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

• URL: http://arxiv.org/abs/2412.16129v1
• Date: Fri, 20 Dec 2024 18:26:10 GMT
• Title: LEDA: Log-Euclidean Diffeomorphic Autoencoder for Efficient Statistical Analysis of Diffeomorphism
• Authors: Krithika Iyer, Shireen Elhabian, Sarang Joshi,
• Abstract summary: Invertible deformable registration is essential for tracking anatomical variations. Traditional approaches for analyzing deformation fields are computationally expensive and prone to numerical errors. We introduce a loss function to enforce inverse consistency, ensuring accurate latent representations of deformation fields.
• Score: 0.029792392019703937
• License:
• 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 transformation, 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, limiting 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 Diffeomorphic 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.

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