How to obtain radial frequency of objects (Radial Distribution of connected objects)?

I have a single 3D volume object consisting of 5 separate irregularly shaped particles. I have the geometric center of the 3D object and also the complete set of 3D coordinates for each irregularly shaped particles obtained from voxel data. I want to compute the radial frequency of particles at any random radius from the geometric center. In other words lets suppose I am drawing a sphere of radius 'X' from the geometric center of the 3D object then I want to compute how many particles are existing (even partially) in that radius 'X' . Similarly if I take the radius 'Y' which is greater than the boundary of object then it will display frequency as 5 or 'Z' then also 5 as it includes all 5 (blue highlighted).

Kindly any idea how can I perform this in MATLAB with the above mentioned inputs. I have tried to illustrate the 2D view for this but please ask me questions if any point is still unclear. The shaded parts are the individual particles and yellow highlight is the boundary of the 3D object.

Answer 1

[Image Analyst]

See my attached demos to calculate the average radial profile. Adapt as needed. Upload your adapted code if you still need help with it.