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.

- The three-dimensional extension of t-x prediction
- The three-dimensional extension of f-x prediction
- Examples of three-dimensional lateral prediction

2/9/2001