Linear Image Filtering via FFT

[H. Gluender]

Dear experts,

just an observation of a slight discrepancy when applying a _binary_
filter function to the Fourier spectrum of an image by using "FFT >
Custom Filter" and "FFT > FFT" > spectral masking > "FFT > Inverse
FFT":

With the former approach more "ringing" is observed - why?

Any ideas?

Best

--


                   Herbie

          ------------------------

          <http://www.gluender.de>

[Joachim Wesner]

Hi,

would you have some example data?

One reason I could think of, is that actually the FFT filtering by Hartley
transform in ImageJ IMHO is a bit "broken by design" (no pun intended), I
tried to
express that problem already superficially in some earlier posts, but not
very specifically, I.e.:

The Hartley transform always assumes that the "initial" and the" final"
domains (after backwards transform) are fully real. This however imposes
certain symmetry restrictions on the FFT domain, i.e. the negative
frequency component must be always the complex conjugate of the positive
frequency one. Yet, in the FFT domain in ImageJ, you can define/draw
arbitrary (binary) filters that violate that constraint. so the inverse
transformed result after applying such a "non-conformant filtering" is
actually complex (has an imag part) and is no longer simply real,

Still, the filter options only will give you back some "real" results
whatever filtering you do, so something must "go wrong" resp. "be lost"
here.
And indeed I see artifacts coming up in the results if you violate that
symmetry condition (I should try to set up an simple example).

Maybe your two different ways of filtering internally use different "flows
of information", so this is the reason for the varying ringing you see.
(However, the artifacts I could generate by FFT filtering and violating the
symmetry were more likely "echos" of the initial structure at
wrong/"mirror" positions, I did not yet put too much time into the details
to understand what exactly happens)

Hope this helps

JW



                                                                                                                                       
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Dear experts,

just an observation of a slight discrepancy when applying a _binary_
filter function to the Fourier spectrum of an image by using "FFT >
Custom Filter" and "FFT > FFT" > spectral masking > "FFT > Inverse
FFT":

With the former approach more "ringing" is observed - why?

Any ideas?

Best

--


                   Herbie

          ------------------------

          <http://www.gluender.de>



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