# Metamorphic image registration using a semi-Lagrangian scheme

arXiv: https://arxiv.org/abs/2106.08817 · HTML: https://mlsanity.com/paper/2106.08817/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 19 references that are in the map.
- First posted on arXiv 16 Jun 2021.

## Builds on (most cited first, 2 of 2)

- [Image reconstruction through metamorphosis](https://mlsanity.com/paper/1806.01225/) (2018)
- [Metamorphosis of Images in Reproducing Kernel Hilbert Spaces](https://mlsanity.com/paper/1409.6573/) (2014)

## Built on by (most cited first, 7 of 7)

- [A deep residual learning implementation of Metamorphosis](https://mlsanity.com/paper/2202.00676/) (2022)
- [MetaMorph: Learning Metamorphic Image Transformation With Appearance Changes](https://mlsanity.com/paper/2303.04849/) (2023)
- [MetaRegNet: Metamorphic Image Registration Using Flow-Driven Residual Networks](https://mlsanity.com/paper/2303.09088/) (2023)
- [Automatic classification of deformable shapes](https://mlsanity.com/paper/2211.02530/) (2022)
- [VPREG: An Optimal Control Formulation for Diffeomorphic Image Registration Based on the Variational Principle Grid Generation Method](https://mlsanity.com/paper/2510.13109/) (2025)
- [Benchmarking Intra-Patient 3D Deformable Multimodal Image Registration](https://mlsanity.com/paper/2609.15669/) (2026)
- [Intrinsic Geometry Matching: learning observation-equivariant process geometry](https://mlsanity.com/paper/2610.16995/) (2026)

## Abstract (arXiv)

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.