  A common task in cryo-electron microscopy (cryo-EM) data processing is to
compare three-dimensional density maps of macromolecules. In this paper, we
propose an algorithm for aligning three-dimensional density maps that exploits
common lines between projection images of the maps. The algorithm is fully
automatic and handles rotations, reflections (handedness), and translations
between the maps. In addition, the algorithm is applicable to any type of
molecular symmetry without requiring any information regarding the symmetry of
the maps. We evaluate our alignment algorithm on publicly available density
maps, demonstrating its accuracy and efficiency. The algorithm is available at
https://github.com/ShkolniskyLab/emalign.
