Three-dimensional lateral prediction has two important advantages over two-dimensional prediction. The first is that, in a three-dimensional volume, any output sample is close to more samples in the input than in the two-dimensional case. Having more nearby samples allows better random noise attenuation. Second, the assumption that events are linear within a two-dimensional window or three-dimensional subvolume can be relaxed. As pointed out by Chase 1992 and Gulunay et.al. 1993, events that are nonlinear in one direction but linear in another are predicted exactly with a three-dimensional filter.
Prediction over a three-dimensional volume can be done with two passes of a two-dimensional process or with a true three-dimensional technique. Since two passes of either two-dimensional technique does not allow processors to take full advantage of the opportunities three-dimensional data presents, we have extended the two-dimensional techniques to true three-dimensional techniques using three-dimensional filters.