The Earth Mover’s Distance

Abstract

A ground distance between single visual image features can often be found by psychophysical experiments. For example, perceptual color spaces have been devised in which the Euclidean distance between two colors approximately matches the human perception of their difference. Measuring perceptual distance becomes more complicated when sets of features, rather than single features, are being compared. In Section 2 we showed the problems caused by dissimilarity measures that do not handle correspondences between different bins in the two histograms. Such correspondences are key to a perceptually natural definition of the distances between sets of features. This observation led to distance measures based on bipartite graph matching [65, 108], defined as the minimum cost of matching elements between the two histograms.

The great God endows his children variously. To some He gives intellect— and they move the earth...

—Mary Roberts Rinehart, 1876–1958