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Abstract
Cortical shape correspondence is a crucial problem in medical image analysis, primarily focused on aligning cortical geometric patterns across individuals. This task is particularly challenging due to the intricate geometry of the cortex and the substantial anatomical variability among individuals. In this work, we introduce a novel approach comprising (1) a spherical diffusion process and (2) a spectral attention for robust shape correspondence construction, wherein a score function from the diffusion process guides a deformation to align cortical geometric features on sphere. Specifically, we propose a smooth diffusion process on sphere by introducing a stochastic differential equation in a spherical harmonic space, where we learn the score function that encodes the distribution of subjects. Furthermore, to effectively guide the alignment of cortical geometric patterns using the learned score function, we propose a novel attention mechanism that computes frequency correlations in the spectral domain, enabling efficient conditioning of the score function in this domain. Experimental results demonstrate that our method achieves highly accurate shape correspondence while minimizing the distortions. The code is available at https://github.com/Shape-Lab/SPHARM-Reg-Diffusion.
Links to Paper and Supplementary Materials
Main Paper (Open Access Version): https://papers.miccai.org/miccai-2025/paper/1268_paper.pdf
SharedIt Link: Not yet available
SpringerLink (DOI): Not yet available
Supplementary Material: Not Submitted
Link to the Code Repository
https://github.com/Shape-Lab/SPHARM-Reg-Diffusion
Link to the Dataset(s)
N/A
BibTex
@InProceedings{LeeSeu_Spherical_MICCAI2025,
author = { Lee, Seungeun and Pyatkovskiy, Sergey and Yoo, Jaejun and Lyu, Ilwoo},
title = { { Spherical Diffusion Process for Score-Guided Cortical Correspondence via Spectral Attention } },
booktitle = {proceedings of Medical Image Computing and Computer Assisted Intervention -- MICCAI 2025},
year = {2025},
publisher = {Springer Nature Switzerland},
volume = {LNCS 15975},
month = {September},
page = {551 -- 561}
}
Reviews
Review #1
- Please describe the contribution of the paper
This paper proposes an interesting approach to the cortical surface registration problem, addressing a relevant problem in medical imaging. The method combines a Riemannian diffusion model defined for the S2 spherical manifold with a spectral attention-based deformation network. The key contribution lies in the cascaded design: the model first generates a score using the diffusion model, and this score is then used as a condition for the subsequent deformation network that has been modified with cross-attention layers.
- 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 an important and well-established problem in neuroimaging: cortical surface registration.
The proposed method is clearly described, and the Methods section is structured in a way that makes the overall pipeline easy to follow.
The application of a score-based generative model to guide surface registration along with attention is relatively uncommon in this context and provides a potentially useful direction.
The use of a spectral attention mechanism within the deformation network is a reasonable and intelligent design choice that aligns with the geometric structure of the spherical domain and helps avoid the computational overhead associated with operating in the spatial domain.
- 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.
While the paper addresses a clinically relevant problem, its technical novelty appears limited. The proposed method is built upon existing components: the deformation network from Lee et al. and the diffusion model from Huang et al. The integration of these elements lacks a clearly articulated motivation, and no new theoretical or empirical insights are offered to support this combination.
In the introduction, the paper claims to “propose a novel score-based diffusion model.” This appears to be an overstatement. The method builds on the existing formulation of diffusion models (Huang et al.) that is defined for general Riemannian manifolds and extends it to the S2 (sphere) domain using spherical harmonics. While this adaptation is non-trivial, it does not constitute a fundamentally new diffusion model.
The task is framed as cortical surface correspondence, yet both the methodological setup and the baseline comparisons (FreeSurfer, Spherical Demons, MSM, HSD, Lee et al.) are rooted in surface “registration”. While registration and correspondence tasks are related, they serve distinct purposes. This may be misleading, especially since evaluation in this work is limited to registration metrics (Dice score, MSE, distortion) and does not include standard correspondence measures such as generalization or specificity of statistical shape models learned from such surface to surface registration/matching.
Although recent deep learning-based cortical surface registration methods [Cheng et al., Zhao et al., Zhuo et al.] are cited in the introduction, they are not included in the experimental comparisons. The only deep learning baseline used is Lee et al., which is also part of the proposed pipeline’s deformation network. There is no justification provided for excluding these other methods, and it would strengthen the paper to evaluate against approaches like DiffuseReg (Zhuo et al.) that also leverage diffusion modeling.
The rationale for combining diffusion modeling and spectral attention together is not clearly presented in the methods. While the paper includes an ablation study, it lacks a systematic exploration of each component’s impact (e.g., comparing base model + attention vs. base + diffusion vs. full model) instead of incremental ablation.
The dataset description and evaluation strategy are insufficiently detailed. It is unclear how the train/test split is performed, and whether reported results are based on the training set or an independent test set.
Quantitative improvements over the baselines are modest, and the baseline selection appears limited and biased. The method is compared against four “traditional” registration methods and only one deep learning-based method, the latter being reused as part of the proposed method. Validation via downstream tasks is missing , and the broader clinical relevance or practical impact of the method is not convincingly demonstrated. Adding this could have justified the innovative aspect of the proposed methodology.
In the results, the proposed method shows improved Dice scores over the baselines in only a few (three) cortical regions. This selective improvement and degradation of different regions is not discussed in depth. It is unclear why the method fails to improve in other regions—whether due to anatomical complexity, model limitations, or clinical irrelevance. This lack of analysis limits the interpretation of the reported improvements.
- 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
Figure 3: The figure could be improved for clarity. The axes are not clearly labeled, and the use of asterisks appears to interfere with readability. Additionally, the caption lacks clarity as some baseline methods are not properly described (citation numbers are missing), and Region 17 is mentioned twice, which may be a typo unless it’s a deliberate distinction that should be clarified.
Figure 4: The caption could be revised for better readability. There is a typo (“2–3th rows”), and it would be helpful to explicitly state what the heatmaps represent in the captions to aid interpretation of the figure.
Citation issue (Page 2, Line 10): The reference to Brehmer et al. is incorrect in this context. The cited work does not relate to diffusion models or the Riemannian Laplace-Beltrami operator, and a more relevant citation would be appropriate here.
Typo (Page 2, Line 12): The word “asphere” appears to be a typo and should likely be corrected.
- 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?
While the paper addresses a relevant problem in neuroimaging and presents a clearly written methodology, the overall technical novelty is limited. The proposed approach primarily combines existing architectures without introducing new theoretical insights or strong empirical justification for their integration. The evaluation lacks comparisons with several relevant deep learning-based methods, and the framing of the task as correspondence is somewhat misleading given the registration-focused design and metrics. Additionally, the reported performance gains are modest, and key details regarding evaluation strategy and dataset splits are missing.
- Reviewer confidence
Confident but not absolutely certain (3)
- [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
Review #2
- Please describe the contribution of the paper
The method aims to achieve robust shape correspondence by guiding the alignment of cortical geometric features on a sphere. This mechanism computes frequency correlations in the spectral domain, enabling efficient conditioning of the score function., experimental results demonstrate that the proposed approach achieves highly accurate shape correspondence while minimizing distortions.
- 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 combination of spherical diffusion and spectral attention is novel and addresses the challenges of cortical shape correspondence effectively.
- The method shows improved robustness in aligning cortical geometric patterns, even with substantial anatomical variability among individuals.
- Reasonable validation and comparison with freesurfer.
- 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.
- I think the performance improvement is only marginal. in terms of MSE, NCC and Dice scores. But then this is expected as freesurfer has been developed over 20 years and is a very mature software.
- 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.
- 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.
(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?
Novel and interesting method but marginally better results. Still a good contribution in my opinon.
- 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 address a problem that has been studied for more than two decades, so the expected performance improvement is small. The proposed approach is novel and interesting.
Review #3
- Please describe the contribution of the paper
This paper tackles the problem of cortical shape correspondence. The authors make 2 important contributions. They introduce an i) approach for defining a diffusion process on the sphere and ii) an attentional mechanism that relies on the spherical harmonic decomposition. They build upon a previously defined deformation network that performs both rigid and non-rigid alignments between a source and a target surface. On top of that, a diffusion process is formulated as the solution of a heat equation using spherical harmonics (on the sphere).
- 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.
Clever integration of ideas that have been separately proposed before and using them properly. However, this is simply not an application of different methods. Instead, the authors have demonstrated a diffusion model for spherically parameterized surfaces with an important application to cortical shape correspondences. This is a clear strength.
Both the diffusion model and the spherical attention are shown to improve shape correspondence results.
The method also yields lower average areal distortion across subjects.
The authors have performed extensive experimental evaluation and comparison of their method.
- 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 idea of using the heat equation on the sphere using spherical harmonics to represent spherical coordinates is not novel. This idea is fundamental to the approach proposed in the paper.
Similarly, the idea of constructing a diffusion process on the sphere is not novel.
In Figure 1, the network architecture is confusing. The blocks and the lines are ambiguous. Shouldn’t the deformation net g_\psi also take M as an input? Both M and F are needed to compute the score s_\epsilon.
Shouldn’t the Reverse Diffusion Process block also take M as an input.
The notation needs considerable improvement. For e.g. the deformation network is denoted by g_\psi. What is \psi here? Does one really need an additional notation g_\psi?
What does s_\epsilon mean? It is used as a a score as well as used to denote the neural network. Is it SPHARM-NET? This is not defined properly anywhere.
Numerically, the authors have shown improved performance over other state of the art methods. However, the improvement is modest.
The diffusion model is not well motivated. I.e. the model seems to show a small improvement over existing methods, including the classical (non deep-learning) methods. Thus the reason why a diffusion model should be a better approach for this problem is not well justified.
- 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.
- 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
From Figure 2, it is observed that increasing the regularization normalized cross-correlation (accuracy measure) also increase areal distortions. While this is to be expected, can the authors comment on why this graph looks almost linear? At even higher regularization values, do they see the NCC start dropping?
It is interesting to see that the traditional method of Freesurfer performs nearly as well as modern neural network based methods including the new method that the authors propose (for multiple regions).
In Figure 3 are there typos in the region labels? They mention region 17 and region 1 twice.
- 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?
While this paper builds upon previously developed methods, it does make a novel contribution by implementing a diffusion model on the sphere for the purpose of cortical shape correspondence. Thus even if the improvements in registration are moderate, this paper does contribute to a new technique.
- 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 reviewers have satisfactorily answered my concerns. My rating (accept) has not changed after reading the other reviews and the author response.
Author Feedback
We thank the reviewers for their feedback and recognition of our method as a novel and well-motivated approach to cortical shape correspondence, highlighting clever/novel integration/design of spherical diffusion and spectral attention (R1,R2,R3), robust performance in alignment and distortion (R2,R3), and clear problem setting (R1). Please find our responses below.
Technical Novelty (R1-W1,W2,R2-W1): Our method introduces a novel closed-form diffusion process tailored for a spherical manifold. Existing Riemannian models (Huang et al.) target arbitrary manifolds and rely on stochastic or numerical approximation for diffusion. In contrast, we focus on the spherical manifold and define diffusion using a spherical harmonics-based analytic kernel (Sec. 1&2.3). Although individual components have been previously explored, this is the first work to propose a closed-form spherical diffusion model. We also propose a novel spectral attention that enables learning from high-resolution spatial data.
Motivation & Ablation (R1-W5,R2-W4): As discussed in Sec.1, relying solely on geometric descriptors can limit performance. Learning a generative prior via representation learning further captures richer latent features [17,21,28]. Incremental ablation was done as the spectral attention requires the latent features extracted from the diffusion process.
Task Framing (R1-W3): We agree that shape correspondence can be established through various methods. Cortical surface registration is widely used for computing dense correspondence [5,11,18,20,24,26]. If descriptors (geometry, annotation, etc.) reliably define corresponding locations, shape correspondence can be assessed based on the similarity metrics of any valid descriptor. Indeed, registration performance is evaluated at locations defined “by shape correspondence” from surface registration. Statistical shape models use Euclidean statistics to evaluate “absolute coordinates”. Though feasible, the approach is seldom applied to brain surfaces as Euclidean proximity poorly reflects manifold proximity; e.g., points on opposite sulcal walls seem close but are far on the surface.
Evaluation (R1-W4,W6,W7-2,R2-C2): DiffuseReg deforms volumetric space so must compute vertex-wise correspondence as a nontrivial extra step unlike surface registration. Other DL methods use private, incomplete, or undocumented code, making fair comparisons difficult. We thus used classical methods like FreeSurfer, which remain public, widely used, and maintained over decades, as also noted by R3. We did not include non-registration methods like point cloud matching, as they typically rely on absolute coordinates for similarity metrics, which is hard to distinguish narrow sulci; they are thus rarely used in neuroscience studies. We used a full set of HCP for training (sorry for the missing info!) and Mindboggle for test to assess generalization.
Performance Gain (R1–W7-1,R2-W3,R3-W1): Although absolute gain may seem modest especially in distortion due to its log scale, our method offers 4.84% & 9.02% reductions in mean areal & edge distortion without log scale over the SOTA (Lee et al.). All reported improvement is statistically significant and exceeds typical margins reported in recent studies [5,24,27].
Dice Score (R1-W8,R2-C3): “17” denotes “the number of regions” with statistically significant improvement, not a region index. Our method outperforms all others in over half of the 32 regions. This can be useful for neuroscience studies targeting these areas.
Typos & Others (R1-C1,C2,C3,C4,R2-W2,C1): (R1) We will revise figures, fix typos (e.g., asphere), and correct the citation of Brehmer et al. (R2-W2) M is input to the deformation network, and \psi denotes its parameters. s_\eps is the denoising network, and we simplified the output notation as s_\eps(\cdot). Fig.1 will be revised for clarity. (R2-C1) Strong regularization reduces both distortion and NCC. NCC converges at zero distortion under rigid alignment.
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’
N/A