Radially Averaged Autocorrelation vs Radial Distribution Function

I am trying to calculate the Radial Distribution Function by analyzing Optical Microscopy Images in order to identify the distance between first neighbors.
The macro Radial Distribution Function did not work in my case, I do not know the reason…
I found that the result of Radially Averaged Autocorrelation looks very much to what I want if I reverse it…
has anybody tried it? In its “manual”
https://imagejdocu.tudor.lu/doku.php?id=macro:radially_averaged_autocorrelation
they refer to the the “…first side maximum of the autocorrelation gives the typical distance between two particles or holes…”
My question is, the following: What is the first side maximum? If I reverse it then the minimum becomes maximum… Is it correct to refer to it as the distance of first neighbors?
Thank you for your help!!!

Hi Lalas,

what exactly are you interested in? Is it the distance between the particle centers?
Then you need the Radial Distribution Function macro
https://imagejdocu.tudor.lu/macro/radial_distribution_function

What was the problem when you say “it did not work”?
The Radial Distribution Function macro needs an image where “Find Maxima” can correctly find the objects of interest with “Light Background” on. You can change these options in the macro, in line with run("Find Maxima...

What does “If I reverse it then the minimum becomes maximum…” refer to?
If you invert an image, the autocorrelation will remain the same. The radial average will also remain the same if you flip an image horizontally or vertically.
Or do you simply want to know what the first minimum of the radially averaged autocorrelation is related to? This depends on particle size and shape as well on the radial distribution function; I think that there is no simple rule that determines its position.

–Michael

Hi Michael,
Thank you for your fast response to my topic…
I want to know the distance between first neighbors. I understand this can be done with RDF. This did not work with me means results were not valid…
Beyond that, I used Radially Averaged Autocorrelation, and the results were good. By saying “reverse” I meant the results plot, not the image itself…
I want to know if the first minimum of the Radially Averaged Autocorrelation corresponds to the first neighbor distance. If so I am OK with Radially Averaged Autocorrelation.
Thank you once again!

Hi Lalas,

if you want the distance between the centers, go for the Radial Distribution Function.
If you have trouble using it with your image, use “Find maxima” with output type=“Single Points” and then apply the Radial Distribution Function macro to the output. Make sure that “Black background” is off (deselected) in Process>Binary>Options, so the output of “Find maxima” are black points on a white background.
The Radially Averaged Autocorrelation macro won’t give you the exact answer for the radial distribution function. E.g., larger particles will get more weight than small ones, and depending on the size, shape, and distribution of the particles, 2nd-nearest neighbors might may have an influence on the position of the maximum that you use for the nearest neighbors.

–Michael