List of Papers By topics Author List
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Authors
Fenqiang Zhao, Zhengwang Wu, Li Wang, Weili Lin, Gang Li
Abstract
Spherical mapping of cortical surface meshes provides a more convenient and accurate space for cortical surface registration and analysis and thus has been widely adopted in neuroimaging field. Conventional approaches typically first inflate and project the original cortical surface mesh onto a sphere to generate an initial spherical mesh which contains large distortions. Then they iteratively reshape the spherical mesh to minimize the metric (distance), area or angle distortions. However, these methods suffer from two major issues: 1) the iterative optimization process is computationally expensive, making them not suitable for large-scale data processing; 2) when metric distortion cannot be further minimized, either area or angle distortion is minimized at the expense of the other, which is not flexible to generate application-specific meshes based on both of them. To address these issues, for the first time, we propose a deep learning-based algorithm to learn the mapping between the original cortical surface and spherical surface meshes. Specifically, we take advantage of the Spherical U-Net model to learn the spherical diffeomorphic deformation field for minimizing the distortions between the icosahedron-reparameterized original surface and spherical surface meshes. The end-to-end unsupervised learning scheme is very flexible to incorporate various optimization objectives. We further integrate it into a coarse-to-fine multi-resolution framework for better correcting fine-scaled distortions. We have validated our method on 800+ cortical surfaces, demonstrating reduced distortions than FreeSurfer (the most popularly used tool), while speeding up the process from 20 minutes to 5 seconds.
Link to paper
DOI: https://link.springer.com/chapter/10.1007/978-3-031-16446-0_16
SharedIt: https://rdcu.be/cVRSW
Link to the code repository
N/A
Link to the dataset(s)
N/A
Reviews
Review #1
- Please describe the contribution of the paper
This paper proposes a spherical mapping of cortical surfaces using spherical convolution [29]. The proposed method infers a deformation field to adjust triangles on the unit sphere to minimize the mapping distortions. Three distortion metrics are used for computing deformation fields, and L2 regularity is introduced for a smooth velocity field. The experimental results show that the proposed method achieves a fast spherical mapping compared to the baseline methods.
- 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.
A spherical mapping is key in many surface-based analysis for cortical surface registration, parcellation, etc. In this paper, a fast spherical mapping was proposed that significantly reduces the computing time over the classic approach such as FreeSurfer. The approach is non-supervised, which is also an advantage of the proposed method.
- 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.
See the comments below.
- 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
Seems reproducible.
- Please provide detailed and constructive comments for the authors. Please also refer to our Reviewer’s guide on what makes a good review: https://conferences.miccai.org/2022/en/REVIEWER-GUIDELINES.html
The proposed method utilizes existing spherical CNNs [29]. The central idea of spherical deformation is based on Spherical Demons that employs diffeomorphic deformation over a stationary vector field using the scaling and squaring approach. This is also used in [24] for spherical CNNs-based surface registration. Although a combination of several metric losses is incorporated, this paper technically reads an application of what was proposed in [24]. A hierarchical optimization has been widely adapted in classic surface registration. I think the paper needs some acknowledgement of the previous studies. In terms of their methodological descriptions.
Local charts of the velocity field are presumably predefined. To learn deformation fields, spherical CNNs need to support rotation-equivariance as initial mappings are not necessarily aligned. As such is absent in [29], rigid alignment and possibly data augmentation may be required for the proposed framework. In particular, [29] defines a spatial filter on an icosaherdral mesh with a specific order of neighborhoods, where the performance may depend on the alignment of initial mappings. The authors claim that the IAP is used due to its popularity, but the proposed method perhaps works because the initial mappings are already roughly well aligned?
Please provide more in-depth rationale of the average convexity for this work. The average convexity roughly captures overall sulcal patterns but offers a rougher representation than other fine geometry such as mean curvature. Fine features might work better to capture local deformation.
As the authors pointed, FreeSurfer has an extra step after spherical mapping that unfolds self-intersection. This is another bottleneck in FreeSurfer. Even if the proposed approach models diffeomorphism, the resulting deformation can practically have self-intersection since the re-tessellation introduces sampling errors and the deformation field is defined on an icosahedral mesh.
The experimental results also need to be interpreted carefully. For example, if some method uses a conformal mapping, large distortion in distance or area is somewhat expected. Indeed, an isometric mapping is not possible, so any mappings have their pros. and cons. depending on which metric they optimize over. Since spherical mappings have several types (conformal, area preserving, etc.), I think a more fair comparison in this work would be to show performance of individual component (loss). This also lies along what the authors claim in the introduction.
What was the step size for the scale and squaring approach? What is the memory requirement for the proposed method? It looks like the reported runtime of the proposed method exclude that of that of the IAP. This is misleading as the IAP is preprocessing in this work.
This paper cites about a third of papers from a specific group, and some of them seem not strongly related to this work. Please focus rather on relevant studies. There are yet other studies for spherical mappings. For instance,
- Choi et al., FLASH: Fast Landmark Aligned Spherical Harmonic Parameterization for Genus-0 Closed Brain Surfaces
- Nadeem et al., Spherical Parameterization Balancing Angle and Area Distortions
- Rate the paper on a scale of 1-8, 8 being the strongest (8-5: accept; 4-1: reject). Spreading the score helps create a distribution for decision-making
4
- Please justify your recommendation. What were the major factors that led you to your overall score for this paper?
See my comments above.
- Number of papers in your stack
5
- What is the ranking of this paper in your review stack?
3
- Reviewer confidence
Very confident
- [Post rebuttal] After reading the author’s rebuttal, state your overall opinion of the paper if it has been changed
4
- [Post rebuttal] Please justify your decision
The authors addressed some of my concerns, but there are still two main points that are not fully addressed.
Technical contribution: I am still not fully convinced by the authors’ claim that the proposed framework fundamentally differs from [24] or Spherical Demons because the way of spherical deformation is identical to what was proposed in [24] or SD. The only difference to spherical registration is that no template is required. I believe the paper is an application of [24] with slight tweak of problem definition (i.e., replacing existing losses (e.g., [11]) and input channels). The authors claim that the CNN part or deformation can be replaced, but this is also true for [24] if diffeomorphism holds.
Evaluation: since this work is about methodology and isometric mapping is theoretically not possible, I think that more intuitive way of evaluation comes from well-known mapping perspectives (area/conformal) and compares some area-preserving/conformal methods to validate how the proposed method works. As also stated by the authors, there is no consensus in spherical mapping in the field, and users should be hence able to decide a proper mapping (area, conformal, or mix) for their study based on what is reported. Please update the inference time or caption in Table 1. The table is not self-contained.
Review #2
- Please describe the contribution of the paper
- Proposes a very efficient method to obtain deformation field to map between spherical mesh and brain mesh.
- The method achieves results with less distortion.
- The method works in an end-to-end manner in an unsupervised way.
- 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.
- Efficiency: proposed framework runs fast.
- Clear writing: the paper is well written.
- 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.
- Lack of experiment with ground truth.
- 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
Probably reproducible.
- Please provide detailed and constructive comments for the authors. Please also refer to our Reviewer’s guide on what makes a good review: https://conferences.miccai.org/2022/en/REVIEWER-GUIDELINES.html
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How is the coarse-to-fine mesh exactly generated? “reparameterize it again using an icosahedron with higher resolution” may not be sufficient and perhaps a reader would like to know the differences between the coarse and fine meshes after reprarmeterization. What properties are maintained after the transform?
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I am wondering if the authors have done any toy experiment with ground truth, although not reported in this paper. I understand that this method operates without supervision; but such an analysis would have been helpful.
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How much of a change is expected at each iteration? Is there a way to control how much to update per iteration (e.g., learning rate) so as to transform the mesh faster or slower?
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- Rate the paper on a scale of 1-8, 8 being the strongest (8-5: accept; 4-1: reject). Spreading the score helps create a distribution for decision-making
6
- Please justify your recommendation. What were the major factors that led you to your overall score for this paper?
Clear novelty and outstanding performance.
- Number of papers in your stack
4
- What is the ranking of this paper in your review stack?
1
- Reviewer confidence
Very confident
- [Post rebuttal] After reading the author’s rebuttal, state your overall opinion of the paper if it has been changed
Not Answered
- [Post rebuttal] Please justify your decision
Not Answered
Review #3
- Please describe the contribution of the paper
In this paper, the authors proposed a novel framework based on Spherical U-Net for spherical mapping of cortical surface meshes. Compared with FreeSurfer, which is the most popular tools for brain images, the proposed method have fewer distortions and achieve a speedup for more than 200 folds.
- 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.
In this paper, the authors proposed a novel framework based on Spherical U-Net for spherical mapping of cortical surface meshes. Compared with FreeSurfer, which is the most popular tools for brain images, the proposed method have fewer distortions and achieve a speedup for more than 200 folds.
- 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 weakness of this work is that Spherical U-Net has been previously proposed. This paper utilized it for spherical mapping.
- 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
The paper meets the requirements of the checklist.
- Please provide detailed and constructive comments for the authors. Please also refer to our Reviewer’s guide on what makes a good review: https://conferences.miccai.org/2022/en/REVIEWER-GUIDELINES.html
More than 800 cortical surfaces were processed by the method. Is there any failed case? If so, what is the reason for the failed cases.
- Rate the paper on a scale of 1-8, 8 being the strongest (8-5: accept; 4-1: reject). Spreading the score helps create a distribution for decision-making
7
- Please justify your recommendation. What were the major factors that led you to your overall score for this paper?
FreeSurfer plays a significant role in medical imaging. The proposed work has fewer distortions and is 200-times faster than FreeSurfer.
- Number of papers in your stack
5
- What is the ranking of this paper in your review stack?
1
- Reviewer confidence
Very confident
- [Post rebuttal] After reading the author’s rebuttal, state your overall opinion of the paper if it has been changed
Not Answered
- [Post rebuttal] Please justify your decision
Not Answered
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.
This paper proposes a novel and fast method to compute the spherical mapping of cortical surfaces, and demonstrated its performance over a large dataset. There is some concern about its novelty relative to the spherical-u-net (ref 29). Also there is a need of clarification with respect to previous works as pointed out by reviewer 1.
- 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). If this paper is among the bottom 30% of your stack, feel free to use NR (not ranked).
5
Author Feedback
We thank all reviewers’ comments and recognition of our contributions: R1: “a fast spherical mapping method significantly reduces the runtime over FreeSurfer”, “non-supervised is also an advantage”; R2: “a very efficient method”, “clear novelty and outstanding performance”, ranking 1/4 in R2 stack; R3: “compared with the most popular tool FreeSurfer, this work has fewer distortions and is 200 times faster”, ranking 1/5 in R3 stack.
R1 and meta-reviewer have concern on the novelty relative to Spherical U-Net [29] and S3Reg [24]. Although our work uses [29] and surface warping layer in [24] as sub-components, it fundamentally differs from them and has novelties in both methodology and application. 1) Methodologically, our whole framework, including the problem formulation, the end-to-end unsupervised learning scheme, the input metric properties and output metric losses, is completely newly designed and proved to be effective and efficient. Moreover, it is very generic, where [29] and [24] can be replaced by other Spherical CNN and surface moving operation. 2) As for application, our method is the first deep learning method developed for spherical mapping of cortical meshes, while Spherical U-Net and S3Reg are for cortical surface parcellation and registration respectively. It achieves smaller distortions and is 200 times faster than the most popular FreeSurfer, demonstrating high potential in clinical practice. As MICCAI welcomes both methodology and application studies, we believe our paper with novelties and contributions in both sides is well suitable for MICCAI audiences. We will highlight these novelties in revision.
R1 questions “rationale of the average convexity used in the work”. We did emphasize twice that “the average convexity is for display purposes ONLY and not used in the model” one in Fig 1’s caption, one in Experiment setting. So this is a big MISUNDERSTANDING of our paper from R1. To clarify again, our method only requires vertices’ coordinates as input, not vertices’ geometric features (e.g., average convexity) that are often used in spherical registration. We will clarify the differences between spherical mapping and registration by citing [4, 5] more clearly.
R1 questions whether initial mappings are roughly aligned. The answer is yes. As a routine preprocess in neuroimage analysis pipeline, e.g., FreeSurfer and HCP pipeline, brain MR images are typically first rigidly aligned and thus subsequent surface reconstruction and initial mappings are also roughly aligned.
R1 suggests a fair comparison and interpretation of individual loss, which is exactly what we showed in Table 1 and why we compared with model trained with smaller area weight. We understood the concern and did emphasize that “all three standard distortion metrics are reported in case that one metric is optimized at the cost of the other” and interpreted all metrics for all methods in Page 7.
R1 concerns that “reported runtime exclude that of IAP which is misleading”. R1 might overlook our paper again since we already clarified that in Page 8, “note that our method uses IAP strategy to generate initial spherical mesh which takes extra ∼7 sec. Nevertheless, it is still much faster than FreeSurfer”, which also takes the extra ~7 sec.
R1 suggests comparing with Choi et al and Nadeem et al’s methods. We previously run Choi’s method and the results are 41.84±5.88%, 74.71±8.36%, 1.34±0.21° for metric, area and angle distortions respectively. The area and metric distortions are much worse than ours in Table 1. Surfaces with so large area distortion are not practically useful for downstream analysis. We did not report these results due to page limit, but we will add them in revision. Nadeem’s code is not public available.
R1 concerns on potential self-intersections. In our experiment with 864 surfaces, we did not find any self-intersections. Even if there are self-intersections in very rare cases, they can be easily unfolded by classic algorithms.
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 rebuttal addresses most of the concerns from the reviewers. The novel method and the good performance from the work justifies the acceptance of this paper.
- 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/n (best paper in your stack) and n/n (worst paper in your stack of n papers). If this paper is among the bottom 30% of your stack, feel free to use NR (not ranked).
4
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.
The reviewers have converged to accept decision after the rebuttal, major concerns have been addressed.
- 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/n (best paper in your stack) and n/n (worst paper in your stack of n papers). If this paper is among the bottom 30% of your stack, feel free to use NR (not ranked).
2
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.
The paper makes a good contribution for MICCAI. While there were issues raised with citing previous work, the authors have addressed the reviewer concerns in the rebuttal.
- 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/n (best paper in your stack) and n/n (worst paper in your stack of n papers). If this paper is among the bottom 30% of your stack, feel free to use NR (not ranked).
7