# Sliding at first order: Higher-order momentum distributions for discontinuous image registration

arXiv: https://arxiv.org/abs/2303.07744 · HTML: https://mlsanity.com/paper/2303.07744/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 40 references that are in the map.
- First posted on arXiv 14 Mar 2023.

## Builds on (most cited first, 1 of 1)

- [Higher-order Spatial Accuracy in Diffeomorphic Image Registration](https://mlsanity.com/paper/1412.7504/) (2014)

## Built on by (most cited first, 1 of 1)

- [A Diffeomorphism Groupoid and Algebroid Framework for Discontinuous Image Registration](https://mlsanity.com/paper/2603.11806/) (2026)

## Abstract (arXiv)

In this paper, we propose a new approach to deformable image registration that captures sliding motions. The large deformation diffeomorphic metric mapping (LDDMM) registration method faces challenges in representing sliding motion since it per construction generates smooth warps. To address this issue, we extend LDDMM by incorporating both zeroth- and first-order momenta with a non-differentiable kernel. This allows to represent both discontinuous deformation at switching boundaries and diffeomorphic deformation in homogeneous regions. We provide a mathematical analysis of the proposed deformation model from the viewpoint of discontinuous systems. To evaluate our approach, we conduct experiments on both artificial images and the publicly available DIR-Lab 4DCT dataset. Results show the effectiveness of our approach in capturing plausible sliding motion.