@article{Kaijser1998ComputingTK,
title={Computing the Kantorovich Distance for Images},
author={Thomas Kaijser},
journal={Journal of Mathematical Imaging and Vision},
year={1998},
volume={9},
pages={173-191}
}

Computing the Kantorovich distance for images is equivalent to solving a very large transportation problem. The cost-function of this transportation problem depends on which distance-function one uses to measure distances between pixels. In this paper we present an algorithm, with a computational complexity of roughly order $$\mathcal{O}$$ (N2), where N is equal to the number of pixels in the two images, in case the underlying distance-function is the L1-metric, an approximation of the L2… CONTINUE READING