  Statistically sound crystallographic symmetry classifications are obtained
with information theory based methods in the presence of approximately Gaussian
distributed noise. A set of three synthetic images with very strong Fedorov
type pseudosymmetries and varying amounts of noise serve as examples. The
correct distinctions between genuine symmetries and their Fedorov type
pseudosymmetry counterparts failed only for the noisiest image of the series
where an inconsistent combination of plane symmetry group and projected Laue
class was obtained. Contrary to traditional crystallographic symmetry
classifications with an image processing program such as CRISP, the
classification process does not need to be supervised by a human being. This
enables crystallographic symmetry classification of digital images that are
more or less periodic in two dimensions (2D) as recorded with sufficient
spatial resolution from a wide range of samples with different types of
scanning probe microscopes. Alternatives to the employed objective
classification methods as proposed by members of the computational symmetry
community and machine learning proponents are briefly discussed in an appendix
and are found to be wanting because they ignore Fedorov type pseudosymmetries
completely. The information theory based methods are more accurate than visual
classifications at first sight by most human experts.
