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A comparison theorem for a piecewise Lipschitz continuous Hamiltonian and application to Shape-from-Shading problems

Tourin, Agnès (1992), A comparison theorem for a piecewise Lipschitz continuous Hamiltonian and application to Shape-from-Shading problems, Numerische Mathematik, 62, 1, p. 75-85. http://dx.doi.org/10.1007/BF01396221

Type
Article accepté pour publication ou publié
Date
1992
Journal name
Numerische Mathematik
Volume
62
Number
1
Publisher
Springer
Pages
75-85
Publication identifier
http://dx.doi.org/10.1007/BF01396221
Metadata
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Author(s)
Tourin, Agnès
Abstract (EN)
The reconstruction from a shaded image of a Lambertian and not self-shadowing surface illuminated by a single distant pointwise light source may be written as a first-order Hamilton-Jacobi equation. In this paper, we continue the investigation begun in E. Rouy and A. Tourin into the uniqueness of the solution of this equation; the approach is based on the viscosity solutions theory and the dynamic programming principle. More precisely, we concentrate here on the uniqueness of the viscosity solution of this equation in case the measured luminous intensity reflected by the surface is discontinuous along a smooth curve. We prove a general comparison result for a piecewise Lipschitz continuous Hamiltonian and illustrate it by numerical experiments.
Subjects / Keywords
dynamic programming principle; viscosity solutions theory; Hamilton-Jacobi equation

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