[Insight-users] (Fast) Fourier Filters

[Luis Ibanez]

Hi Bjorn,

1) We don't have an FFT filter in ITK yet.
       The element for creating one are all there though.

       VNL (the mathematical library used in ITK) provides
       a ready to use fft function for 1D:
       http://www.itk.org/Insight/Doxygen/html/classvnl__fft1d.html

       So, an easy implementation could be done by using the
       same infrastructure of the RecursiveSeparableImageFilter
       because it is a separable filter applied line by line,
       which is the same approach required for an FFT.
http://www.itk.org/Insight/Doxygen/html/classitk_1_1RecursiveSeparableImageFilter.html

       However, FFT requires some additional machinery,
       and brings up some design issues, for example:
       The output of an FFT is an image whose pixels
       are complex and could be represented by:

       1.1) ITK images are templated over pixel type
            so we can easily create itk::Image< complex<float>,3>
       1.2) An alternative representation is to produce two
            escalar images with real and imaginary parts.
       1.3) yet another approach is to produce two escalar
            images with magnitude and phase.

       We could probably take 1.1, that is,  using native
       complex images and adress 1.2 and 1.3 by using ImageAdaptors
       and ImageFilters. ImageAdaptors will easily allow to access
       the real or imaginary part of a complex image as it the image
       were has a scalar component. See for example the use of Adaptors
       in RGB images for getting access to one of the channels:

       Insight/Testing/Code/Common/itkImageAdaptorTest.cxx

       Filters for extracting {real/imaginary/magnitud/phase} from
       complex pixels can be easile implemented using the
       UnaryFunctorImageFilter:

       Insight/Code/BasicFilters/itkUnaryFunctorImageFilter.h

       It is enough to add a Functor class defining how the input
       complex pixel should be converted into an output scalar value.
       See for example:

       Insight/Code/BasicFilters/itkSinImageFilter.h



2) An FFT is maybe not what you need. According to
     your email, you want to smooth a binary image and
     remove holes an peaks.

        2.1) This sounds like a good match for Mathematical
        Morphology operators. A sequence of erosion and dilation
        (also known as an openning or closing operation depending
        on how you defined your object and background on the
        binary image). The available filters are described in:
http://www.itk.org/Insight/Doxygen/html/group__MathematicalMorphologyImageFilters.html

        Note that some of them are GrayScale, so you can apply them
        before thresholding your output (although in theory,
        thresholding and erosion/dilation are commutative operators).

        These filters use a clever approach involving the Neighborhood
        operators designed and implemented by Josh Cates at Utah.
        The median filter also use neighborhood operators but requires
        less computations per neighborhood than the Median filter.


        2.2) You may also take advantage of the recently
        added filter:
        http://www.itk.org/HTML/AntiAliasBinaryImageFilterExample.html

http://www.itk.org/Insight/Doxygen/html/classitk_1_1AntiAliasBinaryImageFilter.html

        but Morphological Operators will probably give you a better
        performance.




Please let us know if you find an acceptable alternative,


       Thanks

         Luis


=========================================

Bjorn Hanch Sollie wrote:
    > Is there a fourier-filter implemented in ITK?  I was looking for it
    > but I didn't find anything.  Are there any recommended ways of
    > implementing it if it's not already there?
    >
    > I have performed some fast march and level set segmentation, and the
    > results so far look very promising!  However, I need to smooth the
    > binary output images I get in order to remove small "holes" inside the
    > segmented region and sharp peaks and gaps along the edges.  A median
    > filter does this very very well, practically to the point of being
    > ideal for the purpose, but it takes a bit (too) long to run,
    > unfortunately.  A gaussian, for example, doesn't perform nearly as
    > well.
    >
    > Aside from medians and fouriers, are there any other filters in ITK
    > that are particularly suited for such a task?
    >
    > Finally, a big thanks goes to Luis Ibanez and everyone else on this
    > list who have patiently answered my questions (you know who you are).
    > I wouldn't have made it this far without your help.
    >
    > -Bjorn
    >