2025/01/01 by Liu, Yechen, Younes, Laurent
#46C99 #49N90 #FOS: Mathematics #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.2501.04031
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.