Given a STEM image showing a grain boundary and simulated grain boundary patterns, we aim to find which of these patterns occur in the image and where. As an example, we consider the A and T structural units of dislocation cores in the sigma 7 grain boundary.

In this talk, we present a novel mathematical framework to detect patterns in the form of atomic arrangements from density-functional theory (DFT) simulations in scanning transmission electron microscopy (STEM) images and to quantify the differences by estimating the deformation between experimental and simulational atomic arrangement based on variational methods. To this end, a given simulated atomic arrangement is first converted to a synthetic image patch, whose occurrences in the STEM image are found using template matching. On each matching patch, we then estimate the deformation between the simulated atomic column arrangement to the positions in the STEM image using bump fitting. The fitting of the position is split into two steps: First, we determine the affine part of the deformation and then the remaining nonlinear part. From the resulting fit, we derive feature descriptors that allow to determine which of the given patterns is present, in case there are multiple competing candidate patterns.