Invariant classification of molecular views in electron micrographs

Biological macromolecules can exhibit many different orientations in electron microscopical preparations. In particular in vitreous-ice-embedded specimens, the number of different views can be high. Existing techniques of analysis require the alignment of the molecular views relative to one or more reference images with cross-correlation ("matched filtering") techniques and are somewhat unsatisfactory because of the high noise level and the large number of different views in such images. We here propose a method in which first rotation-, translation- and mirror-invariant functions are derived from the large set of input images. These functions are subsequently classified automatically using multivariate statistical classification techniques. The different molecular views in the images can therewith be found without bias, provided that a statistically significant number of copies of the views are present in the data set. The basic ideas are exemplified with realistic model data.