Novel Approaches to the Parametric Cubic-Spline Interpolation

Abstract

The cubic-spline interpolation (CSI) scheme can be utilized to obtain a better quality reconstructed image. It is based on the least-squares method with cubic convolution interpolation (CCI) function. Within the parametric CSI scheme, it is difficult to determine the optimal parameter for various target images. In this paper, a novel method involving the concept of opportunity costs is proposed to identify the most suitable parameter for the CCI function needed in the CSI scheme. It is shown that such an optimal four-point CCI function in conjunction with the least-squares method can achieve a better performance with the same arithmetic operations in comparison with the existing CSI algorithm. In addition, experimental results show that the optimal six-point CSI scheme together with cross-zonal filter is superior in performance to the optimal four-point CSI scheme without increasing the computational complexity.

Cubic-Spline Interpolation for Sparse-View CT Image Reconstruction With Filtered Backprojection in Dynamic Myocardial Perfusion Imaging

“…Compared with a single high-order polynomial function, spline interpolation should provide a more accurate approximation of f ( x ), particularly if there exists local abrupt changes (such as the edges between high- and low-contrast regions). A cubic spline is a spline constructed of piecewise third-order polynomials (12, 13). Let us consider 3 consecutive data points, namely, x i − 1 , x i , x i + 1 .…”

“…The assumption of boundary conditions can be made to obtain 2 additional equations that are required to solve for all the unknowns. Conventionally, we can assume the first and second derivatives at the end points x 0 and x n , respectively, are zero: Pi′(x0)=Pi′(xn)=0; Pi′′(x0)=Pi′′(xn)=0 The cubic-spline interpolation is based on the least squares method with the cubic convolution interpolation function (12, 13). Taking equations (1) to equations (6) into account, the cubic-spline interpolation function I(x ) can be expressed as follows (14): I(x)=∑icis(x−xih) where x i are the interpolation nodes, S is the spline interpolation kernel as defined above, h is the sampling interval, and c i is selected so that the interpolation function is continuous.…”

A Novel Approach For 3D Surface Reconstruction Of LV Endocardium Based On SPCNN And MC

“…In order to produce a smooth surface after 3D reconstruction, we firstly increase the resolution between slices via recovering interlayer images. Considering the accurate and smoothness of the image interpolation result, here, we use the cubic spline interpolation [19]which is a kind of piecewise interpolation.When providing function values from 0 to n nodes and two boundary conditions, we can get interpolation function having continuous first and second order derivative at the nodes.Using it can better adapt to different requirements of smoothness and restore the interlayer missing images accurately. We assume the gray value of point (u, v) on the i th image to be (u, v), the cubic spline interpolation function y(x) calculated by three moment method [20] is as follows:…”

Adaptive image coding based on cubic-spline interpolation

“…because it provides a better PSNR performance in the CSI scheme with the same arithmetic operations 8 . The 1-D CCI function with 1 α = − , illustrated in Fig.…”