Cosine-Weighted B-Spline Interpolation: A Fast and High-Quality Reconstruction Scheme for the Body-Centered Cubic Lattice

Abstract

In this paper, Cosine-Weighted B-spline (CWB) filters are proposed for interpolation on the optimal Body-Centered Cubic (BCC) lattice. We demonstrate that our CWB filters can well exploit the fast trilinear texture-fetching capability of modern GPUs, and outperform the state-of-the-art box-spline filters not just in terms of efficiency, but in terms of visual quality and numerical accuracy as well. Furthermore, we rigorously show that the CWB filters are better tailored to the BCC lattice than the previously proposed quasi-interpolating BCC B-spline filters, because they form a Riesz basis; exactly reproduce the original signal at the lattice points; but still provide the same approximation order.

Towards an Unbiased Comparison of CC, BCC, and FCC Lattices in Terms of Prealiasing

“…Here the major goal is to demonstrate the superior potential of the BCC and FCC volume representations themselves regardless of the increased complexity of non‐separable reconstruction filters. In contrast, papers belonging to the second category aim at efficient GPU implementations that can utilize the theoretical advantages in practice [CH06, FEVDVM10, DC10, DC11, Csé13]. This paper clearly corresponds to the first category.…”

“…However, we think that our results should certainly be taken into account when in future works practical non‐Cartesian reconstruction schemes are proposed, analyzed, or compared to Cartesian reconstruction schemes in terms of numerical accuracy and visual quality. Recently, promising reconstruction techniques [FEVDVM10, DC11, Csé13] have been published that provide just slightly worse performance compared to that of the most popular CC‐based techniques. Nevertheless, to decide between CC, BCC, and FCC representations not just the rendering speed counts but also numerical and visual quality, which in our opinion should be compared as fairly as possible.…”

“…Therefore, the aliasing spectra also contribute to the reconstructed signal causing postaliasing effects [ML94]. In the literature on volume visualization, the design of filters that minimize the postaliasing artifacts to achieve high image quality is a core topic [ML94, EM06, Csé08b, CD09, Csé10, CD10, Csé13]. One might argue that the reduction of the prealiasing is not a visualization problem and it is more related to data acquisition or tomographic reconstruction, since in the visualization stage it is already too late to do anything against prealiasing.…”

Cosine‐Weighted B‐Spline Interpolation on the Face‐Centered Cubic Lattice

“…In this paper, we generalize Cosine-Weighted triLinear B-spline (CWLB) interpolation [Csé13] to the FCC lattice. Our method can be implemented on the GPU as efficiently as the previously proposed interleaved trilinear interpolation [QEE * 05] and provides the same approximation order.…”

Compactly Supported Biorthogonal Wavelet Bases on the Body Centered Cubic Lattice

“…Kim presented a quartic box spline with even smaller support but the same smoothness as the quintic box spline, as well as a tensor product style box spline (with larger support but reasonable evaluation speed due to the structure of the spline) [Kim13]. There are also DC‐splines [DC10, Csé13, AO15], which attempt to bring the advantages of tri‐linear interpolation to the BCC lattice; we suspect these are not a new family of splines, but rather a sub‐family of the exponential box splines [Ron88].…”