Aliasing properties of voxels in three-dimensional sampling lattices

Abstract

It is well-known that band limited functions can be represented more efficiently on the body centered cubic (bcc) and face centered cubic (fcc) lattices than on the standard cartesian (cubic) lattice. We examine sampling properties of these lattices for non band-limited functions and see that, with respect to preserving the energy of the sampled function, the bcc and fcc lattices perform better than the cubic lattice for a given sampling density, indicating that sampling on these lattices will produce less aliasing errors. We study the aliasing errors within a cross section of a three dimensional, rotational invariant pattern through the origin and how these errors depend on the normal of the cross section. The results are in line with the theory, showing that the bcc and fcc lattices have superior sampling qualities with respect to aliasing errors. © 2012 Springer-Verlag.