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Pitfalls of topology-aware image segmentation

T0 review · 3 major / 4 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read This paper argues that standard benchmarking of topology-aware image segmentation is unreliable: connectivity choice alone can invert method rankings, ground-truth artifacts can account for a large share of measured topological error, and…

desk verdict A benchmarking critique with a real message, but the headline ranking-inversion claim is built on single-seed statistics that need more support. read the letter →

arxiv 2412.14619 v1 pith:VYCATFLA submitted 2024-12-19 cs.CV cs.AIcs.LG

Alexander H. Berger , Laurin Lux , Alexander Weers , Martin Menten , Daniel Rueckert , Johannes C. Paetzold This is my paper · ORCID
classification cs.CVcs.AIcs.LG
keywords topology-awaresegmentationmodelevaluationconnectivityBettinumbersmatchingerrorgroundtruthartifactsbenchmarkingpitfallsmedicalimage
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 argues that the standard way of benchmarking topology-aware image segmentation methods is broken. It identifies three practice-level pitfalls: choosing the wrong voxel connectivity for a dataset, leaving topological artifacts in ground-truth labels, and using metrics such as VOI or aggregated Betti scores that mix volume and topology. On three widely used benchmarks (DRIVE, CREMI, Roads), the authors show that switching between the two common connectivity conventions alone flips method rankings, with an average Spearman correlation of -0.63, and that cleaning small label artifacts cuts measured topological error by up to 43%. The paper concludes with concrete reporting and evaluation guidelines designed to make future comparisons trustworthy.

What carries the argument

The analysis is built on two formal tools. The first is the pair of connectivity conventions A and D, which correspond to opposite foreground/background adjacency choices and, in cubical complex terms, to T- versus V-construction; the paper proposes a simple susceptibility score, e.g., |β0(PD) − β0(PA)|, to quantify how much a dataset's topological metrics move when connectivity changes. The second is the comparison of before/after artifact removal on DRIVE, using a 5-pixel component-size threshold, to isolate the contribution of label noise and connectivity artifacts to Betti number and Betti matching errors.

What would settle it

Compute the A-versus-D Spearman rank correlation for a new, topologically rich segmentation dataset using the authors' protocol; if the correlation is systematically positive or near zero, the claim that connectivity choice inverts rankings does not generalize. More directly, re-run the DRIVE artifact experiment with a 10-pixel or 3-pixel removal threshold and check whether the 43% reduction in BM1 error persists or disappears, which would test whether the effect is an artifact of the threshold.

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Extended reading notes

Core claim

The central claim is that reported rankings of topology-aware segmentation methods are largely artifacts of arbitrary evaluation choices. By training and evaluating six methods on the CREMI dataset under both the A connectivity (all-connectivity foreground, direct background) and the D connectivity (the reverse), the authors find that ranks invert on nearly every metric, including negative Spearman correlations on Betti errors. On DRIVE, removing ground-truth components up to 5 pixels, which visually correspond to label noise and connectivity artifacts, reduces the Betti matching 1 error by about 43% and Betti number 1 error by about 29%, while leaving Dice and VOI nearly unchanged. The paper also shows that distributional metrics (VOI, ARE/ARI) entangle volumetric and topological errors, and that aggregating Betti errors across dimensions hides the metric that matters for the downstream task, e.g., BM0 for vessels and BM1 for neurons.

Load-bearing premise

The quantitative conclusions rest on the authors' manual choice, guided by visual inspection, of which connectivity is semantically correct for each dataset (A for DRIVE, D for CREMI and Roads) and of the 5-pixel component-size cutoff for treating ground-truth objects as artifacts; a different reasonable choice could change the magnitudes and possibly the ranking flips.

Editorial extensions

If this is right

  • Method papers should report which connectivity they use, e.g., β0A versus β0D, and choose the semantics-preserving one per dataset.
  • Rankings in existing papers that omit connectivity reporting may not transfer to downstream applications.
  • Topological metrics should be reported without dimension aggregation, and always paired with a purely volumetric metric.
  • Datasets should be screened for small background components before benchmarking, except where such components carry semantic meaning, as in CREMI neuron beginnings.
  • The connectivity susceptibility score can be computed cheaply for any dataset before it is adopted as a benchmark.

Reading between the lines

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

  • The susceptibility measure generalizes: any 2D or 3D segmentation benchmark could be screened with it, and datasets with high susceptibility should be reported with multiple connectivity choices until a semantic consensus is reached.
  • The finding that connectivity can invert rankings suggests that some published method comparisons in the topology-aware segmentation literature may need to be re-run under standardized connectivity before their conclusions can be considered stable.
  • The artifact-removal result implies that weakly supervised or iterative label-cleaning steps could be integrated into evaluation pipelines, though the 5-pixel threshold would need task-specific justification.
  • The paper's recommendation to use Betti matching errors over Betti numbers may itself depend on the matching algorithm's sensitivity to connectivity, which the paper does not fully dissect.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper argues that current benchmarking practices for topology-aware medical image segmentation are unreliable because of three pitfalls: (1) inadequate connectivity choices that can distort method rankings, (2) topological artifacts in ground-truth labels that inflate measured topological error, and (3) inappropriate use of evaluation metrics that entangle volumetric and topological information or aggregate different topological dimensions. The authors empirically study these issues using the DRIVE, CREMI, Roads, and MSSEG2 datasets and six topology-aware segmentation methods. They report that switching between the two standard connectivity conventions (A and D) can produce negative correlations between method rankings across metrics, that removing small ground-truth components reduces Betti matching error by up to ~43% (Table 4, BM1A), and that distributional metrics such as VOI/ARE are not consistently correlated with topological metrics. They propose recommendations: dataset-specific connectivity choices with transparency, removal of semantic artifacts, and reporting of disaggregated Betti matching errors alongside volumetric metrics. They also introduce a connectivity susceptibility metric.

Significance. If the findings are robust, the paper addresses a real and timely problem: many topology-aware segmentation papers report rankings that may be artifacts of evaluation choices rather than genuine method quality. The work is constructive in proposing concrete reporting standards and a susceptibility metric, and it ships code and uses publicly available datasets. The main claims are empirical and falsifiable. However, the central ranking-inversion claim currently rests on a small number of methods trained with single seeds, which undermines the strength of the conclusion as presented. The paper is nevertheless a valuable contribution to benchmarking methodology, provided the statistical grounding is improved.

major comments (3)
  1. [Section 3.1, Table 2] The ranking-inversion claim is supported only by single training runs per method per connectivity setting. With n=6 methods, none of the reported Spearman coefficients (range -0.37 to -0.85) reaches the critical value of approximately 0.886 at alpha=0.05 (two-tailed), and the average of -0.63 could plausibly arise from training stochasticity. Please provide multi-seed experiments with confidence intervals or explicitly moderate the conclusion that 'the ranking of the methods changes drastically' to a statement that rankings are unstable under connectivity changes.
  2. [Discussion (unnumbered paragraph)] The headline statistic 'avg. Spearman's ρ = -0.63' does not match the mean of the seven values in Table 2, which is approximately -0.59. This inconsistency undermines the reported summary statistic; please correct the value or clarify how the average is computed (e.g., whether the average is over metrics or over some other grouping).
  3. [Section 3.2, Table 4] The artifact-removal experiment uses a manually chosen threshold of components with fewer than 5 pixels, and the reported claim that artifacts can comprise up to 43% of measured topological error (BM1A relative change) is threshold-dependent. The paper does not provide a sensitivity analysis over thresholds for the metric changes, although Table 5 reports component counts for several thresholds. Please either add such an analysis or explicitly state that the 43% figure is an example under a specific threshold, and discuss how the conclusion depends on this choice.
minor comments (4)
  1. [Section 3.2, Table 4] The caption for Table 4 repeats the phrase 'adapted ground truth' for both blocks; the second block should refer to the original ground truth.
  2. [Section 3.1, Eq. (1) and Table 3] The connectivity susceptibility values in Table 3 appear to be per-image averages (e.g., for DRIVE, the total foreground component difference of 18,718 divided by 40 images gives 467.95), but the text defines the metric for 'a label G' without specifying whether the reported values are per-image averages or totals. Please clarify the normalization.
  3. [Section 3.1] The claim that 'only one paper reports their connectivity choice' for the DRIVE dataset would benefit from a citation to that specific paper to make the statement verifiable.
  4. [Section 3.3, Figure 4] In Figure 4, the panels illustrate 'unfavorable' and 'favorable' predictions, but the caption does not state which prediction the authors consider preferable in each case; adding explicit labels would improve interpretability.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central claims are empirical benchmark observations, not derivations from the paper's own definitions or fitted parameters.

full rationale

The manuscript's central claims are empirical findings about existing methods and metrics: connectivity choices invert rankings (Table 2), small-component removal changes measured topological errors (Table 4), and distributional or aggregated metrics misrepresent topological accuracy (Section 3.3). These claims are supported by direct experiments, not by equations that presuppose the conclusions. The only formal definition, connectivity susceptibility in Eq. (1), is a descriptive measure of label partitions; the paper's statement that high susceptibility 'indicates' large score discrepancies is an empirical correlation, not an identity. Self-citations (TopoGraph [28], Betti matching [42], ClDice [40], and related prior work) appear as baselines or as prior metrics, and the paper explicitly re-tests the Betti-matching claim ('We investigate this statement empirically'), so no load-bearing argument reduces to a self-citation. Manual choices, such as the semantically favorable connectivity per dataset and the 5-pixel artifact threshold, are assumptions based on visual inspection; they affect the magnitude of reported effects but do not make the conclusions true by construction. The single-seed, six-method statistical weakness is a validity concern, not a circularity. Accordingly, no circular step is present.

Assumptions & free parameters 1 free parameters · 4 assumptions · 0 invented entities

The central claim rests on a small number of domain-specific semantic judgments: which connectivity is 'correct' for each dataset and which small components are 'artifacts'. The 5-pixel threshold is a free parameter. No new entities (particles, forces, dimensions) are introduced.

free parameters (1)
  • Small component removal threshold = ≤ 5 pixels
    Used to define topological artifacts in DRIVE and Roads (Section 3.2, Table 4). Chosen by visual inspection, not optimized or validated. Table 5 shows a sweep over 1, 2, and 5 pixels, but the headline 43% effect uses 5 pixels.
assumptions (4)
  • standard math Jordan curve theorem requires opposite connectivity for foreground and background (A or D)
    Assumed in Section 3.1 to justify the two feasible connectivity settings.
  • domain assumption The 'semantically favorable' connectivity is A for DRIVE, D for CREMI, and D for Roads
    The paper asserts these choices capture dataset semantics (Sections 3.1 and 3.2) based on visual inspection, not external validation.
  • ad hoc to paper Small connected components (≤5 pixels) in DRIVE and Roads are artifacts without semantic meaning
    The artifact-removal experiment depends on this; the paper notes the same removal would be harmful in CREMI, so it is dataset-specific.
  • domain assumption VOI and ARE entangle volumetric and topological errors
    Borrowed from cited works (Funke et al., Nunez-Iglesias et al.), used to justify disentangled metrics.

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Cite this review

Pith. "Pith review of Pitfalls of topology-aware image segmentation." pith.science (2026). https://pith.science/paper/VYCATFLA

@misc{pith2026241214619,
  author       = {Pith},
  title        = {Pith review of: Pitfalls of topology-aware image segmentation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VYCATFLA}},
  note         = {Machine review of arXiv:2412.14619}
}
read the original abstract

Topological correctness, i.e., the preservation of structural integrity and specific characteristics of shape, is a fundamental requirement for medical imaging tasks, such as neuron or vessel segmentation. Despite the recent surge in topology-aware methods addressing this challenge, their real-world applicability is hindered by flawed benchmarking practices. In this paper, we identify critical pitfalls in model evaluation that include inadequate connectivity choices, overlooked topological artifacts in ground truth annotations, and inappropriate use of evaluation metrics. Through detailed empirical analysis, we uncover these issues' profound impact on the evaluation and ranking of segmentation methods. Drawing from our findings, we propose a set of actionable recommendations to establish fair and robust evaluation standards for topology-aware medical image segmentation methods.

Figures

Figures reproduced from arXiv: 2412.14619 by the authors.

Figure 1
Figure 1. Topological errors are present across distinct medical image segmentation tasks, e.g., in neuron, Circle of Willis, and retinal segmentation (top). We identify three critical pitfalls (bottom) in the evaluation of topology-aware segmentation methods. These include inadequate connectivity choices that misrepresent a dataset’s semantics (left, e.g., representing a single vessel as multiple components), overlooked topo… view at source ↗
Figure 2
Figure 2. Example of the importance of making the correct connectivity choices for the DRIVE and CREMI datasets. In the DRIVE dataset, small vessels are disconnected with 4-connectivity for the FG. In the CREMI dataset, synaptic clefts can become disconnected with 4-connectivity for the BG. Making the correct connectivity choice is essential to accurately capture the domain-specific semantics of the underlying data. Investiga… view at source ↗
Figure 3
Figure 3. Examples of topological artifacts. The two left columns show connectivity artifacts and label noise in the DRIVE dataset. The right column shows resolution artifacts in the Roads dataset. Arrows and circles indicate topological artifacts. errors can lead to topological artifacts. Single-pixel label noise is a common phenomenon in segmentation labels. These errors only have a negligible impact on pixel-wise metrics. … view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Examples for the impact of inappropriate reporting practice on DRIVE (top) and unsuitable evaluation metrics on the Roads dataset (bottom). Left: Image with an overlay of the segmentation label. Middle: Unfavorable predictions, with detached vessels BM = 2 (top) and di…

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Cited by 1 Pith paper

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Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.