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| Statistical and Geometrical Way of Model Selectionfor a Family of Subdivision Schemes |
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Citation： |
Ghulam MUSTAFA.Statistical and Geometrical Way of Model Selectionfor a Family of Subdivision Schemes[J].Chinese Annals of Mathematics B,2017,38(5):1077~1092 |
| Page view： 2962
Net amount： 1317 |
Authors： |
Ghulam MUSTAFA; |
Foundation： |
This work was supported by the National Research Program
for Universities (No.3183). |
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| Abstract： |
The objective of this article is to introduce a generalized
algorithm to produce the $m$-point $n$-ary approximating subdivision
schemes (for any integer $m, n\geq 2).$ The proposed algorithm has
been derived from uniform B-spline blending functions. In
particular, we study statistical and geometrical/traditional methods
for the model selection and assessment for selecting a subdivision
curve from the proposed family of schemes to model noisy and noisy
free data. Moreover, we also discuss the deviation of subdivision
curves generated by proposed family of schemes from convex polygonal
curve. Furthermore, visual performances of the schemes have been
presented to compare numerically the Gibbs oscillations with the
existing family of schemes. |
Keywords： |
Approximating subdivision schemes, B-spline blending function,
Convex polygon, Statistical and geometrical methods, Model selection
and assessment |
Classification： |
65D17, 65D10, 65D05, 62P30 |
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