2011-09-01, English, Article, Report edition: Transportation Distances on the Circle.(Report) Rabin, Julien; Delon, Julie; Gousseau, Yann

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Physical Description
  • Report
  • Magazine/​Journal article
Published
  • Springer, 2011 Sept
Language
  • English

Edition details

Title
  • Transportation Distances on the Circle.(Report)
Also Titled
  • Transportation Distances on the Circle.
Appears In
  • Journal of Mathematical Imaging and Vision, v.41, no.1-2, 2011 Sept, p.147(21) (ISSN: 0924-9907)
Author
  • Rabin, Julien
  • Delon, Julie
  • Gousseau, Yann
Published
  • Springer, 2011 Sept
Physical Description
  • Report
  • Magazine/​Journal article
Subjects
Target Audience
  • Academic
Summary
  • Byline: Julien Rabin (1), Julie Delon (2), Yann Gousseau (2) Keywords: Optimal mass transportation theory; Earth Mover's Distance; Circular histograms Abstract: This paper is devoted to the study of the Monge-Kantorovich theory of optimal mass transport, in the special case of one-dimensional and circular distributions. More precisely, we study the Monge-Kantorovich problem between discrete distributions on the unit circle S .sup.1, in the case where the ground distance between two points x and y is defined as h(d(x,y)), where d is the geodesic distance on the circle and h a convex and increasing function. This study complements previous results in the literature, holding only for a ground distance equal to the geodesic distance d. We first prove that computing a Monge-Kantorovich distance between two given sets of pairwise different points boils down to cut the circle at a well chosen point and to compute the same distance on the real line. This result is then used to obtain a dissimilarity measure between 1-D and circular discrete histograms. In a last part, a study is conducted to compare the advantages and drawbacks of transportation distances relying on convex or concave cost functions, and of the classical L .sup.1 distance. Simple retrieval experiments based on the hue component of color images are shown to illustrate the interest of circular distances. The framework is eventually applied to the problem of color transfer between images. Author Affiliation: (1) CMLA, ENS de Cachan, 61, Avenue du President Wilson, 94230, Cachan, France (2) CNRS LTCI, Telecom ParisTech, 46 rue Barrault, 75634, Paris Cedex 13, France Article History: Registration Date: 29/​03/​2011 Online Date: 06/​05/​2011 Article note: This work has been supported by the French National Research Agency (project OTARIE) under grant BLAN07-2_183172.
Terms of Use
  • COPYRIGHT 2011 Springer
Language
  • English
Database
  • Gale Academic OneFile
Identifier
  • 262882492

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