[Insight-users] FFT Confusion

[Gaëtan Lehmann]

Le 25 janv. 11 à 15:28, David Doria a écrit :

>> This is the "normal" FFT -- a real image produces a complex image,  
>> but there is
>> complex conjugate symmetry of the first half of the transform because
>>
>> sin(-x) = - sin(x) (odd)
>> cos(-x) = cos(x)   (even)
>>
>> exp(ix) = cos(x) + isin(x)
>>
>> This complex conjugate symmetry is sometimes called Hermitian  
>> symmetry, but I
>> have been told that is an incorrect term.
>>
>> Regards,
>> Matt
>
> Thanks Matt. Maybe you could explain this in the documentation of the
> class (right now it is basically empty)? (and explain the choice of
> the name of the class too - i.e. why not just VnlFFTImageFilter? ).
>
> Also, should I just use UnaryFunctorImageFilter to compute the complex
> conjugate of the resulting image? I'm surprised not to find a
> ConjugateImageFilter or similar.

David,

You will find one at

   http://mima2.jouy.inra.fr/darcs/contrib-itk/deconv/itkComplexConjugateImageFilter.h

Hopefully this class will be in ITK soon.

Gaëtan


> For a normalized correlation of
> images A and B in the frequency domain, I believe you are supposed to
> do
>
> FFT(A) * conj(FFT(B))
>
> Thanks,
>
> David
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-- 
Gaëtan Lehmann
Biologie du Développement et de la Reproduction
INRA de Jouy-en-Josas (France)
tel: +33 1 34 65 29 66    fax: 01 34 65 29 09
http://voxel.jouy.inra.fr  http://www.itk.org
http://www.mandriva.org  http://www.bepo.fr

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