Those are the common resampling modes used in basically every
AFNI program that does resampling, though it seems that none of
them includes much of a description, sorry.

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When resampling is necessary, you essentially have a new point
(at the center of a voxel) that is in the middle of old points,
say. Imagine that point inside a shoe box of 8 surrounding
neighbors (2 in 1-D, 4 in 2-D, 8 in 3-D), or it happens to be
on a corner, side or face of the box, but let's ignore those
cases for now.

So now we have a new point inside a shoe box, and where each of
the 8 corners of the shoe box has an old value. What value
should be assigned to the new point?

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NN (nearest neighbor): the closest of the 8 points is the
nearest neighbor. The new point gets that value. There is
no actual interpolation.

Li (linear): the new value gets a linear combination of the
neighbors, weighted by 1 minus the fractional distance along
each of the axes.

Cu (cubic): similar to Li, but apply a cubic field along each
axis (which means using second neighbors, not just the 8 in
the original bounding box).

Bk (block): between NN and Li, this is heavily weighted toward
the boundries of the shoe box, i.e. even approaching one side
makes the values at the other side almost irrelevant.

Higher order polynomial interpolation is akin to cubic, and
applies neighbors from even farther away.

There is also Fourier interpolation, which is different enough
to leave out of the discussion at this point.

Does that help?

- rick