  An approach for the analysis of atomically resolved scanning transmission
electron microscopy data with multiple ferroic variants in the presence of
imaging non-idealities and chemical variabilities based on a rotationally
invariant variational autoencoder (rVAE) is presented. We show that an optimal
local descriptor for the analysis is a sub-image centered at specific atomic
units, since materials and microscope distortions preclude the use of an ideal
lattice as a reference point. The applicability of unsupervised clustering and
dimensionality reduction methods is explored and are shown to produce clusters
dominated by chemical and microscope effects, with a large number of classes
required to establish the presence of rotational variants. Comparatively, the
rVAE allows extraction of the angle corresponding to the orientation of ferroic
variants explicitly, enabling straightforward identification of the ferroic
variants as regions with constant or smoothly changing latent variables and
sharp orientational changes. This approach allows further exploration of the
chemical variability by separating the rotational degrees of freedom via rVAE
and searching for remaining variability in the system. The code used in the
manuscript is available at
https://github.com/saimani5/ferroelectric_domains_rVAE.
