On Bivariate Interpolatory Mask Symbols, Subdivision and Refinable Functions

Rabarison, Andrianarivo Fabien; Villiers, Johan de

doi:10.1007/978-3-642-16876-5_13

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2012

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“…To circumvent this difficulty, in this paper we follow a different approach motivated by the work of Rabarison and de Villiers [12] on the characterization of interpolatory bivariate mask symbols. The proposed strategy proceeds by splitting the correction symbol m(z 1 , z 2 ) into two components which can be individually characterized as solutions of Bezout-like equations for univariate polynomials with coefficients over an integral domain.…”

Section: Introductionmentioning

confidence: 99%

A constructive algebraic strategy for interpolatory subdivision schemes induced by bivariate box splines

2012

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This paper describes an algebraic construction of bivariate interpolatory subdivision masks induced by three-directional box spline subdivision schemes. Specifically, given a three-directional box spline, we address the problem of defining a corresponding interpolatory subdivision scheme by constructing an appropriate correction mask to convolve with the three-directional box spline mask. The proposed approach is based on the analysis of certain polynomial identities in two variables and leads to interesting new interpolatory bivariate subdivision schemes.

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Section: Introductionmentioning

confidence: 99%