Posted by
Stephan Preibisch on
Dec 29, 2008; 5:18pm
URL: http://imagej.273.s1.nabble.com/FFT-filter-conversion-to-real-space-tp3694163p3694166.html
Hi,
maybe this might help you as well. I recently presented my Stitching Tools
at the ImageJ conference, they are Fourier based and compute the
correlation between n-dimensional images.
Have a look here:
http://fly.mpi-cbg.de/~preibisch/software.html#StitchingThere is also a conference paper explaining everything in detail:
http://fly.mpi-cbg.de/~preibisch/pubs/imagejpaper2008.pdfConcerning padding of the images what was discussed as well it turned out
best for us if one extends the images by their mirrored content which is
faded using a exponential function.
Btw, I use an extended version of Dave Hale's 1D FFT. It is by far the
fastest one I have seen under Java, I have the multithreaded ImageJ
version on my website as well:
http://fly.mpi-cbg.de/~preibisch/software.html#FFTAnd if you are interested in polar FFTs, I can suggest you two algorithms
from two different groups which deal with that:
Fast Fourier transforms for nonequispaced data, Potts et. al.
http://www-user.tu-chemnitz.de/~potts/nfft/http://www-user.tu-chemnitz.de/~potts/nfft/polar.phpFast and Accurate Polar Fourier Transform, Averbuch et. al.
http://www.cs.tau.ac.il/~amir1/PS/Polar_Paper_New.pdfhttp://www.math.umn.edu/~focm/c_/Elad.pdfAll the best, hope it helps,
Stephan
> Dear All,
>
> I would like to take the opportunity to ask another question regarding
> Fourier operations. I would like to perform spatiotemporal image
> correlation in the Fourier domain because of speed and memory
> considerations.
> If I understand correctly, convolution of two images (i.e.
> correlation) in the spatial domain, equals mere multiplication of the
> Fourier transformed images in the frequency domain.
> However, when multiplying two FFT images, the resulting images is no
> longer expressed in polar coordinates and therefore cannot be
> transformed back by inverse FFT. I tried FD Math correlate, but this
> operation requires two square images of fixed dimensions and I'm not
> sure if enlarging the canvas size goes without consequences for the
> correlation outcome. I have noticed that the latter operation appears
> to give a similar resulting image whether one uses the original images
> as input or the Fourier transformed.
> Could anybody please share on how to do this the right way?
> Many thanks in advance and best wishes,
>
> Winnok
>
> ps: the archives were unaccesible, so apologies if this is a duplicate
> query.
>