Approximation by the third-order splines on uniform and non-uniform grids and image processing

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Approximation by the third-order splines on uniform and non-uniform grids and image processing. / Burova, I. G.; Muzafarova, E. F.; Narbutovskikh, I. I.

In: WSEAS Transactions on Mathematics, Vol. 19, 01.01.2020, p. 65-73.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{4bb43835823c4c988cef556e3b06763e,

title = "Approximation by the third-order splines on uniform and non-uniform grids and image processing",

abstract = "This work is one of a series of papers that is devoted to the further investigation of polynomial splines and trigonometric splines of the third order approximation. Polynomial basis splines are better known and therefore more commonly used. However, the use of trigonometric basis splines often provides a smaller approximation error. In some cases, the use of the trigonometric approximations is preferable to the polynomial approximations. Here we continue to compare these two types of approximation. The Lebesgue functions and constants are discussed for the polynomial splines and the trigonometric splines. The examples of the applications of the splines to image enlargement are given.",

keywords = "Enlarging image, Image processing, Interpolation, Lebesgue constant, Polynomial splines, Trigonometric splines",

author = "Burova, {I. G.} and Muzafarova, {E. F.} and Narbutovskikh, {I. I.}",

year = "2020",

month = jan,

day = "1",

doi = "10.37394/23206.2020.19.7",

language = "English",

volume = "19",

pages = "65--73",

journal = "WSEAS Transactions on Mathematics",

issn = "1109-2769",

publisher = "WORLD SCIENTIFIC PUBL CO PTE LTD",

}

RIS

TY - JOUR

T1 - Approximation by the third-order splines on uniform and non-uniform grids and image processing

AU - Burova, I. G.

AU - Muzafarova, E. F.

AU - Narbutovskikh, I. I.

PY - 2020/1/1

Y1 - 2020/1/1

N2 - This work is one of a series of papers that is devoted to the further investigation of polynomial splines and trigonometric splines of the third order approximation. Polynomial basis splines are better known and therefore more commonly used. However, the use of trigonometric basis splines often provides a smaller approximation error. In some cases, the use of the trigonometric approximations is preferable to the polynomial approximations. Here we continue to compare these two types of approximation. The Lebesgue functions and constants are discussed for the polynomial splines and the trigonometric splines. The examples of the applications of the splines to image enlargement are given.

AB - This work is one of a series of papers that is devoted to the further investigation of polynomial splines and trigonometric splines of the third order approximation. Polynomial basis splines are better known and therefore more commonly used. However, the use of trigonometric basis splines often provides a smaller approximation error. In some cases, the use of the trigonometric approximations is preferable to the polynomial approximations. Here we continue to compare these two types of approximation. The Lebesgue functions and constants are discussed for the polynomial splines and the trigonometric splines. The examples of the applications of the splines to image enlargement are given.

KW - Enlarging image

KW - Image processing

KW - Interpolation

KW - Lebesgue constant

KW - Polynomial splines

KW - Trigonometric splines

UR - http://www.scopus.com/inward/record.url?scp=85083836252&partnerID=8YFLogxK

U2 - 10.37394/23206.2020.19.7

DO - 10.37394/23206.2020.19.7

M3 - Article

AN - SCOPUS:85083836252

VL - 19

SP - 65

EP - 73

JO - WSEAS Transactions on Mathematics

JF - WSEAS Transactions on Mathematics

SN - 1109-2769

ER -

ID: 53627032