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 $\mathbb{R}^2$
. Despite
various existence and uniqueness theorems for smooth solutions,
we show that this problem is unstable, which is catastrophic for
general numerical algorithms.