Prefiltered B-Spline Reconstruction for Hardware-Accelerated Rendering of Optimally Sampled Volumetric Data

In this paper odd-order B-spline filters are proposed to reconstruct volumetric data sampled on an optimal Body-Centered Cubic (BCC) grid. To make these filters nearly interpolating, we adapt a previously published framework, which is based on a discrete frequency-domain prefiltering. It is shown that a BCC-sampled B-spline kernel is not invertible, therefore the interpolation constraint cannot be satisfied by a discrete prefiltering. To remedy this problem, we use a slightly modified discrete Bspline for prefiltering, which is proven to be invertible. Although this modification leads to an approximation, the proposed prefiltered B-spline reconstruction of BCC-sampled data still provides much higher image quality than the interpolating prefiltered B-spline reconstruction of volume data sampled on an equivalent Cartesian Cubic (CC) grid. Furthermore, our method directly supports an efficient implementation on a conventional graphics hardware, unlike the previous reconstruction methods developed for the BCC grid.