Quantitative Analysis of Similarity Measures of Distributions

Eric Bazan (1, 2) , Petr Dokládal (1, 2) , Eva Dokladalova (3, 4)

1 CMM - Centre de Morphologie Mathématique
2 Mines Paris - PSL (École nationale supérieure des mines de Paris)
3 ESIEE Paris
4 LIGM - Laboratoire d'Informatique Gaspard-Monge

There are many measures of dissimilarity that, depending on the application, do not always have optimal behavior. In this paper, we present a qualitative analysis of the similarity measures most used in the literature and the Earth Mover's Distance (EMD). The EMD is a metric based on the theory of optimal transport with interesting geometrical properties for the comparison of distributions. However, the use of this measure is limited in comparison with other similarity measures. The main reason was, until recently, the computational complexity. We show the superiority of the EMD through three different experiments. First, analyzing the response of the measures in the simplest of cases; one-dimension synthetic distributions. Second, with two image retrieval systems; using colour and texture features. Finally, using a dimensional reduction technique for a visual representation of the textures. We show that today the EMD is a measure that better reflects the similarity between two distributions.

Domaines: Traitement des images [eess.IV]; Traitement du signal et de l'image [eess.SP]

Eric Bazan, Petr Dokládal, Eva Dokladalova. Quantitative Analysis of Similarity Measures of Distributions. British Machine Vision Conference (BMVC), Sep 2019, Cardiff, United Kingdom. ⟨hal-02299826⟩