Two Dimensional Spline Interpolation Algorithms

1993 ◽  
Author(s):  
Helmuth Späth
Keyword(s):  
Spline Interpolation ◽  
Two Dimensional ◽  
Interpolation Algorithms

Two-dimensional empirical mode decomposition by finite elements

2006 ◽  
Vol 462 (2074) ◽  
pp. 3081-3096 ◽  
Author(s):  
Y Xu ◽  
B Liu ◽  
J Liu ◽  
S Riemenschneider
Keyword(s):  
Finite Element ◽  
Linear Combination ◽  
Empirical Mode Decomposition ◽  
Spline Interpolation ◽  
Basis Functions ◽  
Two Dimensional ◽  
Element Analysis ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Mode Decomposition

Empirical mode decomposition (EMD) is a powerful tool for analysis of non-stationary and nonlinear signals, and has drawn significant attention in various engineering application areas. This paper presents a finite element-based EMD method for two-dimensional data analysis. Specifically, we represent the local mean surface of the data, a key step in EMD, as a linear combination of a set of two-dimensional linear basis functions smoothed with bi-cubic spline interpolation. The coefficients of the basis functions in the linear combination are obtained from the local extrema of the data using a generalized low-pass filter. By taking advantage of the principle of finite-element analysis, we develop a fast algorithm for implementation of the EMD. The proposed method provides an effective approach to overcome several challenging difficulties in extending the original one-dimensional EMD to the two-dimensional EMD. Numerical experiments using both simulated and practical texture images show that the proposed method works well.

ACCURATE NONLINEAR REGISTRATION FOR TWO-DIMENSIONAL GEL ELECTROPHORESIS IMAGES

2013 ◽  
Vol 21 (03) ◽  
pp. 1350020
Author(s):  
HUA-MEI XIN ◽  
YUEMIN ZHU
Keyword(s):  
Thin Plate ◽  
Gel Electrophoresis ◽  
Protein Identification ◽  
Distance Measure ◽  
Spline Interpolation ◽  
Thin Plate Spline ◽  
Two Dimensional ◽  
Registration Accuracy ◽  
Two Dimensional Gel Electrophoresis ◽  
Nonlinear Registration

Two-dimensional gel electrophoresis (2DGE) images are an important support for the analysis of proteins in proteomics. The registration of 2DGE images is considered as one of key elements in protein identification while it is a difficult problem. This paper proposes a new accurate nonlinear registration approach for 2DGE images, based on the exploitation of both spot distance measure and spot intensity. The method consists of three steps: multi-resolution affine registration, spot pairing and thin-plate spline interpolation. The results on both simulated and real gel images show that the proposed method significantly improves registration accuracy in comparison with thin-plate spline registration techniques.

BICUBIC SPLINE INTERPOLATION AS A METHOD FOR TREATMENT OF POTENTIAL FIELD DATA

Geophysics ◽  
1969 ◽  
Vol 34 (3) ◽  
pp. 402-423 ◽  
Author(s):  
B. K. Bhattacharyya
Keyword(s):  
Field Data ◽  
Spline Interpolation ◽  
Amplitude Spectrum ◽  
Accurate Method ◽  
Fourier Series Expansion ◽  
Small Scale ◽  
Spline Functions ◽  
Two Dimensional ◽  
Potential Field Data ◽  
Bicubic Spline

A method for the generation of bicubic spline functions is presented in this paper. From this method it becomes apparent that these functions derive their potential strength in accurate and reliable representation of two‐dimensional data by maintaining continuity of the variable and its slope and curvature throughout the area of observation. The results obtained by computing horizontal and vertical derivatives with model and field data illustrate the exceptional accuracy achieved with spline functions. The piecewise cubic polynomial functions expressing observed data analytically in space are used to estimate amplitude and phase spectra of magnetic anomalies. At relatively long wavelengths the amplitude spectrum thus calculated displays remarkable similarity with the true spectrum and is found to be superior to that obtained with two‐dimensional Fourier series expansion. A cubic spline method is also presented for computing values of an observed variable at equispaced points along two orthogonal directions with the help of irregularly distributed data. The interpolation technique applied to field data shows high resolution by maintaining the separation of neighboring anomalies and the small‐scale features. The shapes, peaks, and troughs of both large and small amplitude anomalies are faithfully reproduced. The gradients of the magnetic field do not undergo any appreciable distortion. It can thus be concluded that cubic splines are a reliable and accurate method of interpolation.

Two Dimensional Damage Localization Using the Interpolation Method

2013 ◽  
Vol 569-570 ◽  
pp. 860-867 ◽  
Author(s):  
Maria Pina Limongelli
Keyword(s):  
Interpolation Method ◽  
Spline Interpolation ◽  
Error Function ◽  
Mode Shapes ◽  
Fe Model ◽  
Two Dimensional ◽  
Operational Mode ◽  
Spline Surface ◽  
The Difference ◽  
Definition Of

This paper presents a vibration based procedure for locating reductions of stiffness in two-dimensional structures that can be modeled as plates. This procedure is a generalization to the two-dimensional case of the previously published Interpolation Damage Detection Method (IDDM). The method is based on the definition of a damage sensitive feature in terms of the accuracy of a spline function in interpolating the operational displacement shapes of the structure. These latter are recovered from frequency response functions (FRFs) measured at different locations of the structure during vibrations. At the i-th location, the FRF is calculated through spline interpolation using the FRF’s recorded at the all the instrumented locations but the i-th. For two-dimensional structures a spline surface is defined to interpolate the operational shapes. The accuracy of the spline interpolation is measured by an error function defined as the difference between the measured and interpolated operational mode shapes. At a certain location an increase (statistically meaningful) of the interpolation error, with respect to a reference configuration, points out a localized variation of the operational shapes thus revealing the existence of damage. The two dimensional IDDM algorithm is checked herein through numerical simulations, using the FE model of a plate and modeling local reductions of stiffness through a reduction of the elastic modulus of the material of one or more elements of the model.

Sign in / Sign up

Export Citation Format

Share Document