Title: Fast Interpolation and Approximation of Scattered Multidimensional and Dynamic Data Using Radial Basis Functions
Authors: Skala, Václav
Citation: WSEAS Transaction on Mathematics. 2013, vol. 12, no. 5, p. 501-511.
Issue Date: 2013
Publisher: WSEAS
Document type: konferenční příspěvek
URI: http://hdl.handle.net/11025/11330
ISSN: 2224-2880
Keywords: počítačové zpracování obrazu;radiální bázové funkce
Keywords in different language: computer image processing;radial basis functions
Abstract: Interpolation or approximation of scattered data is very often task in engineering problems. The Radial Basis Functions (RBF) interpolation is convenient for scattered (un-ordered) data sets in k-dimensional space, in general. This approach is convenient especially for a higher dimension k > 2 as the conversion to an ordered data set, e.g. using tessellation, is computationally very expensive. The RBF interpolation is not separable and it is based on distance of two points. It leads to a solution of a Linear System of Equations (LSE) Ax=b. There are two main groups of interpolating functions: ‘global” and “local”. Application of “local” functions, called Compactly Supporting RBF (CSFBF), can significantly decrease computational cost as they lead to a system of linear equations with a sparse matrix. In this paper the RBF interpolation theory is briefly introduced at the “application level” including some basic principles and computational issues and an incremental RBF computation is presented and approximation RBF as well. The RBF interpolation or approximation can be used also for image reconstruction, inpainting removal, for solution of Partial Differential Equations (PDE), in GIS systems, digital elevation model DEM etc.
Rights: Original article published under copytright license: © 2013 WSEAS
Appears in Collections:Konferenční příspěvky / Conference Papers (KIV)

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