A Fast Marching Method for the Area Based Affine Distance

Authors:
Moacyr A. Silva;Ralph Teixeira;Sinésio Pesco;Marcos Craizer
Affiliations:
FGV, Fundação Getulio Vargas, Rio de Janeiro, Brazil;FGV, Fundação Getulio Vargas, Rio de Janeiro, Brazil;Departamento de Matemática, PUC---Rio, Rio de Janeiro, Brazil;Departamento de Matemática, PUC---Rio, Rio de Janeiro, Brazil
Venue:
Journal of Mathematical Imaging and Vision
Year:
2008

Citing 4
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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.