Quincunx fundamental refinable functions in arbitrary dimensions

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Article number20
Journal / PublicationAxioms
Volume6
Issue number3
Online published6 Jul 2017
Publication statusPublished - Sep 2017

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Abstract

In this paper, we generalize the family of Deslauriers–Dubuc’s interpolatory masks from dimension one to arbitrary dimensions with respect to the quincunx dilation matrices, thereby providing a family of quincunx fundamental refinable functions in arbitrary dimensions. We show that a family of unique quincunx interpolatory masks exists and such a family of masks is of real value and has the full-axis symmetry property. In dimension , we give the explicit form of such unique quincunx interpolatory masks, which implies the nonnegativity property of such a family of masks.

Research Area(s)

  • Checkerboard lattice, Full-axis symmetry, Fundamental refinable functions, Interpolatory masks, Interpolatory subdivision schemes, Nonnegative masks, Quincunx lattice, Sum rule

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