The triangulation of images has become an active research area in recent years for its compressive representation and ease of image processing and visualization. However, little work has been done on how to faithfully recover image intensities from a triangulated mesh of an image, a process also known as image restoration or decoding from meshes. The existing methods such as linear interpolatio...

The triangulation of images has become an active research area in recent years for its compressive representation and ease of image processing and visualization. However, little work has been done on how to faithfully recover image intensities from a triangulated mesh of an image, a process also known as image restoration or decoding from meshes. The existing methods such as linear interpolatio...

We propose a new approach for the radial basis function (RBF) interpolation of large scattered data sets. It uses the space subdivision technique into independent cells allowing processing of large data sets with low memory requirements and offering high computation speed, together with the possibility of parallel processing as each cell can be processed independently. The proposed RBF interpol...

Coupled with the concept of particular solutions and radial basis functions, a simple and effective numerical method for solving a large class of partial differential equations can be achieved. One of the difficulties of globally applying MAPS is that these methods result in a large dense matrices which in turn severely restricts the number of interpolation points, thereby affecting our ability...

We propose a Semi-Lagrangian scheme coupled with Radial Basis Function interpolation for approximating a curvature-related level set model, which has been proposed by Zhao et al. in [19] to reconstruct unknown surfaces from sparse, possibly noisy data sets. The main advantages of the proposed scheme are the possibility to solve the level set method on unstructured grids, as well as to concentra...

Abstract. Radial basis function (RBF) approximation has the potential to provide spectrally accurate function approximations for data given at scattered node locations. For smooth solutions, the best accuracy for a given number of node points is typically achieved when the basis functions are scaled to be nearly flat. This also results in nearly linearly dependent basis functions and severe ill...

The question in the title is answered using tools of potential theory. Convergence and divergence rates of interpolants of analytic functions on the unit interval are analyzed. The starting point is a complex variable contour integral formula for the remainder in RBF interpolation. We study a generalized Runge phenomenon and explore how the location of centers affects convergence. Special atten...