Grain analysis of atomic force microscopy images via persistent homology.

Atomic force microscopy (AFM) is an established technique in nanoscale grain analysis due to its accuracy in producing 3-dimensional images. Even though height threshold and watershed algorithms are commonly used to determine the grain size and number of grains, they mostly require image processing that result in the change of topographical features of the surface that generates misleading conclusions. In this study, we use persistent homology, a method of representing topological features, to obtain more accurate information about the granular surfaces from unprocessed AFM images than the conventional methods. The method is also useful as a robust alternative to common parameters describing the topography of the AFM images. Most of these parameters such as arithmetic roughness and root-mean-squared roughness are represented by a single number which results in uncertainty in characterization of different surfaces. Persistent homology provides more precise summary about surface properties than a single parameter.