[Numpy-discussion] nd_image.affine_transform edge effects

[James Turner]

Hi Zach,

 > Based on my reading of the two excellent Unser papers (both the one
 > that ndimage's spline code is based on, and the one that Travis
 > linked to), it seems like a major point of using splines for
 > interpolation is *better* behavior in the case of non-band-limited
 > data than the traditional 'anti-aliasing [e.g. lowpass] filter' +
 > 'resampling' + 'reconstruction [e.g. lowpass] filter' procedure.

It's certainly true that intermediate-order spline interpolants will
cause less ringing than an "ideal" sinc function. So their behaviour
is better for non-band-limited data than applying simplistic formulae
derived from the Sampling Theorem. This fact would help you out if
you don't use a low-pass filter. However, I wouldn't go as far as to
say that splines *replace* some form of low-pass filtering. I haven't
read Unser's papers in much detail, though (at least not recently)
and my applications are different from yours; it may depend exactly
what you're trying to do.

 > So it seems that something is wrong if the spline interpolation
 > tools in ndimage only work properly in the band-limited case, or
 > require lowpass filtering.

It depends what you mean by working properly -- but in this case it
does look like something is wrong and that you figured it out in your
next post :-).

James.