Information theory-based plane symmetry classifications: revealing pseudo-symmetries in the presence of noise

Abstract

Information theory-based methods [1][2][3][4] for the classification of more or less 2D periodic images from real-world crystals with atomic or molecular resolution into plane symmetry groups and projected Laue classes are described and applied to both synthetic patterns and experimental transmission electron microscope images of intrinsic membrane proteins. The synthetic patterns are per design either free of noise or contain approximately Gaussian distributed noise and are also highly pseudo-symmetric so that it is, for human beings on the basis of a visual inspection alone, very difficult to identify the underlying plane symmetry of the noisy patterns. This is because all genuine symmetries and pseudo-symmetries are broken by the added noise so that their differences are diminished. The new information theory-based classification methods, on the other hand, overcomes such challenges.