A fast algorithm for particle simulations
Journal of Computational Physics
SIAM Journal on Scientific and Statistical Computing
Diffeomorphisms Groups and Pattern Matching in Image Analysis
International Journal of Computer Vision
Variational problems on flows of diffeomorphisms for image matching
Quarterly of Applied Mathematics
Computational anatomy: an emerging discipline
Quarterly of Applied Mathematics - Special issue on current and future challenges in the applications of mathematics
A new class of radial basis functions with compact support
Mathematics of Computation
Improved Fast Gauss Transform and Efficient Kernel Density Estimation
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
IEEE Transactions on Pattern Analysis and Machine Intelligence
SIAM Journal on Scientific Computing
Geodesic Shooting for Computational Anatomy
Journal of Mathematical Imaging and Vision
Fast Radial Basis Function Interpolation via Preconditioned Krylov Iteration
SIAM Journal on Scientific Computing
IPMI'05 Proceedings of the 19th international conference on Information Processing in Medical Imaging
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Reproducing kernel Hilbert spaces play an important role in diffeomorphic matching of shapes and in which they intervene in the construction of Riemannian metrics on diffeomorphisms and shape spaces. In such contexts, they are directly involved in the expressions of geodesic equations, and in their numerical solutions via particle evolutions. Solving such equations, however, involves computing kernel sums over irregular grids which can be a big computational overhead if the number of particles is large. In this paper we introduce and establish properties of a finitely generated kernel class in which the kernel is defined using a double interpolation from a discrete kernel supported by a regular grid covering the domain of the system of particles under consideration. It not only speeds up the calculations by utilizing standard algorithms for faster computations over regular grids, but also maintains the exactness and consistency of the system. We provide experimental results in support of this, comparing in particular the computation time and accuracy to similar competing methods.