# The ICICS/CS Reading Room

## UBC CS TR-91-02 Summary

- No on-line copy of this technical report is available.

- A Multigrid Method for Shape from Shading, April 1991 Uri M. Ascher and Paul M. Carter, 17 pages
The shape-from-shading problem has received much attention in the
Computer Vision literature in recent years. The basic problem is to
recover the {\em shape z(x,y)} of a surface from a given map of its {\em
shading}, i.e. its variation of brightness over a given domain.
Mathematically, one has to solve approximately the {\em image irradiance
equation}\\
\begin{center}
E(x,y)
\end{center}
relating a given image irradiance {\em E(x,y)} to the radiance of the
surface
at each point {\em (x,y)}, with {\em R(p,q)} a given {\em reflectance
z_ {x}$ and $q = z_
{y}$.
\nA possible presence of noise and lack of adequate boundary conditions
adds to the difficulty of this problem. A number of different
approaches towards its solution have been proposed in the Vision
literature, including various regularization models. However, a
reliable, efficient solution method for practical instances has remained
elusive so far.
\nIn this paper we analyze the various solution models proposed with the
aim of applying an efficient multigrid solver. A combination of an
FMG-continuation technique with an appropriate discretization of one such
solution model proposed by B. Horn yields an efficient solver. Our
results are demonstrated by examples.

If you have any questions or comments regarding this page please send mail to
help@cs.ubc.ca.