A rigorous setting for the reinitialization of first order level set equations

DOI HANDLE Open Access

Abstract

In this paper we set up a rigorous justification for the reinitialization algorithm. Using the theory of viscosity solutions, we propose a well-posed Hamilton-Jacobi equation with a parameter, which is derived from homogenization for a Hamiltonian discontinuous in time which appears in the reinitialization. We prove that, as the parameter tends to infinity, the solution of the initial value problem converges to a signed distance function to the evolving interfaces. A locally uniform convergence is shown when the distance function is continuous, whereas a weaker notion of convergence is introduced to establish a convergence result to a possibly discontinuous distance function. In terms of the geometry of the interfaces, we give a necessary and sufficient condition for the continuity of the distance function. We also propose another simpler equation whose solution has a gradient bound away from zero.

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Details 詳細情報について

  • CRID
    1390290699772196352
  • NII Article ID
    120006459763
  • DOI
    10.14943/84218
  • HANDLE
    2115/69878
  • Text Lang
    en
  • Data Source
    • JaLC
    • IRDB
    • CiNii Articles
  • Abstract License Flag
    Allowed

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