Interpretable Structural Evaluation of Metal-Oxide Nanostructures in Scanning Transmission Electron Microscopy (STEM) Images via Persistent Homology

Persistent homology is a powerful tool for quantifying various structures, but it is equally crucial to maintain its interpretability. In this study, we extracted interpretable geometric features from the persistent diagrams (PDs) of scanning transmission electron microscopy (STEM) images of self-assembled Pt-CeO₂ nanostructures synthesized under different annealing conditions. We focused on PD quadrants and extracted five interpretable features from the zeroth and first PDs of nanostructures ranging from maze-like to striped patterns. A combination of hierarchical clustering and inverse analysis of PDs reconstructed by principal component analysis through vectorization of the PDs highlighted the importance of the number of arc-like structures of the CeO₂ phase in the first PDs, particularly those that were smaller than a characteristic size. This descriptor enabled us to quantify the degree of disorder, namely the density of bends, in nanostructures formed under different conditions. By using this descriptor along with the width of the CeO₂ phase, we classified 12 Pt-CeO₂ nanostructures in an interpretable way.