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REVIEW 4 major objections 6 minor 1 cited by

Mesh2SSM++: A Probabilistic Framework for Unsupervised Learning of Statistical Shape Model of Anatomies from Surface Meshes

T0 review · 4 major / 6 minor · reviewed 2026-08-08 · deepseek-v4-flash

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Pith's one-line read Mesh2SSM++ claims that statistical shape models can be learned from raw surface meshes unsupervised, with per-point aleatoric uncertainty, matching or beating established tools.

desk verdict A genuinely useful but modest extension of Mesh2SSM; the headline uncertainty claim is mislabeled as aleatoric and needs fixing before publication. read the letter →

arxiv 2502.07145 v1 pith:6NTN2CQB submitted 2025-02-11 cs.CV

Krithika Iyer , Mokshagna Sai Teja Karanam , Shireen Elhabian This is my paper · ORCID
classification cs.CV
keywords statisticalshapemodelingsurfacemeshesunsupervisedcorrespondencelearningnormalizingflowsaleatoricuncertaintypointdistributionmodelsmeshautoencodermedicalimageanalysis
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper tries to establish that a statistical shape model of an anatomical structure can be learned directly from surface meshes without correspondence annotations, a pre-existing shape model, or per-sample optimization. The key claim is that deforming a single template point cloud into each subject's mesh, guided by a permutation-invariant mesh encoder and an implicit-field decoder, yields correspondence-based shape models whose quality is competitive with established optimization-based tools. The paper further claims that replacing the previous variational-autoencoder analysis module with a normalizing flow in the latent space simplifies training and adds reliable aleatoric uncertainty estimates for every predicted correspondence point. If these claims hold, clinical shape analysis becomes faster, more scalable, and more interpretable, because new subjects are processed in a single forward pass and regions of high prediction ambiguity are flagged automatically.

What carries the argument

The central object is a decoupled-prior variational autoencoder with a continuous normalizing flow in the latent space. This combines a DGCNN mesh encoder that produces a variational posterior, an invertible flow that maps the representation space to a standard Gaussian sampling space, and an implicit-field decoder (IM-NET) that deforms a shared template point cloud into subject-specific correspondences. The flow's change-of-variables formula gives the latent prior density and supports sampling new shapes; the decoder's Chamfer-distance loss is supplemented by a softmin surface-projection step that pulls predicted correspondences onto the mesh surface, and vertex masking adds robustness. This machinery carries the argument because it replaces the separately trained shape-variation autoencoder of the predecessor method with a single end-to-end probabilistic pipeline that yields a template, a shape distribution, and per-point uncertainty.

What would settle it

Run Mesh2SSM++ on the same five cohorts without the initial rough alignment, or on one cohort with deliberately varied poses, and compare surface accuracy and surface-to-surface distance against the aligned setting; if these metrics degrade materially or the deformed template no longer lands on the same anatomical landmarks, the alignment assumption is confirmed as load-bearing. Alternatively, inject synthetic noise into the meshes and check whether the reported uncertainty-error correlation survives, since controlled noise should keep the calibration claim testable.

Watch

Extended reading notes

Core claim

Mesh2SSM++ claims that a probabilistic autoencoder with a normalizing-flow prior can learn a correspondence-based statistical shape model from surface meshes alone. The encoder maps each mesh to a low-dimensional latent representation; the decoder, an implicit field network, uses that representation to deform a common template point cloud onto the subject's surface, so the same ordered points across all subjects form the correspondence model. The normalizing flow links the encoder's representation space to a Gaussian sampling space, enabling end-to-end training, population-informed template updates, and sampling of new shape instances. To keep predicted particles on the anatomy, the method projects them onto the mesh surface via softmin-weighted displacements, and it augments training by masking and perturbing vertices. Aleatoric uncertainty is obtained by decoding multiple latent samples and fitting a Gaussian to the resulting correspondence predictions; the paper reports that this uncertainty correlates with prediction error in most tested organs and can flag out-of-distribution shapes.

Load-bearing premise

The cohort of meshes must already be roughly aligned before training begins; if they are not, the shared template deformation no longer puts corresponding points on the same anatomical locations, so the learned shape model loses anatomical meaning.

Editorial extensions

If this is right

  • If the central claim is right, statistical shape models for a new anatomical cohort can be built directly from segmented meshes, without manual landmarks, atlas initialization, or pre-computed shape models.
  • A single forward pass produces correspondences for a new subject, so inference no longer requires per-sample re-optimization, making large-scale and near-real-time shape analysis practical.
  • The learned latent space doubles as a shape-statistics space, so population modes of variation can be read off either the correspondences or the latent codes, and new synthetic shapes can be generated from the flow prior.
  • Per-correspondence aleatoric uncertainty gives a ready-made reliability map for clinical workflows, flagging noisy regions and out-of-distribution anatomy such as atypical liver lobes or thin left-atrium structures.
  • Because the method matches or outperforms optimization-based and deep baselines on surface accuracy, SSM metrics, and downstream classification, it offers a drop-in alternative for shape-based diagnosis studies.
  • The mesh-to-correspondence pipeline can scale to large cohorts and multiple anatomies with a single learned template, as demonstrated by the reported multi-class vertebra classification experiment.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The paper does not test active learning, but its calibrated uncertainty suggests a natural extension: retraining on the highest-uncertainty meshes would likely improve the model where correspondence is currently ambiguous.
  • The stated alignment assumption points to a stress test the paper does not run: removing the pre-alignment step or adding large pose variation should reveal where the pipeline breaks, and an alignment-free variant would considerably widen clinical applicability.
  • The interpretable latent-space modes shown for liver and left atrium hint at a biomarker-discovery tool, since latent scores could be correlated with clinical variables beyond the group-difference analysis the paper reports.
  • The softmin surface projection keeps particles close to the mesh, but the underlying Chamfer loss may still be sensitive to missing regions or spurious surfaces; replacing it with signed-distance or implicit-surface supervision, which the authors themselves suggest, is a plausible next test.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. The paper proposes Mesh2SSM++, an unsupervised deep learning framework for constructing correspondence-based statistical shape models (SSMs) directly from surface meshes. It extends Mesh2SSM by introducing a normalizing flow in the latent space of a mesh autoencoder, a soft surface-projection step, vertex masking augmentation, and an uncertainty-estimation procedure that the authors call aleatoric. The method is evaluated on five anatomical datasets (femur, spleen, pancreas, liver, left atrium) against ShapeWorks, Deformetrica, FlowSSM, and Mesh2SSM, using distance metrics, SSM metrics, and downstream tasks including group-difference analysis and lumbar vertebra classification. The main claims are that the method outperforms existing approaches, learns a population-specific template, and quantifies aleatoric uncertainty.

Significance. If the central claims are supported, Mesh2SSM++ would be a practically valuable contribution to medical shape analysis: it offers fast, unsupervised SSM construction from meshes, a learned template, and uncertainty estimates for correspondence predictions. The paper is strong in experimental breadth: five datasets, multiple baselines, downstream tasks, and public code. The probabilistic framing is appealing, and the surface-projection and data-augmentation ideas are sensible engineering additions. However, the key conceptual contribution advertised in the abstract and introduction—aleatoric uncertainty quantification—is not supported as stated; the quantity actually computed is posterior predictive (epistemic) variance. Several other claims are also stronger than the evidence, and the alignment assumption is acknowledged only as a limitation without analysis. For these reasons the paper needs substantive revision even though the underlying method appears to be useful and the experiments are commendable.

major comments (4)
  1. [III-C.4, Abstract, Introduction] The quantity called 'aleatoric uncertainty' is the variance of the posterior predictive distribution, which is epistemic uncertainty, not aleatoric uncertainty. The decoder f_theta is deterministic, and the training loss in Eq. (6) is a Chamfer distance, not the negative log-likelihood of a stochastic output distribution. The procedure in Section III-C.4 samples z_n^{(s)} ~ q_phi(z|X_n) and computes C_n^{(s)} = f_theta(z_n^{(s)}); the variance of these decoded samples reflects posterior uncertainty over the latent code z given the input, i.e., epistemic (model) uncertainty. The authors explicitly contrast aleatoric and epistemic at the start of the section, then compute an epistemic quantity. Since the abstract and introduction advertise aleatoric uncertainty as a key feature and basis for clinical reliability, this is a load-bearing mischaracterization. The uncertainty estimates in Table I may still be useful as predictive variances, but they must be relabeled and the associated claims revised.
  2. [III-C.2, Eqs. (7)-(10)] The surface-projection step does not guarantee that predicted correspondences lie on the mesh surface. The update in Eq. (10) is c_i^proj = sum_j W_ij v_j, i.e., a convex combination of all mesh vertices, which lies in the convex hull of the entire mesh and, for a closed volumetric mesh, can be in the interior. Only in the limit of zero softmin temperature would the result coincide with the nearest vertex; for any finite sigma it is generally off the surface. The claim that the projection 'aligns predicted correspondences precisely onto the surface' is therefore inaccurate. The authors should either implement a hard projection onto the closest face or empirically verify with a point-to-surface metric that projected points are on the surface within a small tolerance, and soften the wording to 'encourage'.
  3. [VI and Section I] The method assumes the cohort of shapes is roughly aligned, as stated in Section VI. This assumption is load-bearing for learning meaningful correspondences: without alignment, deforming a common template cannot establish anatomically valid correspondences. The paper gives no details of the alignment preprocessing used on its five datasets and no experiment quantifying sensitivity to misalignment. Consequently, the repeated claim that Mesh2SSM++ operates 'directly on meshes' (Abstract, Introduction) is overstated. The authors should either document the alignment step explicitly or provide a misalignment-robustness experiment (e.g., by perturbing rigid poses and reporting the degradation in metrics).
  4. [Abstract and Section V-A] The claim that Mesh2SSM++ 'outperforms existing methods' is too broad. The results in Section V-A show that for the femur and spleen datasets, Deformetrica and ShapeWorks achieve the lowest Chamfer distance, with the proposed models 'closely follow' (Figure 3). The proposed methods are consistently strong on S2S and on some SSM metrics, but not uniformly across all metrics and anatomies. The abstract and conclusion should be rephrased to indicate that Mesh2SSM++ is comparable or superior on specific metrics and datasets, rather than universally outperforming all baselines.
minor comments (6)
  1. [Eq. (5)] The equation sets a loss L to a negative expected log-likelihood plus a KL term, while the text says the training 'maximizes the likelihood'; the sign convention should be clarified (e.g., state explicitly that the objective is minimized).
  2. [Eqs. (3)-(4) and Figure 2.A] The notation for the normalizing flow direction is inconsistent: Eqs. (3)-(4) treat z0 = g_eta(z), whereas Figure 2.A and the text describe mapping from z0 to z via g_eta^{-1}. Please align the notation to avoid confusion about forward and inverse transformations.
  3. [Section III-C.4] The number of latent samples S used for the uncertainty estimate is not specified; please state it and whether it is tuned or held fixed across datasets.
  4. [Section IV-C] The exclusion of FUSS is explained, but the reader cannot verify the inability to reproduce its reported performance; providing the attempted configuration (e.g., exact hyperparameters, software versions) in a supplement would be helpful for reproducibility.
  5. [Table II] The M++AE and M++Flow rows report identical accuracy and F1 values to three decimal places; please confirm this is not a copy error and add a brief comment on why the two variants behave identically in this task.
  6. [Section VI] The caveat that Chamfer distance and the projection step may fail with missing regions, spurious surfaces, or noise is useful but placed far from the method description; consider moving a short version of this caveat next to the surface-projection discussion in Section III-C.2.

Circularity Check

0 steps flagged · score 2.0 of 10

No circular derivation found; the correspondence model is trained against external reconstruction targets and evaluated on held-out data against independent baselines, with only non-load-bearing self-referential design choices.

full rationale

Mesh2SSM++'s derivation chain is not circular. The correspondence generation module is trained by minimizing Chamfer and vertex reconstruction losses against the input meshes (Eq. 1 and Eq. 6), which is supervision from the data rather than from the model's own outputs. The probabilistic latent-space objective (Eq. 5) is a standard VAE/NF training target, and the template update described in Section III-C.1-c is a self-referential training choice, not a fitted parameter renamed as a prediction; moreover, all methods are evaluated on held-out test splits against independent baselines such as ShapeWorks and Deformetrica. The uncertainty calibration analysis in Section V-B and Table I is post hoc and does not feed back into training, so no prediction is forced by construction. The main concern raised by the skeptic is the aleatoric-versus-epistemic labeling in Section III-C.4: the reported variance is computed by sampling latent codes z from the approximate posterior and decoding deterministically, which is posterior predictive (epistemic) variance rather than aleatoric noise. That is a correctness or interpretation issue, not a circularity, because it does not make any output equal to its input by construction. Self-citations to Mesh2SSM, dpVAEs, and ShapeWorks are used as architectural and baseline references and are not load-bearing circular justifications for the paper's central claims.

Assumptions & free parameters 6 free parameters · 4 assumptions · 0 invented entities

The method relies on standard unsupervised deep learning assumptions (Gaussian posterior, Chamfer-driven correspondence) and an explicit alignment assumption. No new physical entities are introduced. The free parameters are standard hyperparameters, but the paper does not report their values or ablations, which reduces reproducibility.

free parameters (6)
  • alpha (L1 Chamfer weight) = not specified
    Hyperparameter in Eq. 1 weighting the L1 Chamfer term; chosen by hand, no ablation reported.
  • gamma (MSE reconstruction weight) = not specified
    Hyperparameter in Eq. 1 weighting the vertex reconstruction loss.
  • sigma (softmin temperature) = not specified
    Controls softness of projection in Eq. 8; affects how strictly correspondences are pulled to the surface.
  • Number of correspondences M = 1024 (stated for comparisons)
    Fixed number of correspondence points, chosen by the user, not learned.
  • Number of template update samples = 500
    Number of prior samples decoded and averaged to update the template each epoch.
  • Latent dimension L = not specified
    Dimensionality of representation space z; not reported, affects model capacity.
assumptions (4)
  • domain assumption The shape cohort is roughly aligned.
    Explicitly stated in Section VI as a limitation; if meshes are not aligned, template deformation cannot establish meaningful correspondences.
  • domain assumption Minimizing Chamfer distance between the deformed template and each target mesh yields anatomically corresponding points.
    The core unsupervised objective (Eq. 6); assumes closest-point matching on the surface reflects anatomical correspondence, which is not guaranteed.
  • domain assumption The variational posterior q_phi(z|X) is Gaussian.
    Used for reparameterization sampling and for computing aleatoric uncertainty; standard VAE assumption.
  • domain assumption The predictive distribution p(C|z) can be approximated by a Gaussian.
    Section III-C.4 fits a Gaussian to decoded samples; the paper acknowledges this may not always hold.

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Cite this review

Pith. "Pith review of Mesh2SSM++: A Probabilistic Framework for Unsupervised Learning of Statistical Shape Model of Anatomies from Surface Meshes." pith.science (2026). https://pith.science/paper/6NTN2CQB

@misc{pith2026250207145,
  author       = {Pith},
  title        = {Pith review of: Mesh2SSM++: A Probabilistic Framework for Unsupervised Learning of Statistical Shape Model of Anatomies from Surface Meshes},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6NTN2CQB}},
  note         = {Machine review of arXiv:2502.07145}
}
read the original abstract

Anatomy evaluation is crucial for understanding the physiological state, diagnosing abnormalities, and guiding medical interventions. Statistical shape modeling (SSM) is vital in this process. By enabling the extraction of quantitative morphological shape descriptors from MRI and CT scans, SSM provides comprehensive descriptions of anatomical variations within a population. However, the effectiveness of SSM in anatomy evaluation hinges on the quality and robustness of the shape models. While deep learning techniques show promise in addressing these challenges by learning complex nonlinear representations of shapes, existing models still have limitations and often require pre-established shape models for training. To overcome these issues, we propose Mesh2SSM++, a novel approach that learns to estimate correspondences from meshes in an unsupervised manner. This method leverages unsupervised, permutation-invariant representation learning to estimate how to deform a template point cloud into subject-specific meshes, forming a correspondence-based shape model. Additionally, our probabilistic formulation allows learning a population-specific template, reducing potential biases associated with template selection. A key feature of Mesh2SSM++ is its ability to quantify aleatoric uncertainty, which captures inherent data variability and is essential for ensuring reliable model predictions and robust decision-making in clinical tasks, especially under challenging imaging conditions. Through extensive validation across diverse anatomies, evaluation metrics, and downstream tasks, we demonstrate that Mesh2SSM++ outperforms existing methods. Its ability to operate directly on meshes, combined with computational efficiency and interpretability through its probabilistic framework, makes it an attractive alternative to traditional and deep learning-based SSM approaches.

Figures

Figures reproduced from arXiv: 2502.07145 by the authors.

Figure 1
Figure 1. Correspondences are sets of ordered points on different shapes [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Overview of Mesh2SSM++ Framework: (A) The generative model leverages a decoupled representation and generation process. The latent variable z is mapped from the generation space z0 ∼ p(z0) to the representation space through the invertible mapping g −1 η (z0), while X ∼ pθ(X|z) represents data sampled in the data space. Inference is performed via qϕ(z|X), which maps the input mesh X to its latent representation z. (… view at source ↗
Figure 3
Figure 3. Distance Metrics: Boxplots show the error distribution across test sets for each model in mm. M++AE, the template is updated as the mean correspondence of all the predicted training samples. All SW, Mesh2SSM, and Mesh2SSM++ based methods use 1024 correspondence points, whereas Deformetrica and FlowSSM establish vertex￾wise correspondences. Note that we attempted to replicate the results of the FUSS [25] using the co… view at source ↗
Figures from the paper (9 more)
Figure 4
Figure 4. Figure 4: SSM Metrics: A compactness plot displays the cumulative variance ratio as a function of PCA mode count. Generalization and specificity reconstruction error plotted as a function of PCA mode count. For all datasets, a maximum of 30 modes that account for at least 99% of…
Figure 6
Figure 6. Figure 6: B presents the correlation between aleatoric uncer [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]
Figure 6
Figure 6. Figure 6: (A) Comparison of Group Differences Identified by ShapeWorks vs. Mesh2SSM++: The figure illustrates the mean shapes of the control group. Color mapping indicates the distance between the control and CAM FAI mean. Both ShapeWorks and Mesh2SSM++successfully capture the c…
Figure 7
Figure 7. Figure 7: C presents scatter plots of aleatoric uncertainty [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]
Figure 7
Figure 7. Figure 7: A. Group Difference Statistical Significance: The p-values of the group differences overlayed over the mean mesh. The color showcases statistical significance. (B). LDA Map Shape mapping to linear discrimination of variation between population means for the groups of p…
Figure 9
Figure 9. Figure 9: Modes of Variation in Latent Space: The first two modes were identified by performing PCA in the latent space of the M++Flow model for the liver, left atrium, and pancreas datasets. PCA modes in [PITH_FULL_IMAGE:figures/full_fig_p010_9.png]
Figure 10
Figure 10. Figure 10: Lumbar Vertebra: The first row represents the examples of the lumbar vertebra. The second row represents the mean predictions from the Mesh2SSM++ model for each vertebrae. Color denotes correspondence. The next two rows represent the PCA modes of variations identified…
Figure 6
Figure 6. Figure 6: A, further validating the utility of Mesh2SSM++for [PITH_FULL_IMAGE:figures/full_fig_p011_6.png]
Figure 11
Figure 11. Figure 11: Modes of Variation: The first two modes were identified by performing PCA on the predicted correspondences [PITH_FULL_IMAGE:figures/full_fig_p014_11.png]

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Pith tools

Reviewed August 8, 2026 · model on record in the stance chip above.