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Statistically sound crystallographic symmetry classifications are obtainedwith information theory based methods in the presence of approximately Gaussiandistributed noise. A set of three synthetic images with very strong Fedorovtype pseudosymmetries and varying amounts of noise serve as examples. Thecorrect distinctions between genuine symmetries and their Fedorov typepseudosymmetry counterparts failed only for the noisiest image of the serieswhere an inconsistent combination of plane symmetry group and projected Laueclass was obtained. Contrary to traditional crystallographic symmetryclassifications with an image processing program such as CRISP, theclassification process does not need to be supervised by a human being. Thisenables crystallographic symmetry classification of digital images that aremore or less periodic in two dimensions (2D) as recorded with sufficientspatial resolution from a wide range of samples with different types ofscanning probe microscopes. Alternatives to the employed objectiveclassification methods as proposed by members of the computational symmetrycommunity and machine learning proponents are briefly discussed in an appendixand are found to be wanting because they ignore Fedorov type pseudosymmetriescompletely. The information theory based methods are more accurate than visualclassifications at first sight by most human experts.

Information-theoretic symmetry classifications of crystal patterns in  the presence of noise and strong Fedorov type pseudosymmetries for an optimal  subsequent crystallographic processing of these patterns