Paper Info Reviews Meta-review Author Feedback Post-Rebuttal Meta-reviews

# Authors

Jian Wang, Miaomiao Zhang

# Abstract

This paper presents a novel hierarchical Bayesian model for unbiased atlas building with subject-specific regularizations of image registration. We develop an atlas construction process that automatically selects parameters to control the smoothness of diffeomorphic transformation according to individual image data. To achieve this, we introduce a hierarchical prior distribution on regularization parameters that allows multiple penalties on images with various degrees of geometric transformations. We then treat the regularization parameters as latent variables and integrate them out from the model by using the Monte Carlo Expectation Maximization (MCEM) algorithm. Another advantage of our algorithm is that it eliminates the need for manual parameter tuning, which can be tedious and infeasible. We demonstrate the effectiveness of our model on 3D brain MR images. Experimental results show that our model provides a sharper atlas compared to the current atlas building algorithms with single-penalty regularizations. Our code is publicly available at https://github.com/jw4hv/HierarchicalBayesianAtlasBuild

# Link to paper

SharedIt: https://rdcu.be/cyhPP

# Reviews

### Review #1

• Please describe the contribution of the paper

This paper propose a method to build an atlas using a hierarchical bayesian model. The model uses subject-specific regularisations and the LDDMM framework. The model automatically selects parameters of the diffeomorphic deformations.

• Please list the main strengths of the paper; you should write about 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.

Main strength: The motivation of the paper is relevant as indeed, tuning parameters is an issue in deformation-based analysis. Also, the method is clearly presented.

• Please list the main weaknesses of the paper. Please provide details, for instance, if you think a method is not novel, explain why and provide a reference to prior work.

Main weakness: Results are not conclusive as there is no analysis of the results. There is no information about computation time nor memory usage.

• Please rate the clarity and organization of this paper

Very Good

• Please comment on the reproducibility of the paper. Note, that authors have filled out a reproducibility checklist upon submission. Please be aware that authors are not required to meet all criteria on the checklist - for instance, providing code and data is a plus, but not a requirement for acceptance

Method is well described, making possible, though not straightforward, the implementation of the method from the paper.

• Please provide detailed and constructive comments for the authors. Please also refer to our Reviewer’s guide on what makes a good review: https://miccai2021.org/en/REVIEWER-GUIDELINES.html
• Results and experiment do not really support the method. For example, at Figure 1 it is very difficult to see differences between the different results.
• There is no significance test run on the different metrics (sharpness and dice). This would help to understand how the method affect the results.
• It could be interesting to have information about the estimated subject-specific parameters, for each considered structures.
• I think the important here, is to show that the method does at least as good as when parameters are manually chosen by expert. The principal issue being to choose those parameters. Therefore I would expect analysis on the selected parameters rather than on the accuracy of the method (which is needed to say that the method does what it is meant to do, but it is not sufficient for the problem raised).
• As atlas are build for statistical analysis, I feel a bit frustrated not to see such analysis, even if I acknowledge that the length of the paper might need to rewrite the whole section 4 or provide to do it here (as authors said, they will do it in a future work), which make this point a minor comment.
• Please state your overall opinion of the paper

accept (8)

• Please justify your recommendation. What were the major factors that led you to your overall score for this paper?

The method is well presented and seems promising despite the limited results section.

• What is the ranking of this paper in your review stack?

1

• Number of papers in your stack

3

• Reviewer confidence

Very confident

### Review #2

• Please describe the contribution of the paper

A Bayesian atlas building algorithm where individual regularization factors are treated as random realizations from a shared hyper-prior and marginalized. Experiments show through improved atlas crispness and improved Dice score between warped anatomical masks that the proposed approach generates more accurate transformations than standard LDDMM with fixed regularization.

• Please list the main strengths of the paper; you should write about 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.

Excellent theoretical background. While works stemming from the same theoretical framework had been used to generate atlases with either ML or MAP optimal regularization parameters, this paper is the first that successfully marginalizes regularization parameters at the subject level.

• Please list the main weaknesses of the paper. Please provide details, for instance, if you think a method is not novel, explain why and provide a reference to prior work.

Works in a similar line of work have repeatedly pointed the benefit of marginalizing deformations when building atlases. While this method marginalizes regularization, it does not integrate deformations out. While there may be decent reasons for it (one of them being the computational cost of HMC on velocity fields – even though the Fourier representation is supposed to alleviate this problem in part), they should be discussed in the manuscript.

• Please rate the clarity and organization of this paper

Excellent

• Please comment on the reproducibility of the paper. Note, that authors have filled out a reproducibility checklist upon submission. Please be aware that authors are not required to meet all criteria on the checklist - for instance, providing code and data is a plus, but not a requirement for acceptance
• Code not available
• Optimization parameters are provided.
• Please provide detailed and constructive comments for the authors. Please also refer to our Reviewer’s guide on what makes a good review: https://miccai2021.org/en/REVIEWER-GUIDELINES.html

• In the hyper-prior section, the possible use of an inverse-wishart distribution as a prior for alpha is mentioned. The inverse wishart is a conjugate prior for covariance matrices. Since L acts more like a precision matrix, the gamma distribution (or the Wishart, which reduces to Gamma in dimension 1) is the appropriate prior.
• The equations stop being numbered suddenly in section 3. It would help numbering them as well.
• Is there a typo in equation (2), (4) and in the second equation of section 3? Given the way L is defined, I would assume that the inner product should be <v, Lv> (with L positive definite) instead of <Lv, Lv>.
• Please state your overall opinion of the paper

strong accept (9)

• Please justify your recommendation. What were the major factors that led you to your overall score for this paper?

The theory is sound and the validation convincing. The methods shows the advantage of marginalizing subject-level variables when building population atlases.

• What is the ranking of this paper in your review stack?

1

• Number of papers in your stack

4

• Reviewer confidence

Very confident

### Review #3

• Please describe the contribution of the paper

This article merges the Bayesian formulation for atlas construction proposed in [29] with the Fourier approximation of diffeomorphic registrations from [28]. The only novelty is a, I would say controversial, subject-specific deformation regularity.

• Please list the main strengths of the paper; you should write about 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 correctly points out the need for an automatic, reproducible and consistent method for atlas construction
• Differently from [29], the regularization hyper-parameters are now estimated and not fixed by the user
• Please list the main weaknesses of the paper. Please provide details, for instance, if you think a method is not novel, explain why and provide a reference to prior work.
• The only novelty of this paper is the definition of a subject specific regularization term. It’s not clear why different subjects would need a different regularization if they belong to the same population and above all how to compute statistics with the estimated deformations, since they would not come from the same distribution.
• Results are not convincing
• Please rate the clarity and organization of this paper

Good

• Please comment on the reproducibility of the paper. Note, that authors have filled out a reproducibility checklist upon submission. Please be aware that authors are not required to meet all criteria on the checklist - for instance, providing code and data is a plus, but not a requirement for acceptance
• Authors do not give access to their code (and don’t say they will do it after review)
• There are not enough computational details to reproduce the experiments shown in the paper (for instance, about how to truncate the convolutions or how many samples S are used for Eq.6)
• Please provide detailed and constructive comments for the authors. Please also refer to our Reviewer’s guide on what makes a good review: https://miccai2021.org/en/REVIEWER-GUIDELINES.html

The use of a subject-specific regularization implies that subjects need a different kind of regularization and thus that their deformations come from different distributions. Is it really the case? Or is it the case only for subjects belonging to different clinical populations (i.e., healthy Vs patients)? Have the authors looked at the estimated $\alpha_n$? Are they different? And above all, how to compute statistics with your new framework? Have authors considered estimating a single $\alpha$ for the entire population instead than one for each subject? It would be interesting to compare the results. I think that these are important questions that authors should consider answering in a next version of the paper.

• Please state your overall opinion of the paper

reject (3)

• Please justify your recommendation. What were the major factors that led you to your overall score for this paper?
• The novelty is quite incremental with respect to [29] and [28] and results do not show a statistically significantly improvement over the framework of [29]
• It is not clear when and why a subject-specific deformation regularization would be useful and how to compute statistics with it
• What is the ranking of this paper in your review stack?

2

• Number of papers in your stack

3

• Reviewer confidence

Confident but not absolutely certain

# Primary Meta-Review

• Please provide your assessment of this work, taking into account all reviews. Summarize the key strengths and weaknesses of the paper and justify your recommendation. 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.

Summary: This paper propose a method of atlas construction using the LDDMM framework within a hierarchical Bayesian model, which allows subject-specific regularisations settings to be determined. This one split the reviewers. One objected to it being incremental and that there should not be subject-specific regularisation, whereas the other two were much more positive. The authors should try to satisfy that reviewer.

Positives:

• Tuning regularisation settings is an important, and overlooked, issue in registration.
• Good theoretical background, and the first work to successfully marginalize regularization parameters at the subject level.
• Clearly presented, but more could be done regarding reproducibility (link to where code will eventually reside).

Negatives:

• Considered to be too incremental by one reviewer, given how much it builds on previous work.
• Unclear why different subjects would need a different regularization if they come from the same population. This really needs to be justified.
• Results are not conclusive and probably need some statistical analysis to demonstrate any benefits.
• No information about computation time or memory usage.
• What is the ranking of this paper in your stack? Use a number between 1 (best paper in your stack) and n (worst paper in your stack of n papers).

3

# Author Feedback

We thank the valuable feedback and suggestions provided by all reviewers. The reviewers’ major questions are addressed below:

[To Meta & R1 & R2 & R3] Reproducibility We will work on releasing the code when this work is published.

[To Meta & R3] Novelty We appreciate both R1 and R2’s positive comments on the motivation of the paper, as well as pointing out that our work is the first to successfully marginalize regularization parameters of registration-based atlas building at the subject level. For R3’s question on the novelty, we’d also like to emphasize that the methodological development of hyper-prior combined with the MCEM sampling is newly introduced to the atlas building problem.

[To Meta & R1 & R3] Adding statistical analysis of the estimated results Thanks to all suggestions on the statistical analysis of the estimated results. As R1 suggested, we will add significance tests on the metrics of sharpness and dice in the revised version of our paper. We will also consider running population-based statistics by using the estimated atlas in an extended journal version of the current manuscript.

[To Meta & R2] Computational time and memory consumption The computational complexity of the proposed algorithm majorly lies on the sampling (E step) and gradient-based optimization of registration (M step). Our low-dimensional framework with Fourier representations enables the entire inference much more computationally feasible than baselines conducted in the high-dimensional image domain (as R2 mentioned). We will add a figure of averaged computational time and memory consumption in the revised version of our paper.

[To Meta & R3] Motivations/Reasonings of subject-specific regularization
Thanks for this question. We agree with R3 that the regularizations could be similar if the group data has small variability. However, the ‘one-fits-all’ fails in cases where large geometric variations occur, i.e., brain shape changes of Alzheimer’s disease group. Allowing the subject-specific (data-driven) regularization can substantially affect the sharpness and quality of the atlas (this was discussed in Yeo et.al., 2008). We also showed a comparison between our method and single regularization parameter estimation in Fig.1 and Fig. 2. Another motivation to develop subject-specific regularization is that our current model can be easily extended to multi-atlas settings where much higher degree of variations exist in the population studies. We will add the clarifications in the revised paper.

[To R1] Information of estimated parameters & comparison with parameters manually selected by experts Thanks for R1’s great suggestions. We will add the statistics (i.e., mean and variance) of the samples of each subject-specific parameter. We will also try to find experts to manually select the regularization parameters and compare them with our estimates.

All minor comments will be carefully addressed in the revised paper.

# Post-rebuttal Meta-Reviews

## Meta-review # 1 (Primary)

• Please provide your assessment of the paper taking all information into account, including rebuttal. Highlight the key strengths and weaknesses of the paper, clarify how you reconciled contrasting review comments and scores, indicate if concerns were successfully addressed in the rebuttal, and provide a clear justification of your decision. If you disagree with some of the (meta)reviewer statements, you can indicate so in your meta-review. Please make sure that the authors, program chairs, and the public can understand the reason for your decision.

The authors say that their revised version will address most of the concerns of the one critical reviewer, although no promises are made about releasing code and the authors say that one of the statistical analyses will be left for an extended journal version. Other reviewers are very positive about the work, and the authors have made some effort to motivate their use of subject-specific regularisation.

• After you have reviewed the rebuttal, please provide your final rating based on all reviews and the authors’ rebuttal.

Accept

• What is the rank of this paper among all your rebuttal papers? Use a number between 1 (best paper in your stack) and n (worst paper in your stack of n papers).

1

## Meta-review #2

• Please provide your assessment of the paper taking all information into account, including rebuttal. Highlight the key strengths and weaknesses of the paper, clarify how you reconciled contrasting review comments and scores, indicate if concerns were successfully addressed in the rebuttal, and provide a clear justification of your decision. If you disagree with some of the (meta)reviewer statements, you can indicate so in your meta-review. Please make sure that the authors, program chairs, and the public can understand the reason for your decision.

This work proposes a Bayesian atlas-building strategy based on LDDMM. In particular, the goal is to avoid tuning of hyperparameters by marginalizing over the regularization parameters. The work is interesting and hyperparameter tuning is always hard in registration so a method that can help alleviate this burden is appreciated. However, the rebuttal is a bit unsatisfying, because it does not provide much concrete information as requested by the reviewers (e.g., what is the runtime and the memory consumption? Are results statistically significantly different?). While it is commendable that the authors want to include this information in a final version some of it seems to be simple enough to do so that it could have also been provided for the rebuttal. The biggest reviewer question was if it is useful to have subject-specific regularization. The authors argue (in the rebuttal) that this is useful for atlas sharpness and to obtain good registration results for large deformations for example when warping an atlas for multi-atlas segmentation. This might indeed be the case, but misses (I believe) the point of R3 a bit. My understanding of it is that his/her comment was more related to the statistical analysis of deformations, which becomes unclear if every case is regularized differently. Such potential issues should be acknowledged in a final version. Further, it is unclear to this AC that a sharp atlas is necessarily a good atlas. Minor comment: on page 4 in the hyperprior section there appears to be a missing reference (shown as ??) which should be fixed.

• After you have reviewed the rebuttal, please provide your final rating based on all reviews and the authors’ rebuttal.

Accept

• What is the rank of this paper among all your rebuttal papers? Use a number between 1 (best paper in your stack) and n (worst paper in your stack of n papers).

8

## Meta-review #3

• Please provide your assessment of the paper taking all information into account, including rebuttal. Highlight the key strengths and weaknesses of the paper, clarify how you reconciled contrasting review comments and scores, indicate if concerns were successfully addressed in the rebuttal, and provide a clear justification of your decision. If you disagree with some of the (meta)reviewer statements, you can indicate so in your meta-review. Please make sure that the authors, program chairs, and the public can understand the reason for your decision.

This paper got mixed reviews, and critiques by all see somewhat limited novelty and need for more comparison/evaluation. There are definitely merits, but this Meta reviewer also sees incremental novelty in particular compared to [28] and [29], with mainly adding a subject-specific regularization. In their rebuttal, authors responded by acknowledging that significant more work related to statistical analysis, population-based analysis and statistics, and that code will need to be made available. Results as presented are validated via common metrics, but with the expectation of getting sharp templates also in comparison to different atlas-building methodologies, they are not fully convincing and conclusive. Enthusiasm of this current version for MICCAI is therefore limited.

• After you have reviewed the rebuttal, please provide your final rating based on all reviews and the authors’ rebuttal.

Reject

• What is the rank of this paper among all your rebuttal papers? Use a number between 1 (best paper in your stack) and n (worst paper in your stack of n papers).

11