Interpretable graph methods for determining nanoparticles ordering in electron microscopy images

An important step in determining the properties of carbon materials is the analysis of images from a scanning electron microscope (SEM). These images show the material surface after the application of metal nanoparticles. The order of these nanoparticles is a key characteristic that affects the material properties. We have previously proposed an approach to formalize the order features based on the identification of lines by nanoparticles in the SEM image. This paper proposes a novel approach to line allocation that is based on the concept of constructing a minimum spanning forest. Additionally, it introduces a set of novel ordering functions that are derived from this approach. The experimental study demonstrates that the combination of these new and previously extracted features improves the recognition quality of SEM images with ordered and disordered nanoparticles arrangements. This approach allows us to gain a better understanding of the nanoparticles arrangement and their effect on the material properties.