Posted by
Joachim Wesner on
Nov 16, 2009; 2:27pm
URL: http://imagej.273.s1.nabble.com/downsampling-methods-tp3690444p3690450.html
>In the context of image processing, downsampling usually refers to
>collecting the integral of that function which is in any case a
>Gaussian.
Honestly I do not see this point, why it has to be a gaussian "in any
case"!
To be exact, even in theory, a Gaussian is not bandlimited at all, because
it extends
ti +/- inf both in real space and FT (whis is also a gaussian, as we all
know)
However, to unite all the arguments in this discussion a bit, clearly any
"reasonable"
downsampling does not mean to sample the input data in coarse steps and try
to generate a "best approximation" from those limited data alone (in some
cases this might
even be the task, too), but should try to take ALL ("high-res") input data
into account to
come up with a "best" low-res equivalent.
This approach has to assume that the input data are no longer aliased wrt
their resolution
(which might also not be the cases in some circumstances, but even more
"downsampling" cannot
really solve this), but the aliasing wrt the new sample spacing has to be
taken into account.
This might (in principle) happen within an extra "prefiltering step", but
can be combined
with the "downsampling" itself, be it in real space ("true", limited
comvolution) or in fourier
space.
Joachim Wesner
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