Objective crystallographic symmetry classifications of noisy and noise-free 2D periodic patterns with strong Fedorov type pseudosymmetries

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.