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Abstract
This paper proposes a probabilistic inverse consistency image
registration network using a sparse BNN for cardiac motion estimation,aiming to simultaneously measure aleatoric and epistemic uncertainty.We construct a sparse BNN to predict the distribution parameters of the inverse consistency transformations between two images. Two symmetric Variational Autoencoders (VAEs) are constructed to predict the distribution parameters of latent variables in deformation space.
The posterior distribution parameters of network weights are estimated during optimization, and only important weights are updated. Our sparse BNNs significantly reduce the computational cost and improve the registration accuracy by Bayesian model averaging (BMA). Experiments on a
public cardiac MR dataset show that our sparse BNNs significantly improve the accuracy of the bidirectional registration for small datasets. It also provides aleatoric and epistemic uncertainty of registration results.
Links to Paper and Supplementary Materials
Main Paper (Open Access Version): https://papers.miccai.org/miccai-2025/paper/4995_paper.pdf
SharedIt Link: Not yet available
SpringerLink (DOI): Not yet available
Supplementary Material: Not Submitted
Link to the Code Repository
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Link to the Dataset(s)
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BibTex
@InProceedings{YanShe_Probabilistic_MICCAI2025,
author = { Yang, Shenglong AND Xu, Kangrong AND He, Zefeng AND Feng, Tianchao AND Yang, Xuan},
title = { { Probabilistic Inverse Consistent Image Registration Using Sparse Bayesian Network } },
booktitle = {proceedings of Medical Image Computing and Computer Assisted Intervention -- MICCAI 2025},
year = {2025},
publisher = {Springer Nature Switzerland},
volume = {LNCS 15963},
month = {September},
page = {414 -- 424}
}
Reviews
Review #1
- Please describe the contribution of the paper
The paper propose an bidirectional image registration model, called ICRnet, for cardiac motion estimation, based on two symmetric variational autoencoders (VAEs) and a sparse Bayesian Neural Network (BNN), which improves the registration accuracy and also simultaneously measure the aleatoric and epistemic uncertainty.
- 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 framework can provide both the aleatoric and epistemic uncertainty for registration, which enhances its reliability.
The use of two symmetric VAEs with the corss-attention mechanism and an inverse consistent networks ensures that the forward and backward transforms are inverse of each other.
The constructed sparse BNN significantly reduces the computational cost while preserving the accuracy. It performs especially well for small datasets.
- 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 is based on a bidirectional image registration, which often requires more computational costs compared to the single directional models. The paper mentions that sparse BNNs significant reduce the computational cost. However, it is obtained compared to their models without using sparse BNNs.
- 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
1) paragraph below eq(5). Here \theta_i is the snapshot of theta with totally L elements. Also each column of \hat{D} is a snapshot of theta but with K columns. Are these two snapshots the same?
2) why a sparse ratio \gamma = 20% was chosen for the sparse BNNs in the experiments? Is \gamma = 20% the best to balance the registration accuracy and the computational efficiency?
3) Sparse BNNs section of the experiments: the computation time of ICRnet with sparse BNNs reduces about 65%. It seems it is the one compared to the model without BNNs? What about the result if compared to the model with BNNs?
- 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?
The paper is well organized, and the experiments show good results compared to other models. However, the two slices used in the experiments are already very similar. It is not clear if the model can handle images with large deformations, which makes the method seem restrictive.
- Reviewer confidence
Very confident (4)
- [Post rebuttal] After reading the authors’ rebuttal, please state your final opinion of the paper.
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- [Post rebuttal] Please justify your final decision from above.
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Review #2
- Please describe the contribution of the paper
The paper introduces ICRnet, a novel complex inverse consistent image registration model using symmetric VAEs (consisting of a T2T module and N layers of Transformer encoders) with diffeomorphic layers in the decoder part followed by an inverse consistency network (with an architecture “similar” [page 4] to two U-Nets with shared parameters) that is trained to make the intermediate transition DVFs of the diffeomorphic layers inverse consistent. In the sense of a sparse BNN, only important weights (determined on the signal-to-noise ratio of currently estimated weight distribution parameters) are updated. The probabilistic model estimates aleatoric (based on the VAEs and caused by data inherent noise) and epistemic (leveraging the BNN and possibly reflecting data “with which the model has less experience” [page 6]) uncertainty for bi-directional DVFs simultaneously. Validation is performed on (depending on the experiment on up to) four publicly available cardiac image datasets using Dice score, Hausdorff distance (HD), bending energy (BE), the number of non-positive Jacobian determinants and the inverse consistency error (ICE) as metrics. Validation experiments include ablation studies and comparison with eight other trained approaches (no traditional methods).
- 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: well-founded novel combination of methods to achieve inverse consistent, diffeomophic registration
- estimation of aleatoric and epistemic uncertainty
- extensive validation including ablation studies, different parameter settings and comparison to other trained methods
- validation shows improvement in most of the metrics (but unclear whether those are statistically significant)
- 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.
- highly complex
- due to the complexity, some details are only included in the supplementary material
- submission does not mention open access to source code: although the description of the algorithm is good, it is doubtful that, due to the complexity of the approach, an exact reimplementation is possible.
- no statistical evaluation of results: it remains unclear against which methods the best-performing method shows a statistically significant improvement and against which it does not (although the abstract contains the word “significantly” twice)
- no comparison to traditional iterative methods
- 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 provide sufficient information for reproducibility.
- Optional: If you have any additional comments to share with the authors, please provide them here. Please also refer to our Reviewer’s guide on what makes a good review and pay specific attention to the different assessment criteria for the different paper categories: https://conferences.miccai.org/2025/en/REVIEWER-GUIDELINES.html
Please consider to include the name of the proposed method (ICRnet) in the abstract.
Page 1: “It has specific advantages for cyclic cardiac motion estimation because it provides more accurate motion whether for end-systolic (ES) to end-diastolic (ED) phase or ED to ES.” Is it possible to provide a reference for this statement?
Page 1: “… dose mapping uncertainty …” unclear which “dose” has to be mapped (possibly for radioablation therapy, but this is not mentioned elsewhere)
LCC (local correlations coefficient) seems in eqn (3) not to be explicitly defined.
The “E” of L_ICE seems not to be explicitly defined.
Page 6: “The metric |J_ϕ| <= 0 is close whether for all cases.“ Is this supposed to mean: The occurrence of non-positive Jacobian determinants is rare (or negligible) across all cases? Consider rephrasing.
Table 1: Is there a reason, why the best method is not highlighted (as in Table 2)?
Table 1-3: It would be interesting to know which results are statistically significantly worse than the best method.
- 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?
The strengths of the paper largely outweigh its weaknesses in my opinion, except for the unfortunately lacking statistical analysis of the results.
- Reviewer confidence
Confident but not absolutely certain (3)
- [Post rebuttal] After reading the authors’ rebuttal, please state your final opinion of the paper.
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- [Post rebuttal] Please justify your final decision from above.
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Review #3
- Please describe the contribution of the paper
This paper proposes a probabilistic inverse consistency image registration network using a sparse Bayesian neural network (BNN) for cardiac motion estimation, aiming to simultaneously measure aleatoric and epistemic uncertainty. The method utilizes symmetric Variational Autoencoders (VAEs) to predict the distribution parameters of latent variables in deformation space and reduces computational cost by updating only important weights in the sparse BNN. Experiments on public cardiac MRI datasets demonstrate that the proposed approach significantly improves bidirectional registration accuracy, especially on small datasets, while providing uncertainty quantification of the registration results.
- 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 key distinguishing aspect of the method presented in this paper lies in its novel probabilistic formulation for inverse consistent image registration. Specifically, the approach introduces the use of two symmetric Variational Autoencoders (VAEs) to predict forward and backward deformation vector fields (DVFs), while ensuring that these DVFs are inverse to each other, which improves the accuracy of bidirectional cardiac motion estimation. This method not only measures aleatoric uncertainty using the latent variables from the VAEs, but also estimates epistemic uncertainty using a sparse Bayesian neural network (BNN). By leveraging sparse BNNs, the model significantly reduces computational costs while preserving registration accuracy, even with a limited subset of important Bayesian weights. This is the first probabilistic model to simultaneously account for both uncertainties in the context of bidirectional DVFs, which sets it apart from previous models that typically address one type of uncertainty or focus on single-directional registration.
- 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.
Outdated Baseline Comparisons: The baseline models used for comparison in the paper are quite old. To strengthen the evaluation, the authors should include more recent and relevant baseline methods to provide a more comprehensive and up-to-date comparison.
- 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
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- 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?
My primary focus is on the innovation and reliability of the experimental results. This paper presents the inverse consistent image registration, combining two symmetric VAEs with a sparse Bayesian Neural Network (BNN) to address both aleatoric and epistemic uncertainty in bidirectional DVFs. The experiments show significant improvements across four public cardiac datasets, particularly for small datasets, and provide valuable uncertainty quantification for clinical applications.
- Reviewer confidence
Confident but not absolutely certain (3)
- [Post rebuttal] After reading the authors’ rebuttal, please state your final opinion of the paper.
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- [Post rebuttal] Please justify your final decision from above.
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Author Feedback
Reviewer #1 and #2 Q1: High computational costs and complex; no BNNs without using sparse are compared.
A1: Bidirectional registration inherently introduces higher computational complexity compared to unidirectional methods. Training traditional BNNs is also computationally intensive [1, 14]. Our BNN training offers two advantages: (1) it avoids repeated parameter sampling; and (2) the incorporation of sparsity further improves training efficiency. The training efficiency of our BNN is comparable to that of standard neural networks. The average epoch time of our model is 2.8 and 1.75 times that of other unidirectional and bidirectional models listed in Table 2. We further implemented a non-sparse BNN using Dropout, which increases computation time by 6% and degrades the Dice by 0.5% compared to ICRnet. In contrast, our model decreases computation cost by 65% and improves the Dice by 0.45%. We choose non-Bayesian methods as baselines for comparison, as their computational efficiency is comparable to that of our proposed method, shown in the last table of the supplementary materials.Q2. Why was γ=20% chosen? Whether the model can handle images with large deformations. Reproducibility of the paper. A2: Experimental results using different γ are provided in the supplementary materials. We selected γ = 20% because it offers a better trade-off between accuracy and efficiency.
Cardiac images are captured at the ED and ES in a cardiac cycle, which inherently involve large deformations. The top and bottom rows in Figure 2 illustrate examples of the source and target images, respectively, which clearly show a large deformation between the two images. The experimental results validate the effectiveness of our model in registration with large deformations.
We have uploaded our code to GitHub: https://github.com/ysl-1314/ICRnet-sBNN.git
Q3: Snapshot of \hat{D}. A3: Each column of \hat{D} is the difference between the snapshot of \theta_i and the average of L snapshots.
Q4: No statistical evaluation of the results is provided, nor is there a comparison to traditional iterative methods.
A4: The t-test was conducted to examine whether there was a significant difference in Dice between our model and other models. It showed a p-value of 0.003, indicating statistical significance at the 0.05 level.
Traditional iterative methods require optimization for each input, resulting in low efficiency in applications. Deep learning-based approaches offer significantly faster inference, making them more suitable for applications, and have become the dominant paradigm in image registration. Our work is developed within the DL-based registration framework; So, traditional iterative methods were not included for comparison.
Reviewer #3 Q1: Outdated Baseline Comparisons.
A1: The baseline models used for comparison in the paper include classical VAE-based ([21,9,11,8]) and inverse-consistent-based ([27,17,24]). The work [11] is the most recent literature related to ours, and other related methods proposed in 2024 and 2023 are all improvements based on it. Therefore, we adopt it as a baseline for comparison. In recent years, there has been limited research focusing on inverse-consistent registration, except for GradICON (2023). However, GradICON aimed to regularize deviations of the Jacobian from the identity maps, which applies to small deformations. We implemented the state-of-the-art models TransMatch (2023), LL-Net (2024), and GradICON (2023). The experimental results indicate that these models lead to a large bending energy of DVF and a large ICE between bidirectional DVFs, with Dice scores on the two test datasets barely reaching, or failing to reach, 0.8. This is lower than the accuracy of our model, which achieved Dice scores of 0.88 and 0.90 on the two test datasets, respectively. The inferior performance of TransMatch and LL-Net is due to insufficient control over DVFs, which is not applicable to cardiac image registration.
Meta-Review
Meta-review #1
- Your recommendation
Provisional Accept
- 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”.
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