3D frequency-domain analysis of non-separable reconstruction schemes by using direct volume rendering

Recently, it has been demonstrated that the optimality of the Body-Centered Cubic (BCC) lattice can be utilized also in practice by using either non-separable box-spline filters or tensor-product B-spline filters for reconstructing an originally continuous signal from its discrete BCC-sampled representation. In order to study the frequency-domain behavior of these filters, a 3D analysis of their frequency responses is required. In this paper, we show that direct volume rendering offers a natural tool for such a 3D analysis. As the frequency responses are analytically known, their characteristic isosurfaces can be rendered separately in the pass band and in the stop band. The visualization of the frequency responses conveys information not just on the absolute postaliasing and oversmoothing effects, but also on their direction dependence. In this sense, the frequency-domain behavior of the non-separable box splines and the tensor-product B-splines on the BCC lattice is evaluated for the first time in this paper. Furthermore, we also analyze how the frequency responses are influenced by a discrete prefiltering, which is necessary to fully exploit the approximation power of the higherorder box-spline and B-spline filters.