Unsupervised Learning for the Automatic Counting of Grains in Nanocrystals and Image Segmentation at the Atomic Resolution

Identifying the grain distribution and grain boundaries of nanoparticles is important for predicting their properties. Experimental methods for identifying the crystallographic distribution, such as precession electron diffraction, are limited by their probe size. In this study, we developed an unsupervised learning method by applying a Gabor filter to HAADF-STEM images at the atomic level for image segmentation and automatic counting of grains in polycrystalline nanoparticles. The methodology comprises a Gabor filter for feature extraction, non-negative matrix factorization for dimension reduction, and K-means clustering. We set the threshold distance and angle between the clusters required for the number of clusters to converge so as to automatically determine the optimal number of grains. This approach can shed new light on the nature of polycrystalline nanoparticles and their structure–property relationships.