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Angular reconstitution: A posteriori assignment of projection directions for 3D reconstruction

Authors
Journal
Ultramicroscopy
0304-3991
Publisher
Elsevier
Publication Date
Volume
21
Issue
2
Identifiers
DOI: 10.1016/0304-3991(87)90078-7
Disciplines
  • Biology
  • Medicine

Abstract

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.

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