An Evaluation of Prefiltered B-Spline Reconstruction for Quasi-Interpolation on the Body-Centered Cubic Lattice

Balázs Csébfalvi

Department of Control Engineering and Information Technology

Budapest University of Technology and Economics  

 

Interpolating Prefiltered Quintic Box-Spline Reconstruction Quasi-Interpolating Prefiltered Cubic B-Spline Reconstruction

Abstract:

In this paper, we demonstrate that quasi-interpolation of orders two and four can be efficiently implemented on the Body-Centered Cubic (BCC) lattice by using tensor-product B-splines combined with appropriate discrete prefilters. Unlike the non-separable box-spline reconstruction previously proposed for the BCC lattice, the prefiltered B-spline reconstruction can utilize the fast trilinear texture-fetching capability of the recent graphics cards. Therefore, it can be applied for rendering BCC-sampled volumetric data interactively. Furthermore, we show that a separable B-spline filter can suppress the postaliasing effect much more isotropically than a non-separable box-spline filter of the same approximation power. Although prefilters that make the B-splines interpolating on the BCC lattice do not exist, we demonstrate that quasi-interpolating prefiltered linear and cubic B-spline reconstructions can still provide similar or higher image quality than the interpolating linear box-spline and prefiltered quintic box-spline reconstructions respectively.

Keywords:

Filtering, Sampling, Volume Visualization.

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