title: Extensions of the Zwart-Powell box spline for volumetric data reconstruction on the cartesian lattice.
abstract: In this article we propose a box spline and its variants for reconstructing volumetric data sampled on the Cartesian lattice. In particular we present a tri-variate box spline reconstruction kernel that is superior to tensor product reconstruction schemes in terms of recovering the proper Cartesian spectrum of the underlying function. This box spline produces a C2 reconstruction that can be considered as a three dimensional extension of the well known Zwart-Powell element in 2D. While its smoothness and approximation power are equivalent to those of the tri-cubic B-spline, we illustrate the superiority of this reconstruction on functions sampled on the Cartesian lattice and contrast it to tensor product B-splines. Our construction is validated through a Fourier domain analysis of the reconstruction behavior of this box spline. Moreover, we present a stable method for evaluation of this box spline by means of a decomposition. Through a convolution, this decomposition reduces the problem to evaluation of a four directional box spline that we previously published in its explicit closed form.
authors.affiliation: School of Computing Science, Simon Fraser University. aentezar@cs.sfu.ca
authors.forename: Alireza
authors.initials: A
authors.lastname: Entezari
authors.forename: Torsten
authors.initials: T
authors.lastname: Möller
mesh_terms: D003196:Computer Graphics; D003205:Computing Methodologies; D003628:Database Management Systems; D016208:Databases, Factual; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D021621:Imaging, Three-Dimensional / Q000379:methods*; D016247:Information Storage and Retrieval / Q000379:methods*; D009716:Numerical Analysis, Computer-Assisted; D014584:User-Computer Interface