HI everyone!

I’m aware that there has been at least one previous topic focused on a similar problem (Quantification of the distribution of vesicles in different sections of a cell (fluorescence intensity)), but I would like to ask a different question.

I can see by eye that most of the cells I’m studying do display polarization of their intracellular vesicles, but want to automate the analysis process so as to prove that observation beyond any reasonable doubt.

However, I am struggling to determine what would be the ideal logical process to create cell subdivision ROIs. I’m calculating the angle of each particle relative to a horizontal line and thought that calculating the average angle of all intracellular particles to then build quadrants around it would be a good approach, since it immediately resolves situations in which there is polarization and does not significantly affect situations in which the particles distribute randomly:

However, I am struggling with the mathematics behind this (and actually think it may be fairly simple, but I don’t know how to define this situation more mathematically): the polarization example would numerically result in e.g. 3 particles having angles between 0 and 45 and the 4th particle having an angle close to 360 degrees, given the calculation relative to the horizontal line - and thus the average angle calculation is skewed to a completely different value than what I would find usable.

How can I perform a “correct” calculation of the average angle?

Thank you in advance!

-PM