A rigorous setting for the reinitialization of first order level set equations
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.
Journal
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- Hokkaido University Preprint Series in Mathematics
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Hokkaido University Preprint Series in Mathematics 1074 1-45, 2015-06-23
Department of Mathematics, Hokkaido University
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Keywords
Details 詳細情報について
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- CRID
- 1390290699772196352
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- NII Article ID
- 120006459763
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- DOI
- 10.14943/84218
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- HANDLE
- 2115/69878
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- Text Lang
- en
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- Data Source
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- JaLC
- IRDB
- CiNii Articles
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- Abstract License Flag
- Allowed