Interpolation by radial basis functions and interpolation by polynomials are both popular methods for function reconstruction from discrete data given on spheres. Recently, there has been an increasing interest in employing these function families together in hybrid schemes for scattered data modeling and the solution of partial differential equations on spheres. For the theoretical analysis of...

In many cases, multivariate interpolation by smooth radial basis functions converges towards polynomial interpolants, when the basis functions are scaled to become “wide”. In particular, examples show that interpolation by scaled Gaussians seems to converge towards the de Boor/Ron “least” polynomial interpolant. The paper starts by providing sufficient criteria for the convergence of radial int...

Radial basis functions are well-known and successful tools for the interpolation of data in many dimensions. Several radial basis functions of compact support that give rise to nonsingular interpolation problems have been proposed, and in this paper we study a new, larger class of smooth radial functions of compact support which contains other compactly supported ones that were proposed earlier...

We present a unified framework for interpolation and regularisation of scalarand tensor-valued images. This framework is based on elliptic partial differential equations (PDEs) and allows rotationally invariant models. Since it does not require a regular grid, it can also be used for tensor-valued scattered data interpolation and for tensor field inpainting. By choosing suitable differential op...

As the core of digital elevation model, interpolation methods have been run through the each link, such as production, quality control, accuracy assessment, analytical applications and etc. The local radial basis function interpolation method based on spatial relationship of natural neighbor was proposed in this paper. The interpolation reference points were chosen by the Delaunay Triangulation...

rainfall erosivity is the ability of rainfall to detach the soil particles. this study was conducted to evaluate spatial variability of rainfall erosivity indices in khouzestan province. the point data of indices (ei30, aim, ke>1 and onchev indices) in 74 stations were used to generate spatial erosivity maps through deterministic and geostatistical interpolation methods (radial basis functions,...

Volume morphing is a technique used for generating smooth 3D image transformations and deformations. In this paper, several algorithms are developed for morphing transformations that create new forms and simulate shape deformation and growth in biomedical applications. 3D biological point landmarks and their movements are deened to guide the morphing transformation using a scattered data interp...