Methods for objective classifications of approximate crystallographic symmetries in digital images that are more or less translation periodic in two dimensions (2D) have recently been demonstrated [1-3]. Classifications into Bravais lattice types, Laue classes, and plane symmetry groups can be made. The objectivity of the crystallographic symmetry classifications is ensured by the selection of the statistically best geometric model for the 2D periodic signal in the images on the basis of geometric Akaike Information Criteria.
Experimental images from transmission electron microscopes that are digital and sufficiently well resolved at the molecular level serve as input data. This data is considered to consist of the pixel-wise sums of more or less Gaussian distributed noise and an unknown underlying signal that is strictly 2D periodic. Structural defects in the molecular 2D array, instrumental image recording noise, and (unavoidable1) inaccuracies in the algorithmic processing of the image data all contribute to one generalized noise term. Because there are many different sources of noise that contribute to the generalized noise term and none of them is assumed to dominate, the central limit theorem justifies the overarching assumption that the generalized noise is approximately Gaussian distributed. The outputs of the methods are the most probable 2D periodic signal distribution from the underlying molecular array in addition to the most probable plane symmetry group, Laue class, and Bravais lattice type.
As recently reviewed , the new crystallographic symmetry classification methods are the only ones that can be considered to be objective, i.e. independent of arbitrarily set thresholds. In the presumed presence of genuine underlying crystallographic site symmetries, the new methods deal effectively with all types of pseudo-symmetries and allow for the calculation of sets of geometric Akaike weights. Such weights represent the probabilities of the correctness of particular crystallographic symmetry classifications. They are relative to the weights of the other geometric models for the input data within the selected model set. Products of geometric Akaike weights for classifications into plane symmetry groups, Laue classes, and Bravais lattice types enable objective classifications of strongly pseudo-symmetric images that are also very noisy.
The new methods are analytic in nature rather than based on machine learning. Machine learning studies have so far ignored pseudo-symmetries in crystallographic symmetry classifications of digital images that are more or less 2D periodic. After having been trained on more than three million noise-free and noisy synthetic images with underlying genuine crystallographic symmetries, a machine learned demonstrably nothing about crystallographic symmetries in digital images . As long as the underlying assumptions are fulfilled, the applications of the new analytical classification methods empower structural biologists with knowledge of the genuine crystallographic symmetries in their crystalline membrane protein samples. If you would like to be empowered by such knowledge, come to this talk (and become aware of the abysmal out-of-training-set performance of contemporarily competing machine learning systems as a byproduct).