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Hierarchical Uncertainty Estimation for Learning-based Registration in Neuroimaging
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Propagates network-predicted voxel-level (aleatoric or MC-dropout epistemic) uncertainty through weighted least-squares fitting of affine, B-spline and Demons transforms to downstream segmentation uncertainty in brain MRI registration.
Problem
Uncertainty estimation in deep learning based brain MRI registration is underexplored and generic voxel-level methods like MC dropout do not capture spatial structure of deformation fields.
Approach
Treat per-location network predictions of coordinates with Gaussian uncertainty as observations and fit transformation models (affine, B-spline, Demons) by precision-weighted least squares, giving closed-form coefficient covariances and sampling that propagate uncertainty to downstream segmentation.
Key results
- Aleatoric uncertainty correlates with coordinate error (Spearman 0.601, Pearson 0.476) far better than MC dropout epistemic uncertainty (Spearman 0.181, Pearson 0.108).
- Uncertainty-aware fitting improves affine Dice on ABIDE from 0.718 to 0.730 and B-spline 10 mm Dice from 0.782 to 0.790 (OASIS3: 0.750 to 0.772).
- Demons fitting with uncertainty gives no Dice change (0.799 on ABIDE), attributed to Demons being used in the training segmentation loss.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use aleatoric uncertainty to weight affine fitting | RbR registration · ABIDE | Dice: 0.718 $\pm$ 0.038 -> 0.730 $\pm$ 0.033 | Helped |
| Use aleatoric uncertainty to weight affine fitting | RbR registration · OASIS3 | Dice: 0.673 $\pm$ 0.056 -> 0.682 $\pm$ 0.055 | Helped |
| Use aleatoric uncertainty to weight B-spline fitting | RbR registration · ABIDE | Dice: 0.782 $\pm$ 0.020 -> 0.790 $\pm$ 0.019 | Helped |
| Use aleatoric uncertainty to weight B-spline fitting | RbR registration · OASIS3 | Dice: 0.750 $\pm$ 0.034 -> 0.772 $\pm$ 0.030 | Helped |
| Use aleatoric uncertainty to weight Demons fitting | RbR registration · ABIDE and OASIS3 | Dice: 0.799 $\pm$ 0.020 -> 0.799 $\pm$ 0.019; 0.783 $\pm$ 0.029 -> 0.783 $\pm$ 0.028 | No clear effect |
| Predict aleatoric rather than MC-dropout epistemic uncertainty | RbR coordinate regression · Validation set | Correlation with coordinate error: 0.181 $\pm$ 0.017 -> 0.601 $\pm$ 0.019 (Spearman); 0.108 $\pm$ 0.012 -> 0.476 $\pm$ 0.021 (Pearson) | Helped |
| Add the atlas segmentation loss to RbR training | RbR · ABIDE and OASIS3 | Dice: 0.739 $\pm$ 0.038 -> 0.767 $\pm$ 0.024 (ABIDE); 0.728 $\pm$ 0.028 -> 0.759 $\pm$ 0.030 (OASIS3) | Helped |
| Set segmentation-loss weight λ_seg to 5 (ablation) | Proposed method · ABIDE and OASIS3 | Dice: 0.759 $\pm$ 0.035 at λ_seg=2 -> 0.790 $\pm$ 0.019 at λ_seg=5; 0.734 $\pm$ 0.036 -> 0.772 $\pm$ 0.030 | Helped |
| Model uncertainty separately for each coordinate direction instead of using one shared channel (ablation) | Proposed method · ABIDE and OASIS3 | Dice: 0.714 $\pm$ 0.054 -> 0.790 $\pm$ 0.019 (ABIDE); 0.687 $\pm$ 0.048 -> 0.772 $\pm$ 0.030 (OASIS3) | Helped |
| Use a Laplacian rather than Gaussian distribution for uncertainty (ablation) | Proposed method · ABIDE and OASIS3 | Dice: 0.785 $\pm$ 0.025 -> 0.790 $\pm$ 0.019 (ABIDE); 0.774 $\pm$ 0.026 -> 0.772 $\pm$ 0.030 (OASIS3) | No clear effect |
| Use L2 rather than L1 coordinate regression loss (ablation) | Proposed method · ABIDE and OASIS3 | Dice: 0.783 $\pm$ 0.024 -> 0.790 $\pm$ 0.019 (ABIDE); 0.763 $\pm$ 0.016 -> 0.772 $\pm$ 0.030 (OASIS3) | Helped |
| Use Demons rather than B-spline as the transformation in the training segmentation loss (ablation) | Proposed method · ABIDE and OASIS3 | Dice: 0.710 $\pm$ 0.022 -> 0.790 $\pm$ 0.019 (ABIDE); 0.700 $\pm$ 0.024 -> 0.772 $\pm$ 0.030 (OASIS3) | Helped |
Surprising findings
- Demons transformation does not benefit from uncertainty-weighted fitting when used in training, but does benefit (0.767 to 0.799 on ABIDE) when training used direct deformation.
- MC dropout epistemic uncertainty correlates very poorly with registration error.
Limitations
- Only two non-linear transformation models were included and registration is restricted to a fixed atlas space.
- Third-level (downstream segmentation) uncertainty is shown only qualitatively.
- Dice is the only proxy for registration accuracy.
Experimental setup
Datasets: HCP ADNI ABIDE OASIS3 MNI ICBM 2009b template
Benchmarks: ABIDE OASIS3
Metrics: Dice Spearman correlation Pearson correlation coordinate error (mm)
Baselines: Registration by Regression (RbR) Monte Carlo dropout
Builds on: Registration by Regression VoxelMorph Monte Carlo dropout SynthSeg NiftyReg
Closest papers by meaning
- Uncertainty Estimation for Pretrained Medical Image Registration Models via Transformation Equivariance (NeurIPS 2026 · similarity 0.91)
- Rate-In: Information-Driven Adaptive Dropout Rates for Improved Inference-Time Uncertainty Estimation (CVPR 2025 · similarity 0.84)
- Efficient Noise Calculation in Deep Learning-based MRI Reconstructions (ICML 2025 · similarity 0.84)
- CARL: A Framework for Equivariant Image Registration (CVPR 2025 · similarity 0.84)
- Estimating Epistemic and Aleatoric Uncertainty with a Single Model (NeurIPS 2024 · similarity 0.84)
- Deep Learning in Medical Image Registration: Magic or Mirage? (NeurIPS 2024 · similarity 0.83)
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