Classification for transmission electron microscope images from different amorphous states using persistent homology

It is difficult to discriminate the amorphous state using a transmission electron microscope (TEM). We discriminated different amorphous states on TEM images using persistent homology, which is a mathematical analysis technique that employs the homology concept and focuses on 'holes'. The structural models of the different amorphous states, that is, amorphous and liquid states, were created using classical molecular dynamic simulation. TEM images in several defocus conditions were simulated by the multi-slice method using the created amorphous and liquid states, and their persistent diagrams were calculated. Finally, logistic regression and support vector classification machine learning algorithms were applied for discrimination. Consequently, we found that the amorphous and liquid phases can be discriminated by more than 85%. Because the contrast of TEM images depends on sample thickness, focus, lens aberration, etc., radial distribution function cannot be classified; however, the persistent homology can discriminate different amorphous states in a wide focus range.