{"id":"59b28e17-0522-44cd-b2e4-a24e9b9d3441","arxiv_id":"2502.07145","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"Mesh2SSM++ learns correspondence-based statistical shape models from unlabeled 3D meshes using a normalizing flow latent space and surface projection, with built-in uncertainty estimates.","lead":"Mesh2SSM++ is a new deep learning method that learns anatomical shape models directly from 3D surface meshes without manual landmark annotations. It also estimates how confident its predictions are, which could help doctors trust automated shape analysis.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The uncertainty quantified as 'aleatoric' is the variance of the posterior predictive, produced by sampling the variational encoder; with a deterministic decoder (Eq. 5-6), this is epistemic uncertainty, so a key claimed contribution is mischaracterized.","rationale":"I reviewed the central claim and the reader's analysis. The reader's weakest_assumption is the rough-alignment requirement, which is a valid limitation and explicitly acknowledged in Section VI. However, I find a more load-bearing concern in the paper's core contribution: the uncertainty labeled 'aleatoric' is computed by sampling the variational posterior q_phi(z|X) and decoding deterministically; this is the posterior predictive variance, an epistemic quantity. This is an internal inconsistency with the paper's own definition of aleatoric uncertainty. It does not require external assumptions or data; it follows from the model equations (Eq. 5-6 and Section III-C.4). While the alignment assumption limits applicability, it is stated and is typical of shape modeling; the uncertainty mischaracterization, by contrast, is an unsupported claim about a headline feature. I therefore partially agree with the reader: they noted the mislabel in the rationale but selected alignment as the weakest assumption. I recommend keeping the verdict CONDITIONAL, requiring the authors to correct the uncertainty definition or re-estimate it with an explicit noise model. I do not recommend rejection because the method still produces useful predictive variance and demonstrates empirical calibration; the issue is addressable.","tokens_in":19218,"tokens_out":9215,"duration_ms":77710,"concrete_test":"Perform an analytical derivation of the predictive variance using Eq. 5-6 and Section III-C.4: if the decoder is deterministic and the likelihood is a Chamfer distance with no noise parameter, the computed variance is posterior predictive (epistemic), which would invalidate the aleatoric label. To confirm, run a synthetic experiment with known heteroscedastic vertex noise and check whether the estimated uncertainty tracks the injected noise; if it does not, the aleatoric claim is unsupported.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper claims a key feature is 'to quantify aleatoric uncertainty' (Abstract), defined in Section III-C.4 as the variance of the conditional distribution p(C_n|z_n). In the model, however, p_theta(C|z) is not a distribution: the decoder f_theta is a deterministic mapping from latent code to correspondences, and the loss in Eq. 5-6 is a Chamfer distance, not a negative log-likelihood of a stochastic output. The procedure in Section III-C.4 samples z_n^{(s)} ~ q_phi(z|X_n) (the approximate posterior), computes C_n^{(s)} = f_theta(z_n^{(s)}), and fits a Gaussian to these samples. The resulting variance is the variance of the posterior predictive p(C|X), arising from posterior uncertainty over the latent code z. That is epistemic uncertainty (model uncertainty about the latent given the input), not aleatoric uncertainty (inherent noise in the data). The authors even contrast aleatoric with epistemic at the start of the section, then compute a quantity that is epistemic by construction. This is not a minor semantic issue: the abstract and introduction advertise aleatoric uncertainty as a core contribution and a basis for clinical reliability. If the quantity is epistemic, the model's own definition of aleatoric uncertainty is unsatisfied, and the claim that Mesh2SSM++ 'quantifies aleatoric uncertainty' is false. The correlation with error shown in Table I is a property of the posterior predictive variance, which can be useful, but it does not make the uncertainty aleatoric. The paper should either remodel the likelihood to include observation noise (e.g., a Gaussian output head with predicted variance) or relabel the uncertainty as posterior predictive / epistemic.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":19566,"tokens_out":6033,"duration_ms":53927,"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":[{"comment":"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.","section":"III-C.4, Abstract, Introduction"},{"comment":"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'.","section":"III-C.2, Eqs. (7)-(10)"},{"comment":"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).","section":"VI and Section I"},{"comment":"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.","section":"Abstract and Section V-A"}],"minor_comments":[{"comment":"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).","section":"Eq. (5)"},{"comment":"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.","section":"Eqs. (3)-(4) and Figure 2.A"},{"comment":"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.","section":"Section III-C.4"},{"comment":"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.","section":"Section IV-C"},{"comment":"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.","section":"Table II"},{"comment":"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.","section":"Section VI"}],"recommendation":"major_revision","confidential_remarks":"The paper is generally well written and the experimental effort is substantial, but the aleatoric-versus-epistemic confusion is likely to be the key bone of contention in review. The authors should be given the opportunity to recharacterize the uncertainty as posterior predictive (epistemic) or to add a genuine aleatoric noise model. The surface-projection issue is also fixable by rewording or by a hard projection. The alignment assumption is a stated limitation, but its impact should be demonstrated empirically. The exclusion of FUSS is understandable but may attract criticism; a supplementary reproducibility report would help. Overall, the method is promising and the release of code is a clear positive."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: Mesh2SSM++ is a real improvement over its predecessor, and the authors evaluate it honestly against strong baselines on five anatomies. But the central uncertainty contribution is mischaracterized, and the abstract overclaims. The stress-test note is correct: what they call aleatoric uncertainty is not aleatoric.\n\nWhat is actually new and good: replacing the SP-VAE with a normalizing flow in the latent space is a sensible architectural change that simplifies training and enables population-informed template updates; the softmin surface projection directly addresses a real weakness of Chamfer-only training; vertex masking as augmentation is reasonable. The experimental breadth is a genuine strength—five anatomies, distance metrics, SSM compactness/generalization/specificity, and two downstream tasks. The comparison to ShapeWorks and Deformetrica is the right kind of benchmark, and the qualitative correspondence results look credible.\n\nThe soft spots, in proportion:\n\n1. The uncertainty label is wrong. Equation (5)–(6) defines a deterministic decoder f_theta with Chamfer loss, not a stochastic likelihood. Sampling z ~ q_phi(z|X) and measuring the spread of f_theta(z) gives posterior predictive variance, which is epistemic uncertainty about the latent code, not aleatoric noise in the data. The authors themselves distinguish aleatoric from epistemic at the start of Section III-C.4 and then compute the epistemic quantity. This is not a minor semantic quibble: the abstract and introduction advertise aleatoric uncertainty as a key clinical-reliability feature. Either add an observation-noise output head or relabel the quantity.\n\n2. The abstract claims the method \"outperforms existing methods.\" The results do not support universal superiority: on femur and spleen, ShapeWorks and Deformetrica achieve lower Chamfer and point-to-mesh distances, with M++Flow close behind. The paper is strongest when it says \"comparable or better,\" and weakest when it overgeneralizes.\n\n3. Excluding FUSS after failing to reproduce its reported performance is understandable, but it means the SOTA comparison is incomplete. The right move is to report the attempt, the discrepancy, and include FUSS with the authors' numbers or an explicit disclaimer.\n\n4. Replication details are thin: alpha, gamma, sigma, number of correspondences, latent dimension, template-update frequency, and training schedules are not given. The stated limitation about rough pre-alignment is honest, but it is load-bearing: without alignment, the template-deformation story collapses.\n\nWho this is for: researchers working on deep statistical shape models for medical anatomy. It is a solid, citable incremental contribution, not a breakthrough. It deserves a serious referee, but the referee should require the uncertainty relabeling, softened claims, and fuller implementation details before acceptance.","headline":"A genuinely useful but modest extension of Mesh2SSM; the headline uncertainty claim is mislabeled as aleatoric and needs fixing before publication.","tokens_in":20127,"tokens_out":1932,"would_cite":true,"duration_ms":21010,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Mesh2SSM++ claims that statistical shape models can be learned from raw surface meshes unsupervised, with per-point aleatoric uncertainty, matching or beating established tools.","keywords":["statistical shape modeling","surface meshes","unsupervised correspondence learning","normalizing flows","aleatoric uncertainty","point distribution models","mesh autoencoder","medical image analysis"],"falsifier":"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.","tokens_in":19025,"feed_emoji":"🩻","tokens_out":4989,"duration_ms":46068,"temperature":0.7,"pith_summary":"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.","feed_headline":"Mesh2SSM++ builds anatomy shape models straight from meshes","feed_subtitle":"A normalizing-flow redesign adds per-point uncertainty and matches established optimizers on five organs.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Supplies the predecessor architecture, the template-deformation correspondence generation idea, and the baselines limitations that Mesh2SSM++ is designed to fix.","marker":"[20]"},{"why":"Provides the EdgeConv dynamic graph convolution operations used in the mesh encoder to capture permutation-invariant local geometric features.","marker":"[37]"},{"why":"Supplies the implicit field decoder architecture that deforms the template point cloud into subject-specific correspondences.","marker":"[46]"},{"why":"Provides the normalizing-flow framework whose invertible transformations and change-of-variables formula create the expressive latent prior in Mesh2SSM++.","marker":"[28], [29]"},{"why":"Supplies the decoupled-prior variational autoencoder design that organizes the latent space into representation and sampling spaces.","marker":"[49]"},{"why":"Serves as a directly compared deep-learning baseline for mesh-based statistical shape modeling with neural flow deformations.","marker":"[22]"},{"why":"Serves as the state-of-the-art particle-based correspondence benchmark and reference point for SSM metrics and downstream group analysis.","marker":"[33]"},{"why":"Provides the spleen and pancreas segmentation datasets used to test the method under limited data and complex anatomical variability.","marker":"[50]"},{"why":"Provides the liver segmentation dataset used to evaluate performance on nonlinear shape variation at scale.","marker":"[51]"}],"fun_headline_variants":["Unsupervised anatomy shape models from raw meshes","Mesh2SSM++ learns shape models directly from meshes","Probabilistic shape modeling without pre-built templates","Mesh2SSM++: meshes to shape models with uncertainty","Aleatoric uncertainty built into unsupervised shape learning"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Unsupervised anatomy shape models from raw meshes","Mesh2SSM++ learns shape models directly from meshes","Probabilistic shape modeling without pre-built templates","Mesh2SSM++: meshes to shape models with uncertainty","Aleatoric uncertainty built into unsupervised shape learning"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000205,"raw_usage":{"total_tokens":1431,"prompt_tokens":1019,"completion_tokens":412,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":635,"completion_tokens_details":{"reasoning_tokens":333}},"tokens_in":635,"tokens_out":412,"duration_ms":4453,"temperature":1.0,"reasoning_tokens":333,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-08T13:39:30.803292+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":"Mesh2ssm: From surface meshes to statis- tical shape models of anatomy,","cited_arxiv_id":null,"evidence_quote":"Supplies the predecessor architecture, the template-deformation correspondence generation idea, and the baselines limitations that Mesh2SSM++ is designed to fix."},{"cited_title":"Im-net: Learning implicit fields for generative shape model- ing,","cited_arxiv_id":null,"evidence_quote":"Supplies the implicit field decoder architecture that deforms the template point cloud into subject-specific correspondences."},{"cited_title":"dpvaes: Fixing sample generation for regularized vaes,","cited_arxiv_id":null,"evidence_quote":"Supplies the decoupled-prior variational autoencoder design that organizes the latent space into representation and sampling spaces."},{"cited_title":"Landmark-free statistical shape modeling via neural flow deformations,","cited_arxiv_id":null,"evidence_quote":"Serves as a directly compared deep-learning baseline for mesh-based statistical shape modeling with neural flow deformations."},{"cited_title":"Shapeworks: Particle-based shape correspondence and visualization software,","cited_arxiv_id":null,"evidence_quote":"Serves as the state-of-the-art particle-based correspondence benchmark and reference point for SSM metrics and downstream group analysis."},{"cited_title":"Abdomenct-1k: Is abdominal organ segmentation a solved problem?","cited_arxiv_id":null,"evidence_quote":"Provides the liver segmentation dataset used to evaluate performance on nonlinear shape variation at scale."}],"review_version":1}