Metamorphic image registration using a semi-Lagrangian scheme

TL;DR

This paper introduces a semi-Lagrangian scheme for image registration using LDDMM and Metamorphosis, demonstrating improved stability and GPU acceleration with a unified cost function for inexact matching.

Contribution

It presents a novel semi-Lagrangian approach for LDDMM and Metamorphosis registration, unifying the problems with a single cost function and implementing GPU acceleration.

Findings

Semi-Lagrangian scheme offers more stability than Eulerian.

GPU implementation using PyTorch accelerates computations.

Unified cost function simplifies the registration process.

Abstract

In this paper, we propose an implementation of both Large Deformation Diffeomorphic Metric Mapping (LDDMM) and Metamorphosis image registration using a semi-Lagrangian scheme for geodesic shooting. We propose to solve both problems as an inexact matching providing a single and unifying cost function. We demonstrate that for image registration the use of a semi-Lagrangian scheme is more stable than a standard Eulerian scheme. Our GPU implementation is based on PyTorch, which greatly simplifies and accelerates the computations thanks to its powerful automatic differentiation engine. It will be freely available at https://github.com/antonfrancois/Demeter_metamorphosis.