Abstract
The problem of recovering a Lambertian surface from a single two-dimensional image may be written as a first-order nonlinear equation which presents the disadvantage of having several continuous and even smooth solutions. A new approach based on Hamilton–Jacobi–Bellman equations and viscosity solutions theories enables one to study non-uniqueness phenomenon and thus to characterize the surface among the various solutions. A consistent and monotone scheme approximating the surface is constructed thanks to the dynamic programming principle, and numerical results are presented.
Keywords
MathematicsViscosity solutionUniquenessMonotone polygonSurface (topology)ViscosityPhotometric stereoNonlinear systemMathematical analysisApplied mathematicsScheme (mathematics)Numerical analysisImage (mathematics)GeometryComputer science
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Publication Info
- Year
- 1992
- Type
- article
- Volume
- 29
- Issue
- 3
- Pages
- 867-884
- Citations
- 647
- Access
- Closed
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Cite This
Elisabeth Rouy,
Agnès Tourin
(1992).
A Viscosity Solutions Approach to Shape-From-Shading.
SIAM Journal on Numerical Analysis
, 29
(3)
, 867-884.
https://doi.org/10.1137/0729053
Identifiers
- DOI
- 10.1137/0729053