Intensity-Based Wasserstein Distance As A Loss Measure For Unsupervised Deformable Deep Registration
Bibliographic record
Abstract
Traditional pairwise medical image registration techniques are based on computationally intensive frameworks due to numerical optimization procedures. While there is increasing adoption of deep neural networks to improve deformable image registration, achieving a clinically suitable solution remains scarce. One of the primary difficulties lies in the choice of tractable distance functions to assess image similarity. Recent works have explored the Wasserstein distance as a loss function in generative deep neural networks. In this work, we evaluate a fast approximation variant - the sliced Wasserstein distance - for deep image registration of brain MRI datasets. Based on a VoxelMorph backbone architecture, which includes a combination of UNet and spatial transformer networks (STN) for deformable registration, we propose three implementation variants to compare the model's performance: the standard sliced Wasserstein, the Radon transform performing a low dimensional embedding, and a novel patch-based method that allows fine-grained deformation comparison. Experiments performed on public datasets of brain images from the Learn2Reg open challenge demonstrate the Wasserstein methods converge faster than the baseline mean square error method, with the proposed patch-based method yielding similar performance to baseline methods, and improved overall accuracy compared with other implementations. This makes the sliced Wasserstein a valuable metric for deep mono-modal and multi-modal deformable medical image registration problems with our proposed implementation.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.007 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".