Topology-preserving augmentation for CNN-based segmentation of congenital heart defects from 3D paediatric CMR

Andrew P. King; Giovanni Montana; Isra Valverde; James R. Clough; Nick Byrne

REVIEW 3 major objections 5 minor 7 references

Topology-preserving augmentation for CNN-based segmentation of congenital heart defects from 3D paediatric CMR

T0 review · 3 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read This paper shows that enforcing ground-truth label topology during data augmentation—via fast-marching correction against a cardiac-topology template—cuts false defect clusters in congenital heart segmentation from 12.0 to 6.5 (p=0.022).

desk verdict Nice idea and a real clinical motivation, but the training protocol has a plausible data-leakage ambiguity that could invalidate the headline result. read the letter →

arxiv 1908.08870 v1 pith:EXVBL5US submitted 2019-08-23 eess.IV cs.CVcs.LG

Nick Byrne , James R. Clough , Isra Valverde , Giovanni Montana , Andrew P. King This is my paper · ORCID

classification eess.IVcs.CVcs.LG

keywords imagesegmentationdataaugmentationtopologypreservationcongenitalheartdiseasecardiacmagneticresonancefastmarchingconvolutionalneuralnetwork3Dprinting

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 identifies a failure mode in CNN training for congenital heart disease segmentation: standard data augmentation transforms and resamples ground-truth label maps, and nearest-neighbour resampling can create or destroy thin tissue interfaces, producing spurious defects in the training labels. The authors propose a pipeline that builds a simplified topological skeleton of each label map, the cardiac contiguous topology (CCT) template, transforms it alongside the labels, and uses fast-marching topology correction to force the resampled blood pool back to the template's topology. In five-fold cross-validation on ten paediatric cardiac MR cases, coupling clinically realistic augmentation with this correction lowers the median number of topologically relevant false-positive error clusters from 12.0 to 6.5, a statistically significant improvement (p=0.022). If correct, the work establishes that label-map topology is a trainable property and that clinically meaningful augmentation does not have to corrupt it.

What carries the argument

The central mechanism is the CCT template: a one-voxel-wide skeleton of the ground-truth blood pool that records how the heart's chambers and vessels are connected, with each sub-class first simplified to ball topology so that trabeculation is removed. The companion mechanism is a fast-marching topology-correction algorithm, which flips only non-simple voxels—voxels whose label can be changed without changing the topology of the object or its complement—until the resampled blood pool has the same topology as the transformed CCT template. Together they let the pipeline repair whatever topological damage the resampling step caused, while changing almost no voxels.

What would settle it

Take one labelled volume with a known thin connection between two chambers, such as an atrial septal defect; construct its CCT template and check whether the one-voxel skeleton still contains that connection. If the erosion step severs the channel, then enforcing the template topology during augmentation would actively train the network to delete the very defect the segmentation is meant to show.

Watch

Extended reading notes

Core claim

When ground-truth labels for the cardiac blood pool are spatially transformed and resampled by nearest-neighbour interpolation during data augmentation, thin interfaces such as the atrial septum can develop spurious holes or connections, which appear in the final segmentation as anomalous congenital defects. The authors' pipeline first constructs, for each training label map, a cardiac contiguous topology (CCT) template: each cardiac sub-class is corrected to ball topology and the recombined blood pool is topologically eroded to a one-voxel skeleton, so the template records only clinically meaningful chamber-to-chamber contiguity. After the image transform, the blood pool label is resampled with trilinear interpolation and corrected with a fast-marching algorithm until its topology matches the transformed CCT template. In five-fold cross-validation on ten paediatric CMR cases, CNNs trained with clinically justified transformations plus this correction produced a median of 6.5 topologically relevant false-positive error clusters, down from 12.0 for the same transformations without topology correction (Wilcoxon p=0.022), and fewer than 0.5% of blood-pool voxels were altered.

Load-bearing premise

The pipeline assumes that the CCT template—obtained by correcting every cardiac sub-class to ball topology and eroding the blood pool to a one-voxel skeleton—preserves exactly the clinically meaningful connections, so that any connection missing from the template is a defect rather than a real anatomical feature.

Editorial extensions

If this is right

Clinically realistic augmentation and label-topology preservation become compatible rather than conflicting objectives.
Median topologically relevant false-positive clusters fall from 12.0 to 6.5 when the correction is applied (Wilcoxon p=0.022), beating both naive clinically justified augmentation and the orthogonal-rotation-only augmentation used in previous work.
The correction is cheap in voxel terms: fewer than 0.5% of blood-pool voxels are altered, and blood-pool overlap is preserved (DSC 0.925 vs 0.918).
Topological correctness can be evaluated separately from overlap, giving a clinically interpretable count of where a segmentation would falsely suggest a defect.

Reading between the lines

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

The same template-plus-correction construction should transfer to any segmentation task whose foreground can be expressed as several well-composed contiguous sub-classes, such as vascular trees, airways, or multi-chamber organs; the only requirement is a clinical definition of which connections count.
A direct next step is to use the paper's topological error metric as a loss term or early-stopping signal during training; the reported results suggest that penalising topologically relevant error clusters could suppress the remaining ~6.5 false-positive clusters further.
The authors are explicit that the myocardium label is still resampled by nearest-neighbour interpolation because its true topology is only partially visible in CMR; extending the topology guarantee to the myocardium would require a clinically agreed definition of muscle topology and would change the correction statistics.
Because the pipeline changes less than 0.5% of blood-pool voxels, the corrective step is acting almost entirely on the handful of voxels that determine thin-interface topology; this suggests a topology-preserving resampler could eventually be implemented as an end-to-end differentiable layer rather than a post-hoc correction.

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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

The short version: this paper introduces a genuinely nice idea—using fast-marching topology correction to keep augmented label maps consistent with the original cardiac topology—and supports it with a new, clinically interpretable cluster-counting metric. The writing is clear, the figures are helpful, and the clinical motivation (thin septal interfaces and 3D printing) is real.

The problem is the training protocol. The authors say 10,000 training examples were "pre-computed by data augmentation" from the ten HVSMR cases. They then run five-fold cross-validation (train on eight, test on two) and randomly crop batches from the augmented data. No statement says that the augmented pool was regenerated per fold from only the eight training subjects. If the pool was built once from all ten cases, then for each fold the two test subjects' augmented replicas—including their topology-corrected labels—are sitting in the training pool. The network would then be directly exposed to the test topology it is later asked to predict. That would explain the reported drop in false-positive clusters (12.0 to 6.5, p=0.022) without any real learning. This is a load-bearing flaw, not a nuisance.

Everything else is softer. The dataset is tiny (ten cases), so confidence intervals are wide; the DSC gains are modest (e.g., +0.007 for blood pool); and the new metric isn't externally validated. No code or trained models are provided, so reproduction would require reimplementation. None of these alone would sink the paper, but the leakage ambiguity is enough to withhold acceptance.

I hope the authors can show that augmentation was done per fold. If they can, the paper is a reasonable contribution: it's the first to my knowledge to combine topology correction with augmentation for CHD segmentation, and the CCT template idea is worth building on. If they can't, the empirical comparison is meaningless.

Verdict: deserves peer review, but as a conditional—authors must clarify the augmentation split and ideally make the augmented data available. I'd bring it to a reading group to discuss the design, not because the result is trustworthy yet.

Referee Report

3 major / 5 minor

Summary. The manuscript addresses the problem of topological errors in CNN-based segmentation of congenital heart defects from 3D CMR, motivated by patient-specific 3D printing. It proposes a topology-preserving augmentation pipeline that applies clinically justified spatial transformations to the image and label maps, then uses a fast-marching algorithm to enforce the 'cardiac contiguous topology' (CCT) of the ground truth labels on the transformed label maps. The authors define CCT as the connectivity between cardiac sub-classes after each is made ball-like, and construct a one-voxel skeleton template via erosion. They also introduce a novel metric that counts clusters of topologically relevant disagreement. Using five-fold cross-validation on the ten HVSMR training cases, they compare clinically justified augmentation with and without topology preservation, and report that the topology-preserving version reduces the median number of false-positive topological clusters from 12.0 to 6.5 (Wilcoxon p=0.022) and improves DSC for blood pool and myocardium.

Significance. If the central claim holds, this is a valuable contribution: it identifies a realistic failure mode of conventional augmentation (topological corruption of thin tissue interfaces), provides a principled correction, and introduces a metric more sensitive than DSC to clinically relevant interface errors. The CCT notion is an elegant way to handle arbitrarily complex combinations of defects, and the authors make a plausible argument for why previous augmentation choices (orthogonal rotations) were suboptimal. However, the evidence base is small (ten subjects, two per test fold), the metric is not externally validated, and the leakage ambiguity described below must be resolved before the empirical claim can be accepted.

major comments (3)

[Section 2.2, Implementation] The Implementation section states that 'From the ten cases provided by the HVSMR Challenge, a total of 10,000 training examples were pre-computed by data augmentation according to figure 2.' It does not state whether the augmentation was regenerated for each of the five folds using only the eight training subjects of that fold. If the pre-computed pool contains augmented examples of a test subject, then during that fold's training the network can see transformed and topology-corrected versions of the subject it is later tested on, directly exposing it to the test subject's CCT. This would invalidate the comparison in Figure 4 and the Wilcoxon test (p=0.022). The authors must either confirm that per-fold separation was enforced at the augmentation level, or re-run the experiments with the augmentation generated separately for each training fold.
[Section 2.1, CCT template construction] The pipeline enforces the topology of a CCT template obtained by (i) correcting each cardiac sub-class to ball topology and (ii) eroding a well-composed blood pool to a one-voxel skeleton. This assumes that the simplified CCT retains all clinically relevant connections and that no important connection is removed or distorted by the erosion. If, for example, a thin but real communication is thinner than one voxel after resampling, the template could break that connection and the augmentation would then train the network to incorrectly separate connected chambers. The manuscript should provide evidence (e.g., expert review of the templates, or quantitative comparison of CCT with the original labels) that the CCT construction preserves the clinically relevant topology in all ten cases.
[Section 2.2, Metrics] The proposed metric counts 'topologically relevant clusters of voxels where inferred and ground truth segmentations disagree' and uses this to measure the 'anomalous appearance of congenital defects.' No validation is provided that these clusters correspond to clinically meaningful defects, nor is the metric compared with an expert assessment or a more established topological descriptor. Since the paper's main quantitative finding is expressed in this metric, the manuscript should include at least an illustrative case-by-case breakdown and ideally a small expert study to support the clinical relevance of the metric.

minor comments (5)

[Figure 4] The figure caption does not define the abbreviations 'CJ' and 'TP' in printed form; the caption should explicitly state that CJ stands for clinically justified, TP for topology-preserving, and *CJ + TP for the proposed pipeline.
[Section 2.1] The term 'well-composed set' is introduced without a citation or formal definition; please provide a reference or a clear definition.
[Section 2.2, Implementation] The description of the fast-marching topology correction is brief; please specify the parameters used (e.g., neighborhood connectivity and stopping criterion) so that the experiments are reproducible.
[Results and discussion] The DSC improvements are reported without confidence intervals or statistical tests; please report these to support the claim of benefit.
[Section 2.2, Implementation] Minor typo: 'MIPA V' should likely be 'MIPAV'.

Circularity Check

1 steps flagged · score 2.0 of 10

Minor definitional circularity in CCT enforcement; central cross-validated result is not forced.

self definitional [Section 2.1 (Topology-preserving augmentation pipeline)]
"We resample the transformed blood pool label using trilinear interpolation, realising an image bounded in the range [0,1]. Akin to a probability map, this is corrected to share the topology of the transformed CCT template, ensuring that the arbitrary CCT of the ground truth labels is maintained (see figure 2(c))."

The CCT template is itself derived from the ground truth labels: each sub-class is corrected to ball topology and the well-composed blood pool is topologically eroded to a one-voxel skeleton. The pipeline then forces each augmented label to share that template's topology. Consequently, the statement that the augmented labels preserve the ground truth CCT is true by construction: the output is constrained to match a template extracted from the same labels. This is a definitional property of the method rather than an empirical finding.

full rationale

The paper's derivation chain separates two distinct claims: (1) the topology-preserving augmentation pipeline maintains the ground truth CCT of augmented labels, and (2) training with this pipeline reduces topological errors in CNN outputs under five-fold cross-validation. Claim (1) is self-definitional: the CCT template is built from the ground truth label by topological correction and erosion, and the fast-marching correction enforces that template on the resampled label. The augmented label therefore matches the template by construction; this is a deliberate design choice, not a circular inference. Claim (2) is the substantive contribution and is supported by held-out cross-validation against baseline augmentation schemes, with a reported Wilcoxon signed-rank test. The evaluation metric is novel but not fitted to the pipeline's output; it counts topologically relevant disagreement clusters between inferred and ground truth labels, which is an external comparison. There is no load-bearing self-citation: the fast-marching method is cited from Bazin et al., an external source, and the paper's own previous work is not invoked to force the central result. A potential data-leakage concern exists because 10,000 augmented examples were pre-computed from all ten cases with no stated per-fold regeneration, but that is a correctness/experimental-design risk, not a circularity of the derivation. Overall, the only circular element is the definitional construction of CCT and its enforcement, which does not invalidate the independent cross-validated evaluation. Score 2 reflects this minor self-referential component.

Assumptions & free parameters 0 free parameters · 6 assumptions · 1 invented entities

The method introduces one new conceptual entity (CCT) and several domain assumptions about clinical plausibility and the correctness of the topology correction tools. No free parameters are fitted to data; the pipeline relies on algorithmic choices (e.g., erosion to one-voxel width) that are not tuned to the results.

assumptions (6)

domain assumption The fast-marching topology correction algorithm of Bazin and Pham [1] can correct any binary label map to a specified template topology.
The pipeline relies on this method as the core correction step; its correctness for arbitrary templates is assumed.
ad hoc to paper Cardiac contiguous topology (CCT), defined by the connections between cardiac sub-classes after each is made ball-like, captures the clinically relevant topology of the blood pool.
This is a new concept introduced by the authors to make the template tractable; no external validation is provided.
standard math A well-composed blood pool label set guarantees that repeated topological erosion yields a one-voxel-wide CCT template.
This is a mathematical property of well-composed sets in digital topology, used in Section 2.1 to justify template construction.
domain assumption Small-angle rotations and non-rigid deformations are clinically justified augmentation transformations for paediatric CMR.
The paper argues these better represent patient variation than orthogonal rotations; this is a clinical assumption.
ad hoc to paper The metric counting topologically relevant clusters of disagreement is a clinically meaningful measure of segmentation quality.
The metric is introduced in this paper and is not validated against clinical endpoints or expert preferences beyond the stated motivation.
domain assumption The expert-corrected ground truth labels are the appropriate reference standard.
Before experiments, an expert modified 0.098% of blood pool and 0.0059% of myocardium labels; the paper assumes these corrections improve the reference standard.

invented entities (1)

Cardiac contiguous topology (CCT)
purpose: A simplified one-voxel-wide representation of the topology of the cardiac blood pool, used as a template for topology correction during augmentation and as the basis for a topological error metric.
CCT is defined in this paper and used both to construct the correction template and to define the evaluation metric; there is no independent falsifiable prediction or external validation.

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Cite this review

Pith. "Pith review of Topology-preserving augmentation for CNN-based segmentation of congenital heart defects from 3D paediatric CMR." pith.science (2026). https://pith.science/paper/EXVBL5US

@misc{pith2026190808870,
  author       = {Pith},
  title        = {Pith review of: Topology-preserving augmentation for CNN-based segmentation of congenital heart defects from 3D paediatric CMR},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EXVBL5US}},
  note         = {Machine review of arXiv:1908.08870}
}

read the original abstract

Patient-specific 3D printing of congenital heart anatomy demands an accurate segmentation of the thin tissue interfaces which characterise these diagnoses. Even when a label set has a high spatial overlap with the ground truth, inaccurate delineation of these interfaces can result in topological errors. These compromise the clinical utility of such models due to the anomalous appearance of defects. CNNs have achieved state-of-the-art performance in segmentation tasks. Whilst data augmentation has often played an important role, we show that conventional image resampling schemes used therein can introduce topological changes in the ground truth labelling of augmented samples. We present a novel pipeline to correct for these changes, using a fast-marching algorithm to enforce the topology of the ground truth labels within their augmented representations. In so doing, we invoke the idea of cardiac contiguous topology to describe an arbitrary combination of congenital heart defects and develop an associated, clinically meaningful metric to measure the topological correctness of segmentations. In a series of five-fold cross-validations, we demonstrate the performance gain produced by this pipeline and the relevance of topological considerations to the segmentation of congenital heart defects. We speculate as to the applicability of this approach to any segmentation task involving morphologically complex targets.

Figures

Figures reproduced from arXiv: 1908.08870 by the authors.

**Figure 1.** An error in the segmentation of thin tissue interfaces such as the septum between left and right atria (LA, RA) can give rise to topological changes and the anomalous appearance of a congenital heart defect (yellow arrow). Whilst the DSC between ground truth (orange) and inferred (green) blood pool is high, (c) demonstrates the presence of five topologically and clinically relevant segmentation errors. orthogonal … view at source ↗

**Figure 2.** Spatial transformation and nearest neighbour resampling of a ground truth label set (a), can result in anomalous topological changes such as defects within the atrial septum (b). Such changes can be corrected by consideration of a CCT template (f). Having two shunts between the respectively topologically spherical left and right heart (ventricular and atrial septal defect), this patient exhibits toroidal CCT. The te… view at source ↗

**Figure 3.** The V-net architecture used. Output feature map sizes at training are indicated. Most often, the sub-valvular apparatus and its association with the papillary muscles are only partially visualised in CMR: the true-to-life topological properties of the myocardium are rarely apparent. Hence, we resample the spatially transformed myocardium label by naive nearest neighbour interpolation. 2.2 Study design Data — We emp… view at source ↗

Figures from the paper (1 more)

**Figure 4.** Figure 4: CNN segmentation performance in terms of spatial overlap (left) and topological accuracy (right), where training data are augmented by spatial transformation which is: CJ - clinically justified; TP - topology-preserving; CJ + TP - clinically justified and topology-pres…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

7 extracted references · 4 canonical work pages

[1]

Computer methods and programs in biomedicine 88(2), 182--190 (2007)

Bazin, P.L., Pham, D.L.: Topology correction of segmented medical images using a fast marching algorithm. Computer methods and programs in biomedicine 88(2), 182--190 (2007)

work page 2007
[4]

In: 3D Vision (3DV), 2016 Fourth International Conference on

Milletari, F., Navab, N., Ahmadi, S.A.: V-net: Fully convolutional neural networks for volumetric medical image segmentation. In: 3D Vision (3DV), 2016 Fourth International Conference on. pp. 565--571. IEEE

work page 2016
[5]

Med Image Comput Comput Assist Interv 9351, 80--88 (2015)

Pace, D.F., Dalca, A.V., Geva, T., Powell, A.J., Moghari, M.H., Golland, P.: Interactive whole-heart segmentation in congenital heart disease. Med Image Comput Comput Assist Interv 9351, 80--88 (2015). doi:10.1007/978-3-319-24574-4\_10

doi:10.1007/978-3-319-24574-4 2015
[7]

In: International Conference on Medical Image Computing and Computer-Assisted Intervention

Yu, L., Cheng, J.Z., Dou, Q., Yang, X., Chen, H., Qin, J., Heng, P.A.: Automatic 3d cardiovascular mr segmentation with densely-connected volumetric convnets. In: International Conference on Medical Image Computing and Computer-Assisted Intervention. pp. 287--295. Springer (2017)

work page 2017
[9]

139--146

Zuluaga, M.A., Biffi, B., Taylor, A.M., Schievano, S., Vercauteren, T., Ourselin, S.: Strengths and Pitfalls of Whole-Heart Atlas-Based Segmentation in Congenital Heart Disease Patients, pp. 139--146. Springer International Publishing, Cham (2017). doi:10.1007/978-3-319-52280-7\_14

work page doi:10.1007/978-3-319-52280-7 2017
[10]

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[11]

write newline

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Pith tools

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

[1] [1]

Computer methods and programs in biomedicine 88(2), 182--190 (2007)

Bazin, P.L., Pham, D.L.: Topology correction of segmented medical images using a fast marching algorithm. Computer methods and programs in biomedicine 88(2), 182--190 (2007)

work page 2007

[2] [4]

In: 3D Vision (3DV), 2016 Fourth International Conference on

Milletari, F., Navab, N., Ahmadi, S.A.: V-net: Fully convolutional neural networks for volumetric medical image segmentation. In: 3D Vision (3DV), 2016 Fourth International Conference on. pp. 565--571. IEEE

work page 2016

[3] [5]

Med Image Comput Comput Assist Interv 9351, 80--88 (2015)

Pace, D.F., Dalca, A.V., Geva, T., Powell, A.J., Moghari, M.H., Golland, P.: Interactive whole-heart segmentation in congenital heart disease. Med Image Comput Comput Assist Interv 9351, 80--88 (2015). doi:10.1007/978-3-319-24574-4\_10

doi:10.1007/978-3-319-24574-4 2015

[4] [7]

In: International Conference on Medical Image Computing and Computer-Assisted Intervention

Yu, L., Cheng, J.Z., Dou, Q., Yang, X., Chen, H., Qin, J., Heng, P.A.: Automatic 3d cardiovascular mr segmentation with densely-connected volumetric convnets. In: International Conference on Medical Image Computing and Computer-Assisted Intervention. pp. 287--295. Springer (2017)

work page 2017

[5] [9]

139--146

Zuluaga, M.A., Biffi, B., Taylor, A.M., Schievano, S., Vercauteren, T., Ourselin, S.: Strengths and Pitfalls of Whole-Heart Atlas-Based Segmentation in Congenital Heart Disease Patients, pp. 139--146. Springer International Publishing, Cham (2017). doi:10.1007/978-3-319-52280-7\_14

work page doi:10.1007/978-3-319-52280-7 2017

[6] [10]

, " * write output.state after.block = add.period write

ENTRY address author booktitle chapter doi edition editor eid howpublished institution journal key month note number organization pages publisher school series title type url volume year label INTEGERS output.state before.all mid.sentence after.sentence after.block FUNCTION init.state.consts #0 'before.all := #1 'mid.sentence := #2 'after.sentence := #3 '...

[7] [11]

write newline

" write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION word.in bbl.in capitalize ":" * " " *...