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

Balázs Csébfalvi, Markus Hadwiger

Department of Control Engineering and Information Technology

Budapest University of Technology and Economics  


linear B-spline cubic B-spline quintic B-spline
Prefiltered B-spline reconstruction from 404040 CC samples.
Prefiltered B-spline reconstruction from 2828282 BCC samples.


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 B-spline 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.


Body-Centered Cubic Grid, Reconstruction, Optimal Regular Volume Sampling, Generalized Interpolation.

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