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Abstract
We present a method, open-source software, and experiments which embed arbitrary deformation vector fields produced by any method (e.g. ANTs or VoxelMorph) in the Large Deformation Diffeomorphic Metric Mapping (LDDMM) framework. This decouples formal diffeomorphic shape analysis from image registration, which has many practical benefits. Shape analysis can be added to study designs without modification to already chosen image registration methods and existing databases of deformation fields can be reanalyzed within the LDDMM framework without repeating image registrations. Pairwise time series studies can be extended to full time series regression with minimal added computing. The diffeomorphic rigor of image registration methods can be compared by embedding deformation fields and comparing projection distances. Finally, the added value of formal diffeomorphic shape analysis can be more fairly evaluated when it is derived from and compared to a baseline set of deformation fields. In brief, the method is a straightforward use of geodesic shooting in diffeomorphisms with a deformation field as the target, rather than an image. This is simpler than the image registration case which leads to a faster implementation that requires fewer user derived parameters.
Links to Paper and Supplementary Materials
Main Paper (Open Access Version): https://papers.miccai.org/miccai-2025/paper/3223_paper.pdf
SharedIt Link: Not yet available
SpringerLink (DOI): Not yet available
Supplementary Material: Not Submitted
Link to the Code Repository
https://github.com/GFleishman/lddmem
Link to the Dataset(s)
N/A
BibTex
@InProceedings{FleGre_LDDMEm_MICCAI2025,
author = { Fleishman, Greg M. AND Fletcher, P. Thomas},
title = { { LDDMEm: Large Deformation Diffeomorphic Metric Embedding: Decoupling Shape Analysis from Image Registration } },
booktitle = {proceedings of Medical Image Computing and Computer Assisted Intervention -- MICCAI 2025},
year = {2025},
publisher = {Springer Nature Switzerland},
volume = {LNCS 15962},
month = {September},
page = {323 -- 332}
}
Reviews
Review #1
- Please describe the contribution of the paper
The paper proposes to use a vector field from any registration method embed it in the LDDMM and then interpolate and extrapolate the deformation. This approach is less computationally expensive way than classic LDDMM, as fitting a deformation field is simpler than fitting an image. The method is applied to synthetic image and to a longitudinal public MR dataset.
- 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 is clearly written, with a good introduction on LDDMM (although probably too long). The proposed method is applied on a both a synthetic toy example and a real clinical dataset. Experiments use and compare 3 SoTA registration methods as the vector field to match. Code is made available.
- 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.
Experiments on real data are inconclusive : the proposed method does not yield better than naïve approaches for interpolation and extrapolation. Unexpected results are observed at t=2, where the method gives better results than direct registration when it should not: the authors say they “have not yet determined an exact reason”. The proposed method is claimed to be simpler and faster than conventional LDDM but no comparison is made with LDDMM and no computation times are not reported. The paper lacks a discussion and conclusion section, and its motivation section is too detailed. In synthetic experiments results are reported on just 1 instance of the momentum field. Also, the MSE is only communicated for t=16.
- 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?
My recommandation is based on 2 factors: 1/the experiments on real data do not show an improvement brought by the method compared to a naive approach. The results raise questions that the authors say they cannot answer. 2/the absence of comparison with classic (image driven) LDDMM. The paper claims the proposed method is simpler but does not prove it experimentally.
- 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.
I stand by my initial review. The authors produce 9 experiments on clinical data. In 6 of these experiments, they expect their method to outperform the naive approach but it does not (the one significant result corresponds to a very small effect). In 3 of these experiments, the method is not expected to outperform the naive approach but it does by a significantly and by wide margin (the authors use the term ‘curiously’ and say they “have not yet determined an exact reason”).
Review #2
- Please describe the contribution of the paper
This work proposes a method for transforming any solution from any non-rigid registration method into an initial velocity field from which conduct shape analysis from the corresponding geodesic shooting path. Depending on the usability of the solutions in real clinical aplications, the proposed method would provide the oportunity to conduct shape analysis in a correct mathematical framwork from any non-rigid registration method. This would displace the need for developing methods based on the EPDiff equation to the need of developing methods whos embeddings provide acceptable results in shape analysis 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.
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The idea is related to the problem of estimating the logarithm map in the manifold of diffeomorphisms. However, the authors extend the motivation to any arbitrary algorithm opening the posibility that all non-rigid registration methods can be used in shape analysis.
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The formulation of the solution is brilliant. Starting from Vialard and Singh approach from Hamiltonian physics, the authors derive the equations for the computation of the embedding from gradient descent.
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The background summary is a good recall of more than 10 years old papers.
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- 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 major weakness of the paper are in the experimental section. Some of the figures are hard to interpret with the information given in the manuscript. In addition, there are fundamental questions that would empirically support the validity of the idea that have not been explored.
- 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
I have some questions, ideas, or suggestions that may help improving the experimental section:
1) The authors should justify the different VoxelMorph models between 2D and 3D experiments. I believe that the 2D experiments included training and testing for the generation of a model that is trained to learn to register this ellipse experiments. So this may be clarified.
2) The paragraph and the results shown in Figure 2 are confusing. I suggest rewriting having the reader in mind. For example, what does the first subfigure show? Displacements, v0s? Besides, why is the vector field from VoxelMorph like that?
Regarding the boxplots, the authors are plotting the MSE from the different experiments. The orange bars show the naive interpolation / extrapolation and the green bars show the embedding interpolation / extrapolation results. Is this right? It is too striking that the green bar at 12 months shows such a low standard deviation.
“The extrapolation effect observed in the synthetic experiments is only present for the ANTs transforms” I was not able to identify this phenomenon in the figures. Did the authors mean the result for Simple ITK?
Why did the authors mention on the experiment between 3 and 36 months? Why did they decided not to show those results?
3) How extreme are the differences between 6, 12, and 24 month images? According to my experience they tend to be quite small.
4) It would be great to include in the study comparison with an EPDiff-based method such as Flash. Would the embedding differ greatly from the real solution?
5) Since there are non-rigid image registration methods that provide highly non-diffeomorphic results I am intrigued on how would the embedding work in aread with very negative Jacobians.
6) I would suggest changing the paragraph with the software implementation. The different modules can be guessed straightforwardly from the numerical description of the method. It would be more informative to improve the explanation of the results, to give results concerning the computational complexity, future work aplications, and providing a convincing conclusion.
- 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?
As I said, I believe that the methodological section of the manuscript is brilliant. The method is of quite relevance to non-rigid registration community. However, the experimental section should be enhanced to demonstrate the potential of the method in important applications of shape analysis. I could change my opinion depending on the rebuttal.
- 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 hope the authors will take into account my comments to improve the quality of the manuscript. Nice work.
Review #3
- Please describe the contribution of the paper
LDDMEm enables the separation of formal diffeomorphic shape analysis from image registration. It can embed deformation vector fields generated by any method (like ANTs or VoxelMorph) into the LDDMM framework.
- 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 presents the Large Deformation Diffeomorphic Metric Embedding (LDDMEm) method, which embeds arbitrary deformation vector fields into the LDDMM framework. This decouples formal diffeomorphic shape analysis from image registration. Instead of directly registering images within the LDDMM framework, LDDMEm works with pre - computed deformation vector fields generated by other methods (such as ANTs or VoxelMorph).
- 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.
- Comparisons of alignment effects were not performed with additional metrics.
- fig 2 is not clear enough
- Does the initially given deformation field affect the performance of the alignment?
- 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.
- 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.
(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?
The work is innovative, but there are no more comparative experiments on whether it depends on a given deformation field.
- Reviewer confidence
Somewhat confident (2)
- [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 are grateful to reviewers and chairs for their time, effort, and insight.
The reviews demonstrate understanding of our methodological contribution. The formulation in eqn (5) is novel and eqns (6) and (7) facilitate hitherto unexplored capabilities in non-rigid registration. This was not disputed in any review.
Some concerns are raised regarding experiments. Thank you for the helpful contributions. First we address a few misunderstandings.
The first point by reviewer 2 to justify their recommendation is incorrect. It contradicts their own prior statement, “Unexpected results are observed at t=2, where the method gives better results than direct registration when it should not…” Results at t=2 are indeed unexpected and evidently better than direct registration. The error is to assume this “should not” be observed. We do not dismiss our experiments when they surprise us, we accept and try to understand them. In hindsight, there are legitimate considerations which may explain this. Post-process regularization is beneficial in many applications, and projecting transforms to a smoother space will regularize. Moreover, a statistically significant improvement in extrapolation is observed for embedded ANTs transforms at 24 months. Reviewer 2 may have overlooked this supportive evidence and mistakenly claimed it is absent. We entreat reviewer 2 to consider their assumptions and re-evaluate our statistically significant results.
The second point made by reviewer 2 contains a fair suggestion (also made by reviewer 1) to compare with LDDMM registration. We would love to include this when we pursue a journal paper with more space. Review guidelines acknowledge that papers are acceptable as works in progress and new experiments cannot be added. We have made a sound and undisputed methodological contribution and supported it with preliminary experiments. Sharing this preliminary work at MICCAI will help us gather more helpful insights, like those provided by our reviewers, so that our contribution can be made more useful to the community.
This second point also contains a misunderstanding. Our claim that LDDMEm is simpler than LDDMM registration is methodologically self-evident. LDDMM registration requires matching noisy images. This is rarely done with MSE and typically requires LCC or MI, which are costly and require hand-picked parameters. LDDMEm instead reconstructs a single given displacement field, for which MSE is always sufficient. This is a simplification.
Now Addressing a few specific points: Pre-trained VoxelMorph 2D-shape and 3D-brain-mri models were both obtained from the VM repository and were each the most appropriate model for their use case.
The fields in figure 2 upper left indeed lack description. We will correct this. The top row are fields produced by the three direct registration methods. The bottom row are embeddings of those fields returned by LDDMEm. The top row VM transform is likely noisy because the ML approach does not explicitly enforce smoothness at evaluation as the classical methods do.
The variance of results in figure 2 scales with the mean. The Index of Dispersion is comparable for all methods and time points.
Extrapolation of ANTs embeddings in figure 2 is significantly better than naive, though with small amplitude. ANTs performed the best of the three registrations before LDDMEm. It is likely the embeddings are higher quality as well and thus extrapolate better.
Brain deformation magnitude over 2 years is indeed quite small relative to the spatial sampling rate and SNR. Measuring it, and extrapolating it, is difficult. Benefits of LDDMEm may be even more salient over longer time scales. We intend to explore this in future work.
We are also very curious to explore how LDDMEm will modify non-diffeomorphic transforms. Though not explored in the present work, correcting topology is a valid LDDMEm application.
We sincerely hope to discuss these and more suggestions and concerns at MICCAI.
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’
N/A
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. You may optionally write justifications for ‘accepts’, but are expected to write a justification for ‘rejects’
After reading the paper, I agree with R1 and R3 on the technical novelty and methodological contribution of this paper. The experimental evaluations are sufficient, although some of them do not have the best performance, I believe the paper itself still has merit that overweighs the meaning of higher numbers. My recommendation is accept.