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A Viscosity Solutions Approach to Shape-From-Shading

Rouy, Elisabeth; Tourin, Agnès (1992), A Viscosity Solutions Approach to Shape-From-Shading, SIAM Journal on Numerical Analysis, 29, 3, p. 867-884. http://dx.doi.org/10.1137/0729053

Type
Article accepté pour publication ou publié
Date
1992
Journal name
SIAM Journal on Numerical Analysis
Volume
29
Number
3
Publisher
SIAM
Pages
867-884
Publication identifier
Metadata
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Author(s)
Rouy, Elisabeth
Tourin, Agnès
Abstract (EN)
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.
Subjects / Keywords
Hamilton–Jacobi equations; viscosity solutions; dynamic programming approximation scheme; shape-from-shading