A Numerical Scheme for the Curvature Equation Near the Singularities

Authors: Craizer Marcos¹; Pesco Sinésio²; Teixeira Ralph³

Source: Journal of Mathematical Imaging and Vision, Volume 22, Number 1, January 2005 , pp. 89-95(7)

Publisher: Springer

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Abstract:

In this paper we propose a modification in the usual numerical method for computing the solutions of the curvature equation in the plane . This modification takes place near the singularities of the image. We propose to use zero as the vertical speed at a saddle point and, at an extremum, the geometric mean of the eigenvalues of the Hessian matrix. This modification is theoretically justified and the preliminary experimental results show that it makes the algorithm more reliable.

Document Type: Research article

DOI: http://dx.doi.org/10.1007/s10851-005-4784-7

Affiliations: 1: Dep. Matemática-PUC-Rio, R. M. de São Vicente, 225, Rio de Janeiro, RJ, Brasil, 22453-900, Email: craizer@mat.puc-rio.br 2: Dep. Matemática-PUC-Rio, R. M. de São Vicente, 225, Rio de Janeiro, RJ, Brasil, 22453-900, Email: pesco@mat.puc-rio.br 3: Fundação Getulio Vargas, Praia de Botafogo, 190, Rio de Janeiro, RJ, Brasil, 22253-900, Email: ralph@fgv.br

Publication date: 2005-01-01