[Insight-users] equivalence of Gaussian and low-pass-FFT

[Kishore Mosaliganti]

If your low pass filter in the frequency domain is a Gaussian, then it
is equivalent to Gaussian filtering in the time domain as well. The
two Gaussian sigmas are related in an inverse relationship, if I
remember correctly.

However, there are a variety of window shapes for low pass filters
that may not be a Gaussian and in that case, you only get a similar
result to time-domain Gaussian filtering.

In other words, Gaussian filtering in the time-domain is a special
case of low-pass filtering (LPF). LPF can be done in the frequency
domain using FFT methods for which you need to specify the windowing
used.

ITK does Gaussian filtering in the time-domain and it is easily
accessible, so I recommend that.

Kishore


On Thu, Nov 12, 2009 at 10:46 AM, Roman Grothausmann
<roman.grothausmann at helmholtz-berlin.de> wrote:
> Dear mailing list members,
>
>
> This problem really bugs me after reading in the Insight-Book:
> - Is the result of applying a Gaussian filter the same as the result of a
> low-pass-FFT-filtering?
> - Or is it only similar (not equivalent) in discrete space?
> - What is the better choice?
> - Is there a relation between the kernel size of the Gaussian and the
> low-pass frequency? (If so, is the relation known?)
>
> Any comments are very much appreciated
> Roman
>
> --
> Roman Grothausmann
>
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