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We introduce and analyze an efficient reconstruction algorithm for FCC-sampled data. The reconstruction is based on the 6-direction box spline that is naturally associated with the FCC lattice and shares the continuity and approximation order of the triquadratic B-spline. We observe less aliasing for generic level sets and derive special techniques to… (More)

In this paper we derive piecewise linear and piecewise cubic box spline reconstruction filters for data sampled on the body centered cubic (BCC) lattice. We analytically derive a time domain representation of these reconstruction filters and using the Fourier slice-projection theorem we derive their frequency responses. The quality of these filters, when… (More)

We introduce a family of box splines for efficient, accurate and smooth reconstruction of volumetric data sampled on the Body Centered Cubic (BCC) lattice, which is the favorable volumetric sampling pattern due to its optimal spectral sphere packing property. First, we construct a box spline based on the four principal directions of the BCC lattice that… (More)

The work presented here describes two methods to incorporate viable illumination models into Fourier Volume Rendering (FVR). The lack of adequate illumination has been one of the impediments for the wide spread acceptance of FVR. Our first method adapts the Gamma Corrected Hemispherical Shading (GCHS) proposed by Scoggins et al. [11] for FVR. We achieve… (More)

In this paper, we propose an interlaced multi-shell sampling scheme for the reconstruction of the diffusion propagator from diffusion weighted magnetic resonance imaging (DW-MRI). In standard multi-shell sampling schemes, sample points are uniformly distributed on several spherical shells in q-space. The distribution of sample points is the same for all… (More)

—We introduce a framework for construction of non-separable multivariate splines that are geometrically tailored for general sampling lattices. Voronoi splines are B-spline-like elements that inherit the geometry of a sampling lattice from its Voronoi cell and generate a lattice-shift-invariant spline space for approximation in. The spline spaces associated… (More)

We demonstrate that non-separable box splines deployed on body centered cubic lattices (BCC) are suitable for fast evaluation on present graphics hardware. Therefore, we develop the linear and quintic box splines using a piecewise polynomial (pp)-form as opposed to their currently known basis (B)-form. The pp-form lends itself to efficient evaluation… (More)

In this article we propose a box spline and its variants for reconstructing volumetric data sampled on the Cartesian lattice. In particular we present a tri-variate box spline reconstruction kernel that is superior to tensor product reconstruction schemes in terms of recovering the proper Cartesian spectrum of the underlying function. This box spline… (More)

This paper presents a user study of the visual quality of an imaging pipeline employing the optimal body-centered cubic (BCC) sampling lattice. We provide perceptual evidence supporting the theoretical expectation that sampling and reconstruction on the BCC lattice offer superior imaging quality over the traditionally popular Cartesian cubic (CC) sampling… (More)