[Insight-users] FFT Confusion

[Bill Lorensen]

Gaëtan ,

I suggest submitting this and associated tests to gerrit.

Bill

2011/1/25 Gaëtan Lehmann <gaetan.lehmann at jouy.inra.fr>:
>
> 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)
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> _____________________________________
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>
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>