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Mind the Gap: Mesh-Guided Repair of Broken Vessels

Gniewosz Drwiega, Wojciech Szymanski, Marek Wodzinski

arXiv:2609.29779v1cs.CV

TL;DR

Voxel-wise overlap can overlook small vessel breaks that disrupt connectivity and downstream analyses. The paper fits a deformable mesh to each nnU-Net mask and uses it to guide targeted reconnection. Repair improves connectivity-sensitive measures while Dice changes only marginally, and FOMAML initialization keeps per-case repair practical.

  • Problem

    Voxel-wise segmentation can achieve high Dice despite broken vessels, because small errors may change connectivity and topology while having little effect on overlap.

    Source: §1 · p. 2

  • Method

    The method fits a deformable mesh to each predicted mask and uses it as a case-specific scaffold to guide conservative reconnection while retaining a voxel-mask output.

    Source: §2.1 · p. 4, §2.4 · p. 7

  • Results

    Connectivity-sensitive metrics improved across datasets, whereas Dice changed only marginally.

    Source: §4.1 · p. 14, §5 · p. 15

  • Takeaways & Limitations

    The results support mesh representations as practical geometric priors for topology repair in vessel segmentation.

    Source: §5 · p. 15

    The method can support incorrect bridges, does not use image intensities or probability maps, and relies on dataset-specific templates and hyperparameters that may need adjustment for new vascular territories.

    Source: §4.2 · p. 14

Abstract

from arXiv · show

Vessel segmentation is commonly optimized as voxel-wise classification, but small local errors can strongly disrupt vascular connectivity while having little effect on overlap scores. This is particularly problematic for downstream analyses that rely on centerlines, branches, connected components, or graph structure. We propose a mesh-guided post-processing framework for repairing broken vessel segmentations produced by nnU-Net. For each predicted binary mask, a deformable template mesh is fitted to the mask surface in physical space and used as a case-specific geometric scaffold. The fitted mesh is not voxelized as the final segmentation; instead, it guides conservative reconnection of disconnected components by proposing or validating thin bridge candidates under foreground-growth constraints. We evaluated this approach in three vascular anatomies using AortaSeg24 and SEGA for the aorta, TopCoW for the Circle of Willis, and PARSE for the pulmonary arteries. Performance is measured using Dice, connected-component Dice (ccDice), and the Betti-0 number. Across these datasets, repair substantially improved connectivity while preserving overlap: Dice remained nearly unchanged, whereas ccDice increased from 0.596 to 0.992 for aorta, from 0.722 to 0.835 for TopCoW, and from 0.028 to 0.862 for PARSE. The FOMAML meta-initialization further accelerated the fitting per-case, supporting practical mesh-based repair of the vascular topology. These results suggest that explicit mesh representations can provide a useful geometric prior for correcting topological failures in otherwise accurate voxel segmentations.

1 Introduction

Voxel-wise overlap can miss small vessel discontinuities that disrupt connectivity and downstream analyses. The paper motivates topology-aware evaluation and proposes mesh-guided repair as a conservative post-processing approach for existing masks.

1 Introduction

  • Small missing bridges can split thin, anisotropic vessels while changing little volume, disrupting centerlines, branch labeling, diameter measurement, and flow analysis.These structural errors are easy to underweight when optimizing or reporting voxel-wise overlap.Source: §1 · p. 2
  • High Dice can coexist with broken vessels, missing branches, false-positive islands, or incorrect loops, motivating evaluation and learning objectives that account for structure.Voxel-wise losses primarily reward local agreement with reference annotations.Source: §1 · p. 2
  • Topology-aware losses and measures such as persistent-homology losses, clDice, centerline-Cross Entropy, and ccDice provide structural signals, but do not directly repair an existing voxel mask.ccDice extends Dice to spatially corresponding connected components.Source: §1 · pp. 2, 4
  • Meshes encode adjacency and allowable paths, but direct voxelized mesh replacement can overfill vessels or introduce implausible shortcuts amid branching, caliber variation, and patient variability.Most prior mesh-based segmentation methods use the mesh as the final anatomical representation.Source: §1 · p. 4
  • The proposed contributions are case-wise mesh scaffolding, conservative path-based reconnection, FOMAML initialization for faster fitting, and evaluation across four vascular datasets.The framework is evaluated with overlap, component-level, and topological metrics.Source: §1 · p. 4

2 Method

The method fits a deformable mesh to each nnU-Net mask and uses it as a geometric guide for conservative connectivity repair. It evaluates the repaired voxel masks across vascular datasets with overlap and topology-oriented measures.

2.1 Pipeline Overview

  • The fitted mesh guides targeted reconnection of disconnected components; the repaired output remains a voxel mask rather than a voxelized mesh.The pipeline extracts the predicted mask surface, deforms a fixed template through successive stages, and uses the fitted mesh as a geometric prior.Source: §2.1 · p. 4, Figure 2 · p. 5

2.2 Datasets and Input Masks

  • Evaluation covers aortic, cerebral, and pulmonary vessels, merging dataset-specific subregions or branch labels into one foreground vessel label.The datasets are SEGA and AortaSeg24, TopCoW, and PARSE, respectively.Source: §2.2 · p. 6

2.3 Mesh Fitting

  • For each mask, a case-specific graph decoder deforms an anatomy-specific template toward the physical-space surface, with Chamfer fitting and geometric regularization.The method selects the best-Chamfer mesh during per-case optimization and uses it only as a local geometric prior.Source: §2.3 · p. 6

2.4 Mesh-Guided Connectivity Repair

  • Repair proposes thin bridges through mesh-graph paths or endpoint connections, accepts only mesh-supported candidates under a foreground-growth limit, and can filter unsupported components.Candidates must merge target components; optional filtering and cleanup address distant false positives and small poorly supported components.Source: §2.4 · p. 7

2.5 FOMAML Meta-Initialization

  • FOMAML treats each case as a fitting task, adapts on support points, updates the shared initialization using query loss, and provides an inference-time warm start.The first-order update avoids backpropagating through the full inner optimization trajectory.Source: §2.5 · p. 8

2.6 Evaluation Metrics

  • The evaluation reports Dice for overlap, ccDice for spatially corresponding connected components, and Betti-0 for the number of mask components.These measures summarize preservation of segmentation quality alongside improved connectivity.Source: §2.6 · pp. 8–9

2.7 Experimental Protocol

  • Raw nnU-Net binary predictions are the baseline, and five-fold evaluation ensures each repaired case was segmented by a model that did not see it during training.The repair stage uses hard binary masks, not image intensities or nnU-Net probability maps.Source: §2.7 · p. 9

3 Results

Across the three vascular settings, repair improved connected-component Dice while Dice stayed nearly unchanged. Qualitative examples show localized reconnections, and FOMAML improved per-case mesh-fitting convergence.

3.1 Visual Assessment of Vessel Reconnection

  • Visual errors varied by anatomy: aortic gaps were small, TopCoW discontinuities often occurred near the posterior communicating artery, and PARSE showed severe peripheral-branch fragmentation.Source: §3.1 · p. 9
  • Repairs added localized connectors, preserving most of the original nnU-Net mask rather than replacing it with a voxelized mesh.Source: §3.1 · p. 9, Figure 3 · p. 10

3.2 Effect on Overlap and Connectivity

  • Betti-0 fell from 3.35 ± 2.61 to 1.01 ± 0.12 in aorta and from 2.58 ± 1.14 to 1.02 ± 0.13 in TopCoW.Source: §3.2 · p. 11
  • Dice remained essentially unchanged across cohorts, while TopCoW false-branch fraction rose from 0.040±0.006 to 0.063±0.007.The reported false-branch fraction remained nearly unchanged in the aortic cohort and PARSE.Source: §3.2 · p. 11
  • In PARSE, Betti-0 fell from 87.46 ± 45.92 to 1.56 ± 1.06.The raw pulmonary-artery masks were highly fragmented.Source: §3.2 · p. 11
  • ccDice rose from 0.596±0.275 to 0.992±0.057 (aorta), 0.722±0.247 to 0.835±0.195 (TopCoW), and 0.028±0.012 to 0.862±0.211 (PARSE).The values compare raw masks with repaired masks.Source: Table 3 · p. 11, §3.2 · p. 11

3.3 Effect of FOMAML Meta-Initialization

  • On 25 held-out TopCoW cases, FOMAML beat standard initialization at every checkpoint and reduced mean Chamfer loss after 100 iterations from 7.79×10−4 to 4.99×10−4.FOMAML outperformed standard initialization in all 25 cases.Source: §3.3 · pp. 11, 13, Figure 5 · p. 13

4 Discussion

Mesh-guided repair chiefly improves connectivity-sensitive measures while changing Dice only marginally, with the most consistent behavior in aortic anatomy. FOMAML keeps per-case fitting practical, while limitations and proposed future work center on bridge selection, evidence sources, and adaptation to new anatomies.

4.1 Mesh-Guided Topology Repair

  • The fitted mesh guides local reconnection rather than replacing the voxel mask, keeping the repaired output close to the original prediction and avoiding a globally generalizing mesh model.Per-case fitting accommodates variation in branching patterns, caliber, and topology; TopCoW and PARSE pose more complex geometry than the aorta.Source: §4.1 · pp. 13–14
  • Connectivity-sensitive metrics show the method’s main effect across datasets, while Dice changes only marginally.The behavior is most consistent for aortic anatomy, where connectivity errors are often localized.Source: §4.1 · p. 14
  • With FOMAML initialization, mesh fitting at approximately 300 optimization steps plus post-repair takes about 30 s per case, versus 44.17 s for nnU-Net inference.The authors report that the added repair stage remains comparable to the original inference time.Source: §4.1 · p. 14

4.2 Limitations

  • Misleading false positives or anatomically implausible shortcuts can produce incorrect bridges, and current binary-mask repair does not use image intensities or nnU-Net probability maps.Dataset-specific templates and hyperparameters may also need adjustment for new vascular territories.Source: §4.2 · p. 14

4.3 Future Work

  • Future work proposes learned bridge scoring, anatomical constraints, and probability-map or image evidence to make repair more adaptive, alongside hemodynamic experiments on downstream effects.The authors also propose combining per-case mesh fitting with learned topology-aware repair.Source: §4.3 · pp. 14–15

5 Conclusion

The conclusion presents mesh-guided post-processing as a practical geometric prior for repairing broken vessel segmentations while preserving the voxel-wise prediction. FOMAML initialization keeps the per-case strategy practical without requiring a globally generalizing mesh prediction model.

5 Conclusion

  • Fitting a deformable mesh to each predicted mask provides a case-specific scaffold for post-processing broken vessel segmentations.The method uses the mesh as a geometric prior for topology repair while preserving the original voxel-wise segmentation.Source: §5 · p. 15
  • FOMAML initialization makes the per-case repair practical without requiring a globally generalizing mesh prediction model.Source: §5 · p. 15
  • The results support mesh representations as practical geometric priors for vessel-topology repair.Source: §5 · p. 15

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