The ability to determine the viewing parameters of objects from their projections has enabled well established tomographic techniques to be employed in the 3D reconstruction of objects from images obtained via modalities where the orientation of the objects cannot be controlled. A method is described for the determination of the viewing parameters of randomly acquired projections of asymmetric objects. It extends upon the common lines algorithm by determining the relative orientation of projections from the location of lines of intersection among the Fourier transforms of the projections in 3D Fourier space. A new technique for finding the lines of intersection in the presence of translational displacement, and for subsequently finding the translational displacement, is presented. The complete algorithm is described and its efficacy is demonstrated using real data. A new technique for dealing with noise is also discussed.
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