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
TypeArticle accepté pour publication ou publié
Journal nameSIAM Journal on Numerical Analysis
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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 / KeywordsHamilton–Jacobi equations; viscosity solutions; dynamic programming approximation scheme; shape-from-shading
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