TY - JOUR

T1 - Local splines of the second and third order, complex-valued splines and image processing

AU - Burova, I. G.

AU - Muzafarova, E. F.

AU - Narbutovskikh, I. I.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - This paper is devoted to the local complex-valued spline interpolation in a circle and image processing using local polynomial and non-polynomial splines. We consider local complex-valued spline interpolation, constructed by using tensor product. For constructing the tensor product we use local basis splines of two variables: A radial variable and an angular variable. The approximation is constructed separately in each elementary segment, formed by two arcs and two line segments. For the approximation of a complex-valued function we use the values of the function in several nodes near this elementary segment and the basis splines. The order of the approximation depends on the properties of splines of one variable which we use in the tensor product. In this paper we suggest using local exponential, local trigonometrical and local polynomial splines of the second and third order of approximation. The local spline interpolation is the most convenient for the approximation and visualization of functions and they may be applied to solving various problems. In this paper we focus on the problem of enlarging images using the local splines.

AB - This paper is devoted to the local complex-valued spline interpolation in a circle and image processing using local polynomial and non-polynomial splines. We consider local complex-valued spline interpolation, constructed by using tensor product. For constructing the tensor product we use local basis splines of two variables: A radial variable and an angular variable. The approximation is constructed separately in each elementary segment, formed by two arcs and two line segments. For the approximation of a complex-valued function we use the values of the function in several nodes near this elementary segment and the basis splines. The order of the approximation depends on the properties of splines of one variable which we use in the tensor product. In this paper we suggest using local exponential, local trigonometrical and local polynomial splines of the second and third order of approximation. The local spline interpolation is the most convenient for the approximation and visualization of functions and they may be applied to solving various problems. In this paper we focus on the problem of enlarging images using the local splines.

KW - Approximation

KW - Complex-valued splines

KW - Exponential spline

KW - Image processing

KW - Interpolation

KW - Polynomial spline

KW - Tensor product

KW - Trigonometric spline

UR - http://www.scopus.com/inward/record.url?scp=85070672174&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:85070672174

VL - 13

SP - 419

EP - 429

JO - International Journal of Circuits, Systems and Signal Processing

JF - International Journal of Circuits, Systems and Signal Processing

SN - 1998-4464

ER -