Scattered data fitting by minimal surface

2017 ◽  
Vol 25 (3) ◽  
Author(s):  
Yong-Xia Hao ◽  
Dianchen Lu
Keyword(s):  
Tikhonov Regularization ◽  
Numerical Experiments ◽  
Data Fitting ◽  
Scattered Data ◽  
B Spline ◽  
Scattered Data Fitting ◽  
Area Minimization ◽  
Regularization Parameters ◽  
The Given ◽  
Minimal Area

AbstractThe goal of this paper is to develop a computational model for obtaining the fitting surface to the given scattered data with minimal area. The basic idea of the model is to utilize the B-spline and area minimization. The model is turned into a Tikhonov regularization model finally. By choosing the regularization parameters with the L-curve criterion and the GCV method, respectively, numerical experiments indicate that the model can provide an acceptable compromise between the minimization of the data mismatch term and the area of the surface.

scholarly journals N-D $C^k$ B-Spline Scattered Data Approximation

2005 ◽  
Author(s):  
Nicholas J. Tustison ◽  
James Gee
Keyword(s):  
Function Class ◽  
Data Fitting ◽  
Scattered Data ◽  
Scattered Data Approximation ◽  
Data Approximation ◽  
B Spline ◽  
B Splines ◽  
Scattered Data Fitting ◽  
Spline Surface ◽  
Ill Conditioning

Since the 1970’s B-splines have evolved to become the {} standard for curve and surface representation due to many of their salient properties. Conventional least-squares scattered data fitting techniques for B-splines require the inversion of potentially large matrices. This is time-consuming as well as susceptible to ill-conditioning which leads to undesired results. Lee {} proposed a novel B-spline algorithm for fitting a 2-D cubic B-spline surface to scattered data in . The proposed algorithm utilizes an optional multilevel approach for better fitting results. We generalize this technique to support N-dimensional data fitting as well as arbitrary degree of B-spline. In addition, we generalize the B-spline kernel function class to accommodate this new image filter.

Scattered data fitting with simplex splines in two and three dimensional spaces

1997 ◽  
Vol 13 (7) ◽  
pp. 295-315 ◽  
Author(s):  
Jingfang Zhou ◽  
Nicholas M. Patrikalakis ◽  
Seamus T. Tuohy ◽  
Xiuzi Ye
Keyword(s):  
Three Dimensional ◽  
Data Fitting ◽  
Scattered Data ◽  
Scattered Data Fitting ◽  
Simplex Splines

Scattered data fitting of Hermite type by a weighted meshless method

2017 ◽  
Vol 44 (3) ◽  
pp. 673-691 ◽  
Author(s):  
M. Esmaeilbeigi ◽  
O. Chatrabgoun ◽  
M. Shafa
Keyword(s):  
Meshless Method ◽  
Data Fitting ◽  
Scattered Data ◽  
Scattered Data Fitting
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