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Abstract
Connectome harmonic analysis has been proposed as a multimodal approach for studying brain dynamics by decomposing functional MRI signals in a Fourier basis informed by the structural connectome derived from diffusion MRI. In this work we pose the following question: is the propensity of the connectomic Fourier basis to reconstruct resting state fMRI signals truly contingent upon anatomical priors? We present evidence that it is not, by demonstrating that when fewer than $n=100$ modes are considered the connectomic eigenbasis obtained through state-of-the-art methodology performs similarly to geometrically transformed versions of that same basis. The main theoretical contribution of this paper is the construction of a regular planar embedding of the left hemisphere’s cortical surface, which we use to compute a smoothly parametrised family of cortical transformations which form
Links to Paper and Supplementary Materials
Main Paper (Open Access Version): https://papers.miccai.org/miccai-2025/paper/2950_paper.pdf
SharedIt Link: Not yet available
SpringerLink (DOI): Not yet available
Supplementary Material: Not Submitted
Link to the Code Repository
https://github.com/riv20/cha_spin_test
Link to the Dataset(s)
HCP: https://www.humanconnectome.org/study/hcp-young-adult/data-releases
BibTex
@InProceedings{VocRap_Does_MICCAI2025,
author = { Vock, Raphaël AND Grigis, Antoine AND Dufumier, Benoît AND Duchesnay, Edouard},
title = { { Does Connectome Harmonic Analysis pass the Spin Test? } },
booktitle = {proceedings of Medical Image Computing and Computer Assisted Intervention -- MICCAI 2025},
year = {2025},
publisher = {Springer Nature Switzerland},
volume = {LNCS 15971},
month = {September},
page = {279 -- 287}
}
Reviews
Review #1
- Please describe the contribution of the paper
In this paper, the authors set out to show that connectome-based methods (particular the CHA method) in reconstructing fMRI signals do not need anatomical priors.
- 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 main strength of the paper is posing the question whether the spin test under the CHA testing is optimal and whether it really needs anatomical constraints. This is a valid and an important question. Another strength of the paper, is that the authors have formulated one approach for comparing fMRI reconstruction accuracies based on a different type of planar embedding. This is indeed valuable to the field.
- 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.
As the main premise of the paper, the authors set to show that the reconstruction performance or accuracy of the connectomic Fourier basis for fMRI signals need not depend on anatomical priors. However, this is not what was proven. Most registration methods or featurization methods (such as the background methods used here) are anatomically constrained or anatomically driven, but not necessarily impose anatomical priors. The authors claim that one could achieve same reconstruction performance without strict anatomical priors. However, in their work, they still rely on a geometric embedding for the cortical surface. Thus there is anatomical information (although it is projected) in the planar embedding that the authors use.
The main aim of the paper was not clear. Is it trying to show “lack of robustness of CHA” or proposing an improved “spin test”?
The authors state that the “The main theoretical contribution of this paper is the construction of a regular planar embedding of the left hemisphere’s cortical surface…” However, this has been done both methodologically and has been extensively used in applications. Further, there are other better distortion minimizing embeddings (conformal maps for e.g.. See the work by Xianfeng Gu, Yalin Wang etc.) that also achieves a planar embedding and has been extensively used for brain registration.
The space of the functional signals is not defined. Is it a space of matrices? What is the dimension of the eigenvectors e_i?
In describing the method of CHA, the authors define a graph Laplacian and compute it’s eigenspectrum, particularly the eigenvectors, onto which the functional signals are projected. However, it is well known that this eigenspectrum is not unique and the multiplicity of eigenvalues is not taken into account. Further the eigenvectors are not rotationally invariant. Additionally, it is possible to improve upon the reconstruction error by increasing the number of nodes of this eigenspectrum. The authors do state (but don’t show any results) that for a node count > 200, they don’t see a difference between reconstruction quality between CHA and their method.
The authors mention that the “The crudeness of this method leads to several shortcomings…” Outside of CHA, the eigenspectrum is widely deployed in cortical registration and cortical morphology analysis. They also mention their method overcomes several shortcomings such as transformations need not be bijective mappings, the transformed basis need not be orthogonal etc… However, this method is not crude. And these are not necessarily drawbacks. For e.g. why is there a need to otherwise relax the bijective mappings (may be void for tumors/lesions etc.) or relax the orthogonality constraint. Finally, the authors themselves say “…finally we orthogonalise the resulting basis using the Gram–Schmidt process.” Why is orthogonalization in their case preferred?
The authors mention, for CHA “we overcome the shortcomings. It is not clear how these shortcomings are overcome. The rotations applied to the 2D embedding are actually bijective maps (this allows the pullback to C). Further to compute the transformations (applying \rho_\theta), they resort to a Euclidean linear assignment problem. This is not always straightforward. The linear assignment ignores any geometric structure. Thus, it seems this method creates other problems. Further, the embedding \phi while injective, is not guaranteed to be invertible. The authors are computing \phi^{-1}, but it may not exist. Thus even if one gets some solution using the Euclidean linear assignment problem, it may be incorrect.
In the Results section, when computing p-values the authors state, “treating subjects as random effects”. This was not clear. Was a mixed effects model used with subjects as a random effect? However, in the paper, the authors used a t-test for the correlations.
- 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 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
In Fig 1, does the last image (4) appear to be also rotated (in addition to smoothing and regularization), or is it an orientation issue for visualization purposes?
In the Results section, the authors use 243 regularly spaced angles between [0, 2\pi). What is the significance of 243? This number was also referred to the points on the interhemispheric boundary for the cortical surface. The angle division and the number of points on the boundary should be independent. Why is the same number used for both the angles and the number of boundary points?
- 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?
The question whether the spin test under the CHA framework is an optimal test is valid. While doubts have been previously raised (for e.g. Pang et al. reference that the authors do cite), no one has systematically performed an experiment to tackle this. The authors present one attempt for answering this question. But there are several weaknesses in the assumptions and the formulation.
- Reviewer confidence
Very confident (4)
- [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.
The author’s response failed to address my concerns. The paper does raise an important question, “whether the spin test under the CHA framework is optimal”. However, the paper failed to provide a robust alternative and did not convince why their approach is optimal. The main goal of the paper was also not clear, whether to “improve robustness in CHA” or to propose an “improved spin test”. There were important conceptual issues raised in my review, which were not addressed. Thus I will keep my original rating.
Review #2
- Please describe the contribution of the paper
The authors aim to test how useful a set of basis functions formed from the eigendecomposition of the graph Laplacian of a population averaged structural connectome adjacency matrix is for the task of low-rank representation of fMRI signals. They suggest that this can be answered by comparing the correlation between the raw FC matrices and those derived under a fixed rank decomposition in the SC-eigenbases vs. some transformation of the same set of functions.
The main methodological contribution is proposing said transformation (phi), where the authors embed a hemisphere manifold into the unit disk in R2, denoted D2, apply a rotation via a rotation angle on D2, and then invert the transformation to get the transformed eigenfunctions: e_{j}(phi^{-1}(x)). The signal is then decomposed over this transformed basis, and the correlation of the FC from either low-rank representation is compared to the raw FC. Results are presented that indicate that, at least for some rotations, the reconstruction power of the basis is essentially the same as for the original eigenbasis.
- 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 well written and very easy to follow.
The authors propose a different embedding space (D2) than is traditionally used for cortical surface based analysis (S2), along with algorithms for approximating the inverse mapping (would be nice to get more detail here, perhaps in the journal version). The alternative embedding space is motivated through several reasonable shortcomings of the S2 approximation (the handing of the hemisphere barrier). It seems like the machinery here can be useful for a variety of other applications beyond the one considered here (the spin test).
- 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.
My main concern is that I am not convinced of the central premise of the test, as articulated in the opening sentence of Section 4:
“Were the connectomic eigenbasis to be truly contingent on anatomical priors, one would expect an arbitrary rotation of the cortical surface to induce a sharp drop-off in the prescribed metric.”
I interpret this as the authors saying essentially: if the eigenfunctions of the structural connectome were particularly information rich for representing the fMRI signals, then applying the prescribed transformation would result in substantial degradation in representational efficiency, i.e. requiring many more basis functions to represent the signal than the original untransformed basis to a given fidelity. However, this interpretation seems problematic. The rotated basis would still contain a lot of structural information encoded into it, as features such as the overall “shape” of the basis functions, their overall smoothness, etc. are retained under the proposed transformation. Wouldn’t a more appropriate “null” basis be some functions that had nothing to do with the SC, e.g. could you form the Laplacian eigenfucntions on the disk, invert them using phi^{-1} and then study the representational capacity of these as compared to the eigenfunctions (at a fixed rank)?
- 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 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
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?
Although I have some concerns on the interpretation of the particular application studied here, the work proposes a surface embedding, along with algorithms to calculating the inverse mapping, that can make this method useful for a variety of applications beyond the so-called spin test treated in this work.
- Reviewer confidence
Somewhat confident (2)
- [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 carefully responded to my major concern, I look forward to seeing the mentioned proof in the final version. I was already of the opinion the paper should be accepted pre rebuttal, and I have no reason to change that.
Review #3
- Please describe the contribution of the paper
The authors evaluate Connectome Harmonic Analysis (CHA) under the lens of a “Spin Test”, to asses whether resting state functional MRI is properly represented with structural harmonics extracted from diffusion MRI.
The authors conclude that, in their settings, CHA did not pass the Spin Test, which raises questions regarding the adequacy of the analytical approach.
- 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.
- An elegant framework is built on the previous Spin Test proposal, addressing several shortcomings clearly and concisely described in the paper.
- Impactful and timely question with the emergence of CHA as an analytical framework.
- The paper reads fluently and is original.
- 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.
- At points, the authors allow themselves some expressions and styles that may not be accessible to all readers.
- 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
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.
(6) Strong Accept — must be accepted due to excellence
- Please justify your recommendation. What were the major factors that led you to your overall score for this paper?
The paper is compelling, with a well-motivated, properly-scoped, and clearly-described experiment of high interest for the neuroimaging community today.
- 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 did not have any major concerns about this paper and therefore there’s no reason to change my suggestion. The rebuttal addresses the comments I raised.
Author Feedback
Dear Reviewers,
We are grateful for the time and attention afforded by the reviewers to our submission.
All reviewers praised the overall clarity of our writing as well as the relevance and timeliness of the question we sought to answer, although opinions varied strongly between reviewers as to whether our work constitutes a valid answer to that question.
All reviewers also raised the point of non-reproducibility as a weakness to our submission. We recognise this as a flaw and will provide pseudocode descriptions to the key algorithms as well as access to the full contents of our code.
We thank Reviewer #1 for their overwhelmingly positive feedback. We will try our best to follow their suggestion concerning our writing style so as to make the final version of our paper accessible to the broadest possible audience.
The authors are grateful for the detailed response given by Reviewer #2 despite their unfavourable recommendation. Let us first clarify the scope of our work. The objective in this paper is to answer the following question (see Abstract): “is the propensity of the connectomic Fourier basis for reconstructing resting state fMRI signals truly contingent on anatomical priors?”. In doing so, we do not claim to improve CHA but instead to question it. The novelty of our contribution lies in an improvement to the Spin Test paradigm which we go on to apply to CHA. Recall that the Spin Test is a framework for generating null models for brain activity via spatial permutations. We will better emphasise the scope and aim of our research in the introduction to the final version.
To answer a few of the technical points raised, let us indicate that the statement that the “eigenspectrum [of the Laplacian matrix] is not unique” is untrue and not relevant to our line of reasoning, because the methodology of CHA is taken as a given based on the wealth of existing literature on the subject. Also, the claim that “the eigenvectors are not rotationally invariant” is not a valid counterpoint; in fact, it can be seen as a direct corollary of our work. We thank Reviewer #2 for bringing to our attention Xianfeng Gu’s work on conformal planar embeddings. Though interesting and tangentially relevant, these embeddings are ultimately unsuitable for our purposes because unlike our radially regularised Tutte embedding they do not impose uniformity in the unit disc, a property that is crucial for our algorithm’s LAP step to work accurately. For the sake of completeness we will add a reference to this work in the final manuscript.
We thank Reviewer #3 for their positive review. They raise the question of whether our method of transforming the harmonic basis by rotating it in embedding space voids it of anatomical information. They suggest that a more appropriate null basis would be the disc harmonics pulled back to the cortical surface via the inverse embedding. To address the former question, let us point out that the action of transforming the Laplacian eigenmodes via a transformation of the cortex, as we have done, is equivalent to first transforming the edges of the graph through that same transformation and then computing the resulting Laplacian eigenmodes (this fact has a proof which we will include in the final paper). Consequently, our suggested method boils down to “rewiring” the white matter tracts through some arbitrary transformation, and considering the resulting eigenmodes. The rotated eigenbasis, which corresponds to an artificial connectome based on non-existent white matter tracts, contains no anatomical information. The suggestion to use disc eigenmodes is a valid alternative to our proposed Spin Test framework (we have currently unpublished research which uses that idea and led us to similar conclusions). Nonetheless, the existence of this alternative does not undermine the validity of our Spin Test framework. We will include this explanation in the revised manuscript.
Sincerely, The Authors
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.
Reject
- Please justify your recommendation. You may optionally write justifications for ‘accepts’, but are expected to write a justification for ‘rejects’
The manuscript was rejected due to the author’s inadequate response to key concerns. It fails to provide a strong alternative or clarify its primary objective, leaving important conceptual issues unresolved. These gaps hinder validation of its contributions.