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Abstract
Rotational digital subtraction angiography (DSA) captures sparse C-arm projections of beating coronary vasculature over a 5–8 s sweep, where each frame conflates two temporally distinct processes: quasi-periodic cardiac motion deforming vessel geometry and monotonic contrast-agent transport modulating opacity. Under sparse views, parameterizing both with a single acquisition timestamp is highly ambiguous. We present CardioGS, a deformation-driven 4D Gaussian Splatting framework that reduces this ambiguity through dual temporal coordinates. A self-supervised ClockNet learns a monotonic cardiac clock u(τ)∈[0,1] via Gauss–Legendre quadrature of a bounded instantaneous frequency, adapting to heart-rate variability without ECG gating. Since u(τ) is monotonic, quasi-periodicity is imposed through cycle-consistency regularization on sparse deformation control nodes. Geometry is conditioned on the learned clock while appearance is conditioned on acquisition time in canonical space. On porcine rotational cardiac DSA with 15–60 views, CardioGS outperforms recent baselines in both 2D synthesis and 3D vessel geometry. The code is available at: https://github.com/131366/cardiogs
Links to Paper and Supplementary Materials
Main Paper (Open Access Version): https://papers.miccai.org/miccai-2026/paper/3507_paper.pdf
SharedIt Link: Not yet available
SpringerLink (DOI): Not yet available
Supplementary Material: Not Submitted
Link to the Code Repository
https://github.com/131366/cardiogs
Link to the Dataset(s)
N/A
BibTex
@InProceedings{LiuYil_CardioGS_MICCAI2026,
author = { Liu, Yilun AND Yang, Jinzhu AND Feng, Chaolu AND Liu, Yao AND Wang, Yongbo AND Bian, Zhaoying AND Xu, Yan},
title = { { CardioGS: Deformation-Driven 4D Gaussian Splatting with Self-supervised Cardiac Clock Learning for Rotational DSA Reconstruction } },
booktitle = {Medical Image Computing and Computer Assisted Intervention -- MICCAI 2026},
year = {2026},
publisher = {Springer Nature Switzerland},
volume = {LNCS 16888},
month = {September},
page = {pending}
}
Reviews
Review #1
- Please describe the contribution of the paper
This paper presents CardioGS, a deformation-driven 4D Gaussian Splatting framework for reconstructing coronary vasculature from sparse rotational digital subtraction angiography (DSA). The key challenge addressed is the non-identifiability caused by cardiac motion under sparse acquisition. The method uses temporal modeling: a self-supervised ClockNet learns a monotonic cardiac clock, after which geometry and appearance are conditioned on temporal variables. This allows improved reconstruction on porcine DSA data.
- 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 addresses a challenging and clinically relevant imaging scenario of rotational DSA, operating under sparse-view acquisition conditions. The proposed method demonstrates improvements over baselines. In addition, the inclusion of ablation studies helps clarify the contribution. Finally, the public release of the code is a strong positive aspect.
- 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 framework combines multiple sophisticated components, which makes the overall method difficult to interpret. Most of mathematical formulations would benefit from additional intuition to improve accessibility. For example, the curriculum design with the parameter beta seems heuristic, and its impact is not evaluated. Furthermore, several limitations could be more explicitly discussed: for example, since the deformation model depends on the learned cardiac clock, inaccuracies in ClockNet negatively affect geometry reconstruction.
- 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 has provided an anonymized link to the source code, dataset, or any other dependencies.
- Based on your review and your understanding of the MICCAI Scientific Code of Ethics, do you believe this submission may involve a potential ethics concern or violation?
N/A
- Optional: If you have any additional comments to share with the authors, please provide them here. Please also refer to our Reviewer’s guide on what makes a good review and pay specific attention to the different assessment criteria for the different paper categories: https://conferences.miccai.org/2026/en/REVIEWER-GUIDELINES.html
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?
Overall, I lean toward a weak accept, as the paper addresses a clinically relevant and challenging problem with improved performance, despite a complex and somewhat heuristic design.
- Reviewer confidence
Somewhat confident (2)
- [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.
Some claims are not formally justified.
Review #2
- Please describe the contribution of the paper
The authors propose a method to decouple opacity changes caused by contrast agent transport from vessel geometry deformations induced by cardiac motion. The paper comes with the design of the architecture that uses three separate modules for three separate tasks to build the time dependent 3D Guassian Splatting representation. The first module’s goal is to predict the patient’s heart rate that is then used by the second module to model vessel geometry changes caused by cardiac motion. The last module is used to estimate gaussian opacity parameters with respect to the time, which gives the model a chance to take into account contrast agent transportation flow between reference frames. The information flow is designed in a way that blocks responsible for opacity never know about geometry deformations and geometry blocks know nothing about the opacity changes, which makes cardiac motion and contrast agent transport influences separated. Authors provide experimental evidence demonstrating that the proposed architecture outperforms prior approaches in terms of 3D 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.
1.The paper is well written and concise. The architecture figure is particularly informative, making the overall approach clear and easy to understand.
2.The idea of splitting time conditioning into two separate factors, cardiac motion and contrast agent transport, rather than using a single temporal input, is both novel and well-motivated. The experimental results indicate that this design choice leads to noticeable improvements in 3D reconstruction quality. More broadly, the findings suggest that modeling different sources of temporal inconsistency separately is beneficial not only for reconstruction performance but also for improving model interpretability.
3.The proposed approach appears adaptable to other 3D reconstruction tasks, such as lung imaging, suggesting broad applicability.
- 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.Regarding the cardiac clock, while the rationale for avoiding direct modeling of the modular phase is well explained, it is not entirely clear why the model predicts heart rate (frequency) instead of directly estimating the final conditioning u(tau). Additional clarification on this design choice would strengthen the methodological justification.
2.The discussion of limitations and future work could be expanded. A slightly more detailed analysis would help readers better understand the broader implications of the proposed approach and its potential impact on the field. The authors adopt a control-node-based approach to manipulate
3.Gaussian geometries. It would be valuable to understand whether this design choice is driven purely by computational efficiency or also by domain-specific considerations related to vessel structures. Additionally, it raises the question of whether directly manipulating Gaussian parameters could further improve reconstruction quality, even at the cost of increased computational complexity.
- 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?
Overall, I find this paper to be solid, well-executed, and meaningful. The proposed architectural design is clear, well-motivated, and supported by experimental results demonstrating improvements in 3D reconstruction quality. In particular, the explicit disentanglement of cardiac motion and contrast agent transport is an interesting and promising idea that contributes to both performance and interpretability, and may have relevance beyond the specific application studied.
That said, I do have several questions, particularly regarding certain design choices, and some aspects of the method could benefit from further clarification or justification. While these concerns are not fundamental flaws, they slightly limit my confidence in the overall strength and generality of the contribution. Addressing these points would strengthen the paper and improve its clarity.
Overall, I lean toward a Weak Accept.
- Reviewer confidence
Confident but not absolutely certain (3)
- [Post rebuttal] After reading the authors’ rebuttal, please state your final opinion of the paper.
Accept
- [Post rebuttal] Please justify your final decision from above.
I would like to thank the authors for their detailed and highly convincing rebuttal. They provided an excellent, mathematically elegant explanation for why the model predicts instantaneous frequency rather than directly regressing the cardiac clock. Integrating this frequency naturally guarantees monotonicity while allowing the extraction of the total cycle count, which is critical for defining the cycle-consistency loss. Furthermore, the authors successfully clarified that the control-node graph is much more than a computationally driven design choice. It actually serves as a vital spatial regularizer that enforces coherent vessel motion and prevents isolated local deformations under highly sparse projections. I also appreciate their willingness to adjust the manuscript’s claims regarding identifiability and their honest discussion concerning dataset limitations. The proposed method for decoupling quasi-periodic cardiac motion from monotonic contrast agent transport is highly innovative and yields strong experimental results. Because the rebuttal thoroughly addressed my main concerns and strengthened my confidence in the paper, I am upgrading my recommendation to Accept.
Review #3
- Please describe the contribution of the paper
The authors have developed a Gaussian Splatter method, CardioGS. CardioGS is a deformation driven 4D Gaussian Splatting framework that reconstructs 3D vessel geometry. THe are doing so by utilizing i) ClockNet, ii) Curriculum learning, and iii) Sparse control node deformation graph with cycle consistency.
- 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.
Major Strengths: 1.Monotonic cardiac clock controls the continuous positional encoding and provides cycle consistency regularization. Instead of using raw timestamp conditioning alone, the model learns a monotonic reparameterization of time through an instantaneous frequency integrated by Gauss–Legendre quadrature. 2.Well discussed theory and components needed for the moving pieces of this work. 3.The deformation module is not an unconstrained per-point warp. It is a sparse control-node graph with KNN-RBF interpolation, plus cycle-consistency regularization. That is a good compromise between flexibility and stability.
- 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 Weakness: 1.Even though the field is queried in canonical space, the 4D hash grid still allows, (i) temporal variation that mimics motion and (ii) especially along projection rays. This is apparent when I looked at the shared repository. 2.ClockNet enforces monotonicity (this is good), but there is a high chance it will learn neal-linear mapping from the data due to KNN based graph formation.
- Please rate the clarity and organization of this paper
Good
- Please comment on the reproducibility of the paper. Please be aware that providing code and data is a plus, but not a requirement for acceptance.
The submission has provided an anonymized link to the source code, dataset, or any other dependencies.
- Based on your review and your understanding of the MICCAI Scientific Code of Ethics, do you believe this submission may involve a potential ethics concern or violation?
N/A
- Optional: If you have any additional comments to share with the authors, please provide them here. Please also refer to our Reviewer’s guide on what makes a good review and pay specific attention to the different assessment criteria for the different paper categories: https://conferences.miccai.org/2026/en/REVIEWER-GUIDELINES.html
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?
There are several inconsistencies. A core reason is the limitation itself. the proposed framework is the inherent ambiguity in disentangling deformation, appearance, and temporal dynamics from projection-only supervision. Despite the use of canonical-space modeling and cycle-consistency regularization, multiple latent configurations can produce similar rendered projections, potentially leading to non-unique or biased solutions.
If the authors can defend this position, I am willing to change my score.
Another issue that I request the authors to fix is their reference section. The formatting and information for some of the reference needs attention.
- 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 authors have responded to my questions properly and I am elevating my score to accept for this work.
Review #4
- Please describe the contribution of the paper
This paper presents CardioGS, a deformation-driven 4D Gaussian Splatting framework that restores identifiability through dual temporal coordinates. The results show its promising performance compared to the SOTA models in both 2D synthesis and 3D 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.
1.This paper proposes a deformation-driven 4D Gaussian Splatting framework to restore 3D vessel geometry under the deformable scenario with cardiac motion.
2.The authors proposes to disentangle quasi-periodic cardiac motion from monotonic contrast transport by introducing a learnable monotonic cardiac clock.
3.Experiments on a porcine rotational cardiac DSA dataset show its promising performance over the SOTA methods.
- 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.Only one private dataset used in this paper, which is a limitation. At least one public dataset should be used for testing.
2.I was wondering how many subjects in the private dataset used? It seems this dataset only contains one subject?
3.In the Figure 2 about the qualitative results, it looks 4DRGS is much better than R2-Gaussian, but in Table 1 about the quantitative comparison, it seems R2-Gaussian is mostly better than 4DRGS? Could you please explain this phenomenon?
- 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 has provided an anonymized link to the source code, dataset, or any other dependencies.
- Based on your review and your understanding of the MICCAI Scientific Code of Ethics, do you believe this submission may involve a potential ethics concern or violation?
N/A
- Optional: If you have any additional comments to share with the authors, please provide them here. Please also refer to our Reviewer’s guide on what makes a good review and pay specific attention to the different assessment criteria for the different paper categories: https://conferences.miccai.org/2026/en/REVIEWER-GUIDELINES.html
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 paper shows a novel framework to solve the 3D vessel reconstruction problem under deformable scenarios, but one limitation is the limited evaluation on one private dataset.
- Reviewer confidence
Not confident (1)
- [Post rebuttal] After reading the authors’ rebuttal, please state your final opinion of the paper.
N/A
- [Post rebuttal] Please justify your final decision from above.
N/A
Author Feedback
We sincerely thank the reviewers and meta-reviewer for constructive comments that help improve the manuscript’s clarity and rigor.
Reference reliability [Meta,R3]. Ref. 13 has an erroneous/incomplete entry due to a verification oversight. It served only as broad DSA background, not to support any method assumption, loss term, comparison, or conclusion. We apologize; it will be corrected or removed, and references re-checked for accuracy and relevance.
Projection ambiguity [Meta,R3]. We agree projection-only supervision cannot guarantee unique disentanglement of appearance, deformation, and temporal dynamics. Similar projections may arise from true displacement or opacity changes that alter apparent vessel location and perceived motion along projection rays. CardioGS does not prove uniqueness; its separated opacity-at-τ and clock-conditioned geometry pathways make the ambiguity more constrained, improving conditioning relative to generic time-conditioned fields. Opacity is queried at canonical undeformed Gaussian positions and acquisition time τ, so it cannot directly move centers/covariances. Geometry uses a spatially coherent, clock-conditioned sparse control-node graph with cycle consistency. We will use “reduces ambiguity” or “improves conditioning,” not “restores identifiability.”
Method design and reliability [R2,R3,R1]. [R2: frequency vs. u(τ)] The learned frequency is the positive cardiac-clock progression rate; integrating gives cumulative progress w(τ)=∫_0^τ f_θ(s)ds, so u(τ) is monotonic while allowing nonuniform progression. With a smooth unwrapped clock rather than a wrapped phase, cycle consistency needs the scale of one cardiac cycle in normalized u-space. The integral gives C=w(1); after normalization, one cycle corresponds to Δu=1/(C+ε). Direct u(τ) regression is possible, but would need extra monotonicity constraints and a separate cycle-scale estimate.
[R3: near-linear clock] A clock close to acquisition time is valid when cardiac progression is regular. ClockNet does not force nonlinearity; it is adaptive, near-linear for regular motion and nonlinear when progression is irregular. Graph topology/RBF weights are built from canonical 3D positions, while node transforms are time-conditioned; thus KNN formation enforces spatial coherence, not temporal linearity.
[R2/R1: deformation prior, beta, clock sensitivity] The graph is not merely computational; it encodes coherent vessel motion. CardioGS remains per-Gaussian, but shared control nodes/KNN-RBF couple deformations, avoiding isolated local geometry explanations under sparse projections; node-number ablation and the graph gain support this expressiveness-regularization trade-off. Beta is a stability curriculum: start with reliable acquisition-time conditioning, then introduce learned-clock conditioning. It was set by stability tuning; fuller hyperparameter study remains future work. If clock prediction is inaccurate, geometry may degrade, especially with irregular motion/poor projections. Yet even in the hardest 15-view case, experiments show no systematic degradation.
Data scope and metric/visual gap [R4]. [R4: private data] Evaluation is on one private in-vivo porcine rotational cardiac DSA dataset; we acknowledge this limitation. To our knowledge, no comparable public cardiac benchmark provides dynamic projections, calibrated geometry, and dense-view 3D reference. Once new public/internal in-vivo DSA data become available, we will expand evaluation for fair comparison.
[R4: metrics vs. visualization] R2-Gaussian is t-independent; 4DRGS models time-dependent rendering. For quality metrics, R2-Gaussian outperforms 4DRGS only on CD/HD at 15 views; its lower GauN is expected for a static model. Its worse PSNR/SSIM and visualization indicate weaker temporal rendering. CD/HD after ICP favor phase-averaged 3D alignment under extreme sparsity, whereas visualization and PSNR/SSIM reflect dynamic 2D synthesis; this is not a contradiction to dynamic modeling.
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 submission proposes coronary reconstruction using 4d gaussian splats. The reviews are found constructive and feedback converges on: appreciation of the disentanglement of cardiac motion and contrast agent propagation, but also on lacking clarity of the method (difficult interpretation of combination of multiple components) and design choices. High suspicion of AI generated text including likely hallucinated references (e.g., 13). Serious clarifications to these major concerns may improve the quality, and better highlight the relevance of the submission. For these reasons, and with respect to the other submissions, the recommendation is towards requesting a rebuttal for serious clarification on methodological inconsistencies, and design choices.
- 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 authors successfully addressed most major methodological concerns regarding the cardiac clock, and spatial regularization in their rebuttal. Although concerns still remains due to lingering doubts about formal disentanglement guarantees, the overall agreement is that there are no major flaws preventing publication of this preliminary work. Recommendation is towards Borderline Acceptance.
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.
The concerns were mainly on overstated claims while rebuttal is mainly to clarify and explain without adding new experiments or results. On an engaged count of two accepts and a deferring reject, with a third standing weak accept, the paper clears the bar. A worry about AI-style text and one likely fake reference is identified, so this MUST be handled in the camera-ready submission. What need to be handled too is “the lack of guarantees for disentanglement” pointed by R1 who vote for accept but still not convinced. I stand with R1 too. I recommend accept but not top of the batch.
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.
The authors have largely clarified the previously unclear points in their rebuttal, and most of the reviewers appear satisfied with the responses, with agreeing on acceptance. The AC therefore recommends acceptance.