Confident Head Circumference Measurement from Ultrasound with Real-time Feedback for Sonographers

Alberto Gomez; Bernhard Kainz; Bishesh Khanal; David Lloyd; Emma Robinson; Jacqueline Matthew; Matthew Sinclair; Nicolas Toussaint; Samuel Budd

REVIEW 4 major objections 6 minor 16 references

Confident Head Circumference Measurement from Ultrasound with Real-time Feedback for Sonographers

T0 review · 4 major / 6 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Probabilistic multi-sampling gives fetal head circumference measurements confidence bounds and variance scores that guide sonographers to better scan planes in real time.

desk verdict Base HC measurement is solid, but the variance-score feedback claim is under-validated and likely overfit to the test set. read the letter →

arxiv 1908.02582 v1 pith:3YBJW5UE submitted 2019-08-07 eess.IV cs.CVcs.LG

Samuel Budd , Matthew Sinclair , Bishesh Khanal , Jacqueline Matthew , David Lloyd , Alberto Gomez , Nicolas Toussaint , Emma Robinson

show 1 more author

Bernhard Kainz

This is my paper · ORCID

classification eess.IVcs.CVcs.LG

keywords fetalheadcircumferenceultrasoundprobabilisticsegmentationMonteCarlodropoutuncertaintyestimationvariancescorereal-timefeedbackconfidencebounds

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 is trying to establish that a fetal head circumference measurement from ultrasound should come with a confidence interval and a quality score, not just a single number. It proposes a probabilistic deep network that, for one image, outputs many plausible head segmentations; fitting an ellipse to each and aggregating the results yields a head circumference plus upper and lower bounds. The spread of the sampled ellipses and masks is condensed into variance scores, and the paper shows that rejecting high-variance images improves average accuracy and that the predicted bounds contain the true measurement for about half the test images when many samples are taken. If this holds in practice, the payoff is real-time feedback that tells a sonographer when to re-scan, which could reduce the inter-operator variability that limits manual fetal ultrasound.

What carries the argument

The machinery is a probabilistic segmentation pipeline that turns one ultrasound image into $N$ candidate head masks. Monte Carlo Dropout (running a U-Net with dropout active during inference) and a Probabilistic U-Net (a U-Net combined with a conditional variational autoencoder) act as samplers; each candidate mask is converted into an ellipse by direct least-squares fitting, and the head circumference is computed from the fitted axes using the Ramanujan II approximation. The mean or median of the $N$ circumferences becomes the reported measurement, the spread of the ellipses defines the confidence margins, and four variance scores built from those samples are thresholded to accept or reject the image. The variance-score threshold is the component that turns the sampler into an operator guidance tool.

What would settle it

Assemble a set of ultrasound images with independent ratings of view quality and ground-truth head circumference, then check whether images the variance score rejects are systematically less accurate or lower quality than images it accepts; if the score separates the two groups no better than chance, or a threshold calibrated on one scanner fails on another, the feedback loop is not carrying the claimed signal.

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Extended reading notes

Core claim

The central claim is that the disagreement among stochastic predictions of a fetal head segmentation network is informative enough to serve as a signal of measurement reliability. The authors show that Monte Carlo Dropout with dropout probability $p=0.6$ on a U-Net trained on 2,848 training images and evaluated on 540 held-out images gives $1.81 \pm 1.65$ mm mean absolute error, matching the deterministic baseline while adding an upper and lower bound on every measurement. With $N=10$ samples, 27.8% of ground-truth head circumferences fall inside the predicted bounds; with $N=1{,}000$ samples that rises to 50.4%, and for cases outside the bounds the average distance from the true value to the margin is $1.82 \pm 1.78$ mm. Each of the four proposed variance scores (ellipse parameter variance, ring area between the union and intersection of sampled masks, mask entropy, and softmax entropy) improves average accuracy when used to reject high-variance images, which the paper reads as evidence that higher sampled variance coincides with sub-optimal scan planes.

Load-bearing premise

The central assumption is that the run-to-run variation in the network's outputs actually tracks how good the ultrasound view is, and that a cutoff for "too variable" learned on one set of images will keep working on new patients, machines, and anatomies.

Editorial extensions

If this is right

A deployed system could show the head circumference with its upper and lower bounds and issue a re-scan warning when the variance score crosses a threshold, pushing operators toward views the model handles well.
Rejecting high-variance images raises the average accuracy of the accepted set, so a stricter acceptance threshold trades extra scan attempts for higher measurement reliability.
Because the same dropout-equipped U-Net supplies both the measurement and the confidence information, the feedback does not require a separate uncertainty network or a slower ensemble.
Consistent use of the feedback would normalize the chosen scan plane toward the training distribution, which should make measurements more reproducible across sonographers.

Reading between the lines

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

The paper leaves the variance-score thresholds and the containment rate as descriptive results; a natural next test is to calibrate the bounds on one dataset so that the stated confidence matches the observed rate, then apply them to a new scanner or population.
An end-to-end user study with real sonographers could test whether showing the re-scan prompt during freehand scanning actually changes the chosen plane and reduces inter-operator spread in the final measurements.
The same rejection mechanism could function as an out-of-distribution detector for abnormal anatomy, since high variance may flag images unlike the training set; the paper lists such cases as future work rather than demonstrating detection.
The variance scores are not calibrated as true uncertainty estimates, so a useful extension is to compare them against independent inter-observer disagreement on the same images to see whether high variance marks exactly the cases where human sonographers also disagree.

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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

Put simply, the paper's base measurement is credible, but its new feedback signal is not yet demonstrated. The authors add MC Dropout and Probabilistic U-Net to their earlier fetal HC pipeline, sample multiple segmentations per image, fit ellipses to each, and derive four 'variance scores' (h1-h4) from the sample spread. The idea is to reject high-variance images during scanning so sonographers get real-time guidance toward better planes. That combination is new in fetal ultrasound, and the clinical motivation is clear.

The paper does some things well. The dataset is large: 2,724 volunteer exams plus HC18, with images labeled by 45 sonographers. The single-sample result (1.81 ± 1.65 mm mean error) is consistent with the group's earlier work and with human-level performance. The authors are also honest: they explicitly say in Section 4 that the variance scores 'cannot claim' to represent model uncertainty directly, which is more than many papers in this area do. The qualitative examples of low-signal images producing wide margins are useful.

The soft spots are where the actual claims live. The variance-score rejection experiment in Section 3 sweeps a threshold between 0 and 1 on the test set, rejects the cases above it, and plots the error of the remaining cases. Because the threshold is chosen after seeing the test errors, the initial performance boost is exactly what you'd expect from selection, even if the scores are meaningless. That's the central new contribution, and there is no validation set or pre-registered threshold. The 50% containment statistic is also not calibrated: N=1000 was selected after watching the coverage curve plateau at 50% (Supplementary Figure 4), so it's not a confidence interval in any principled sense. There's also a notable internal inconsistency: the deterministic single-sample model (1.81 mm) outperforms the multi-sampling mean/median (2.15 mm), so the only benefit comes from rejection, and that rejection is in-sample. No latency measurements support the 'real-time' label, though the underlying U-Net is probably fast enough.

This is not a throwaway paper. The base measurement result is solid and the feedback concept is worth exploring. But the empirical support for the feedback is weak. I'd send it to peer review—a serious editor shouldn't desk reject it—but require an independent validation set, pre-defined thresholds or a proper calibration procedure, and a clear statement of what coverage means. If the authors can show the variance scores transfer to new data, the paper would be genuinely useful. For now, it's a promising report, not a validated system.

Referee Report

4 major / 6 minor

Summary. The paper proposes a probabilistic deep-learning pipeline for fetal head circumference (HC) measurement from 2D ultrasound, built on a U-Net segmentation followed by ellipse fitting. Two stochastic segmentation mechanisms are compared: Monte-Carlo Dropout at inference and a Probabilistic U-Net. For each input image the method draws N segmentation samples, fits an ellipse to each sample, and aggregates the resulting ellipse parameters into a point estimate and an upper/lower bound. It also defines four 'variance scores' (ellipse parameter variance, total ring area, mask classification entropy, softmax confidence entropy) and uses them to reject test images above a threshold, with the aim of steering sonographers toward scan planes for which the network is more reliable. Experiments on a dataset of 2848 training and 540 test images report a mean absolute HC error of 1.81 ± 1.65 mm for the best deterministic single-sample setting, approximately 50% containment of ground-truth HC within the predicted bounds at N=1000 MC samples, and improved average performance on accepted images after rejecting high-variance cases in the test set.

Significance. If the central claims were fully validated, the paper would be a useful clinical-technical contribution: real-time confidence bounds and operator feedback for fetal HC measurement could improve inter-operator consistency, and the base measurement accuracy is in line with prior work. The strengths of the paper are its use of a large clinical dataset with external ground-truth annotations, a plausible and well-motivated pipeline, and a comparison between MC dropout and Probabilistic U-Net under a common evaluation protocol. However, the two elements that constitute the paper's novelty—the 'confidence' containment statistic and the variance-score feedback mechanism—are not yet convincingly validated. The containment percentage is not a calibrated confidence statement because the number of samples N is selected after observing the coverage curve, and the variance-score thresholds are selected and evaluated on the same test set. These issues affect the abstract's headline numbers and the real-time feedback claim, so the manuscript needs substantial additional validation before the main contributions can be accepted.

major comments (4)

[Section 3, Table 2 and Supplementary Figure 4] The 'percentage in upper-lower bound range' statistic is not a calibrated confidence interval. The paper reports that coverage varies significantly with N (14.8% at N=2 and 50.4% at N=1000 for MC dropout) and that the 50% figure is reached only after increasing N to 1000. Because N is chosen after observing the coverage curve, the headline '50% of test images fully contained' is an artifact of the sample-count choice rather than a principled confidence statement. To support the confidence claim, the authors should pre-specify a target coverage level, select N (or the interval construction) on a validation set, and only then evaluate coverage on the held-out test set. Alternatively, they should report coverage as a monotone function of N for a fixed N and avoid claiming a calibrated confidence level.
[Section 3, 'Variance Measure Thresholding', and Figure 2] The variance-score rejection thresholds are selected and evaluated on the same 540-image test set. For each of the four variance scores, the threshold between 0 and 1 is varied over the test data, and the performance improvement after rejecting high-variance cases is reported on the same images. This is in-sample threshold fitting, so the observed initial performance boost can arise from exploiting idiosyncratic noise in the test set even if the variance scores carry no true signal about measurement error. The correct protocol is to select thresholds on a separate validation set (or via cross-validation) and then report accepted-image performance on an independent test set. Without this, the paper's central feedback claim is not supported.
[Section 4, Discussion] The authors concede that the proposed variance scores 'cannot claim' to represent model uncertainty directly, but the real-time feedback contribution depends on these scores tracking measurement error or view quality on unseen images. The only quantitative evidence for their utility is the in-sample threshold experiment in Section 3, which is not transferable evidence. The authors should provide a direct analysis relating each variance score to absolute HC error on held-out data (for example, a correlation or calibration plot), and demonstrate that a fixed, pre-selected threshold transfers to a new dataset or at least to an untouched test split. Without such evidence, the claim that the system can guide sonographers toward better scan planes is speculative.
[Section 3, 'Single-Sampling Experiments', and Table 1] The dropout probability p=0.6 is described as 'value found to be best performing in variety of dropout configurations' from single-sample experiments, with results then reported on the Dataset A test data. If the model configuration was selected using the test set, the reported mean absolute error of 1.81 ± 1.65 mm may be optimistic. The authors should state explicitly whether a held-out validation split was used for hyperparameter selection, and if not, they should re-evaluate the final configuration on a truly held-out set. This is a load-bearing point for the base accuracy claim, although the accuracy itself is plausible.

minor comments (6)

[Section 2, equations h3 and h4] The definitions of mask classification entropy and softmax confidence entropy appear to have sign issues: entropy is conventionally written as -∑ p log p, but the equations as printed omit the leading minus sign, and h4's summation index is unclear (the sum over K_i and the definition of p_i are confusing). Please clarify the notation and verify the signs.
[Section 2 and Table 2] The use of 'MC dropout' is ambiguous: Table 1 reports a 'Dropout' model trained with dropout, while Table 2 reports 'MC(inf.)' for dropout applied during inference. Please label clearly whether dropout is applied during training, during inference, or both, and align the terminology across the text and tables.
[Figure 2] The horizontal axis shows the number of rejected cases, but the text describes thresholds 'between zero and one'. The figures would be easier to interpret if the threshold value itself were shown on a secondary axis, or if curves were plotted against the normalized threshold for each variance score.
[Tables 1 and 2] The reported DICE and Hausdorff distance values are given as mean ± standard deviation, but no confidence intervals or statistical significance tests are provided. Given the small differences between some configurations, a note on variability across runs or a statistical comparison would strengthen the claims.
[Abstract] The abstract states '50% of the test images fully contained within the predicted confidence margins' without mentioning that this percentage is specific to N=1000 MC samples and not a calibrated confidence level. Please qualify this statement in the abstract to avoid overclaiming.
[References] Reference 13 is formatted inconsistently with the other entries (listing the institution name as the author). Please standardize the reference style.

Circularity Check

1 steps flagged · score 6.0 of 10

Variance-score rejection thresholds are extracted and evaluated on the same test set, making the reported guidance benefit an in-sample fit; the HC measurement itself is externally benchmarked.

fitted input called prediction [Section 3, 'Variance Measure Thresholding' (p. 5), Fig. 2 and Fig. 1 caption]
"Finally, we experiment with each of the variance scores produced over the test set as a means to accept/reject images at test time. We assess their performance by counting the number of accepted/rejected cases for a range of thresholds between zero and one, and how this threshold affects the resulting average performance scores after rejected images are removed from the test set. ... As a proof of concept we extract a threshold such that test cases whose variance score is outside the threshold are rejected, and inside are accepted."

The threshold is extracted from the same test set that is then used to measure the benefit of rejection, and Figure 2 reports the resulting improvement on that same test set. No held-out split, cross-validation, or pre-registered threshold is used; the paper even notes that the thresholds 'vary for each score.' Thus the reported initial performance boost is an in-sample fit: a favorable threshold can always be found post hoc on the test set. The conclusion that variance scores indicate sub-optimal image acquisition therefore rests on the very data used to construct the threshold, making the claimed guidance benefit statistically forced rather than independently predicted.

full rationale

The base HC measurement is not circular: it uses a U-Net and ellipse fit evaluated against external ground-truth delineations, with single-sample comparisons reported against the HC18 challenge and prior work, so the 1.81 +/- 1.65 mm MAE stands on its own. The probabilistic upper/lower bounds come from N forward passes and the containment percentage is measured empirically, not derived from ground truth; the 50% figure at N=1000 is an uncalibrated descriptive statistic rather than a circular prediction. The one genuinely circular element is the variance-rejection evaluation: thresholds are selected from and evaluated on the same 540-image test set, so the support for the operator-feedback claim reduces to an in-sample fit. Self-citation of the group's prior U-Net [14] is present but not load-bearing, since this paper retrains and reports its own single-sample results rather than relying on that citation for its central numbers.

Assumptions & free parameters 3 free parameters · 4 assumptions · 1 invented entities

The central claim rests on standard machine-learning assumptions plus domain-specific assumptions about sonographer ground truth and ellipse fitting. The main free parameters (dropout probability, number of samples for the headline coverage, variance-score thresholds) are selected empirically rather than by a calibration principle.

free parameters (3)

MC Dropout probability p = 0.6
Selected as best among several dropout configurations using single-sample experiments (Section 2), not by a principled uncertainty-calibration criterion.
Number of MC samples N for coverage claim = 1000
Coverage rises with N (Supplementary Fig. 4); N=1000 gives the reported 50% containment, while N=10 gives only 27.8%. The choice is not tied to a target confidence level.
Variance-score rejection thresholds = Not reported; one threshold per score in [0,1]
Thresholds are swept on the test set and the resulting performance after rejection is measured on the same test set (Section 3, Variance Measure Thresholding).

assumptions (4)

domain assumption Expert sonographer manual HC annotations are the reference standard for HC.
Ground truth is a single trained sonographer's annotation for HC18 and clinical annotations for Dataset A; any bias in manual measurement propagates to reported error.
domain assumption Ellipse fitting to the segmented skull mask faithfully reproduces the clinical HC measurement process.
The method mimics sonographer actions, and errors in segmentation translate to HC error through the elliptic fit (Section 2).
standard math MC dropout approximates Bayesian posterior inference for the U-Net.
The paper relies on Gal and Ghahramani's result to interpret samples as plausible segmentations; if this approximation is poor for the U-Net, the variance scores lose meaning.
domain assumption The Probabilistic U-Net's latent space captures inter-annotation variability.
Follows the training scheme of Kohl et al. [7]; the model is assumed to produce plausible segmentation variants.

invented entities (1)

Variance scores h1-h4 (ellipse parameter variance, total ring area, mask classification entropy, softmax confidence entropy)
purpose: Quantify measurement robustness and reject sub-optimal scan planes during freehand ultrasound.
The scores are defined in Section 2 and evaluated only on the same test set used to choose rejection thresholds; no external or prospective validation is provided.

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Cite this review

Pith. "Pith review of Confident Head Circumference Measurement from Ultrasound with Real-time Feedback for Sonographers." pith.science (2026). https://pith.science/paper/3YBJW5UE

@misc{pith2026190802582,
  author       = {Pith},
  title        = {Pith review of: Confident Head Circumference Measurement from Ultrasound with Real-time Feedback for Sonographers},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3YBJW5UE}},
  note         = {Machine review of arXiv:1908.02582}
}

abstract

Manual estimation of fetal Head Circumference (HC) from Ultrasound (US) is a key biometric for monitoring the healthy development of fetuses. Unfortunately, such measurements are subject to large inter-observer variability, resulting in low early-detection rates of fetal abnormalities. To address this issue, we propose a novel probabilistic Deep Learning approach for real-time automated estimation of fetal HC. This system feeds back statistics on measurement robustness to inform users how confident a deep neural network is in evaluating suitable views acquired during free-hand ultrasound examination. In real-time scenarios, this approach may be exploited to guide operators to scan planes that are as close as possible to the underlying distribution of training images, for the purpose of improving inter-operator consistency. We train on free-hand ultrasound data from over 2000 subjects (2848 training/540 test) and show that our method is able to predict HC measurements within 1.81$\pm$1.65mm deviation from the ground truth, with 50% of the test images fully contained within the predicted confidence margins, and an average of 1.82$\pm$1.78mm deviation from the margin for the remaining cases that are not fully contained.

Figures

Figures reproduced from arXiv: 1908.02582 by the authors.

**Figure 1.** Overview of our proposed method. We train a probabilistic model using the available training data. During inference we take N samples from our model, fit ellipses to each sample and aggregate these ellipses to extract a HC value and an upper and lower bound on that HC value. Various outputs of the pipeline are used to calculate different variance scores given a set of N samples. As a proof of concept we extract a th… view at source ↗

**Figure 2.** Plots showing performance measures against the number of rejected test cases. Each measure shows improvement after removing a few test cases for each score (these thresholds vary for each score), however after removing an initial low performing set, the scores power to discriminate between ‘good’ and ‘bad’ images deteriorate. ’Percentage in range’ calculated as the percentage of test cases for which the ground truth… view at source ↗

**Figure 3.** Results produced by our model. White line: Ground Truth, Orange dashed line: Mean of sampled ellipse parameters, Pink shaded area: Upper/lower bound range. Top row: High performing images. Bottom row: Low performing images. See Supplementary Material Figures 4 and 5 for more examples and a demo video demonstration [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

Figures from the paper (5 more)

**Figure 4.** Figure 4: Graph showing the effect of taking more samples from the network on the number of ground truth measurements lying between the generated upper and lower bounds. We can see a sharp increase in this percentage as samples increasing, plateauing around 50% for MC Dropout du…

**Figure 5.** Figure 5: Plot showing ground truth HC values against predicted values (N = 1000), Green dots indicate test cases where the ground truth is contained within the generated upper and lower bounds [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]

**Figure 6.** Figure 6: Bland-Altman plots for test cases where the ground truth is contained within the upper and lower bounds, and for cases that this is not true [PITH_FULL_IMAGE:figures/full_fig_p012_6.png]

**Figure 7.** Figure 7: Most uncertain test cases [PITH_FULL_IMAGE:figures/full_fig_p013_7.png]

**Figure 8.** Figure 8: Least uncertain test cases [PITH_FULL_IMAGE:figures/full_fig_p014_8.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

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Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [1]

Journal of Mathematical Analysis and Applications 260(2), 295–306 (8 2001)

Barnard, R.W., Pearce, K., Schovanec, L.: Inequalities for the Perimeter of an Ellipse. Journal of Mathematical Analysis and Applications 260(2), 295–306 (8 2001). https://doi.org/10.1006/JMAA.2000.7128

work page arXiv 2001

[2] [2]

IEEE Trans Med Imag 36(11), 2204–2215 (11 2017)

Baumgartner, C.F., et al.: SonoNet: Real-Time Detection and Localisation of Fetal Standard Scan Planes in Freehand Ultrasound. IEEE Trans Med Imag 36(11), 2204–2215 (11 2017). https://doi.org/10.1109/TMI.2017.2712367

work page arXiv 2017

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Carneiro, G., Georgescu, B., Good, S., Comaniciu, D.: Detection and Measure- ment of Fetal Anatomies from Ultrasound Images using a Constrained Prob- abilistic Boosting Tree. IEEE Trans on Med Imag 27(9), 1342–1355 (9 2008). https://doi.org/10.1109/TMI.2008.928917

work page arXiv 2008

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doi:10.1007/978- 2018

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arXiv 2018