  Motivated by the 2D class averaging problem in single-particle cryo-electron
microscopy (cryo-EM), we present a k-means algorithm based on a
rotationally-invariant Wasserstein metric for images. Unlike existing methods
that are based on Euclidean ($L_2$) distances, we prove that the Wasserstein
metric better accommodates for the out-of-plane angular differences between
different particle views. We demonstrate on a synthetic dataset that our method
gives superior results compared to an $L_2$ baseline. Furthermore, there is
little computational overhead, thanks to the use of a fast linear-time
approximation to the Wasserstein-1 metric, also known as the Earthmover's
distance.
