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I want to determine the distribution of micro glass spheres in SEM (scanning electron microscope) images, which can be obtained after finding the contours of the little spheres. I think the difficulties are the variance of the brightness and the overlap among the spheres.

At the beginning, I guess canny edge detector may help to find the edges. However the result is not very good.

Thank you for your help and share!

The original obtained from a SEM The result with canny detector

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  • $\begingroup$ Can you give precision about what you call "distribution" ? About the variance of the brightness I suggest you to try to perform grey-level histogram equalization on a >100um sliding window. $\endgroup$ – Antoine Bassoul Jun 1 '15 at 12:06
  • $\begingroup$ @AntoineBassoul Thanks for your help. I use the word "distribution" to mean that I want to get the probability distribution of the centers and the radiuses of the circles. $\endgroup$ – xmfbit Jun 1 '15 at 12:38
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The usual next step in such a case would be to obtain the Hough (or Radon) transform and then try to identify the spheres (or, here, circles) in the domain that results from the transform. For more information on how this works please see this link and also related response here.

However, these transforms will not improve the situation of overlapping objects. For this reason, you might also want to check two dimensional frequency domain / matched filter type (or curve-fitting) methods. For more information on this and an indicative technique, please see this paper (and potentially this one too).

A lot of work around this type of problems has been performed in biomedical engineering and specifically the problem of automatically counting blood cells (which can present themselves as ellipsoids) or detecting and automatically counting "spots" (which, again, present themselves as ellipsoids) from an analysis process called "electrophoresis". Searching for "automatic blood cell count wavelets" for example, in a relevant journal search engine, will return a very large number of results. The added benefit to potentially using wavelets here might be that you can find a wavelet mother function that closely resembles the profile of the sphere, which then gives you a better chance at detectability. For more information about this, please see this and this link, towards the end of the latter there is a link to a thesis that provides a very good summary of relevant methods.

Hope this helps.

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