Towards generalized noise-level dependent crystallographic symmetry classifications of more or less periodic crystal patterns

TL;DR

This paper introduces a quantitative, noise-level dependent approach for classifying crystallographic symmetry in 2D images, reducing subjectivity and improving objectivity over traditional threshold-based methods.

Contribution

It presents a novel information-theoretic framework for more objective, generalized symmetry classification that accounts for noise and provides probabilistic inferences across multiple classes.

Findings

Classifications are based on maximal likelihood and information theory.

The approach reduces subjectivity compared to threshold-based methods.

Provides a probabilistic, multi-class inference framework.

Abstract

Geometric Akaike Information Criteria (G-AICs) for generalized noise-level dependent crystallographic symmetry classifications of two-dimensional (2D) images that are more or less periodic in either two or one dimensions as well as Akaike weights for multi-model inferences and predictions are reviewed. Such novel classifications do not refer to a single crystallographic symmetry class exclusively in a qualitative and definitive way. Instead, they are quantitative, spread over a range of crystallographic symmetry classes, and provide opportunities for inferences from all classes (within the range) simultaneously. The novel classifications are based on information theory and depend only on information that has been extracted from the images themselves by means of maximal likelihood approaches so that these classifications are objective. This is in stark contrast to the common practice whereby arbitrarily set thresholds are employed to force crystallographic symmetry classifications into apparently definitive/exclusive states, while the geometric feature extraction results on which they depend are never definitive in the presence of generalized noise, i.e. in all real world applications. Thus, there is unnecessary subjectivity in the currently practiced ways of making crystallographic symmetry classifications, which can be overcome by the approach outlined in this review.