Search results for "Spline interpolation"

Error bounds for a convexity-preserving interpolation and its limit function

2008

AbstractError bounds between a nonlinear interpolation and the limit function of its associated subdivision scheme are estimated. The bounds can be evaluated without recursive subdivision. We show that this interpolation is convexity preserving, as its associated subdivision scheme. Finally, some numerical experiments are presented.

Hermite interpolation: The barycentric approach

1991

The barycentric formulas for polynomial and rational Hermite interpolation are derived; an efficient algorithm for the computation of these interpolants is developed. Some new interpolation principles based on rational interpolation are discussed.

Reconstructions that combine interpolation with least squares fitting

2015

We develop a reconstruction that combines interpolation and least squares fitting for point values in the context of multiresolution a la Harten. We study the smoothness properties of the reconstruction as well as its approximation order. We analyze how different adaptive techniques (ENO, SR and WENO) can be used within this reconstruction. We present some numerical examples where we compare the results obtained with the classical interpolation and the interpolation combined with least-squares approximation. We develop a reconstruction that combines interpolation and least squares fitting.We study the smoothness properties of the reconstruction and its approximation order.We present some nu…

Monotone cubic spline interpolation for functions with a strong gradient

2021

Abstract Spline interpolation has been used in several applications due to its favorable properties regarding smoothness and accuracy of the interpolant. However, when there exists a discontinuity or a steep gradient in the data, some artifacts can appear due to the Gibbs phenomenon. Also, preservation of data monotonicity is a requirement in some applications, and that property is not automatically verified by the interpolator. Hence, some additional techniques have to be incorporated so as to ensure monotonicity. The final interpolator is not actually a spline as C 2 regularity and monotonicity are not ensured at the same time. In this paper, we study sufficient conditions to obtain monot…

Spline Histogram Method for Reconstruction of Probability Density Functions of Clusters of Galaxies

2003

We describe the spline histogram algorithm which is useful for visualization of the probability density function setting up a statistical hypothesis for a test. The spline histogram is constructed from discrete data measurements using tensioned cubic spline interpolation of the cumulative distribution function which is then differentiated and smoothed using the Savitzky-Golay filter. The optimal width of the filter is determined by minimization of the Integrated Square Error function. The current distribution of the TCSplin algorithm written in f77 with IDL and Gnuplot visualization scripts is available from this http URL

Color Correction for Image Stitching by Monotone Cubic Spline Interpolation

2015

This paper proposes a novel color correction scheme for image stitching where the color map transfer is modelled by a monotone Hermite cubic spline and smoothly propagated into the target image. A three-segments monotone cubic spline minimizing color distribution statistics and gradient differences with respect to both the source and target images is used. While the spline model can handle non-linear color maps, the minimization over the gradient differences limits strong alterations on the image structure. Adaptive heuristics are introduced to reduce the minimization search space and thus computational time. Experimental comparisons with respect to the state-of-the-art linear mapping model…

Defining and measuring the development of a country over time

2012

This paper introduces the concept of harmonic growth as an extended acceptation of the notion of development, and discusses its measurement via the Harmonic Growth Index (HGI). The growth is seen as harmonic when the behaviour of a benchmark time series, which here is a measure of wealth, such as per capita GDP, is followed by a similar pattern in socio-economic series. Unlike most widely used indicators in the literature, which take into account the measurement of development over a single time, HGI measures the degree to which a social indicator’s time series pattern matches with the GDP’s. The index is a function, ranging in [0, 1], of the coefficients of the uniform B-splines fitted to …

Cubic Local Splines on Non-uniform Grid

2015

In this chapter, two types of local cubic splines on non-uniform grids are described: 1. The simplest variation-diminishing splines and 2. The quasi-interpolating splines. The splines are computed by a simple fast computational algorithms that utilizes a relation between the splines and cubic interpolation polynomials. Those splines can serve as an efficient tool for real-time signal processing. As an input, they use either clean or noised arbitrarily-spaced samples. On the other hand, the capability to adapt the grid to the structure of an object and minimal requirements to the operating memory are great advantages for off-line processing of signals and multidimensional data arrays.

An exponential spline interpolation for unequally spaced data points

1982

Geometric deformation measurement and correction applied to dynamic streak camera images

2002

The complete procedure of measuring and correcting geometric deformations encountered with dynamic streak camera images in the picosecond range is presented and discussed. First, we describe the experimental setup derived from the well known spacing calibration grid method. The implemented measurement bench, adapted to time-resolved 1D imaging, notably exhibits a great accuracy and repeatability both in space and time thanks to a three-axis motorized translation stage and programmable delay lines. Second, we examine image restoration by two different analytical transform means (local versus global): results and performances of both are compared. Then we deal with final image reconstruction …