Empirical Mode Decomposition (EMD) has been widely used to analyze non-stationary and nonlinear signal by decomposing data into a series of intrinsic mode functions (IMFs) and a trend function through sifting processes. For lack of a firm mathematical foundation, the implementation of EMD is still empirical and ad hoc. In this paper, we prove mathematically that EMD, as practiced now, only give...

A method based on extended cubic B-spline is proposed to solve a linear system of second-order boundary value problems. In this method, two free parameters, [Formula: see text] and [Formula: see text], play an important role in producing accurate results. Optimization of these parameters are carried out and the truncation error is calculated. This method is tested on three examples. The example...

A piecewise rational cubic spline [5] has been used to visualize the positive data in its natural form. The spline representation is interpolatory and applicable to the scalar valued data. The shape parameters in the description of a rational cubic have been constrained in such a way that they preserve the shape of the positive data in the view of positive curve. As far as visual smoothness is ...

This article presents uniform B-spline interpolation, completely contained on the graphics processing unit (GPU). This implies that the CPU does not need to compute any lookup tables or B-spline basis functions. The cubic interpolation can be decomposed into several linear interpolations [Sigg and Hadwiger 05], which are hard-wired on the GPU and therefore very fast. Here it is demonstrated tha...

In this paper a rational cubic algebraic spline with two shape parameters is developed to create a high-order smoothness interpolation using function values and derivative values which are being interpolated. This is a kind of rational cubic interpolation with quadratic denominator. This rational spline interpolant is monotonic interpolant to given monotonic data. The more important achievement...

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-...

In a dose-finding study with an active control, several doses of a new drug are compared with an established drug (the so-called active control). One goal of such studies is to characterize the dose-response relationship and to find the smallest target dose concentration d(*), which leads to the same efficacy as the active control. For this purpose, the intersection point of the mean dose-respo...

With the objective of generating “shape-preserving” smooth interpolating curves that represent data with abrupt changes in magnitude and/or knot spacing, we study a class of first-derivative-based C1-smooth univariate cubic L1 splines. An L1 spline minimizes the L1 norm of the difference between the first-order derivative of the spline and the local divided difference of the data. Calculating t...

A piecewise rational cubic spline has been introduced to visualize the positive data in its natural form. It is attempted that the spline method preserves the shape of the data when it is positive. The spline representation is interpolatory and applicable to the scalar valued data. The shape parameters, in the description of the rational cubic, have been constrained in such a way that they cont...

Based on variational properties, we generalize the approximation properties of the univariate natural cubic spline to splines in arbitrary dimensions. In one dimension, the solution of the variational problem { given a = x1 < · · · < xN = b and values f(x1), . . . , f(xN ) in R, find a function s with s(xi)=f(xi), i=1, . . . ,N , that minimizes ‖s‖L2([a,b]) is given by the natural univariate cu...