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The alternate method that is usually preferable
to looping over input space
is that
our program have a loop over the space of the *outputs,*
and that each output find its input.
The matrix multiply of (2)
can be interpreted this way.
Where the transformation **shrink**s is a small problem.
In that area
many points in the input space are ignored,
where perhaps they should somehow be averaged with their neighbors.
This is not a serious problem unless we are contemplating
iterative transformations back and forth between the spaces.
We will now address interesting questions
about
the reversibility of these deformation transforms.

** Next:** Formal inversion
** Up:** INTERPOLATION AS A MATRIX
** Previous:** Looping over input space
Stanford Exploration Project

12/26/2000