UNSURF: Uncertainty Quantification for Cortical Surface Reconstruction of Clinical Brain MRIs

Ben Glocker; Juan Eugenio Iglesias; Karthik Gopinath; Raghav Mehta

REVIEW 3 major objections 5 minor 38 references

UNSURF: Uncertainty Quantification for Cortical Surface Reconstruction of Clinical Brain MRIs

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read The paper proposes UNSURF, a surface-placement uncertainty measure based on the squared discrepancy between predicted and fitted signed distance functions, and reports that it tracks thickness errors, enables multi-level quality control…

desk verdict UNSURF is a simple, sensible uncertainty measure with solid correlation evidence, but the QC and downstream-AD claims lack the baseline controls needed to back them up. read the letter →

arxiv 2506.00498 v2 pith:EFCJBF73 submitted 2025-05-31 eess.IV cs.CV

Raghav Mehta , Karthik Gopinath , Ben Glocker , Juan Eugenio Iglesias This is my paper

classification eess.IVcs.CV

keywords uncertaintyquantificationcorticalsurfacereconstructionclinicalMRIsigneddistancefunctionqualitycontrolthicknessAlzheimer'sdiseaseclassification

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

UNSURF is proposed as a way to quantify how much a deep-learning cortical surface reconstruction is to be trusted when the input is a clinical MRI of arbitrary orientation, resolution, and contrast. The measure is defined at every voxel as the squared difference between the signed distance function predicted by the network and the signed distance function of the surface that the geometry-processing stage actually fits. The paper reports that this quantity correlates with measured cortical thickness errors, while classical voxel-wise Monte Carlo variance does not, because the discrepancy captures the geometric corrections that variance ignores. Because of this correlation, UNSURF supports automated quality control at the subject, parcel, and mesh-node level and improves Alzheimer's disease versus control classification when high-uncertainty measurements are removed. If the claim holds, large uncurated clinical datasets become more usable for group studies of cortical thickness.

What carries the argument

The object that carries the argument is the signed distance function (SDF), the map from every voxel to its signed distance from a cortical surface, and the fitted-surface SDF $\tilde{D}$ computed after the geometry-processing stage. The UNSURF measure is the squared difference between the network's raw SDF prediction $\hat{D}$ and the SDF of the topologically corrected, deformed surface $\tilde{D}$. Large discrepancies mark voxels where the network's implicit surface disagrees with the final explicit mesh, indicating regions where more than one surface placement is plausible after geometry constraints are enforced.

What would settle it

Take a set of clinical scans for which expert raters manually mark where the reconstructed white-matter or pial surface is misplaced, and compute UNSURF maps on the same scans: if voxels or mesh nodes with the largest $(\hat{D}-\tilde{D})^2$ do not preferentially coincide with the expert-marked misplacements, the measure is not tracking surface placement error. Alternatively, substitute manually edited surfaces for the FreeSurfer-based ground truth in the thickness-error correlation and check whether the reported correlations survive.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central discovery is that uncertainty in cortical surface placement should be measured after the geometry step, not before it. Given predicted signed distance functions $\hat{D}^v_i$ from a neural network and signed distance functions $\tilde{D}^v_i$ computed from the surfaces extracted by topological correction and mesh deformation, the voxel-wise squared discrepancy $U_i^v = (\hat{D}^v_i - \tilde{D}^v_i)^2$ acts as a surface-placement uncertainty estimate. Across the evaluated clinical and downsampled scans, $U$ shows positive Spearman and Pearson correlations with thickness error, whereas ensemble-dropout variance of the predicted SDFs is weakly or even negatively correlated with the same errors. Filtering out high-$U$ parcels and nodes reduces thickness errors, and removing high-$U$ subjects increases the Cohen's d effect size separating Alzheimer's patients from controls.

Load-bearing premise

The load-bearing premise is that thickness error computed against FreeSurfer-derived surfaces from high-resolution scans is a valid proxy for true surface placement error in clinical scans, and that the geometry-processing stage is deterministic, so the measured discrepancy reflects only model and data ambiguity rather than algorithmic variability.

Editorial extensions

If this is right

Automated quality control of cortical surface reconstructions can be performed at the subject, parcel, and mesh-node level on clinical scans without manual review.
Removing high-uncertainty parcels lowers parcel-level cortical thickness error in the evaluated clinical scans.
Node-level filtering within already uncertain parcels further reduces thickness errors relative to parcel-level filtering alone.
Uncertainty-based subject filtering increases the effect size of cortical thickness differences between Alzheimer's and control groups.
Ensemble-dropout variance of predicted SDFs is not a reliable proxy for cortical surface placement uncertainty and should not be used for this purpose.

Reading between the lines

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

UNSURF could be computed in any implicit-surface reconstruction pipeline that has a deterministic post-processing step, not just cortical surfaces; the same squared-discrepancy logic may transfer to other anatomical structures whose surfaces are extracted from predicted distance maps.
Because UNSURF requires no extra network passes at test time, it is cheaper than ensemble dropout or deep ensembles, so a natural next experiment is to measure the computational cost difference directly on the same geometry pipeline.
The lower correlation at 2 mm and 3 mm slice spacings suggests the measure's practical value is highest for heavily downsampled clinical acquisitions; testing UNSURF on near-isotropic but artifact-heavy scans would delimit this boundary.
If post-processing were made stochastic, for example by randomizing mesh initialization or deformation steps, part of the discrepancy $U$ would capture algorithmic variability rather than data ambiguity, so separating those two sources would clarify what $U$ actually means.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Colleague,

The one thing to know: UNSURF is a genuinely simple and well-motivated uncertainty measure—the squared difference between the network's predicted SDF and the SDF of the final geometry-processed surface—and it does correlate with thickness errors on clinical scans. That's a solid contribution. But the paper's QC and downstream-AD claims rest on filtering curves with no random-filtering control and no error bars, so those parts need more work.

What's new: using the consistency between the raw prediction and the post-processing output as an uncertainty proxy. It's cheap (no M×2 hours of geometry), it naturally accounts for topological correction, and it doesn't require any new parameters. The comparison with ensemble dropout variance is fair: variance is essentially blind to geometry, so it performs poorly, while U captures the mismatch that matters. The correlation numbers (e.g., SCC 0.627 subject-level on clinical data) are believable, and the parcel-level maps make sense.

Soft spots, in order of importance. First, the QC claims in Fig. 3d/e and the AD effect-size curves in Fig. 4 have no random-filtering baseline. Any rule that removes high-error cases will push the curves down; with no control group, you can't tell whether U is doing better than random removal, let alone than simple quality proxies like FreeSurfer's own QC metrics. Second, Cohen's d on a shrinking subsample is biased upward, and removing high-uncertainty subjects may also tilt the AD/CN balance—the paper doesn't report the group counts after filtering. Third, the "ground truth" is FreeSurfer on 1mm T1, which is itself not ground truth; the correlations are against a proxy, and the paper doesn't acknowledge this as a limitation. Fourth, there are no confidence intervals on any of the reported correlations.

The central idea holds up; this is not a circular or fitted measure. But the paper should not be accepted as-is. The core contribution is worth publishing and deserves a serious referee, with the request that the authors add a random-filtering baseline, report CIs, and discuss the FreeSurfer-proxy caveat.

For your reading group: it's a useful example of a practical uncertainty measure that works despite being simple. I'd cite it if I worked on surface reconstruction.

Referee Report

3 major / 5 minor

Summary. The paper introduces UNSURF, a per-voxel uncertainty measure for learning-based cortical surface reconstruction, defined as the squared difference between the signed distance function (SDF) predicted by a CNN and the SDF recomputed from the geometrically processed surface mesh. The measure is aggregated to node, parcel, and subject levels and compared with ensemble-dropout variance on two clinical-style datasets. The authors report correlations between UNSURF and thickness errors (with FreeSurfer-derived surfaces as ground truth), show that filtering high-uncertainty parcels/nodes reduces thickness errors, and report that subject-level filtering increases Cohen's d in an AD versus CN classification analysis.

Significance. If the claims are substantiated, UNSURF would be a valuable and low-cost uncertainty signal: it requires no additional training, it is deterministic, and it explicitly reflects the geometric corrections that variance-based measures miss. The paper's strengths are the use of real heterogeneous clinical data, the head-to-head comparison with ensemble dropout variance, and the multi-level aggregation scheme. I also agree that UNSURF is not circular in a parameter-fitting sense; it is an internal consistency measure between the raw network output and the final surface. The main gaps are statistical: the filtering experiments lack random baselines and confidence intervals, and the correlation evidence is reported without uncertainty bounds, so the central QC and downstream-benefit claims are not yet fully supported.

major comments (3)

[Section 3.3, Figure 3(d)-(e); Section 3.4, Figure 4] The QC and downstream-benefit claims are not supported by the reported filtering experiments because there is no baseline that removes the same fraction of data at random, or according to an independent quality measure. Any selection rule correlated with thickness error will mechanically reduce mean error as data are removed, and Cohen's d computed on shrinking subsamples is biased and increasingly noisy. Please add random-filtering control curves with confidence intervals (for example, repeated random subsampling at each kept fraction), and report the number of subjects and the AD/CN group sizes retained at each point in Figure 4.
[Section 3.4, Figure 4] Subject-level filtering by U^s may change the AD/CN composition of the sample: if high-uncertainty subjects are disproportionately from one diagnostic group, the effect-size increase may reflect altered group balance rather than improved measurement quality. The paper should report the AD/CN counts and the age/gender distributions after each filtering step, and should ideally demonstrate that the effect-size trend persists after adjusting for these factors, or when using within-subject parcel- or node-level filtering only.
[Section 3.2, Figure 2; Section 3.3, Figure 3(a)-(c)] The central correlation evidence lacks uncertainty quantification: SCC/PCC values are presented without confidence intervals, p-values, or correction for the large number of parcels in Figure 3(a). Moreover, the ground-truth thickness errors are computed against FreeSurfer surfaces derived from 1 mm T1 scans, which are themselves an imperfect proxy for true surface placement error; this should be explicitly acknowledged and ideally bounded by a repeatability or inter-method analysis. Without these, it is difficult to judge whether the reported differences between variance and UNSURF are statistically meaningful.

minor comments (5)

[Figure 2 caption] The text says "Person correlation coefficient" but the standard term is "Pearson correlation coefficient."
[Section 2.1] The word "wihtout" should be "without" in the sentence describing the Euler characteristic.
[Section 3.3, Figure 3 caption] The caption says "At 100, all subjects are kept" but the filtering in panels (d) and (e) is applied to parcels and nodes; please clarify the exact denominator and the data unit being kept in each panel.
[Section 2.2] The proposed measure is called "uncertainty" but is defined as a deterministic discrepancy; the paper would benefit from a brief discussion of what sources of error this discrepancy captures (geometric correction, smoothing, topological changes) and what it cannot capture (systematic bias shared by the prediction and the geometry-processing step).
[Section 3.4, Figure 4] The red dashed line for Recon-All is not clearly defined; please specify whether this is FreeSurfer applied to the original 1 mm T1 or to a native low-resolution scan, and how the mean effect size is computed across parcels.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: UNSURF is an independent discrepancy measure empirically correlated with thickness error; the only self-citation is a non-load-bearing component citation.

full rationale

UNSURF is defined as U_v^i = (Dhat_v^i - Dtilde_v^i)^2, a deterministic discrepancy between the network-predicted SDF and the SDF of the final geometrically processed surface. Thickness errors are computed separately as differences between reconstructed thickness and FreeSurfer-derived ground-truth thickness. No equation in the paper derives thickness error from U, nor is U fitted to thickness errors; the reported correlations are empirical findings, not reductions by construction. The fact that the SDF predictor is trained on FreeSurfer targets may explain why U tracks proximity to FreeSurfer geometry, but this is a mechanistic explanation, not a logical circularity. The QC and downstream filtering experiments (Figs. 3d/e and 4) lack random-filtering baselines, confidence intervals, and p-values, which weakens the statistical support for those claims, but this is a validity/statistical concern rather than a circular derivation. Self-citations to recon-all-clinical [14,15] and to SynthSR/SynthSeg [4,21] are component and prior-work citations; UNSURF itself is evaluated against independent held-out clinical data with FreeSurfer ground truth, so these citations are not load-bearing for the central UNSURF claim. The score of 2 reflects one minor non-load-bearing self-citation, not an actual circular step.

Assumptions & free parameters 0 free parameters · 2 assumptions · 0 invented entities

The central claim (UNSURF correlates with errors) rests on the assumptions that the synthetic training distribution covers the clinical test distribution, and that FreeSurfer is an acceptable reference standard for surfaces. These are domain assumptions, not ad-hoc entities or dubious free parameters.

assumptions (2)

domain assumption The synthetic data generation pipeline (domain randomization) produces scans diverse enough to make the model generalize to clinical data.
The model is trained on synthetic data, and the test performance on clinical scans depends on this assumption (Section 2.1).
domain assumption FreeSurfer reconstructions on 1mm T1 scans are a valid ground truth for cortical surfaces in this evaluation.
The ground truth surfaces and thickness errors are derived from FreeSurfer (Sections 3.1 and 3.2).

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Cite this review

Pith. "Pith review of UNSURF: Uncertainty Quantification for Cortical Surface Reconstruction of Clinical Brain MRIs." pith.science (2026). https://pith.science/paper/EFCJBF73

@misc{pith2026250600498,
  author       = {Pith},
  title        = {Pith review of: UNSURF: Uncertainty Quantification for Cortical Surface Reconstruction of Clinical Brain MRIs},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EFCJBF73}},
  note         = {Machine review of arXiv:2506.00498}
}

read the original abstract

We propose UNSURF, a novel uncertainty measure for cortical surface reconstruction of clinical brain MRI scans of any orientation, resolution, and contrast. It relies on the discrepancy between predicted voxel-wise signed distance functions (SDFs) and the actual SDFs of the fitted surfaces. Our experiments on real clinical scans show that traditional uncertainty measures, such as voxel-wise Monte Carlo variance, are not suitable for modeling the uncertainty of surface placement. Our results demonstrate that UNSURF estimates correlate well with the ground truth errors and: \textit{(i)}~enable effective automated quality control of surface reconstructions at the subject-, parcel-, mesh node-level; and \textit{(ii)}~improve performance on a downstream Alzheimer's disease classification task.

Figures

Figures reproduced from arXiv: 2506.00498 by the authors.

**Figure 1.** Overview of the proposed uncertainty estimation method (UNSURF). thickness. Despite its importance, uncertainty quantification remains underexplored in cortical surface reconstruction because standard techniques are not applicable due to the topological and geometric constraints involved (e.g., lack of self-intersections). Without confidence estimates, it is difficult to determine whether surface errors arise from … view at source ↗

**Figure 2.** Comparison of uncertainty estimates vs. thickness error for Variance - (σ 2 ) s (left) and U s (right) on high-resolution (T1-1mm) and clinical scans. SCC and PCC stand for Spearman and Person correlation coefficient. of geometry, variance-based uncertainty exhibits weak or even negative correlation with thickness errors across both high-resolution and clinical-quality scans, making it unreliable for identifying su… view at source ↗

**Figure 3.** Evaluation of parcel-level and node-level uncertainty estimates on clinical scans. (a) SCC between uncertainty and thickness error for all parcels. (b) U p vs. thickness error for four different parcels and varying slice thickness. (c) SCC across slice thicknesses. (d) Thickness error as a function of percent of kept data based on parcel-level uncertainty (U p ). The x-axis refers to the percent of kept dataset bas… view at source ↗

Figures from the paper (1 more)

**Figure 4.** Figure 4: Effect size (ES) as a function of the kept dataset percentage based on uncertainty (U s ). (Left) Mean ES across all parcels for RAC (both FL and T1 MRI). The red dashed line represents ES for Recon-All. (Right) ES per parcel for RA and RAC. 4 Conclusion This paper pr…

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

[1] [1]

ICLR (2020)

Ashukha, A., Lyzhov, A., Molchanov, D., Vetrov, D.: Pitfalls of in-domain uncer- tainty estimation and ensembling in deep learning. ICLR (2020)

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NeurIPS Benchmarking track (2022) 10 Mehta and Gopinath et al

Band, N., Rudner, T.G., Feng, Q., Filos, A., Nado, Z., Dusenberry, M.W., Jerfel, G.,Tran,D.,Gal,Y.:Benchmarkingbayesiandeeplearningondiabeticretinopathy detection tasks. NeurIPS Benchmarking track (2022) 10 Mehta and Gopinath et al

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In: MICCAI

Baumgartner, C.F., Tezcan, K.C., Chaitanya, K., Hötker, A.M., Muehlematter, U.J., Schawkat, K., Becker, A.S., Donati, O., Konukoglu, E.: Phiseg: Capturing uncertainty in medical image segmentation. In: MICCAI. pp. 119–127 (2019)

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In: CVPR

Bongratz, F., Rickmann, A.M., Pölsterl, S., Wachinger, C.: Vox2Cortex: Fast ex- plicit reconstruction of cortical surfaces from 3D MRI scans with geometric deep neural networks. In: CVPR. pp. 20773–20783 (2022)

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In: WACV

Cruz, R.S., Lebrat, L., Bourgeat, P., et al.: DeepCSR: A 3D deep learning approach for cortical surface reconstruction. In: WACV. pp. 806–815 (2021)

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Medical image analysis 57, 226–236 (2019)

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[8] [8]

In: MICCAI

Durso-Finley, J., Falet, J.P., Mehta, R., Arnold, D.L., Pawlowski, N., Arbel, T.: Improving image-based precision medicine with uncertainty-aware causal models. In: MICCAI. pp. 472–481. Springer (2023)

work page 2023