  Cryo-electron microscopy is a state-of-the-art method for determining
high-resolution three-dimensional models of molecules, from their
two-dimensional projection images taken by an electron microscope. A crucial
step in this method is to determine a low-resolution model of the molecule
using only the given projection images, without using any three-dimensional
information, such as an assumed reference model. For molecules without
symmetry, this is often done by exploiting common lines between pairs of
images. Common lines algorithms have been recently devised for molecules with
cyclic symmetry, but no such algorithms exist for molecules with dihedral
symmetry. In this work, we present a common lines algorithm for determining the
structure of molecules with $D_{2}$ symmetry. The algorithm exploits the common
lines between all pairs of images simultaneously, as well as common lines
within each image. We demonstrate the applicability of our algorithm using
experimental cryo-electron microscopy data.
