-end 3D U-Net framework for CAC quantification trained primarily with a loss function leveraging a differentiable Agatston score approximation, along with limited supervision over a small set of scans with per-voxel annotations. We trained and evaluated Proxy-CAC on an in-house, clinical dataset of 27,700 gated CT scans with associated Agatston scores from a large hospital. Proxy-CAC outperforms baseline models trained on segmentation masks at predicting Agatston scores by a substantial margin, increasing Cohen’s Kappa values from 0.71 to 0.81 when stratifying patients into standard risk tiers. This work opens the door to automated, interpretable CAC risk prediction relying only on the limited, clinically relevant supervision available in real-world clinical datasets.
Links to Paper and Supplementary Materials
Main Paper (Open Access Version): https://papers.miccai.org/miccai-2026/paper/4314_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)
Stanford COCA Dataset: https://aimi.stanford.edu/datasets/coca-coronary-calcium-chest-ct
BibTex
@InProceedings{SatSan_ProxyCAC_MICCAI2026,
author = { Sato Imuro, Sandra Emi AND Khan, Salman Siddique AND Balakrishnan, Guha AND Alkhaleefah, Mohammad AND Al-Kindi, Sadeer AND Sabharwal, Ashutosh},
title = { { Proxy-CAC: Learning Coronary Calcium Segmentation from Volume-Level Scores } },
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 main contribution of the paper is the design of a differentiable cost function for the automated regression of the Agatston score from ECG-gated CT using deep learning networks. Using this cost function, and with some prior labeled dataset for lesion segmentation, they generate a network that segments calcifications from the regression of the Agatston score.
- 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.
Novelty. The authors tackle the problem of segmenting structures from an aggregated measurement (the Agatston score). While generating segmentations from aggregated measurements is a problem tackled in the literature (see [Cano20], below, also in the computation of the Agatston score), the proposed method shows novelty by training on a process non-differentiable score, such as the Agatston. Equations 2-4 are a clever way to make the Agatston discrete value continuous. The approximation of the Agatston score in this work (Eq. 2) is computed in a per-voxel basis. However, in the original score, the computation is in a per lesion basis, as the authors explain in equation 1.It is surprising that with this approximation, the network improves in the phase II.
[Cano20] C. Cano-Espinosa, G. González, G. R. Washko, M. Cazorla and R. S. J. Estépar, “Biomarker Localization From Deep Learning Regression Networks,” in IEEE Transactions on Medical Imaging, vol. 39, no. 6, pp. 2121-2132, June 2020, doi: 10.1109/TMI. 2020.2965486.
- 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.
The authors perform a sequential training, where first a pure segmentation network is trained and then refined with the proposed method. Why to forget the segmentation data after the first step? Wouldn’t it make sense to keep it within the optimization, but evaluating the term of the cost function only on the cases where the data is available? The scans are resampled to 0.3x0.3x3.0 mm. Why such large slice thickness? It is better to show Bland-Altman plots than correlation plots in Fig 2. The comparison of Proxy-CAC against AI-CAC and S2CAC is unfair, as, as the authors acknowledge, testing is done on the Dc dataset, which is out of distribution for the other methods, but not for Proxy-CAC.
- Please rate the clarity and organization of this paper
Good
- Please comment on the reproducibility of the paper. Please be aware that providing code and data is a plus, but not a requirement for acceptance.
The submission does not mention open access to source code or data, but provides a clear and detailed description of the algorithm to ensure reproducibility.
- Based on your review and your understanding of the MICCAI Scientific Code of Ethics, do you believe this submission may involve a potential ethics concern or violation?
N/A
- Optional: If you have any additional comments to share with the authors, please provide them here. Please also refer to our Reviewer’s guide on what makes a good review and pay specific attention to the different assessment criteria for the different paper categories: https://conferences.miccai.org/2026/en/REVIEWER-GUIDELINES.html
N/A
- Rate the paper on a scale of 1-6, 6 being the strongest (6-4: accept; 3-1: reject). Please use the entire range of the distribution. Spreading the score helps create a distribution for decision-making.
(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?
Interesting approach to learn segmentations from complex aggregated indices.
- 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.
I think the differentiable Agatston score approximation merits to be shared with the community. The use of dataset with aggregated values is relevant. Evaluation is well performed. I stand with my initial assessment.
Review #2
- Please describe the contribution of the paper
The paper proposes Proxy-CAC, a framework for learning voxel-level CAC segmentation volume-level Agatston score, which are commonly available in real-world clinical datasets but lack dense annotations. The key contribution is the introduction of a differentiable approximation of the Agatston scoring function enabling end-to-end training of a segmentation model using only scalar supervision. The approach combines a 3D-U-Net backbone for voxel-wise prediction, a differentiable Agatston Score module using sigmoid-based relaxations, and a two-phase training strategy leveraging a small annotated dataset and a large score-only dataset. This work aims to bridge the gap between interpretability and data availability, demonstrating improved agreement in risk stratification compared to baseline models.
- 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.Clinically relevant problem formulation : The paper addresses an important and realistic limitation in medical imaging: the lack of dense annotations in large-scale datasets. Most clinical datasets provide only summary scores (e.g., Agatston score), and leveraging such weak supervision is highly valuable. 2.Scalable use of real-world data : The method is demonstrated on a large dataset (27,700 CT scans), showing the feasibility of scaling beyond small, manually annotated datasets. This is a strong practical contribution. 3.Integration of domain knowledge into learning : The differentiable Agatston approximation incorporates prior clinical knowledge (e.g., HU thresholds and density weighting) into the learning process, which is a meaningful design choice compared to purely data-driven regression approaches. 4.Interpretability-oriented design : Unlike direct regression methods, the proposed framework produces voxel-level outputs, which are potentially useful for clinical verification and interpretability. 5.Generalizable idea : The concept of learning dense predictions from structured clinical endpoints via differentiable proxies could be extended to other medical imaging tasks, making the approach broadly relevant.
- 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.Fundamentally ill-posed problem formulation : Learning voxel-level segmentation from a single scalar Agatston score is inherently underdetermined. Multiple segmentation configurations can produce the same score, meaning the supervision signal does not uniquely constrain the solution. This raises concerns about whether the learned segmentations are anatomically meaningful or simply optimized to match the score. 2.Inaccurate approximation of the Agatston scoring process : The proposed differentiable formulation deviates significantly from the true Agatston definition. The original method operates on connected components (lesions) and uses maximum HU per lesion. The proposed method applies voxel-wise weighting without connectivity constraints. This mismatch may lead to incorrect modeling of lesion structure and reduces clinical fidelity. 3.No quantitative evaluation of segmentation quality : A critical limitation is the absence of standard segmentation metrics (e.g., Dice, IoU). Even though large datasets lack voxel-level labels, the dataset includes ground-truth masks, yet no segmentation performance is reported. This omission significantly weakens the validation of the method. 4.Weak and subjective qualitative evaluation : The qualitative analysis is limited to a small number of examples and relies on informal expert assessment. This is insufficient to support claims of interpretability or clinical reliability. 5.Unclear impact on segmentation vs regression : The reported improvement in Cohen’s kappa may primarily reflect improved score regression rather than better segmentation. Since risk categories are derived from score thresholds, gains in regression accuracy naturally improve classification metrics. 6.Unfair or inconsistent comparison with prior work : The proposed method is evaluated on cropped cardiac ROIs, whereas some baselines are applied to full chest CT scans. This introduces a bias and makes the comparison less reliable. 7.Lack of strong baselines : The comparison is limited to a standard 3D U-Net. More competitive baselines, such as Multi-task learning (segmentation + regression) and direct regression models with auxiliary supervision are not included, making it difficult to assess the true advantage of the method.
8.Limited methodological analysis : Several design choices are not sufficiently justified or analyzed:
- Use of SMAPE loss instead of standard regression losses
- Two-phase training with complete removal of segmentation loss in Phase 2
- Temperature annealing schedule for the differentiable approximation
- No ablation or sensitivity analysis is provided.
9.Lack of external validation : The model is evaluated on a single institutional dataset. Generalization to other populations, scanners, or protocols is not demonstrated, limiting clinical applicability. 10.Clinical reliability concerns : The paper acknowledges that segmentation masks may be incomplete or degraded. In clinical settings, incorrect localization of calcifications could reduce trust, even if the overall score is accurate.
- 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.
- 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 paper tackles an important and practically relevant problem, and the idea of leveraging volume-level clinical scores for segmentation is promising. However, several aspects need to be strengthened to improve the scientific rigor:
- Please provide quantitative segmentation evaluation on the annotated subset
- Include stronger baselines, particularly multi-task or regression-based approaches.
- Clarify the impact of the differentiable approximation through ablation studies.
- Provide analysis of training stability and hyperparameter sensitivity.
- Discuss more explicitly the limitations of learning segmentation from scalar supervision, and how degenerate solutions are mitigated. Addressing these points would significantly improve the credibility and impact of 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.
(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?
While the paper presents an interesting and practically motivated idea, it suffers from several critical limitations. The most significant concern is the lack of quantitative evaluation of segmentation quality, despite the method being framed as a segmentation approach. Without such evaluation, it is difficult to assess whether the model produces meaningful voxel-level predictions or simply optimizes for score regression. Additionally, the problem formulation is inherently underdetermined, and the proposed differentiable approximation does not faithfully capture the original Agatston scoring process. Combined with limited experimental rigor, weak baselines, and lack of external validation, the current evidence is insufficient to support the claims. Overall, while the idea is promising, the paper requires more rigorous validation and analysis to meet the standards of a top-tier conference.
- 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.
I thank the authors for their detailed rebuttal. After careful reconsideration, I have updated my recommendation to Accept. The rebuttal addressed several of my primary concerns. The reported Dice scores (Phase I: 0.69 → Phase II: 0.79) demonstrate that scalar supervision meaningfully improves segmentation quality, and the high DAS correlation (r = 0.996) partially alleviates concerns about the approximation fidelity. The two-phase training strategy is also clarified as a deliberate domain adaptation choice, which I find reasonable. While some of these results were not included in the submitted manuscript, the rebuttal collectively suggests that the method is more robust than the paper currently conveys. I encourage the authors to incorporate the segmentation evaluation and ablation analyses into the final version.
Review #3
- Please describe the contribution of the paper
This paper introduces Proxy-CAC, a framework for learning coronary calcium segmentation from volume-level Agatston scores. The method uses a 3D U-Net to predict a voxel-level CAC probability map and couples it with a differentiable approximation of the Agatston score as end-to-end supervision. Training is performed in two stages: first with a smaller segmentation dataset for dense supervision, and then with a much larger set of 27,700 gated CT scans using real clinical Agatston scores only. The paper shows that adding the score-supervised second stage improves agreement with risk strata and overall score correlation relative to mask-only supervision.
- 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 is well aligned with an important clinical problem. The central idea is also genuinely interesting: the Agatston score is a clinically meaningful but non-differentiable target, and the authors convert it into a differentiable supervisory signal so that large numbers of scans with only report-level labels can still be used to train an interpretable segmentation model. That is a strong framing for weakly supervised learning in a clinically grounded setting.
The two-stage training strategy is also sensible. Dense voxel-level supervision is used first to anchor the anatomy, after which score-level supervision expands learning to a much larger real-world dataset. I also found the reported experimental gains meaningful and the statistical presentation stronger than in many application papers. In particular, the improvement in risk-tier agreement appears substantial, and the inclusion of bootstrap confidence intervals for kappa is appreciated.
- 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 main reservation is that the paper ultimately makes a segmentation claim, but the main large-scale evaluation is still largely score-based rather than voxel-based. Improved agreement with the Agatston score does not necessarily imply more accurate coronary segmentation. In principle, a model could still match the overall score while placing calcium in imperfect spatial locations. The qualitative examples suggesting fewer non-coronary false positives are useful, but they do not fully close this gap.
Second, the comparisons with AI-CAC and S2CAC are difficult to interpret cleanly because the benchmarking conditions are not fully matched. In particular, AI-CAC appears to be run on full-chest gated CT, whereas S2CAC and Proxy-CAC are evaluated on coned-down cardiac field-of-view scans, and the compared methods do not appear to have been retrained under identical data and preprocessing conditions. Therefore, part of the observed performance gap may reflect domain or field-of-view mismatch rather than purely methodological advantage.
Third, the differentiable Agatston score remains an approximation of the real scoring procedure. It does not fully reproduce lesion-wise connected-component handling or the original slice-based area computation logic. I do not consider this fatal, but the approximation gap should be acknowledged more explicitly.
Fourth, even the paper’s own qualitative analysis suggests that phase II supervision may introduce some lesion under-coverage, which indicates that the segmentation problem is not fully solved.
Finally, the presentation of the ground-truth mask description on page 8 is somewhat confusing and should be cleaned up for clarity.
- 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
Among the submissions I reviewed, this is one of the stronger ones. The idea is clinically grounded and methodologically meaningful. The paper would be improved further if the claims were calibrated more precisely: the strongest evidence currently supports score prediction and risk stratification under score-level supervision, while full voxel-level clinical equivalence is less directly established. A slightly narrower claim would make the paper more convincing.
- Rate the paper on a scale of 1-6, 6 being the strongest (6-4: accept; 3-1: reject). Please use the entire range of the distribution. Spreading the score helps create a distribution for decision-making.
(4) Weak Accept — marginally above the acceptance threshold, but would not mind if rejected, dependent on rebuttal
- Please justify your recommendation. What were the major factors that led you to your overall score for this paper?
I consider this a high-end weak accept. The paper is not flawless, especially because the segmentation-level validation remains weaker than the score-level validation, but the methodological framing is strong, the clinical supervision design is meaningful, the dataset scale is impressive, and the empirical gains are substantial. Overall, I think the paper is above the acceptance threshold, although some of the claims should be tightened.
- 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 maintain my Accept recommendation based on the methodological contribution of the differentiable Agatston score formulation, which I find genuinely novel and clinically meaningful. The conversion of a non-differentiable clinical scoring procedure into a differentiable supervisory signal, enabling weakly supervised segmentation training on large real-world datasets that lack dense annotations, addresses a generalizable problem in clinical AI development that extends beyond CAC quantification to a broader class of weakly supervised medical imaging tasks. The two-phase training strategy is sensible, the dataset scale is impressive, and the reported risk stratification gains are substantial. While the segmentation-level validation in the submitted manuscript remains weaker than the score-level validation, as I noted in my original review, I do not view this gap as fatal to the methodological contribution. My Accept recommendation is based on the submitted manuscript’s content, with the limitations acknowledged in the paper’s own Discussion section.
Author Feedback
We thank the reviewers for their feedback and recognition of our study’s value. We address the main concerns here and will modify the manuscript accordingly: We acknowledge the need for quantitative segmentation evaluation and concerns about lesion under-segmentation (R2, R3). While our large-scale dataset (Dc) lacks dense masks, a clinical expert annotated 50 random samples from the test set (10/category). We post-process predicted masks by identifying connected pixels within segmented regions above the clinical 130 HU threshold. We observed an increase in Dice score from 0.69 in Phase I to 0.79 in Phase II (0.55 to 0.61 without postprocessing). This jump demonstrates that scalar supervision provides superior lesion identification. Furthermore, Agatston scores derived from the refined masks achieve a Kappa of 0.83 [95% CI: 0.82, 0.84], proving the reliability of the masks. Regarding concerns on the deviation from standard Agatston computation: In the Differentiable Agatston Score (DAS), we replace each non-differentiable operation in the standard Agatston calculation with a soft approximation, while maintaining mathematical fidelity. Using the masks in the COCA dataset, we compared DAS outputs against Agatston scores and obtained a Pearson correlation of 0.996, indicating high accuracy of our approximation. R2 (7.1) raises a valid point regarding the unconstrained nature of scalar supervision. We clarify that the framework is designed to impose constraints: Phase I provides a good initialization for the segmentation model, preventing it from converging on non-anatomical degenerate solutions. Phase II uses the score to refine the model; the DAS module incorporates clinical priors (130 HU thresholding), limiting the solution space to calcified voxels. R1, R2 question the use of a two-phase training approach rather than a simultaneous multi-task strategy. We use Ds to give the segmentation network a reasonable starting point; our focus is performance on Dc, the multi-center dataset for deployment. Since Ds comes from a different system, keeping the Ds mask loss active in Phase 2 would hurt generalization in Dc. Empirically, Phase 2 results in a small drop in segmentation performance on the Ds test set (Dice 0.74 → 0.69) and a large gain in segmentation performance on the Dc test set (Dice 0.61 → 0.79). This is an expected behavior of successful domain adaptation. We agree that external validation is a vital target for future research, we clarify that our Dc dataset represents a heterogeneous “real-world” cohort. It encompasses multi-site and multi-vendor data from a single hospital system, ensuring robustness against variations in clinical practice. We acknowledge concerns about the fairness when comparing Proxy-CAC with external models (AI-CAC and S2CAC). We will clarify that this comparison was intended to highlight a significant gap: available segmentation models trained on external distributions often underperform on other datasets. Our model provides a solution for fine-tuning a real-world dataset with only scalar labels. R2 suggests adding direct regression and multi-task learning baselines. Direct regression may give competitive accuracy, but it removes the main reason for our design choice: inspection of intermediate lesions. Standard multi-task learning, where a shared encoder feeds separate segmentation and regression heads, has the same problem. In our design, the DAS layer computes the scalar directly from the segmentation, so every score is explained by its mask, and any error in the score can be traced back to a lesion. Regarding specific implementation choices, we standardized resampling to 3.0 mm, as it remains the clinical standard for Agatston quantification. L score (SMAPE derived) was selected as it provides scale-invariance, which is essential for accurate risk stratification. We will clarify unclear design choices and improve presentations in line with the reviewer’s suggestions.
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.
This paper offers a method for learning of interpretable CAC segmentation from volume level clinical scores. In the rebuttal, please address the concerns from the reviewers comprehensively.
- 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 reviewers unanimously provided positive recommendations, and I agree with their decision.
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.
Authors satisfactorily addressed all reviewers concerns in the rebuttal and all reviewers agree on accepting the manuscript.
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.
My decision closely aligns with the comments from reviewer #3.In that sense, what I mean is that I find the idea of a differentiable score that can be more or less generalised to other problems for weak supervision is a novel and interesting idea.
Beyond that, looking at the paper and original review comments, there were certain methodological concerns (e.g. lack of segmentation evaluation) that have been successfully addressed with the rebuttal for all three reviewers (and this is highlighted by the overall agreement between all reviewers). I also particularly like the explanation on why an ill-posed problem (segmentation from a score) works with a two-phase approach (segmentation initialisation with score-based refinement). A more formal analysis on how this regularisation works and its limits would be highly welcomed if the authors plan to extend their work. I would also suggest comparison with regression-only methods and potentially ad hoc heatmap methods (e.g. GradCAM) for future work, although I agree with the rebuttal comments on why it is not needed for the current work.
Finally, echoing the reviewers I expect the authors to add the additional results provided in the rebuttal to be included in the camera ready paper.