Topic
Monotone cubic interpolation
About: Monotone cubic interpolation is a research topic. Over the lifetime, 1740 publications have been published within this topic receiving 38111 citations.
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01 Jan 2004
TL;DR: The purpose of this chapter is to present an introduction to thin-plate spline interpolation and indicate how it can be a useful tool in medical imaging applications.
Abstract: The purpose of this chapter is to present an introduction to thin-plate spline interpolation and indicate how it can be a useful tool in medical imaging applications. After a brief review of the strengths and weaknesses of polynomial and Fourier interpolation, the ideas fundamental to the success of cubic spline interpolation are discussed. These ideas include convergence rates of both the interpolants and the derivatives as well as the fact that the clamped cubic spline is the solution of a minimization problem, where the optimal solution is the one exhibiting the fewest “wiggles.” This measure is important because it helps ensure that if slowly oscillating data is interpolated by a spline technique, then the interpolation will also be reasonable. The classical examples of Runge are presented, which dramatically demonstrate the dangers of polynomial interpolation for even the least oscillatory data. While the Fourier interpolants are more stable than the polynomial ones, they have the problem that while the interpolants converge, their derivatives do not. Thus, the spline approach has definite advantages
7 citations
TL;DR: In this article, a rational cubic interpolation with one parameter is proposed for shape preserving interpolation such as positivity, monotonicity, and convexity preservations and constrained data lie on the same side of the given straight line.
Abstract: New rational cubic Ball interpolation with one parameter is proposed for shape preserving interpolation such as positivity, monotonicity, and convexity preservations and constrained data lie on the same side of the given straight line. To produce shape preserving interpolant, the data dependent sufficient condition is derived on the parameter. The rational bicubic Ball function is constructed by using tensor product approach and it will be used for application in image upscaling. Numerical and graphical results are presented by using Mathematica and MATLAB including comparison with some existing scheme.
7 citations
03 Sep 1990
TL;DR: An efficient implementation of a two-stage fractional sampling rate conversion for digital audio signals is presented, based on: local cubic spline interpolation.
Abstract: An efficient implementation of a two-stage fractional sampling rate conversion for digital audio signals is presented, based on: local cubic spline interpolation. The first (up-converter) stage is computationally optimal, using polyphase networks. The second (down-converter) stage generally requires coefficient calculations for each sample, but is also efficient because of the local nature of the cubic spline interpolation. >
7 citations
TL;DR: In the absence of known endpoint derivatives, the usual procedure is to use a "natural" spline interpolant which Kershaw has shown to have e(h4) error except near the endpoints as discussed by the authors.
Abstract: In the absence of known endpoint derivatives, the usual procedure is to use a "natural" spline interpolant which Kershaw has shown to have e(h4) error except near the endpoints. This note observes that either the use of appropriate finite-difference approxima- tions for the endpoint derivatives or a proposed modification of the interpolation algorithm leads to 0(A4) error uniformly in the interval of approximation.
7 citations
01 Jan 1997
TL;DR: In the context of radial basis function interpolation, the construction of native spaces and the techniques for proving error bounds deserve some further clarification and improvement as mentioned in this paper, which can be described by applying the general theory to the special case of cubic splines.
Abstract: In the context of radial basis function interpolation, the construction of native spaces and the techniques for proving error bounds deserve some further clarification and improvement. This can be described by applying the general theory to the special case of cubic splines. It shows the prevailing gaps in the general theory and yields a simple approach to local error bounds for cubic spline interpolation.
7 citations