title: Angular reconstitution: a posteriori assignment of projection directions for 3D reconstruction.
abstract: In computerized tomography as well as in most problems of three-dimensional reconstruction from projections, one knows from the experimental set-up the angular relationships between the projections from which the reconstruction is to be calculated. A serious difficulty is encountered when the angles are not known. In this paper, a method of "angular reconstitution" is described, which allows the a posteriori determination of the relative angular orientations of the projections and thus enables the three-dimensional reconstruction of the object to be calculated. For asymmetric objects, a minimum of three projections is required, which should not be related by a tilt around a single rotation axis. The method can be applied to determine the three-dimensional structure of biological macromolecules based on electron micrographs of randomly oriented individual molecules. Angular reconstitution, in combination with multivariate statistical techniques to classify and average the characteristic views of a molecule forms a complete, self-contained methodology for molecular structure analysis by electron microscopy.
authors.affiliation: Fritz Haber Institute of the Max Planck Society, Berlin Dahlem, Germany.
authors.forename: M
authors.initials: M
authors.lastname: Van Heel
mesh_terms: D046911:Macromolecular Substances; D008433:Mathematics; D008854:Microscopy, Electron / Q000379:methods*; D015999:Multivariate Analysis
chemical_list: D046911:Macromolecular Substances