Quantifying distributions of cryo-EM projections

In cryo-electron microscopy, a set of two-dimensional projections collected from different viewing directions may complicate image processing and subsequent model building if the distribution of these views is non-uniform. View distributions are traditionally represented as color-coded two-dimensional diagrams. However, such diagrams can introduce distortions and are cumbersome to manipulate, store and compare across data sets; they do not provide a commonly accepted quantitative measure of uniformity. In this work, we propose a method to characterize these angular distributions quantitatively and to represent them as simple one-dimensional curves rather than two-dimensional colored diagrams. The suggested measures could be incorporated into databases such as EMDB to provide a compact, standardized description of the angular distribution of particle views.