1 results
Instability of the eikonal equation and shape from shading
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- 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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- Article
- Export citation
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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.
