ResNet-LDDMM: Advancing the LDDMM Framework Using Deep Residual Networks.

Area of Science:

• Medical Image Analysis
• Computer Vision
• Computational Geometry

Background:

• The Riemannian framework, Large Deformation Diffeomorphic Metric Mapping (LDDMM), is crucial for shape and image analysis.
• LDDMM relies on solving flow equations in the space of diffeomorphisms, inspired by fluid dynamics.

Purpose of the Study:

• To develop a novel deep learning approach for solving the LDDMM flow equation.
• To enable efficient and accurate deformable registration of 3D shapes with complex topology-preserving transformations.

Main Methods:

• Utilized deep residual neural networks (ResNets) to solve the non-stationary ordinary differential equation (ODE) of the flow equation.
• Employed an Euler discretization scheme and back-propagation to optimize network parameters for minimizing deformations.
• Represented time-dependent velocity fields as fully connected ReLU neural networks.

Main Results:

• Demonstrated the ability of the ResNet-LDDMM framework to predict diffeomorphic (specifically, bi-Lipschitz) transformations.
• Successfully applied the algorithm to diverse 3D shape registration problems with complex, topology-preserving transformations.
• Showcased how the algorithm partitions space into polytopes for localized, energy-efficient movement of shape parts.

Conclusions:

• The ResNet-LDDMM framework provides a powerful new tool for deformable registration and shape analysis.
• This joint geometric-neural network approach lays foundations for advanced shape variability studies.
• The method offers efficient computation of complex, diffeomorphic transformations essential for medical imaging and computer graphics.