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shape from shading

ESAIM: Mathematical Modelling and Numerical Analysis (1)

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Instability of the eikonal equation and shape from shading
Ian Barnes, Kewei Zhang
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 34 / Issue 1 / January 2000

Published online by Cambridge University Press:

15 April 2002, pp. 127-138

Print publication:

January 2000
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In the shape from shading problem of computer vision oneattempts to recover the three-dimensional shape of an object orlandscape from the shading on a single image. Under theassumptions that the surface is dusty, distant, and illuminatedonly from above, the problem reduces to that of solving theeikonal equation |Du|=f on a domain in $\mathbb{R}^2$ . Despitevarious existence and uniqueness theorems for smooth solutions,we show that this problem is unstable, which is catastrophic forgeneral numerical algorithms.