Statistical and Geometrical Way of Model Selectionfor a Family of Subdivision Schemes

The objective of this article is to introduce a generalizedalgorithm to produce the $m$-point $n$-ary approximating subdivisionschemes (for any integer $m, ngeq 2).$ The proposed algorithm hasbeen derived from uniform B-spline blending functions. Inparticular, we study statistical and geometrical/traditional methodsfor the model selection and assessment for selecting a subdivisioncurve from the proposed family of schemes to model noisy and noisyfree data. Moreover, we also discuss the deviation of subdivisioncurves generated by proposed family of schemes from convex polygonalcurve. Furthermore, visual performances of the schemes have beenpresented to compare numerically the Gibbs oscillations with theexisting family of schemes.