The Earth Mover's Distance is the Mallows Distance: Some Insights from Statistics

The Earth Mover's distance was first introduced as a purely empirical way to measure texture and color similarities. We show that it has a rigorous probabilistic interpretation and is conceptually equivalent to the Mallows distance on probability distributions. The two distances are exactly the same when applied to probability distributions, but behave differently when applied to unnormalized distributions with different masses, called signatures. We discuss the advantages and disadvantages of both distances, and statistical issues involved in computing them from data. We also report some texture classification results for the Mallows distance applied to texture features and compare several ways of estimating feature distributions. In addition, we list some known probabilistic properties of this distance.

• Type: Conference
• Year: 2001
• Where: ICCV
• Authors: Elizaveta Levina, Peter J. Bickel
• Keywords: Computer Vision, Feature Distributions, ICCV 2001, Mallows Distance, Probability Distributions, Rigorous Probabilistic Interpretation, Unnormalized Distributions