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Statistical and geometrical way of model selection for a family of subdivision schemes

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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 ≥ 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.

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Acknowledgments

The author would like to thank the anonymous referee for his helpful suggestions and comments which have showed the way to improve this work.

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Authors and Affiliations

  1. Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur, 63100, Pakistan

    Ghulam Mustafa

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  1. Ghulam Mustafa
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Correspondence to Ghulam Mustafa.

Additional information

This work was supported by the National Research Program for Universities (No. 3183).

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Mustafa, G. Statistical and geometrical way of model selection for a family of subdivision schemes. Chin. Ann. Math. Ser. B 38, 1077–1092 (2017). https://doi.org/10.1007/s11401-017-1024-6

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  • DOI: https://doi.org/10.1007/s11401-017-1024-6

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