Biomedical Engineering Reference
In-Depth Information
Chapter 5
Shape From Shading Models
Xiaoping Shen
1
and Lin Yang
2
5.1 Introduction
In many applications, for instance, visual inspection in robot vision and au-
tonomous land vehicle navigation to name a few, a procedure of recovering
three-dimensional surfaces of unknown objects is of considerable practical in-
terest. In this chapter, we consider one of the reconstruction models: the shape
from shading (SFS) model. The SFS models are not only important for applica-
tions in engineering but also of great intrinsic mathematical interest. We begin
with a portrait of the model.
5.1.1 The Shape from Shading Model
The problem of SFS is to determine the shape of a surface, given a
single
gray
level image of the surface. Mathematically speaking, if we denote the surface of
the object by
Z
=
Z
(
x
,
y
)
,
(
x
,
y
)
∈
with the unit normal to the surface
1
1
+
p
2
N
=
+
q
2
(
−
p
,
−
q
,
1)
T
,
1
Department of Mathematics, Ohio University, Athens, OH 45701, USA
2
Department of EECS, Ohio University, Athens, OH 45701, USA
257
