A Numerical Scheme for the Curvature Equation Near the Singularities

  • Authors:
  • Marcos Craizer;Sinésio Pesco;Ralph Teixeira

  • Affiliations:
  • Dep. Matemática-PUC-Rio, Rio de Janeiro, Brasil 22453-900;Dep. Matemática-PUC-Rio, Rio de Janeiro, Brasil 22453-900;Fundação Getulio Vargas, Rio de Janeiro, Brasil 22253-900

  • Venue:
  • Journal of Mathematical Imaging and Vision
  • Year:
  • 2005

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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.