Generalized n-D C k B-Spline Scattered Data Approximation with Confidence Values

2006 ◽  
pp. 76-83 ◽  
Author(s):  
Nicholas J. Tustison ◽  
James C. Gee
Keyword(s):  
Scattered Data ◽  
Scattered Data Approximation ◽  
Data Approximation ◽  
B Spline

Integration of Moving Least Squares Method and Multilevel B-Spline Method for Scattered Data Approximation

2011 ◽  
Vol 291-294 ◽  
pp. 2245-2249
Author(s):  
Shi Ju Yan ◽  
Bin Ge
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Scattered Data ◽  
Moving Least Squares ◽  
Scattered Data Approximation ◽  
Approximation Accuracy ◽  
Data Approximation ◽  
B Spline ◽  
Moving Least Squares Method ◽  
Method Accuracy

For scattered data approximation with multilevel B-spline(MBS) method, accuracy could be enhanced by densifying control lattice. Nevertheless, when control lattice density reaches to some extent, approximation accuracy could not be enhanced further. A strategy based on integration of moving least squares(MLS) and multilevel B-spline(MBS) is presented. Experimental results demonstrate that the presented strategy has higher approximation accuracy.

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.

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