Stability and Robustness of RBF Interpolation

Vector Field Rbf Interpolation on a Sphere

This paper presents a new approach for Radial Basis Function (RBF) interpolation on a sphere. Standard approaches use the Euclidian metrics for the distance calculation of two points. However, for interpolation on a sphere, more naturally is computation of the distance as the shortest distance over the surface on a sphere, i.e. spherical distance of two points is more natural for interpolation ...

Medical Image Inpainting with RBF Interpolation Technique

Inpainting is a method for repairing damaged images or to remove unwanted parts of an image. While this process has been performed by professional artists in the past, today, the use of this technology is emerging in the medical area – especially in the medical imaging realm. In this study, the proposed inpainting method uses a radial basis function (RBF) interpolation technique. We first expla...

Error bounds for anisotropic RBF interpolation

We present error bounds for the interpolation with anisotropically transformed radial basis functions for both function and its partial derivatives. The bounds rely on a growth function and do not contain unknown constants. For polyharmonic basic functions in R we show that the anisotropic estimates predict a significant improvement of the approximation error if both the target function and the...

Filtering , Stability , and Robustness

The theory of nonlinear filtering concerns the optimal estimation of a Markov signal in noisy observations. Such estimates necessarily depend on the model that is chosen for the signal and observations processes. This thesis studies the sensitivity of the filter to the choice of underlying model over long periods of time, in the framework of continuous time filtering with white noise type obser...

Efficient and exact mesh deformation using multiscale RBF interpolation