A frequently used method to handle scattered data approximation problems on different structures is the interpolation by linear combinations of a single positive definite kernel. Here the underlying positive definite kernel is responsible for the quality of the common estimates of the two main issues in this approximation process. Firstly the approximation error and secondly the stability of th...

Introduction: Diffusion MRI was the first imaging modality to allow the visualization of white matter fibre paths in vivo, and non-invasively. The process by which the white matter tracts are reconstructed from diffusion tensor data is called tractography. Tensor interpolation methods have often been used to improve the reproducibility and reliability of tractography results (e.g [1]). In this ...

We present several mesh smoothing schemes based on the concept of optimal Delaunay triangulations. We define the optimal Delaunay triangulation (ODT) as the triangulation that minimizes the interpolation error among all triangulations with the same number of vertices. ODTs aim to equidistribute the edge length under a new metric related to the Hessian matrix of the approximated function. Theref...

We consider some algorithms for unconstrained minimization without derivatives that form linear or quadratic models by interpolation to values of the objective function. Then a new vector of variables is calculated by minimizing the current model within a trust region. Techniques are described for adjusting the trust region radius, and for choosing positions of the interpolation points that mai...

Alexa’s method for linearly interpolating matrices is well-suited for application to camera matrices. This paper discusses implementation issues that arise when applying this method to camera interpolation. We show how to include the perspective matrix, even though Alexa’s operators cannot be applied directly to it. We discuss cases where Alexa’s operators fail to converge and show how to work ...

Polynomial and rational interpolation and multipoint evaluation are classical subjects, which remain central for the theory and practice of algebraic and numerical computing and have extensive applications to sciences, engineering and signal and image processing. In spite of long and intensive study of these subjects, several major problems remained open. We achieve substantial progress, based ...