Posted by
Herbie on
Feb 07, 2017; 7:30pm
URL: http://imagej.273.s1.nabble.com/create-image-from-radial-profile-tp5018029p5018052.html
Dear Michael and all those who are interested!
The approach that I should like to propose for the computation of the
"Radially Symmetric Function from its Profile"
makes use of the
"Central Slice Theorem"
of the Fourier calculus.^1
Processing steps:
1.
The horizontal 1D profile function is centered to a [ n * n ] image support.
2.
The image is 2D Fourier-transformed which leads to the vertical
projection of the 1D Fourier-transform of the profile.
3.
Rotated versions of the resulting 2D Fourier-spectrum are summed.
The angle increment must at least be [ 360 / (n * PI) ] and the
rotations go from 0...180 deg.^2
4.
The resulting sum of Fourier-spectra is then Fourier re-transformed and
gives the desired radially symmetric function.
The quality of the resulting radially symmetric image function can be
improved by increasing the resolution of the Fourier-spectrum which is
achieved by simply using a larger image support in step 1.
The approach is well-suited for macro-implementations, because all
time-consuming operations (ffts & rotations) are performed by
core-plugins of ImageJ.
Best
Herbie
_____________________
^1
_Bracewell (1956)_
<
http://adsabs.harvard.edu/full/1956aujph...9..198b>
_Glünder (1986)_
<www.gluender.de/Writings/WritingsTexts/HardText.html#Gl-1986-2>
^2
_Herman G.T. (1980)_ "Image reconstruction from projections". Academic.
_Platzer H. (1981)_ "Optical image processing". In: Oja E. and Simula O.
(eds.) The second Scandinavian conference on image analysis. Pattern
Recognition Society of Finland, Espoo/Finland, pp. 128-138.
_Glünder (2013)_
<www.gluender.de/Writings/WritingsTexts/HardText.html#Gl-2013-1>
::::::::::::::::::::::::::::::::::::::::::::
Am 05.02.17 um 16:08 schrieb Michael Elbaum:
> Thanks Herbie,
>
> This is just what I was looking for, to generate a radially symmetric
> image from a given profile. I have the profile only as a list,
> though, rather than a function, so it should be interpolated from 1D
> on "x" to the radius. I vaguely remember seeing something that can do
> this in ImageJ, but might be imagining.
>
> best, Michael
>
> ________________________________________ From: ImageJ Interest Group
> [
[hidden email]] on behalf of Herbie [
[hidden email]] Sent:
> Sunday, February 05, 2017 14:41 To:
[hidden email] Subject: Re:
> create image from radial profile
>
> Dear Michael,
>
> the valuable ImageJ-plugin "Radial Profile" sums the image values on
> concentric circles and displays the normalized sums as a function of
> the radii of these circles. Consequently, the result is a
> 1-dimensional curve with the radius as the abscissa.
>
> Due to the circular summing, this operation can't be reversed or, as
> you've put it, it can't be "inverted".
>
> What you may achieve however, is to generate a radially symmetric
> image from a profile. If the profile is given analytically you can
> use
>
> "Process > Math > Macro"
>
> as it was suggested by Jerome Mutterer:
> <
http://forum.imagej.net/t/image-generation-donut-with-a-gaussian-cross-section/2379>
>
> Here is his example macro using a shifted Gaussian profile:
>
> newImage( "Image from Profile", "8-bit black", 256, 256, 1 ); run(
> "Macro...", "v=255*exp(-((d-50)*(d-50)/w)/2)" );
>
> HTH
>
> Herbie
>
> :::::::::::::::::::::::::::::::::::::::::::: Am 05.02.17 um 08:47
> schrieb Michael Elbaum:
>> Dear list, I'm wondering if there's a plugin available to do
>> the "inverse" of the Radial Profile: given a theoretical curve I
>> want to simulate an image. thanks, Michael
>>
>> -- ImageJ mailing list:
http://imagej.nih.gov/ij/list.html>>
>
> -- ImageJ mailing list:
http://imagej.nih.gov/ij/list.html>
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