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Help prepare sci.image.processing FAQ on FFTs

Edward J. Huff huff at mcclb0.med.nyu.edu
Wed Jun 10 23:36:40 EST 1992

sci.image.processing (you have voted, haven't you?) will have a
number of FAQ (answers to frequently asked questions) postings.  Further
details will be available in files accessible by FTP, gopher, and WAIS
from an archive site.

The end result should be a free online textbook of image processing.
I expect that the authors should retain the copyright, granting
license for unlimited electronic but limited printed copies.
(Generally, postings to USENET are considered to be in the public
domain, but if you attach a copyright notice, you retain some rights.
I imagine that posting to USENET implicitly grants license for
unlimited electronic copies).

One of the FAQs will cover Finite Fourier Transforms in great detail.
This is a call for contributions to that file.  Since 
sci.image.processing doesn't exist yet, please follow up to sci.optics,
and also, please mail your posting to image-proc at oce.orst.edu.

Here are some possible questions.  No doubt we need more.

What does FFT stand for?

Contrast an FFT with a continuous Fourier Transform.

What other related transforms are there?

What does the imaginary part of the FFT mean?

What is the difference between the forward and reverse transforms?

Contrast spatial frequency with ordinary (time) frequency.

Give examples of aliasing.  List some other pitfalls of FFT's.

Contrast one, two, and three dimensional FFT's.

What is a four dimensional FFT?

Show images and their 2D FFT's.  Predict what will happen
if certain parts of the 2D FFT are attenuated.  This would
be a good place for an interactive program, where the student
gets to erase the parts and see what the results are.

Conversely, given input and output images, take the FFT of
the input, erase the appropriate spikes in the transform,
and take the inverse FFT to produce the output.

What is the effect of rotating an image before taking the 2D FFT?
What is the effect of rotating the FFT before taking the inverse?

What happens if the image is not "flat," i.e. the intensity around the
edges is not constant?

Where can I get source code for FFT algorithms in Fortran,
Pascal, C, 680x0 assember, 80x86 assembler, TI DSP assembler,
ATT DSP assembler, etc.?  (I would hope to collect public domain
copies of all of these in one place.  The code can't be THAT big.)

Which image processing packages have (or do not have) FFT facilities?

Are any of the transform algorithms encumbered with patents?  If
so, please provide the text of the patents.

What is convolution?  What is deconvolution?  Does the definition
depend on the number of dimensions?

Explain the convolution theorm.  Why should multiplication in
the frequency domain correspond to convolution in the space or
time domain?  Why should division in the frequency domain
correspond to deconvolution?

Give a bibliography.  This is one area which needs to be kept up-to-date.

If you can't find the sci.image.processing CFV, I will gladly mail
you a copy.

Edward J. Huff   huff at mcclb0.med.nyu.edu   (212)998-8465
Keck Laboratory for Biomolecular Imaging
NYU Chemistry Deptartment, 31 Washington Place, New York NY 10003

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