A continuous scale space of diffeomorphisms

Yechen Liu; Laurent Younes

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arXiv · 2501.04031

A continuous scale space of diffeomorphisms

Yechen Liu·Laurent Younes

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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.

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Yechen Liu, Laurent Younes. 2025-01-01. A continuous scale space of diffeomorphisms. https://arxiv.org/abs/2501.04031

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