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Journal of Mathematical Imaging and Vision

, Volume 30, Issue 1, pp 1–12 | Cite as

A Fast Marching Method for the Area Based Affine Distance

  • Moacyr A. H. B. da SilvaEmail author
  • Ralph Teixeira
  • Sinésio Pesco
  • Marcos Craizer
Article

Abstract

In a previous paper, it was proved that the area based affine distance of a convex region in the plane satisfies a non-homogeneous Monge-Ampère differential equation. Based on this equation, in this paper we propose a fast marching method for the computation of this distance. The proposed algorithm has a lower computational complexity than the direct method and we have proved its convergence. And since the algorithm allows one to obtain a connection from any point of the region to the boundary by a path of decreasing distance, it offers a dynamic point of view for the area based affine distance.

Keywords

Affine distances Affine geometry Fast marching methods Monge-Ampère equation 

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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Moacyr A. H. B. da Silva
    • 1
    Email author
  • Ralph Teixeira
    • 1
  • Sinésio Pesco
    • 2
  • Marcos Craizer
    • 2
  1. 1.FGVFundação Getulio VargasRio de JaneiroBrazil
  2. 2.Departamento de MatemáticaPUC–RioRio de JaneiroBrazil

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