Calibration of the Marschner-Lobb Signal on CC, BCC, and FCC Lattices

The well-known Marschner-Lobb (ML) signal has been originally proposed for visually comparing 3D resampling filters applied on the traditional Cartesian Cubic (CC) lattice. Recently, this popular benchmark is also used for evaluating reconstruction schemes designed for the optimal Body-Centered Cubic (BCC) lattice and the suboptimal Face-Centered Cubic (FCC) lattice. Nevertheless, to the best of our knowledge, it has not been thoroughly studied whether the ML signal meets the assumptions that the theory of optimal regular volume sampling is based on. In this paper, we try to find equivalent CC, BCC, and FCC representations for unbiased comparisons. For the continuous reconstruction, we use comparable approximations of the ideal low-pass filter, and increase the sampling frequency until the aliasing effects completely vanish. Based on these experiments, we show that the ML signal is appropriate for comparing the CC and BCC lattices, but it is inappropriate for fairly comparing the FCC lattice to the CC and BCC lattices regarding the visual quality of the corresponding reconstructions. In fact, the ML signal very strongly prefers the FCC sampling due to the special shape of its spectrum. However, this property can hardly be expected from a general signal.