# LEDA: Log-Euclidean Diffeomorphism Autoencoder for Efficient Statistical Analysis of Diffeomorphisms

arXiv: https://arxiv.org/abs/2412.16129 · HTML: https://mlsanity.com/paper/2412.16129/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 46 references that are in the map.
- First posted on arXiv 20 Dec 2024.

## Builds on (most cited first, 5 of 5)

- [VoxelMorph: A Learning Framework for Deformable Medical Image Registration](https://mlsanity.com/paper/1809.05231/) (2018)
- [HyperMorph: Amortized Hyperparameter Learning for Image Registration](https://mlsanity.com/paper/2101.01035/) (2021)
- [A Survey of Non-Rigid 3D Registration](https://mlsanity.com/paper/2203.07858/) (2022)
- [textttGradICON: Approximate Diffeomorphisms via Gradient Inverse Consistency](https://mlsanity.com/paper/2206.05897/) (2022)
- [ICON: Learning Regular Maps Through Inverse Consistency](https://mlsanity.com/paper/2105.04459/) (2021)

## Built on by (most cited first, 1 of 1)

- [MORPH-LER: Log-Euclidean Regularization for Population-Aware Image Registration](https://mlsanity.com/paper/2502.02029/) (2025)

## Abstract (arXiv)

Image registration is a core task in computational anatomy that establishes correspondences between images. Invertible deformable registration, which computes a deformation field and handles complex, non-linear transformations, is essential for tracking anatomical variations, especially in neuroimaging applications where inter-subject differences and longitudinal changes are key. Analyzing the deformation fields is challenging due to their non-linearity, which limits statistical analysis. However, traditional approaches for analyzing deformation fields are computationally expensive, sensitive to initialization, and prone to numerical errors, especially when the deformation is far from the identity. To address these limitations, we propose the Log-Euclidean Diffeomorphism Autoencoder (LEDA), an innovative framework designed to compute the principal logarithm of deformation fields by efficiently predicting consecutive square roots. LEDA operates within a linearized latent space that adheres to the diffeomorphisms group action laws, enhancing our model's robustness and applicability. We also introduce a loss function to enforce inverse consistency, ensuring accurate latent representations of deformation fields. Extensive experiments with the OASIS-1 dataset demonstrate the effectiveness of LEDA in accurately modeling and analyzing complex non-linear deformations while maintaining inverse consistency. Additionally, we evaluate its ability to capture and incorporate clinical variables, enhancing its relevance for clinical applications.