The Body-Centered Cubic (BCC) and Face-Centered Cubic (FCC) lattices have been analytically shown to be more efficient sampling lattices than the traditional Cartesian Cubic (CC) lattice, but there has been no estimate of their visual comparability. Two perceptual studies (each with N = 12 participants) compared the visual quality of images rendered from BCC and FCC lattices to images rendered from the CC lattice. Images were generated from two signals: the commonly used Marschner-Lobb synthetic function and a computed tomography scan of a fish tail. Observers found that BCC and FCC could produce images of comparable visual quality to CC, using 30-35 percent fewer samples. For the images used in our studies, the L(2) error metric shows high correlation with the judgement of human observers. Using the L(2) metric as a proxy, the results of the experiments appear to extend across a wide range of images and parameter choices.

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 lattice. We asked 12 participants to choose the better of two images: one image rendered from data sampled on the CC lattice and one image that is rendered from data sampled on the BCC lattice. We used both synthetic and CT volumetric data, and confirm that the theoretical advantages of BCC sampling carry over to the perceived quality of rendered images. Using 25% to 35% fewer samples, BCC sampled data result in images that exhibit comparable visual quality to their CC counterparts.

We propose a three dimensional multi-resolution scheme to represent volumetric data in resolutions which are powers of two, resolving the rigidity of the commonly used separable Cartesian multi-resolution schemes in 3D that only allow for change of resolution by a power of eight. Through in-depth comparisons with the counterpart resampling solutions on the Cartesian lattice, we demonstrate the superiority of our subsampling scheme. We derive and document the Fourier domain analysis of this representation. Using such an analysis one can obtain ideal and discrete multidimensional filters for this multi-resolution scheme.