[Numpy-discussion] nd_image.affine_transform edge effects

[James Turner]

PS... (sorry for all the posts, for anyone who isn't interested...)

> Agreed, it looks like aliasing. Nevertheless, any resampling
> procedure is supposed to deal with this internally, right? Either by
> lowpass filtering (traditional case), or by spline fitting (spline
> case as described by Unser and understood by me) -- it shouldn't be
> letting aliasing bubble through, correct?

In the general case, I don't think it is appropriate for the resampling
procedure to use low-pass filtering internally to avoid artefacts,
except perhaps when downsampling. It probably makes sense for computer
graphics work, but there are cases where the input data are band
limited to begin with and any degradation in resolution is unacceptable.
Where needed, I think low-pass filtering should either be the
responsibility of the main program or an option. It's not even possible
for the resampling procedure to prevent artefacts in every case, since
the aliasing in a badly undersampled image cannot be removed post
factum (this is for undersampled photos rather than artificial graphics,
which I think are fundamentally different because everything is defined
on the grid, although I haven't sat down and proved it mathematically).
I'm also not sure how the procedure could decide on the level of
smoothing needed for a given dataset without external information.

Of course intermediate-order splines will probably keep everyone happy,
being reasonably robust against ringing effects without causing much
smoothing or interpolation error :-).

By the way, I think you and Stefan might be interested in a medical
imaging paper by Lehmann et al. (1999), which gives a very nice overview
of the properties of different interpolation kernels:

http://ieeexplore.ieee.org/Xplore/login.jsp?url=/iel5/42/17698/00816070.pdf?arnumber=816070

For what it's worth, I'd agree with both of you that the numeric
overflow should be documented if not fixed. It sounds like Stefan has
figured out a solution for it though. If you make sense of the code in
"ni_interpolation.c", Stefan, I'd be very interested in how to make it
calculate one less value at the edges :-).

Cheers,

James.