Computer analysis of rotational symmetry in CBED patterns

A method for efficient detection of the dominant local rotational symmetry in grey level images of convergent beam electron diffraction (CBED) patterns is described. A general approach is to define a local measure of rotational symmetry that transforms the symmetry detection problem to an optimization problem, and obtain the symmetric regions by an efficient global optimization algorithm. In this paper, we present a correlation function as the measure of rotational symmetry. The value depends on the center of the supporting region, its size, and the rotational angle. The genetic algorithm is used to search the global maximum of the rotational symmetry. According to the unique characteristic of CBED patterns, some segmentation methods are applied to the images of CBED patterns to reduce the search space of the global optimization algorithm, thus this method is shown in experiments to be both effective and quick