  The advent of high-resolution electron and scanning probe microscopy imaging
has opened the floodgates for acquiring atomically resolved images of bulk
materials, 2D materials, and surfaces. This plethora of data contains an
immense volume of information on materials structures, structural distortions,
and physical functionalities. Harnessing this knowledge regarding local
physical phenomena necessitates the development of the mathematical frameworks
for extraction of relevant information. However, the analysis of atomically
resolved images is often based on the adaptation of concepts from macroscopic
physics, notably translational and point group symmetries and symmetry lowering
phenomena. Here, we explore the bottom-up definition of structural units and
symmetry in atomically resolved data using a Bayesian framework. We demonstrate
the need for a Bayesian definition of symmetry using a simple toy model and
demonstrate how this definition can be extended to the experimental data using
deep learning networks in a Bayesian setting, namely rotationally invariant
variational autoencoders.
