| Issue |
ESAIM: ProcS
Volume 79, 2025
CJC-MA 2023 - Le Congrès des Jeunes Chercheuses et Chercheurs en Mathématiques et Applications 2023
|
|
|---|---|---|
| Page(s) | 69 - 82 | |
| DOI | https://doi.org/10.1051/proc/202579069 | |
| Published online | 01 December 2025 | |
A right-invariant sub-Riemannian setting for Large Deformation models
ENS Paris-Saclay
e-mail: thomas.pierron@ens-paris-saclay.fr
The Large Deformation Diffeomorphic Metric Mapping (LDDMM) framework introduced in [BMTY05, Tro95, DGM98] is a widely recognized method in shape analysis and computational anatomy. It aims at finding a diffeomorphism that deforms optimally a given shape into another one using tools from Riemannian geometry. It was acknowledged in Arguillère’s Ph.D. thesis [AT17, Arg20, ATTY15, Arg15] that this approach amounts to endowing the group of deformations DiffC0k(ℝd) with a strong right-invariant sub-Riemannian structure.
In this paper, we extend these ideas to the category of half-Lie groups and we study right-invariant strong sub-Riemannian metrics on them. Several illustrative examples are discussed.
© EDP Sciences, SMAI 2025
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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