Insights into traditional and deep-learning diffeomorphic registration methods: to infinity and beyond in the LDDMM-verse
Short Course part of Seminars in AI and Robotics
Non-rigid image registration is one of the fundamental pillars of medical image analysis, enabling the alignment of anatomical structures across subjects, time points, and imaging modalities. Among its various formulations, diffeomorphic registration stands out for ensuring smooth and invertible deformations that preserve anatomical topology. These properties are essential for accurately capturing complex morphological variations while maintaining the structural integrity of the anatomies being analyzed.
Computational Anatomy is a recently emerging discipline that aims to model and analyze anatomical structures through mathematical and computational frameworks, enabling quantitative studies of shape variability, disease progression, and population trends. A fundamental tool in this field is diffeomorphic image registration. Traditional methods, such as Large Deformation Diffeomorphic Metric Mapping (LDDMM) and its Euler-Poincaré formulation (EPDiff-LDDMM), provide a solid theoretical foundation but often suffer from high computational costs. To mitigate these limitations, faster approximations like Stationary LDDMM, diffeomorphic Demons, and FLASH introduce notable efficiency gains while maintaining registration fidelity. With the advent of deep learning, supervised and non-supervised data-driven methods such as QuickSilver and VoxelMorph have reshaped the field, offering rapid inference while maintaining diffeomorphic constraints. More recently, Implicit Neural Representations (INRs) and Neural Ordinary Differential Equations (NODEs) have emerged as a promising paradigms, bridging traditional physics-based models with modern deep-learning frameworks. This short course provides a structured journey through the evolution of diffeomorphic registration and its application into Computational Anatomy, covering key methodologies from classical optimization-based techniques to state-of-the-art deep-learning approaches.
Through theoretical insights and hands-on demonstrations, participants will gain a comprehensive understanding of the LDDMM-verse, its challenges, and its past and future directions in medical image analysis.