An algorithm for choosing a good shape parameter for radial basis functions method with a case study in image processing

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dc.authoridTofigh Allahviranloo / 0000-0002-6673-3560en_US
dc.authorscopusidTofigh Allahviranloo / 8834494700en_US
dc.authorwosidTofigh Allahviranloo / V-4843-2019en_US
dc.contributor.authorGhalichi, Shabnam Sadat Seyed
dc.contributor.authorAmirfakhrian, Majid
dc.contributor.authorAllahviranloo, Tofigh
dc.date.accessioned2022-11-07T07:02:53Z
dc.date.available2022-11-07T07:02:53Z
dc.date.issued2022en_US
dc.departmentİstinye Üniversitesi, Mühendislik ve Doğa Bilimleri Fakültesi, Matematik Bölümüen_US
dc.description.abstractSome 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 ?.en_US
dc.identifier.citationGhalichi, 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.2022.100337en_US
dc.identifier.doi10.1016/j.rinam.2022.100337en_US
dc.identifier.scopus2-s2.0-85139070821en_US
dc.identifier.scopusqualityN/Aen_US
dc.identifier.urihttps://hdl.handle.net/20.500.12713/3235
dc.identifier.volume16en_US
dc.identifier.wosWOS:000870458600001en_US
dc.identifier.wosqualityN/Aen_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.institutionauthorAllahviranloo, Tofigh
dc.language.isoenen_US
dc.publisherElsevier B.V.en_US
dc.relation.ispartofResults in Applied Mathematicsen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectInterpolationen_US
dc.subjectRadial Basis Functionsen_US
dc.subjectScattered Dataen_US
dc.subjectShape Parameteren_US
dc.subjectZoomingen_US
dc.titleAn algorithm for choosing a good shape parameter for radial basis functions method with a case study in image processingen_US
dc.typeArticleen_US

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