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Abstract

Accurate 3D modeling of the ventricles through cine cardiovascular magnetic resonance (CMR) imaging benefits precise clinical assessment of cardiac morphology and motion. However, the existing short-axis stacks exhibit low spatial resolution in the inter-slice orientation compared to the intra-slice direction, resulting in a sparse representation of the realistic heart. The anisotropic short-axis images pose challenges in directly reconstructing meshes from them. In this work, we propose a surface fitting approach based on the algebraic sphere, which serves as a previous step for various mesh-based applications, to reconstruct a natural ventricular shape from the segmented wireframe-type point cloud. Considering the sparse and layered nature of the point clouds, we first estimate the normals of the point cloud based on dynamic programming and neighborhood selection, followed by fitting a point set surface using a non-compact kernel adapted by layers. Finally, an implicit scalar field representing the signed distance between the query point and the projection point is obtained, and the manifold mesh is extracted by meshing zero iso-surface. Experimental results on two publicly available datasets demonstrate that the proposed framework can accurately and effectively reconstruct ventricular mesh from a single image with better cross-domain generalizability.

Links to Paper and Supplementary Materials

Main Paper (Open Access Version): https://papers.miccai.org/miccai-2024/paper/2017_paper.pdf

SharedIt Link: https://rdcu.be/dVZei

SpringerLink (DOI): https://doi.org/10.1007/978-3-031-72378-0_16

Supplementary Material: https://papers.miccai.org/miccai-2024/supp/2017_supp.zip

Link to the Code Repository

https://github.com/hejin9/algebraic-sphere-surface-fitting

Link to the Dataset(s)

N/A

BibTex

@InProceedings{He_Algebraic_MICCAI2024,
        author = { He, Jin and Liu, Weizhou and Zhao, Shifeng and Tian, Yun and Wang, Shuo},
        title = { { Algebraic Sphere Surface Fitting for Accurate and Efficient Mesh Reconstruction from Cine CMR Images } },
        booktitle = {proceedings of Medical Image Computing and Computer Assisted Intervention -- MICCAI 2024},
        year = {2024},
        publisher = {Springer Nature Switzerland},
        volume = {LNCS 15001},
        month = {October},
        page = {169 -- 178}
}

Reviews

Review #1

  • Please describe the contribution of the paper

    This work presents a surface fitting method based on the algebraic sphere to reconstruct a ventricular shape from the segmented wireframe point cloud.

    Contributions:

    1. Addressing the challenge of reconstructing mesh from a single CMR image without the need for datasets or efficient and accurate training.
    2. Given the specificity of wireframe-type data, this paper proposes an algebraic spherical fitting framework and introduces hierarchical adaptive non-tight kernels and normal estimation methods.
    3. The proposed method outperforms several benchmark methods and exhibits good generalization performance.
  • 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.

    This is a graphics-based method, its greatest advantage lies in not requiring training, with fast inference speed and high efficiency, which will make a significant contribution to this field.

  • 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.

    1. Overall, the general process of the paper is quite similar to the APSS method, but it lacks comparative experiments with this baseline.

    2. Can the results of normal estimation be visualized? As one of the contributions, the specific experimental effects are not demonstrated.

    3. There is a lack of ablation studies on different kernel functions.

    4. The validation in the ACDC dataset is conducted in this paper, but as far as I know, this dataset contains many different types of disease data, and the hearts of different diseases can differ significantly in morphology. Could more examples be visualized?

  • 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.

  • Do you have any additional comments regarding the paper’s reproducibility?

    If the code is open-sourced, it would be a valuable contribution.

  • Please provide detailed and constructive comments for the authors. Please also refer to our Reviewer’s guide on what makes a good review. Pay specific attention to the different assessment criteria for the different paper categories (MIC, CAI, Clinical Translation of Methodology, Health Equity): https://conferences.miccai.org/2024/en/REVIEWER-GUIDELINES.html

    In addition to addressing the main weaknesses mentioned, it is requested to include more formula derivations in the supplementary materials.

  • 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

    Weak Reject — could be rejected, dependent on rebuttal (3)

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

    While this paper makes a certain contribution to the field, it is noted that the method bears similarity to APSS and lacks ablation validation of the proposed modules.

  • Reviewer confidence

    Confident but not absolutely certain (3)

  • [Post rebuttal] After reading the author’s rebuttal, state your overall opinion of the paper if it has been changed

    Weak Accept — could be accepted, dependent on rebuttal (4)

  • [Post rebuttal] Please justify your decision

    Due to the method not requiring training and the promise to open-source the code, it has made a certain contribution to the field.



Review #2

  • Please describe the contribution of the paper

    This work introduces a mesh reconstruction algorithm from point cloud data based on algebraic sphere surface fitting and dynamic programming-based normal estimation. The method was evaluated on two public datasets and compared to three alternative methodologies, demonstrating comparable or even superior performance.

  • 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.

    Simplicity: The proposed methodology is simple, efficient, and involves no learnable strategies, thereby eliminating the need for extensive training data or high-computing resources. Versatility: In addition to its simplicity, the method seems versatile enough to be of interest in a multitude of scenarios (as evidenced by Fig. 4). However, it is not clear whether the methodology can be applied without modifications across all scenarios given (multi-chambers, time-series, etc.), and if any potential limitation exist in each, or whether modifications are required (e.g., can it handle all chambers at once, or do you apply per chamber and visualize altogether?).

  • 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.

    Experimental details missing: Replicating the experiments is challenging given the lack of specific details regarding how test and reference data were generated. More detailed comments follow below. Lack of ablation study: The absence of an ablation study and evidence supporting the advantages or necessity of certain algorithmic decisions significantly hinders a reader’s ability to understand the contribution of each component of the proposed method. More detailed comments follow below. Limited SOTA comparison: While the authors compare their approach against three alternative reconstruction strategies, they made no comparison against recent neural network-based strategies referenced in the introductory section. Despite the potential advantages associated with the proposed methodology (see strengths above) and the theoretical limitations associated with some of these past methods, the lack of a direct comparison prevents one from reaching any conclusion regarding the proposed methodology’s ability to replace previously approaches. This is particularly relevant considering potential limitations (not discussed) of the present method (slice misalignment, segmentation errors, etc.). Detailed comments follow below.

  • Please rate the clarity and organization of this paper

    Very 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.

  • Do you have any additional comments regarding the paper’s reproducibility?

    The authors have adequately described their methodology. The data used is publicly available, which facilitates reproducing the study. However, further details about the MMWHS experiments are required to effectively allow reproducing the results and enable comparison: (1) How many test samples (point clouds extract from the meshes of MMWHS) were generated and used for the results in Table 1? 1 per patient? (2) How did you simulate the acquisition of the SAx stack and resulting point cloud (number of slices, inter-slice distance, etc.)? (3) What parameters were used in PSR to create the reference mesh? A similar comment (to a lower extent) could be made about ACDC – e.g., how was the initial point cloud data generated from the GT mask? The authors could consider publicly sharing their test data for comparative purposes.

  • Please provide detailed and constructive comments for the authors. Please also refer to our Reviewer’s guide on what makes a good review. Pay specific attention to the different assessment criteria for the different paper categories (MIC, CAI, Clinical Translation of Methodology, Health Equity): https://conferences.miccai.org/2024/en/REVIEWER-GUIDELINES.html

    1) The authors argue that a key issue with past methods (namely SSM-based ones) is the failure to match segmented 2D contours. However, one may also argue that segmentation errors may exist, and a reconstruction algorithm may serve as a post-processing method (especially if based on learnable shapes). How does your method handle segmentation errors? Please discuss and consider including a few sentences on possible limitations of your method. 2) Past studies have also dwelt significantly on the issues faced by misaligned slices, which largely preclude the direct application of interpolation techniques. How does your method handle these issues? This should be addressed in the discussion. 3) Can your strategy be adapted to account for the long-axis views (and resulting contours/point sets) that are typically available? Please comment. 4) In the MMWHS experiment, PSR is used to create a reference mesh. How adequate is this reference given that PSR is a generic reconstruction algorithm (can itself be used to solve your research question, no?), and why can’t you derive a reference mesh from the GT meshes available with the dataset? 5) An ablation study is needed to understand some of the algorithmic decisions made and their advantages over alternatives. For example, a. What is the influence of beta (eq. 1) on sphere fitting? b. How much better (quantitatively) is the fitting when using the proposed adaptive rational kernel, rather than the conventional rational kernel or a Gaussian one? c. How much better (quantitatively) is the fitting using your normal estimates vs. the “traditional normal estimation methods” referenced on this section? d. How much better is the sphere fitting mesh compared to the coarse triangular mesh obtained during normal estimation? e. How does your proposed method compare to generic PSR (used as reference in MMWHS) on ACDC? 6) In what sense is the point cloud “hierarchical”? Please clarify. 7) How is the proposed normal estimation method “coarse-to-fine”? From the description, it seems DP is used to connect points in different slices, followed by a mesh smoothing operation. Is it applied (somehow) sequentially in point sets with distinct resolutions (e.g., number of points per layer)? Please clarify.

    Minor comments:

    • Throughout the manuscript, the authors repeatedly refer to “layer”. From the description, it seems that a layer in the point cloud represents the set of points belonging to one SAx slice. Is my interpretation correct? If yes, consider explicitly mentioning it in the beginning of the methodology section to improve readability. If not, please clarify.
  • 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

    Weak Reject — could be rejected, dependent on rebuttal (3)

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

    The methodology presents promising aspects in terms of simplicity, versatility, and potential effectiveness. However, the absence of an ablation study or comparison with recent learnable methods hinders a comprehensive understanding of the proposed methodology’s added value. Consequently, the manuscript lacks substantiation for the claims, hypotheses, and proposals made by the authors. Can it deal with misaligned slices? Segmentation errors? Multi-view inputs? What is the gain in performance, both in terms of reconstruction quality and computational efficiency, against these other methods? If such results are readily available, they would substantially improve the manuscript.

  • Reviewer confidence

    Very confident (4)

  • [Post rebuttal] After reading the author’s rebuttal, state your overall opinion of the paper if it has been changed

    Weak Reject — could be rejected, dependent on rebuttal (3)

  • [Post rebuttal] Please justify your decision

    While I commend the authors for committing to release the source code and data upon acceptance—addressing potential reproducibility issues—my initial concerns regarding the absence of an ablation study and limited comparison with SOTA methods remain unresolved. Without these elements, the study introduces an alternative methodology for solving the problem of LV mesh reconstruction without clarifying the relevance of its components to the task, nor providing evidence of its superiority over existing approaches. My initial recommendation for rejection with the possibility of rebuttal was based on the assumption that these results, though not initially disclosed, would be available (given the strong claims made) and could be included upon revision.



Review #3

  • Please describe the contribution of the paper

    This work proposes an algebraic sphere surface fitting method to reconstruct a 3D mesh for the myocardium from cardiac cine images (known for its different in-plane and through-plane resolutions). The authors then compare the accuracy of their reconstructed mesh to the other established methods in the literature in both simulated and real-world datasets.

  • 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.
    1. Leveraging the standard computer graphics methods on surface reconstruction from point clouds with insights about the data in hand (i.e. the cardiac surface is a smooth manifold) sounds nice and promising.
    2. The authors provide nice comprehensive results comparison with some of the other methods in the literature using several evaluation metrics.
    3. Generalizing the employed algorithm to the different chambers on the heart and to the temporal direction in cine images was a good addition! Many algorithms in this area are usually tought to generalize out of the box.
  • 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.
    1. The author didn’t sufficiently address the main challenge in this area, i.e. most of the reconstruction methods gives unsatisfactory results when the wireframe point cloud is too sparse or have different resolutions in the different direction which is known to be the case in cine CMR images where through-plane is much lower than the in-plane resolution. This is the real issue that should have had more attention throughout the work.
  • Please rate the clarity and organization of this paper

    Very 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.

  • Do you have any additional comments regarding the paper’s reproducibility?

    The author will release the code and testdata on Github for reproducible research.

  • Please provide detailed and constructive comments for the authors. Please also refer to our Reviewer’s guide on what makes a good review. Pay specific attention to the different assessment criteria for the different paper categories (MIC, CAI, Clinical Translation of Methodology, Health Equity): https://conferences.miccai.org/2024/en/REVIEWER-GUIDELINES.html

    computer graphics is the sparse point cloud and the different resolution in the different directions. However, the authors didn’t address these factors in their methods at all! It would have been much better to show how the proposed algorithm performs at different variations of these factors (sparsity level and different resolution)? How would its performance degrade at different sparsity factor and resolution difference? How does this rate of degradation compare with the other algorithms? Investigating the different resolution are the different resolution ratio (in-plane to through-plane) is also worthy to have.

    1. For “Generalization Analysis”: Was the algorithm directly used as-is for the other chambers and cine? or the author had to employe some fine tuning on some of their parameters for each case? Please, list these parameters if any or just state that no fine-tuning was needed for any parameters.

    Minor:

    1. References citations are not ordered properly. e.g. The first citations in the text are 1,3,5,10,26!
    2. Too many decimal points in the results numbers in Table 1 and 2. This just distracts the reader and doesn’t add any significant information. Please, limit this to one or two decimal points at most.
  • 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

    Weak Accept — could be accepted, dependent on rebuttal (4)

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

    The work is good, but the main target hypothesis needs to be more thoroughly addressed.

  • Reviewer confidence

    Very confident (4)

  • [Post rebuttal] After reading the author’s rebuttal, state your overall opinion of the paper if it has been changed

    Accept — should be accepted, independent of rebuttal (5)

  • [Post rebuttal] Please justify your decision

    The authors didn’t properly address the algorithm performance under different resolution conditions. However, they claimed the work to be validated for the typical cine imaging resolution till it can further validated for different resolution in a later version of the work.



Author Feedback

We thank all the reviewers for their detailed reviews and the insightful feedback on our manuscript, highlighting its ability to “generalize out of the box”, being “versatile enough to be of interest in a multitude of scenarios”, providing a “nice comprehensive results comparison”, and having the potential to “make a significant contribution to this field”. Going forward, we’re going to address the concerns.

Application scenarios (R1, R3, R5) {Can it be applied without modifications across scenarios, including other chambers, cine, multi-view inputs, and different diseases?} Our algorithm can be directly used without fine-tuning any parameters for other chambers, cine, multi-view inputs, and different disease morphologies. The input, being a point cloud and lacking explicit topological connectivity, allows our approach to adapt to various scenarios. We will do our best to include more detail. (R5) {Can it deal with misaligned slices? Segmentation errors?} The misalignment in the slices originates from the imaging stage, while segmentation errors stem from the segmentation algorithm itself. Our future work will integrate methods for motion correction and segmentation quality control.

Experiment (R1) {Comparing degradation rates under different resolution ratios} Thanks for having a consensus on the main challenge in this area. Graphics methods can reconstruct surfaces from sparse point clouds but struggle with the data in hand [page3]. Our method specifically tackles this issue. Additionally, cine imaging typically has a plane resolution of 8-10mm and in-plane resolution of <2mm [4, a]. Exp2 validates the performance under different resolution conditions, demonstrating the advantage of our algorithm in handling cine data. we will more thoroughly highlight this in a final version. [a] Wang, C., Li, Y., Lv, J. et al. Recommendation for Cardiac Magnetic Resonance Imaging-Based Phenotypic Study: Imaging Part. Phenomics 1, 151–170 (2021).

Ablation studies (R3, R5) {Lacking ablation experiments with Gaussian kernel function and comparative experiments with APSS} As mentioned in our Layered Adaptive Rational Kernel [page5], The Gaussian kernel is not capable of handling our data, which is used by APSS. (R3, R5) {Lacking ablation experiments for normal estimation} Normal existing methods such as those in open3d/meshlab and [14, 15] produce failed results when directly estimating normals from point clouds. Therefore, we propose this module. We acknowledge that the failure cases section is missing in the paper and will include these cases in the supplementary material.

Some implementation details (R3) {Can the results of normal estimation be visualized} The visualization results of normal estimation can be seen in Fig2, represented by the blue small arrows on the point cloud. We will emphasize in the final version that these indicate the surface normals. (R5) {Why use sphere fitting mesh instead of coarse mesh} The mesh obtained after normal estimation lacks proper topology. (R5) {Why create a reference mesh instead of using the GT meshes of the dataset} MMWHS dataset does not provide GT meshes. (R5) {No comparison to recent learnable methods in the introduction} These methods mentioned in the introduction differ from the problem we aim to address, and we have compared recently learnable method. (R5) {How “coarse-to-fine”} We use DP for global normal consistency across adjacent layers, followed by smoothing to obtain adjusted normals. (R5) {clarification of certain concepts} A “layer” in the point cloud represents a set of points belonging to a single SAX slice. Each point’s nearest neighbors are within the same layer, which we called “hierarchical”.

(R1, R3, R5) We will do our best to include more detail. And we will release the code and test data on Github for reproducible research. Finally, we want to thank the reviewers for their valuable feedback and hope we could clarify some uncertainties/ambiguities.



Meta-Review

Meta-review #1

  • 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’

    Congratulations. I hope the authors will integrate the source code into a major open source framework such it can be used on a broader scale by others.

  • 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).

    Congratulations. I hope the authors will integrate the source code into a major open source framework such it can be used on a broader scale by others.



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’

    I have checked all the reviews and authors’ rebuttal of this paper. No issue was found.

  • 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).

    I have checked all the reviews and authors’ rebuttal of this paper. No issue was found.



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