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Quartic Box-Spline Reconstruction on the BCC Lattice
Feb. 2013 (vol. 19 no. 2)
pp. 319-330
Minho Kim, Sch. of Comput. Sci., Univ. of Seoul, Seoul, South Korea
This paper presents an alternative box-spline filter for the body-centered cubic (BCC) lattice, the seven-direction quartic box-spline M7 that has the same approximation order as the eight-direction quintic box-spline M8 but a lower polynomial degree, smaller support, and is computationally more efficient. When applied to reconstruction with quasi-interpolation prefilters, M7 shows less aliasing, which is verified quantitatively by integral filter metrics and frequency error kernels. To visualize and analyze distributional aliasing characteristics, each spectrum is evaluated on the planes and lines with various orientations.
Index Terms:
splines (mathematics),data visualisation,filtering theory,polynomial approximation,signal reconstruction,distributional aliasing characteristics,quartic box-spline reconstruction,BCC lattice,alternative box-spline filter,body-centered cubic lattice,seven-direction quartic box-spline,approximation order,eight-direction quintic box-spline,lower polynomial degree,quasiinterpolation prefilter reconstruction,integral filter metrics,frequency error kernels,Lattices,Spline,Polynomials,Approximation methods,Kernel,Rendering (computer graphics),FCC,quasi-interpolation,Volume reconstruction,BCC lattice,box-spline
Citation:
Minho Kim, "Quartic Box-Spline Reconstruction on the BCC Lattice," IEEE Transactions on Visualization and Computer Graphics, vol. 19, no. 2, pp. 319-330, Feb. 2013, doi:10.1109/TVCG.2012.130
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