Complete parameterization of piecewise-polynomial interpolation kernels
Journal
IEEE Transactions on Image Processing
Journal Volume
12
Journal Issue
11
Date Issued
2003-11-01
Author(s)
Abstract
Every now and then, a new design of an interpolation kernel shows up in the literature. While interesting results have emerged, the traditional design methodology proves laborious and is riddled with very large systems of linear equations that must be solved analytically. In this paper, we propose to ease this burden by providing an explicit formula that will generate every possible piecewise-polynomial kernel given its degree, its support, its regularity, and its order of approximation. This formula contains a set of coefficients that can be chosen freely and do not interfere with the four main design parameters; it is thus easy to tune the design to achieve any additional constraints that the designer may care for.
Subjects
Compactly supported kernels | Order of approximation | Piecewise polynomial approximation | Sampling | Spline functions | Uniform samples
Type
journal article