Volumic particles density

Can you show me how to determine the particle density (number of spherical particles) per unit volume (not per unit area).

I feel like this is a very generic question and not related to Fiji/ImageJ, right?
Can you elaborate on the link with ImageJ?


May be it’s true, but some users of ImageJ could also met the same problem. And since this is a forum, may be some one could help me.
The problem is that (to my knowledge) ImageJ gives the number of particles per unit area, but how do you get this number per unit volume.

Try searching internet with term “focal volume”. The area you are measuring has certain thickness, so you just need to know that then you could calculate the volume where your counted particles are.

Basically you want to do what particle analyzer in the standard ImageJ setup does for 2D, but in 3D.

For the 2D case this is pretty straight forward:

  • count the number of particles that particle analyzer detects (there is an option to populate a ResultsWindow, where you can just scroll to the bottom and look at the last line number, this is the number of detected particles)
  • calculate the area of the image (if you need to get into proper units, then Image>Properties has the calibration info)
  • particle density in 2D is then (number of particles) / area

For 3D there are multiple options, so here is one example using the 3D objects counter:

  • Personally I tend to threshold my image beforehand to get a little more control over thresholding (say if I want to use an automatic thresholding method), but 3D objects counter will threshold for you as well
  • in menus: Analyze>3D Objects Counter, you shouldn’t need to fiddle with much here, but you might care about excluding objects on the edge
  • Run this, it might be a little bit slow depending on your image volume
  • You will get a table of statistics as output, plus a few image-based renderings of the results
  • Use the number of objects reported in the table of statistics as your number of particles
  • Calculate image volume this time (instead of area) using the same procedure for getting the image calibration information, if you need it (and you probably do because the voxel size along the Z-axis is rarely the same as the X and Y)
  • The volumetric particle density is ( number of objects ) / ( image volume )


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Thank you for the response, i will try this procedure


How to calculate image volume when it is a hollow tube in shape?
I have to normalize 3D objects that spans 10-11 z-stacks and then I need to normalize it with the volume of the tube.