An algorithm for choosing a good shape parameter for radial basis functions method with a case study in image processing
Yükleniyor...
Tarih
2022
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Elsevier B.V.
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
Some efficient radial basis functions (RBFs) have a free parameter called the shape parameter that controls the shape of approximating function. This parameter is mainly selected by trial and error related to the problem. Because of the significant role of this value in the accuracy and stability of the RBF method, we propose an algorithm to choose a good value as a shape parameter. In this work, we focus on the interpolating of scattered data approximation and attempt to find a better value of the shape parameter for RBF interpolation. The proposed algorithm selects a good value for the shape parameter by minimizing a cost function which imitates the error between the radial interpolant and the unknown function f that the data points sampled from the function f. The algorithm can be applied to a multidimensional problem of any dimension and for any radial basis function. Also, many experiments including interpolation of one and two dimensional data sets as well as zooming pictures consider investigating the efficiency of this procedure. Also, we show that this algorithm consistently finds a good value for a shape parameter ?.
Açıklama
Anahtar Kelimeler
Interpolation, Radial Basis Functions, Scattered Data, Shape Parameter, Zooming
Kaynak
Results in Applied Mathematics
WoS Q Değeri
N/A
Scopus Q Değeri
N/A
Cilt
16
Sayı
Künye
Ghalichi, S. S. S., Amirfakhrian, M., & Allahviranloo, T. (2022). An algorithm for choosing a good shape parameter for radial basis functions method with a case study in image processing. Results in Applied Mathematics, 16 doi:10.1016/j.rinam.2022.100337
