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A Fast Marching Method for the Area Based Affine Distance

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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.

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Authors and Affiliations

  1. FGV, Fundação Getulio Vargas, Rio de Janeiro, Brazil

    Moacyr A. H. B. da Silva & Ralph Teixeira

  2. Departamento de Matemática, PUC–Rio, Rio de Janeiro, Brazil

    Sinésio Pesco & Marcos Craizer

Authors
  1. Moacyr A. H. B. da Silva
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  2. Ralph Teixeira
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  3. Sinésio Pesco
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  4. Marcos Craizer
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Correspondence to Moacyr A. H. B. da Silva.

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da Silva, M.A.H.B., Teixeira, R., Pesco, S. et al. A Fast Marching Method for the Area Based Affine Distance. J Math Imaging Vis 30, 1–12 (2008). https://doi.org/10.1007/s10851-007-0038-1

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  • DOI: https://doi.org/10.1007/s10851-007-0038-1

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