PEF-based texture synthesis can only achieve the results of the Fourier transform
method (Figures 2 and 3) in the limit
, which is unrealistic in practical situations, where *N*_{d} is
very large.
Least squares estimation of the filter in this case is certainly costlier than three
Fast Fourier transforms. On the other hand, if the filter size can be limited
without compromising quality, which is the case for stationary, simply correlated
images, then
the PEF-based method is more flexible. Unlike the Fourier transform
a PEF can be estimated easily when data are missing. Figure 8
shows that the PEF estimated from the incomplete data captures enough features
of the data's spectrum to make a fairly convincing texture synthesis result.
The output of the PEF-based method can be of any size, while the output of a
Fourier transform is generally constrained to be the same size as the input.

4/20/1999