A Quality-Preserving Cartesian to Body-Centered Cubic Downsampling Transform

Abstract

The body-centered cubic lattice is the optimal sampling lattice in three dimensions. However, most volumetric datasets are acquired on the well-known Cartesian cubic lattice. In order to leverage the approximation capabilities of the body-centred cubic lattice, we propose a factor-of-four Cartesian to body-centered downsampling transform. We derive a Fourier domain post-aliasing error kernel and use it to optimize the cosine-weighted trilinear B-spline kernel. We demonstrate that our downsampling transform preserves fidelity when an oversampled function of interest is reconstructed with trilinear interpolation on the fine-scale Cartesian grid, and optimized cosine-weighted trilinear approximation on the coarse-scale body-centered cubic grid.