Interpolatory Subdivision Schemes Induced by Box Splines

✍ Scribed by Rong-Qing Jia

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 77 KB
• Volume: 8
• Category: Article
• ISSN: 1063-5203
• DOI: 10.1006/acha.1999.0287

✦ Synopsis

This paper is devoted to a study of interpolatory refinable functions. If a refinable function φ on R s is continuous and fundamental, i.e., φ(0) = 1 and φ(α) = 0 for α ∈ Z s {0}, then its corresponding mask b satisfies b(0) = 1 and b(2α) = 0 for all α ∈ Z s {0}. Such a refinement mask is called an interpolatory mask. We establish the existence and uniqueness of interpolatory masks which are induced by masks of box splines whose shifts are linearly independent.