http://imagej.273.s1.nabble.com/create-image-from-radial-profile-tp5018029p5018066.html
Thanks Jeremy and Herbie! off list the Polar Transform plugin was also recommended.
> On 8 בפבר׳ 2017, at 17:39, Jeremy Adler <
[hidden email]> wrote:
>
> Dear All,
> A rather crude method would be to first turn the image into one where the distances from the designated centre of the circle are marked - a distance map from a single point.
> Then use a LUT to change the distances into the sequence of intensities that you want.
> LUTs are just lists of numbers, so they can be created and edited quite easily.
> The intensities/colours imposed by the LUT can then be made permanent.
> A limitation is that only 256 different intensities are available with a LUT - but the final image could always be smoothed to create intermediate values and Transform/Bin with differential x and y axis compression/stretch would create ovals.
>
> -----Original Message-----
> From: ImageJ Interest Group [mailto:
[hidden email]] On Behalf Of Herbie
> Sent: den 7 februari 2017 20:30
> To:
[hidden email]
> Subject: Re: create image from radial profile
>
> 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-cros>> s-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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