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

TL;DR

LEDA is a novel autoencoder framework that efficiently models and analyzes complex non-linear deformation fields in neuroimaging, improving statistical analysis and inverse consistency in image registration tasks.

Contribution

The paper introduces LEDA, a log-Euclidean autoencoder that predicts deformation field square roots within a linearized diffeomorphism space, enabling robust and efficient statistical analysis.

Findings

LEDA accurately models complex deformations in neuroimaging data.

The framework maintains inverse consistency in deformation representations.

LEDA enhances clinical variable analysis in neuroimaging studies.

Abstract

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.