  Single particle cryogenic electron microscopy (cryo-EM) is an imaging
technique capable of recovering the high-resolution 3-D structure of biological
macromolecules from many noisy and randomly oriented projection images. One
notable approach to 3-D reconstruction, known as Kam's method, relies on the
moments of the 2-D images. Inspired by Kam's method, we introduce a
rotationally invariant metric between two molecular structures, which does not
require 3-D alignment. Further, we introduce a metric between a stack of
projection images and a molecular structure, which is invariant to rotations
and reflections and does not require performing 3-D reconstruction.
Additionally, the latter metric does not assume a uniform distribution of
viewing angles. We demonstrate uses of the new metrics on synthetic and
experimental datasets, highlighting their ability to measure structural
similarity.
