Subsampling models and anti-alias filters for 3-D automultiscopic displays

A new type of three-dimensional (3-D) display recently introduced on the market holds great promise for the future of 3-D visualization, communication, and entertainment. This so-called automultiscopic display can deliver multiple views without glasses, thus allowing a limited "look-around" (correct motion-parallax). Central to this technology is the process of multiplexing several views into a single viewable image. This multiplexing is a complex process involving irregular subsampling of the original views. If not preceded by low-pass filtering, it results in aliasing that leads to texture as well as depth distortions. In order to eliminate this aliasing, we propose to model the multiplexing process with lattices, find their parameters and then design optimal anti-alias filters. To this effect, we use multidimensional sampling theory and basic optimization tools. We derive optimal anti-alias filters for a specific automultiscopic monitor using three models: the orthogonal lattice, the nonorthogonal lattice, and the union of shifted lattices. In the first case, the resulting separable low-pass filter offers significant aliasing reduction that is further improved by hexagonal-passband low-pass filter for the nonorthogonal lattice model. A more accurate model is obtained using union of shifted lattices, but due to the complex nature of repeated spectra, practical filters designed in this case offer no additional improvement. We also describe a practical method to design finite-precision, low-complexity filters that can be implemented using modern graphics cards.