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Abstract
Accurate 3D models of the human heart require not only correct outer surfaces but also realistic inner structures, such as the ventricles, atria, and myocardial layers. Approaches relying on implicit surfaces, such as signed distance functions (SDFs), are primarily designed for single watertight surfaces, making them ill-suited for multi-layered anatomical structures. They often produce gaps or overlaps in shared boundaries. Unsigned distance functions (UDFs) can model non-watertight geometries but are harder to optimize, while voxel-based methods are limited in resolution and struggle to produce smooth, anatomically realistic surfaces. We introduce a pairwise-constrained SDF approach that models the heart as a set of interdependent SDFs, each representing a distinct anatomical component. By enforcing proper contact between adjacent SDFs, we ensure that they form anatomically correct shared walls, preserving the internal structure of the heart and preventing overlaps, or unwanted gaps. Our method significantly improves inner structure accuracy over single-SDF, UDF-based, voxel-based, and segmentation-based reconstructions. We further demonstrate its generalizability by applying it to a vertebrae dataset, preventing unwanted contact between structures.
Links to Paper and Supplementary Materials
Main Paper (Open Access Version): https://papers.miccai.org/miccai-2025/paper/0227_paper.pdf
SharedIt Link: Not yet available
SpringerLink (DOI): Not yet available
Supplementary Material: https://papers.miccai.org/miccai-2025/supp/0227_supp.zip
Link to the Code Repository
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Link to the Dataset(s)
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BibTex
@InProceedings{LeHie_PairwiseConstrained_MICCAI2025,
author = { Le, Hieu and Xu, Jingyi and Talabot, Nicolas and Yang, Jiancheng and Fua, Pascal},
title = { { Pairwise-Constrained Implicit Functions for 3D Human Heart Modeling } },
booktitle = {proceedings of Medical Image Computing and Computer Assisted Intervention -- MICCAI 2025},
year = {2025},
publisher = {Springer Nature Switzerland},
volume = {LNCS 15975},
month = {September},
page = {388 -- 398}
}
Reviews
Review #1
- Please describe the contribution of the paper
The paper introduces interdependent pairwise signed distance functions (SDFs) that enforce topological constraints between anatomical structures—specifically, maintaining a desired contact ratio between adjacent components (as demonstrated in 3D heart modeling) and ensuring a minimum separation distance (as demonstrated in spine modeling). These constraints are enforced via additional loss terms that dynamically adjust the individual SDFs to satisfy the pairwise relationships.
- 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.
Well-Written and Clear Presentation: The manuscript is clearly written, with a logical flow that makes the motivation, method, and results easy to follow. Technical concepts are well explained, aiding comprehension.
Interesting and Intuitive Idea: The core idea—modeling anatomical structures as interdependent signed distance functions (SDFs) to regulate their spatial relationships—is both original and conceptually appealing. It aligns well with how anatomical parts are expected to interact in the human body.
Potential Clinical Relevance: The method has clear usability in the medical domain, where anatomical shapes exhibit consistent and meaningful spatial relationships. Enforcing these relationships during shape reconstruction has the potential to improve downstream applications such as surgical planning or diagnosis.
Novel Formulation of Pairwise SDF Constraints: The paper introduces a novel formulation in which interdependent pairwise SDFs are optimized to enforce topological constraints—including a desired contact ratio (demonstrated on heart modeling) and a minimum separation distance (demonstrated on spine structures). These constraints are incorporated through additional loss terms that guide the SDFs toward anatomically plausible configurations.
- 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 method claims to eliminate unwanted overlap and ensure sufficient contact between structures, but this is only shown qualitatively. There is no direct quantitative comparison with other methods or ground truth on this specific aspect—only indirect evidence via improved per-structure metrics.
Table 1 results are unclear—it’s not specified what the values represent. Is the Chamfer Distance an average over all five reconstructed structures?
The ablation study (Table 4) is limited to a single out-of-distribution (OOD) example pair, which is insufficient. A proper evaluation should report average performance drops over all test pairs, both in-distribution and OOD, to justify the importance of each loss component.
For the spine scenario, there is only a comparison with a baseline SDF method. Broader baseline comparisons are needed to validate performance.
The paper lacks technical details about training the proposed method, including architecture specifics (e.g., whether DeepSDF was used as-is), training schedules, loss balancing, and hyperparameters. Training details for the compared methods are also missing.
There’s an inconsistency in the stated constraints: the method section says vertebrae must maintain a 1mm gap, while another section mentions a 1-pixel minimum gap. This contradiction needs clarification.
The “area difference” metric is mentioned without explaining how it is calculated or specifying its units (e.g., mm²), making it hard to interpret the results.
The ratios used for enforcing anatomical priors are derived from the training set, but it’s unclear whether this set is representative of the broader population. There’s no analysis on how these ratios vary across subjects or whether they form a reliable prior.
The title suggests the method is focused on the heart, but only part of the method is heart-specific; the rest deals with maintaining minimum distances between any adjacent structures, making the title slightly misleading.
There are typos and awkward phrasing, such as in Section 3.1: “touch each other –other than– within a small tolerance…” This is grammatically incorrect and unclear.
The layout of figures and tables is confusing. For instance, results on the heart (Figure 1, Table 1) appear near a spine figure, making it harder to follow the narrative.
Ground truth (GT) values are missing in Table 3, which would help contextualize and evaluate the results more effectively. There’s a typo in the conclusion: “adjacent vertebrae DO not touch each other” likely should be “do not.”
The method may remove or introduce parts that do not exist, especially in out-of-distribution cases. This is a significant limitation. Among evaluated methods, NVF seems more robust in such scenarios.
The issue of unwanted overlap or insufficient contact may be a representation problem rather than a segmentation one. For example, the UNet segmentation has a well-defined shared surface, while implicit reconstructions over- or under-estimate contact. Perhaps constraints should be enforced directly on segmentation outputs rather than through implicit modeling.
The paper lacks comparisons with recent, relevant works:
- Liu et al., AAAI 2024: Implicit Modeling of Non-Rigid Objects with Cross-Category Signals
- Yang et al., MICCAI 2024: Generating Anatomically Accurate Heart Structures via Neural Implicit Fields
- 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
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- 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?
I am recommending a weak accept because the paper presents a novel and conceptually sound method—interdependent pairwise SDFs with topological constraints—that is well-motivated and potentially useful in medical applications. While the idea is interesting and the paper is clearly written, the work is limited by insufficient quantitative evaluation, unclear metrics, and a lack of broader comparisons and ablations.
- Reviewer confidence
Confident but not absolutely certain (3)
- [Post rebuttal] After reading the authors’ rebuttal, please state your final opinion of the paper.
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- [Post rebuttal] Please justify your final decision from above.
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Review #2
- Please describe the contribution of the paper
Summary of paper:
- The authors propose adding constraints (through loss functions) to a (multi-)SDF fitting to ensure properties such as contact region size are learned correctly.
- The results show that the these additional constraints result in improved representation learning.
- The authors show that there exists a inter-patient consistency (see beg. of section 3) when it comes to shared surfaces.
- The authors ablate the introduced constraints well.
- 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.
Strengths:
- The technical parts of the paper are easy to follow and I felt it is generally well written. Some parts are a little unclear (for example it is said that points are sampled closer to the surface, but it isn’t said how exactly this is done. But I understand the space constraint).
- The method seems to provide better results given the constraints.
- Figures nicely illustrate the results
- A comprehensive comparison to other approaches is made.
- 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.
Weaknesses
- It is unclear to me what the task/goal of the paper is. The abstract makes it sound like this is a representation learning paper, in which the authors introduce an improved representation learning approach. But the abstract also mentions that they compare themselves to a segmentation based approach (which makes it sound like segmentation is part of the task). Generally, I still don’t understand where the ground truth model of the hearts is coming from. In Section 4 the authors state that they fit their approches to the output of nnU-Net, so I suspect this is the ground truth? If so, how does Table 2 explain that the output of nnU-Net (a) is different from the Ground truth (d). If my above assumption is correct, the authors should mention this much earlier in the document (in the introduction). Something similar to: “We start from MRI scans segmented by nnU-Net, then convert them into ground-truth surfaces, then fit an SDF (or multiple SDFs) subject to geometric constraints.”
- Ultimately, this is method is learning an SDF with additional constraints. The evaluation shows that the SDF successfully learns the constraints. The authors must make it more clear where the ground truth is coming from. Otherwise, the main message of the paper is more along the lines of “the network trained with constraints better fulfills the constraints”. This wouldn’t be a contribution.
- The authors should make it more clear why we want an SDF representation. Why not use a mesh?
- 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
More Comments:
- The abstract should state why the internal structures are important.
- SDFs don’t directly lend themselves to multi-segment representation learning. But occupancy functions do. There is existing work that should be discussed. Methods for implicit learning of segmented objects (with internal parts) exist (which seem to use a cross-entropy loss to allow the definition of segments). I found a few using the google scholar query:
organ occupancy network - The authors should discuss what problems such constraints can cause. For example for patients that are out of distribution regarding contact ratios etc.
- 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?
The paper is well written and easy to follow. The method is interesting. The method needs to be introduced better and some key points regarding the ground truth data needs to be explained better.
- Reviewer confidence
Very confident (4)
- [Post rebuttal] After reading the authors’ rebuttal, please state your final opinion of the paper.
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- [Post rebuttal] Please justify your final decision from above.
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Review #3
- Please describe the contribution of the paper
This paper proposes a pairwise-constrained signed distance function(SDF) to model the human heart, aiming to form anatomical correct walls, and avoid unwanted misplacements.
- 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.
- This paper proposes a pairwised implicit function approach to enforce anatomical contacts, and model the heart as a set of SDFs. The method could ensure accurate anatomical structures of human heart in an robusted way.
- The proposed method is validated on 3D MRI dataset, and compared with single-SDF, UDF-based and voxel-based approaches. An additional vertebrae dataset is also applied for the validation.
- This paper used a sample based vertification strategy for ratio measurement between different components.
- 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.
This paper provides a novel pairwised SDF method to reconstruct 3D human heart, and achieves good result on 3D MRI datasets. Just a few weekness inside this work.
- The definition of the contact distance is vague in method part, if the authors can describe it using a figure, the readers can understand it in a better way.
- An overall flowchart that clearly illustrate the pipeline of this work could be presented in this paper.
- 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
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- 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?
The paper addresses a clinically important problem (accurate 3D modeling of the human hearts), and proposes a novel pairwised SDF method to generate a precise 3D reconstruction result. The method takes the SDFs of given object and prior contact ratio to enforce correct shared surface areas. The method is reasonable and innovative, the experiment result demonstrates the advantage of the proposed method. The drawback of this paper is lack of figure to illustrate the method, leading to a vague description inside method part.
- Reviewer confidence
Confident but not absolutely certain (3)
- [Post rebuttal] After reading the authors’ rebuttal, please state your final opinion of the paper.
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- [Post rebuttal] Please justify your final decision from above.
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Author Feedback
We appreciate the thoughtful feedback from the reviewers and would like to provide clarifications for a few key points that were raised during the review process.
- How is the ground truth defined?
- The ground truth annotation is provided directly from the datasets. Following prior work, we apply Laplacian smoothing to these meshes for consistency and to reduce noise.
- Is there quantitative evidence for improved contact enforcement or overlap reduction?
- Yes. While we could not include these results in the main paper due to space limitations, our method does improve quantitative metrics related to contact and overlap enforcement.
- Why use SDFs instead of meshes or occupancy networks?
- nnU-Net, which we use as a reference, is effectively an occupancy-based method. However, such methods are resolution-limited and do not produce smooth surfaces. We also experimented with mesh-based modifications, but found it challenging to adjust meshes locally without compromising global structural integrity. SDFs provide a continuous, flexible representation better suited for enforcing geometric constraints.
- How consistent or generalizable are the anatomical priors across subjects?
- They are quite consistent, as demonstrated in Table 2 of the paper. This supports the use of priors like contact ratios in our approach.
- What are the method’s limitations, especially for out-of-distribution (OOD) cases? What if the constraints are not guaranteed?
- This is an excellent point. Our method primarily targets cases where the anatomical constraints are expected to hold. In scenarios where this assumption may not apply, a preliminary measurement or detection mechanism should be used. Identifying and quantifying constraint violations could even serve as a useful diagnostic tool in itself.
- Could constraints be applied to segmentation outputs directly, rather than SDFs?
- We explored this idea initially but found it difficult to formulate global constraints—such as contact ratios or minimum distances—directly on segmentation masks. SDFs provide a natural and differentiable way to define and enforce such constraints. Nonetheless, developing constraint-based approaches in the segmentation space remains an interesting direction for future work.
We hope these clarifications are helpful for readers and researchers interested in extending this work. We will open source our code and welcome further discussion on our GitHub page and via email. We thank the reviewers and area chair once again for their constructive comments and kind consideration.
Meta-Review
Meta-review #1
- Your recommendation
Provisional Accept
- 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”.
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