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BiCC: Bidirectional Connected-Component Loss for Instance-Aware Segmentation
Luc Bouteille, Frederic Jonske, Jens Kleesiek, Alexander Jaus
TL;DR
Voxel-wise segmentation losses give larger lesions more influence, while annotation-derived instance regions do not give false-positive components their own term. BiCC pairs reference- and prediction-derived partitions, and across five datasets it generally improves lesion-wise F1 over CC-DiceCE while outperforming blob loss.
Problem
Voxel-wise losses weight lesions in proportion to volume, and annotation-derived instance regions leave false-positive components without their own instance-level term.
Source: §1 · p. 1Method
Results
Across five diverse 3D datasets at α=0.5, BiCC consistently outperforms blob loss, matches or improves upon DiceCE, and generally improves upon CC-DiceCE in instance-level F1.
Source: §5 · p. 8Takeaways & Limitations
Training-time α adjustment provides control along the lesion-wise precision-recall frontier that post-hoc thresholding cannot replicate, and BiCC substantially reduces false positives on lesion-free scans.
Source: §5 · p. 8On CMB, CC-DiceCE has higher mean F1 than BiCC, though not significantly; for its smallest, most uniform lesions, the prediction-derived branch may over-penalize components without improving precision.
Source: §4.1 · p. 6
Abstract
from arXiv · showhide
Common segmentation losses aggregate errors voxel-wise, so lesions influence the objective in proportion to their volume, giving small but clinically critical lesions disproportionately little weight. Instance-aware losses aim to address this mismatch by assigning each lesion its own term. However, blob loss and CC-DiceCE derive their regions solely from annotations, so false-positive components receive no instance-level term. This matters in computer-assisted review, where each false-positive component may require separate inspection, making precision and false-positive burden important alongside recall. We introduce the bidirectional connected-component loss (BiCC), which pairs annotation- and prediction-derived partitions to score predicted components on their own scale. By deriving instances from the predictions, this branch directly penalizes false-positive components regardless of their size. The balance parameter $α$ allows control over the lesion-wise precision-recall trade-off. Across five datasets with five-fold cross-validation using nnU-Net, BiCC outperforms CC-DiceCE in lesion-wise F1 on four datasets and blob loss on all five. It significantly improves over DiceCE on three datasets and matches it on two; CC-DiceCE instead loses up to 0.363 precision by favoring recall. Code is available at https://github.com/TIO-IKIM/BiCC-Loss.
1 Introduction
Voxel-wise losses let lesion size shape each lesion’s influence, while annotation-derived instance regions still leave false positives without their own term. BiCC pairs reference- and prediction-derived partitions, with a branch designed to score unambiguous false positives.
1 Introduction
- False-positive components receive no instance-level term under annotation-derived regions, despite each potentially requiring separate inspection.Voxel-wise aggregation also gives larger lesions more influence than smaller ones.Source: §1 · pp. 1–2
- BiCC pairs reference- and prediction-derived partitions so every predicted component defines its own training region.For unambiguous false-positive regions, it uses a mass-weighted mean of predicted probability; α balances the two branches.Source: §1 · p. 2
- The paper compares BiCC with DiceCE, blob loss, and CC-DiceCE across five datasets, and studies α as a control along the lesion-wise precision-recall frontier.The datasets span MRI, CT, and PET/CT.Source: §1 · p. 2
2 Method
The method builds instance losses from both reference- and prediction-derived partitions, assigning each component a Voronoi cell. It separately scores ground-truth-empty prediction cells and combines the directional losses through a balance parameter.
2.1 Bidirectional Formulation
- Reference and prediction components define partitions by nearest component in physical Euclidean distance, with ties resolved deterministically; each component contributes one Voronoi-cell loss weighted equally regardless of volume.The regional loss is DiceCE restricted to the cell.Source: §2.1 · pp. 2–3
2.2 Scoring GT-Empty Cells
- In ground-truth-empty prediction cells, smoothed Dice has an effectively zero gradient with small ε, while larger ε makes gradient strength depend on component size.BiCC instead uses a prediction-mass score with total derivative constant across component sizes; surrounding voxels avoid an arbitrary component cutoff.Source: §2.2 · p. 3
2.3 Combined Loss Function
- The complete objective combines the global DiceCE loss with an instance term weighted 1:1 against it, while α controls the relative reference- and prediction-partition contributions.The instance-term budget remains fixed as α varies.Source: §2.3 · p. 3
3 Experiments
The experiments use five datasets spanning modalities, lesion sizes, and lesion counts, with a shared nnU-Net training setup and lesion-wise evaluation. Ablations examine branch balance, false-positive scoring, and whether post-hoc thresholding can reproduce α tuning.
3.1 Data
- Five datasets cover MRI, CT, and PET/CT tasks with differing lesion sizes and counts, including 1,014 FDG and 597 PSMA PET/CT studies in AutoPET III.The data include CMB, BraTS-METS, LiTS, AutoPET III, and ISLES.Source: §3.1 · p. 4
3.2 Experimental Setup
- All methods use the same self-configured 3D nnU-Net and differ only in objective, with α=0.5, five-fold cross-validation, and 500 training epochs.AutoPET III and BraTS-METS folds are grouped by patient to prevent leakage.Source: §3.2 · p. 4
3.3 Evaluation
- Lesion-wise precision, recall, and F1 use 26-connected components matched one-to-one at IoU > 0.1; empty-GT scans are separately evaluated by mean predicted components.Metrics are macro-averaged over scans, with empty-GT scans excluded from the five main metrics.Source: §3.3 · pp. 4–5
3.4 Ablations
- Ablations sweep α, replace false-positive scoring with smoothed Dice, and shift DiceCE logits to test thresholding, using ISLES and AutoPET III.These datasets were chosen because BiCC matches DiceCE on ISLES and outperforms it on AutoPET III.Source: §3.4 · p. 5
4 Results and Discussion
BiCC generally improves or maintains lesion-wise F1 relative to DiceCE while providing a better precision-recall balance than CC-DiceCE. Ablations show that α controls this balance, while post-hoc thresholding does not reproduce its operating range.
4.1 Comparison with Baselines
- CC-DiceCE raises recall on every dataset but lowers precision on four by up to 0.363; BiCC produces the fewest empty-GT components on all five.On four datasets, CC-DiceCE’s recall gain does not prevent significantly lower F1 than DiceCE; BiCC significantly reduces empty-GT components versus both baselines on four.Source: §4.1 · pp. 5–6
- Compared with DiceCE, BiCC gains up to +0.014 in CC-Dice on AutoPET III, gives up at most 0.009 on ISLES, yet remains below CC-DiceCE on all five datasets.This ordering is consistent with CC-Dice’s recall. Relative to DiceCE, global Dice changes by −0.011 to +0.019 and is secondary to lesion-wise metrics because it is dominated by large lesions and insensitive to missed or falsely detected small lesions.Source: §4.1 · pp. 5–6
- Across five datasets, BiCC significantly raises lesion-wise F1 over DiceCE on three and is comparable on two, while beating CC-DiceCE in precision and F1 on four.The main results are means over held-out cases from five-fold cross-validation.Source: §4.1 · p. 5, Table 2 · p. 6
- On an NVIDIA RTX A6000, BiCC adds 17–23% training time per epoch over DiceCE and 7–10% over CC-DiceCE, with no additional inference cost.Source: §4.1 · p. 6
- On CMB, CC-DiceCE has higher mean F1 than BiCC, though not significantly; its smallest, most uniform lesions may make reference-cell overlap sufficient to penalize false positives.For this lesion profile, the prediction-derived component loss may over-penalize predicted components without improving precision.Source: §4.1 · p. 6
4.2 Ablations
- Across the α sweep, precision rises while recall falls; at α = 1/4, about 70% of the precision change and almost 90% of maximum F1 improvement are attained.F1 then remains nearly constant, supporting α = 1/2 as a robust default without dataset-specific tuning; global Dice is comparatively stable and empty-scan false positives fall substantially.Source: §4.2 · p. 7
- Replacing the false-positive scoring rule with smoothed Dice returns results near α = 0; mixed cells retain DiceCE, with precision penalties limited to unambiguous false positives.The authors attribute the smoothed-Dice result to an effectively zero gradient for unambiguous false positives when the smoothing constant is small.Source: §4.2 · p. 7
- Shifting DiceCE logits cannot reproduce α tuning: thresholding spans a narrower precision-recall range on ISLES and is strictly dominated across shared recall on AutoPET III.At high thresholds on ISLES, components falling below the IoU > 0.1 matching cutoff make precision reverse rather than continue improving; thresholding reaches comparable peak F1 there.Source: §4.2 · pp. 7–8, Figure 2 · p. 8
5 Conclusion
BiCC pairs reference- and prediction-derived partitions to evaluate missed lesions and false positives at their own spatial scale. Across five diverse 3D datasets, it improves on blob loss and generally improves on CC-DiceCE in instance-level F1, while α provides training-time control of the lesion-wise precision-recall trade-off.
5 Conclusion
- BiCC pairs reference- and prediction-derived partitions to evaluate missed lesions and false positives at their own spatial scale with a size-independent training signal.Source: §5 · p. 8
- Across five diverse 3D datasets at fixed α = 0.5, BiCC consistently outperforms blob loss, matches or improves upon DiceCE, and generally improves upon CC-DiceCE in instance-level F1.It also substantially reduces false positives on lesion-free scans.Source: §5 · p. 8
- α provides training-time control along the lesion-wise precision-recall frontier, and post-hoc decision thresholding cannot replicate that control.Source: §5 · p. 8
- BiCC requires no architectural changes or inference overhead, making it a practical drop-in loss for instance-aware 3D medical image segmentation.Source: §5 · p. 8
Data Use.
- BraTS-METS and AutoPET III are provided under CC BY-NC 4.0, VALDO under CC BY-NC-SA 4.0, LiTS under CC BY-NC-ND 4.0, and ISLES’26 under ATLAS Terms of Use.Source: Data Use · p. 8