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The Earth Mover's distance is the Mallows distance: some insights from statistics
Abstract
The Earth Mover's distanc1e was first introduced as a purely empirical ways 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.
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Cites
The Hungarian method for the assignment problem
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Metadata
- Authors
- Levina, E., & Bickel, P.
- Venue
- Proceedings Eighth IEEE International Conference on Computer Vision. ICCV 2001
- Publisher
- IEEE Comput. Soc
- Published
- 2002-11-13
- Volume
- 2
- Pages
- 251-256
- OpenAlex
- W2171235719
- Cited by
- 562
- References
- 1
- FWCI
- 3.62
- Type
- conference paper
- Language
- en
- Open access
- closed
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