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Extensions of the Zwart-Powell Box Spline for Volumetric Data Reconstruction on the Cartesian Lattice
September-October 2006 (vol. 12 no. 5)
pp. 1337-1344
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 $C^2$ 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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Index Terms:
Volumetric data interpolation, reconstruction, box splines
Citation:
Alireza Entezari, Torsten Möller, "Extensions of the Zwart-Powell Box Spline for Volumetric Data Reconstruction on the Cartesian Lattice," IEEE Transactions on Visualization and Computer Graphics, vol. 12, no. 5, pp. 1337-1344, Sept. 2006, doi:10.1109/TVCG.2006.141
