A continuous scale space of diffeomorphisms
Numerical Analysis
2025-01-09 v1 Numerical Analysis
Abstract
In this paper, we define and study a nested family of reproducing kernel Hilbert spaces of vector fields that is indexed by a range of scales, from which we construct a reproducing kernel Hilbert space of scale-dependent vector fields. We provide a characterization of the reproducing kernel of that space, with numerical approximations ensuring quick evaluations when this kernel does not have a closed form. We then introduce a multiscale version of the large deformation diffeomorphic metric mapping (LDDMM) problem and prove the existence of solutions. Finally, we provide numerical experiments performing landmark matching using multiscale LDDMM.
Keywords
Cite
@article{arxiv.2501.04031,
title = {A continuous scale space of diffeomorphisms},
author = {Yechen Liu and Laurent Younes},
journal= {arXiv preprint arXiv:2501.04031},
year = {2025}
}