I have circularity and length measures for thousands of different particles and I want to test whether these particles have gotten more rounded over time (due to mechanical stress) using shape parameters. I have tried to use circularity but, as far as I am concerned, circularity depends on the area and the perimeter of a particle and therefore is intrinsically related to maximum Feret’s diameter. A change in the area of a particle (perimeter = constant) means the aspect ratio must change (and consequently Feret’s diameter). A change in the perimeter of the particle (area = constant) means the particle has to become more irregular-shaped (which also means a change in Feret’s diameter). Correct me if I’m wrong.
I have found a formula that corrects the circularity by the aspect ratio (R score) (Takashimizu & Iiyoshi, 2016), which can be easily calculated or obtained with the Extended Geometries plugin. Correcting circularity by aspect ratio reduces the dependence on Feret’s diameter. However, to me there still seems to be an intrinsic relation between the R score and Feret’s diameter. Is this correct? How can I plot Feret’s diameter of a particle with it’s shape describing roundness without having any intrinsic relation between these two?