204 research outputs found
Local interpolation schemes for landmark-based image registration: a comparison
In this paper we focus, from a mathematical point of view, on properties and
performances of some local interpolation schemes for landmark-based image
registration. Precisely, we consider modified Shepard's interpolants,
Wendland's functions, and Lobachevsky splines. They are quite unlike each
other, but all of them are compactly supported and enjoy interesting
theoretical and computational properties. In particular, we point out some
unusual forms of the considered functions. Finally, detailed numerical
comparisons are given, considering also Gaussians and thin plate splines, which
are really globally supported but widely used in applications
Scattered data fitting on surfaces using projected Powell-Sabin splines
We present C1 methods for either interpolating data or for fitting scattered data associated with a smooth function on a two-dimensional smooth manifold Ī© embedded into R3. The methods are based on a local bivariate Powell-Sabin interpolation scheme, and make use of local projections on the tangent planes. The data fitting method is a two-stage method. We illustrate the performance of the algorithms with some numerical examples, which, in particular, confirm the O(h3) order of convergence as the data becomes dens
Hybrid spherical approximation
In this paper a local approximation method on the sphere is presented. As
interpolation scheme we consider a partition of unity method, such as the
modified spherical Shepard's method, which uses zonal basis functions (ZBFs)
plus spherical harmonics as local approximants. Moreover, a spherical zone
algorithm is efficiently implemented, which works well also when the amount of
data is very large, since it is based on an optimized searching procedure.
Numerical results show good accuracy of the method, also on real geomagnetic
data
A well-balanced meshless tsunami propagation and inundation model
We present a novel meshless tsunami propagation and inundation model. We
discretize the nonlinear shallow-water equations using a well-balanced scheme
relying on radial basis function based finite differences. The inundation model
relies on radial basis function generated extrapolation from the wet points
closest to the wet-dry interface into the dry region. Numerical results against
standard one- and two-dimensional benchmarks are presented.Comment: 20 pages, 13 figure
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