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The Impact Label Noise and Choice of Threshold has on Cross-Entropy and Soft-Dice in Image Segmentation
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Shows theoretically and experimentally that under Gaussian-field label noise, soft-Dice optima can be recovered by thresholding cross-entropy optima at an a priori unknown, efficiently computable threshold, which matches soft-Dice performance while keeping cross-entropy stability.
Problem
Cross-entropy and soft-Dice segmentation losses yield different predictions under label noise, and the common fixed 0.5 threshold is suboptimal for Dice; the mechanism behind this discrepancy is not well understood.
Approach
Introduces a Gaussian field deformation label-noise model with closed-form marginals, characterizes optimal segmentations for cross-entropy and soft-Dice, and shows that thresholding the cross-entropy optimum at a computable threshold t_m = sup Dice/2 recovers the soft-Dice optimum.
Key results
- On the esophagus, CE with the computed threshold (CE(*)) outperforms CE with 0.5 threshold, closing the gap to SD(0) as noise increases; on kidney and aorta the gap is smaller.
- Performance of CE(0) and SD(0) is indistinguishable at zero noise and diverges as noise strength a increases to 0.03.
- Theory: optimal CE thresholded at t_m = sup Dice/2 gives the soft-Dice optimal segmentation (Eq. 23).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the alternative threshold instead of 0.5 with cross-entropy | 3D U-Net trained with cross-entropy · TotalSegmentator kidney, aorta, and esophagus segmentation | Dice | Helped |
| Use soft-Dice instead of cross-entropy, both with threshold 0.5 | 3D U-Net · TotalSegmentator kidney, aorta, and esophagus segmentation with increasing label noise | Dice | Helped |
| Use cross-entropy instead of soft-Dice, both with threshold 0.5 | 3D U-Net · TotalSegmentator kidney, aorta, and esophagus segmentation with increasing label noise | Accuracy | Helped |
| Increase label noise | Cross-entropy and soft-Dice with threshold 0.5 · TotalSegmentator kidney, aorta, and esophagus segmentation | Dice | Mixed |
Surprising findings
- The noise model is approximately volume preserving, yet optimal segmentations under noise are systematically reshaped (corners smoothed, thin structures and holes removed).
Limitations
- Experiments are limited to noise produced by the proposed noise model.
- Threshold must be computed for every prediction, adding overhead for large images or many classes.
- Soft-Dice equivalence with expectation-based definitions holds only approximately when noise volume variance is small.
Experimental setup
Datasets: TotalSegmentator
Benchmarks: TotalSegmentator (kidney, aorta, esophagus)
Metrics: Dice
Baselines: CE(0) SD(0)
Builds on: soft-Dice Dice optimal segmentation characterization (Nordström et al.) threshold classifiers (Ye and Zhong)
Closest papers by meaning
- On Image Segmentation With Noisy Labels: Characterization and Volume Properties of the Optimal Solutions to Accuracy and Dice (NeurIPS 2022 · similarity 0.88)
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