Statistical and Geometrical Way of Model Selection for a Family of Subdivision Schemes

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.