  The Wasserstein metric or earth mover's distance (EMD) is a useful tool in
statistics, machine learning and computer science with many applications to
biological or medical imaging, among others. Especially in the light of
increasingly complex data, the computation of these distances via optimal
transport is often the limiting factor. Inspired by this challenge, a variety
of new approaches to optimal transport has been proposed in recent years and
along with these new methods comes the need for a meaningful comparison.
  In this paper, we introduce a benchmark for discrete optimal transport,
called DOTmark, which is designed to serve as a neutral collection of problems,
where discrete optimal transport methods can be tested, compared to one
another, and brought to their limits on large-scale instances. It consists of a
variety of grayscale images, in various resolutions and classes, such as
several types of randomly generated images, classical test images and real data
from microscopy.
  Along with the DOTmark we present a survey and a performance test for a cross
section of established methods ranging from more traditional algorithms, such
as the transportation simplex, to recently developed approaches, such as the
shielding neighborhood method, and including also a comparison with commercial
solvers.
