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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 [8].

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Supplemental Material
Citation
Category
Paper in Conference Proceedings or in Workshop Proceedings (Full Paper in Proceedings)
Event Title
IEEE Visualization (VIS) 2006
Divisions
Visualization and Data Analysis
Subjects
Computergraphik
Event Location
Baltimore, Maryland
Event Type
Conference
Event Dates
Oct 29 - Nov 3
Date
October 2006
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