Model selection for the Dubuc-Deslauriers family of subdivision schemes

Mustafa, Ghulam; Ivrissimtzis, Ioannis; Cripps, Robert J.; Mullineux, Glen; Sabin, Malcolm A.

Abstract

We propose two methods for model selection for the DubucDeslauriers family of subdivision schemes. In particular, we study model selection under the statistical method of cross-validation and the geometric method of minimizing the absolute discrete total curvature. Our results show that schemes with large support and arity can be better models of noisy data. Our findings give a justification to the continuing research on large support and large arity schemes, even though currently such schemes are rarely used in practice.

Citation

Mustafa, G., Ivrissimtzis, I., Cripps, R. J., Mullineux, G., & Sabin, M. A. (2013). Model selection for the Dubuc-Deslauriers family of subdivision schemes. In Mathematics of surfaces - XIV. The proceedings of a conference on the Mathematics of Surfaces, organised by the Institute of Mathematics and its Applications held at the University of Birmingham in September 2013 (155-162)

• Conference Name: 14th IMA Conference on Mathematics of Surfaces
• Conference Location: Birmingham, England
• Start Date: Sep 11, 2013
• End Date: Sep 13, 2013
• Acceptance Date: Jun 11, 2013
• Publication Date: Sep 13, 2013
• Deposit Date: May 5, 2016
• Publisher: Institute of Mathematics and its Applications
• Pages: 155-162
• Book Title: Mathematics of surfaces - XIV. The proceedings of a conference on the Mathematics of Surfaces, organised by the Institute of Mathematics and its Applications held at the University of Birmingham in September 2013.
• Publisher URL: http://www.ima.org.uk/conferences/conferences_calendar/14th_mathematics_of_surfaces.cfm.html
• Related Public URLs: https://www.researchgate.net/profile/Ghulam_Mustafa15/publication/262179373_Model_selection_for_the_Dubuc-Deslauriers_family_of_subdivision_schemes/links/00b7d536d0f964247d000000.pdf
• Additional Information: Conference date: Wednesday 11 - Friday 13 September 2013