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Journal Article

A Viscosity Solutions Approach to Shape-From-Shading

Elisabeth Rouy and Agnès Tourin
SIAM Journal on Numerical Analysis
Vol. 29, No. 3 (Jun., 1992), pp. 867-884
Stable URL: http://www.jstor.org/stable/2158283
Page Count: 18
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A Viscosity Solutions Approach to Shape-From-Shading
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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.

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