Objective crystallographic symmetry classifications of a noisy crystal pattern with strong Fedorov type pseudosymmetries and its optimal image-quality enhancement

TL;DR

This paper introduces an information theory-based method for automatically classifying crystallographic symmetry in noisy 2D crystal images, improving accuracy over traditional visual and software-based methods, and enhancing image quality.

Contribution

It presents a novel, unsupervised, and threshold-free symmetry classification approach that outperforms existing methods in noisy conditions, enabling better image processing and structural analysis.

Findings

Accurate symmetry classification in noisy images using information theory.

Method outperforms traditional visual and software classifications.

Enhances signal-to-noise ratio and structural resolution in crystal images.

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 patterns with strong Fedorov type pseudosymmetries and varying amounts of noise serve as examples. 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 and is free of any subjectively set thresholds in the geometric model selection process. This enables crystallographic symmetry classification of digital images that are more or less periodic in two dimensions (2D), a.k.a. crystal patterns, as recorded with sufficient structural resolution from a wide range of crystalline samples with different types of scanning probe and transmission electron microscopes. Correct symmetry classifications enable the optimal crystallographic processing of such images. That processing consists in the averaging over all asymmetric units in all unit cells in the selected image area and significantly enhances both the signal to noise ratio and the structural resolution of a microscopic study of a crystal. For sufficiently complex crystal patterns, the information-theoretic symmetry classification methods are more accurate than both visual classifications by human experts and the recommendations of one of the popular crystallographic image processing programs of electron crystallography.