Three-dimensional lateral prediction has two important advantages over two-dimensional prediction. The first is that, in a 3-dimensional volume, any output sample is close to more samples in the input than in the 2-dimensional case. Having more nearby samples allows better random noise attenuation. Second, the assumption that events are linear within a 2-dimensional window or 3-dimensional sub-volume 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 3-dimensional filter.
Prediction over a 3-dimensional volume can be done with two passes of a 2-dimensional process or with a true 3-dimensional technique. Since two passes of either the t-x or f-x 2-dimensional techniques do not allow processors to take full advantage of the opportunities 3-dimensional data presents, I have extended the 2-dimensional techniques to true 3-dimensional techniques using 3-dimensional filters.