Paper containing detailed description and first comparison of algorithms:

https://arxiv.org/abs/1610.03368

This benchmark for testing discrete optimal transport algorithms consists of 10 classes.

Each class contains 10 images in each of the 5 different resolutions from 32×32 to 512×512
(in doubling steps per dimension). This allows for a total of 45 computations of Wasserstein distances
between two images for any one class at any fixed resolution.

Classes 1–7 are random simulations based on various probability distributions.
Images at different resolutions are generated independently from each other but according to the
same laws. Classes 8–10 were obtained by ad-hoc choices of simple geometric
shapes, classic test images and images of mitochondria acquired using STED
super-resolution microscopy. For geometric shapes and classic test
images the various resolutions available are coarsenings of a single image. For
the microscopy images different clippings of various sizes have been selected
from larger images to obtain the various resolutions.