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

[C.Cagatay Bilgin]

Your question is actually independent of the ITK
usage. Convolution in time domain corresponds
to multiplication in frequency domain, so gaussian
filtering your image is actually multiplying the FFT
of your image with the FFT of the gaussian filter you
used (you might need some padding as most probably
your gaussian filter is was smaller than your image).

If you want to clean up your image a little, I would say
do not go to FFT just do it in time domain using the
gaussian filters provided in the toolkit as you will
need less number of lines of code.

By the way, is the Insight-Book are you referring
the software manual or something else ?

Regards,
----------------------------------------------------------------------------
Cemal Cagatay Bilgin,
Ph.D Candidate in Computer Science Department at RPI
bilgic at cs.rpi.edu - http://www.cs.rpi.edu/~bilgic
Lally 01A, 110 8th Street Troy, NY 12180-3590, USA.
Tel: (518) 276-8489, Fax:(518) 276-4033

On Nov 12, 2009, at 10:46 AM, Roman Grothausmann 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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