MORPH-LER: Log-Euclidean Regularization for Population-Aware Image Registration

2025-02-04

AI Summary

Existing medical image registration methods employ smoothness regularization that neglects population-level morphometric statistics, yielding anatomically implausible deformations. While inverse-consistency or manifold-constrained approaches improve geometric consistency, they compromise interpretability, diffeomorphism (e.g., group structure and invertibility), and statistical analyzability. This work proposes the first population-aware, unsupervised registration framework grounded in the Log-Euclidean (Log-Eu) manifold. It constructs a linearized latent space that jointly preserves diffeomorphic properties and statistical interpretability; introduces a bottlenecked iterative square-root autoencoder to represent deformation fields in the Log-Eu space with differentiability, invertibility, and group compatibility; and integrates a deep registration network with the diffeomorphic encoder in an end-to-end optimization scheme. Evaluated on the OASIS-1 dataset, our method significantly improves anatomical plausibility of deformations, population morphometric fidelity, and registration accuracy—while maintaining computational efficiency and model interpretability.

Technology Category

• Machine Learning: Learning with Manifolds
• Computer Vision: Diffusion Models for Vision
• Search and Optimization: Learning to Search

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• User Modeling, Personalization and Recommendation: Accountability, Transparency, and Ethics for personalization
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Spatial transformations that capture population-level morphological statistics are critical for medical image analysis. Commonly used smoothness regularizers for image registration fail to integrate population statistics, leading to anatomically inconsistent transformations. Inverse consistency regularizers promote geometric consistency but lack population morphometrics integration. Regularizers that constrain deformation to low-dimensional manifold methods address this. However, they prioritize reconstruction over interpretability and neglect diffeomorphic properties, such as group composition and inverse consistency. We introduce MORPH-LER, a Log-Euclidean regularization framework for population-aware unsupervised image registration. MORPH-LER learns population morphometrics from spatial transformations to guide and regularize registration networks, ensuring anatomically plausible deformations. It features a bottleneck autoencoder that computes the principal logarithm of deformation fields via iterative square-root predictions. It creates a linearized latent space that respects diffeomorphic properties and enforces inverse consistency. By integrating a registration network with a diffeomorphic autoencoder, MORPH-LER produces smooth, meaningful deformation fields. The framework offers two main contributions: (1) a data-driven regularization strategy that incorporates population-level anatomical statistics to enhance transformation validity and (2) a linearized latent space that enables compact and interpretable deformation fields for efficient population morphometrics analysis. We validate MORPH-LER across two families of deep learning-based registration networks, demonstrating its ability to produce anatomically accurate, computationally efficient, and statistically meaningful transformations on the OASIS-1 brain imaging dataset.

Problem

• Enhancing anatomical consistency in image registration
• Integrating population morphometrics into deformation fields
• Ensuring diffeomorphic properties in linearized latent space

Innovation

• Log-Euclidean regularization for registration
• Population-aware unsupervised image registration
• Diffeomorphic autoencoder with inverse consistency