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

TL;DR

This paper introduces an information-theoretic approach for automatically classifying symmetries in noisy crystal images, effectively distinguishing genuine symmetries from pseudosymmetries without human supervision.

Contribution

It presents a novel, unsupervised, information-theoretic method for crystallographic symmetry classification that outperforms traditional visual methods and ignores pseudosymmetries better.

Findings

Accurate symmetry classification in noisy images

Automatic process does not require human supervision

Outperforms traditional visual classification methods

Abstract

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.