| Issue |
ESAIM: M2AN
Volume 34, Number 1, January/February 2000
|
|
|---|---|---|
| Page(s) | 127 - 138 | |
| DOI | https://doi.org/10.1051/m2an:2000134 | |
| Published online | 15 April 2002 | |
Instability of the eikonal equation and shape from shading
1
Department of Mathematics, Macquarie University,
Sydney NSW 2109, Australia. (barnes@maths.mq.edu.au)
2
Department of Mathematics, Macquarie University,
Sydney NSW 2109, Australia. (kewei@maths.mq.edu.au)
Received:
1997
Revised:
19
August
1999
In the shape from shading problem of computer vision one
attempts to recover the three-dimensional shape of an object or
landscape from the shading on a single image. Under the
assumptions that the surface is dusty, distant, and illuminated
only from above, the problem reduces to that of solving the
eikonal equation |Du|=f on a domain in 
. Despite
various existence and uniqueness theorems for smooth solutions,
we show that this problem is unstable, which is catastrophic for
general numerical algorithms.
Mathematics Subject Classification: 57N05 / 57M05 / 26A16 / 54C20
Key words: Eikonal equation / shape from shading / instability / numerical analysis.
© EDP Sciences, SMAI, 2000
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