[Insight-users] Re: DFT-2D and 3-D

[Luis Ibanez]

Hi Josiane,

As you probably know, the Fourier Transform of most
images with natural scenes have a very high content
in low frequencies. Therefore the output of the FFT
filter typically looks like a bright spot in the middle
with an exponential decay towards the borders.

It is not rare to use a logarithmic intensity transformation
in order to display the FFT output and still be able to "see"
something.


Please be more specific in your comments.

for example:


1) What images do you find with constant intensity ?
    The output of the FFT ?

    Note that those are Real and Imaginary parts.

    How did you arrived to the conclusion that they
    have contant values ?
    did you generated their histograms ?
    did you just opened them with a naive viewer ?


2) What images are homogeneous ?
    and what you mean by "homogeneous" ?
    do you mean that all the intensities among the
    pixels are very similar ?

    and yet,... the "intensities change" ?



I'm guessing that you are doing something like
running an FFT and then right away running an
inverse FFT. In order to verify if you recover
the same image.

Is that what your are trying to do  ?

If so, beware the you should avoid the conversion
of the FFT output into a integer pixel type since
you will lose a lot of spectral contributions
specially for the high frequencies.


Please give us a better context of what you are
trying to do.



Regards,



     Luis



-------------------------------------------------
Josiane Yankam Njiwa--DEA Clarysse--Fin 11/04 wrote:

> Hi Luis,
> 
> Thanks a lot for your answer, I tested the example that youtalk about.
> Unfortunately, the FFT result images i have seem to me not relevant,
> because :
>           1- If i left the rescale filter you apply on the result, i have 
>  images with constant intensities
>           2- If i don't apply the rescale filter, the images are
> homogeneous,but the image intensities change.
> And I don't understand why,can you give me more explanation about the
> operation of these three filters?
>  "itkVnlFFTRealToComplexConjugateImageFilter.h"
>  "itkComplexToRealImageFilter.h"
> "itkComplexToImaginaryImageFilter.h"
> 
> Thank you for all, Regards.
> 
> Josiane.
> 
> 
> 
> 
> 
>>Hi Josiane,
>>
>>
>>1) Yes, it is possible to do Fast Fourier Transforms (FFT)
>>    with ITK.
>>
>>    Please look at the example
>>
>>          Insight/Examples/Filtering/
>>                              FFTImageFilter.cxx
>>
>>     This was added last week to the CVS repository.
>>
>>
>>
>>2)  For the Inverse FFT please look at last week's email
>>
>>http://www.itk.org/pipermail/insight-users/2004-November/011128.html
>>
>>     In summary, you can get the equivalent of the Inverse
>>     Fourier Transform by running a Direct Fourier Transform
>>     and then flipping the output.
>>
>>
>>
>>3) The behaviour of this filter will be independent of the
>>    image dimension. In other words, you can use it for 1D,
>>    2D, 3D, 4D... etc.
>>
>>
>>
>>Please let us know if you have any further questions,
>>
>>
>>   Thanks
>>
>>
>>
>>      Luis
>>
>>
>>
>>  -----------------------------------------------------
>>Josiane Yankam Njiwa--DEA Clarysse--Fin 11/04 wrote:
>>
>>
>>>Hi every body,
>>>
>>>I have a problem with the Discrete Fourier Transform of images (2D an
>>>3D).
>>>I would like to know if it is possible to compute FFT and inverse FFT
>>>with
>>>itk. I saw the file itkFFTRealToComplexConjugateImageFilter.h,but i
>>>don't
>>>know how it works and i have any explanation. If you can help me, i will
>>>be very glad.
>>>Best Regards.
>>>
>>>Josiane.
>>>
>>>_______________________________________________
>>>Insight-users mailing list
>>>Insight-users at itk.org
>>>http://www.itk.org/mailman/listinfo/insight-users
>>>
>>>
>>
>>
>>
>>
> 
> 
>