Graphics Reference
In-Depth Information
d
p
u
(s)
x
z
1
b
0
=
d
p
u
(s)
x
−
t
2
b
0
=
(1.100)
z
d
p
v
(s)
d
p
v
(s)
y
z
1
b
0
2
b
0
=
=
which yield the expressions
u
(s)
1
x
=
t
u
(s)
1
−
u
(s)
2
v
(s)
1
y
=
t
(1.101)
u
(s)
1
−
u
(s)
2
b
0
d
p
1
z
=
t
u
(s)
2
for the coordinates
x
,
y
, and
z
. The difference
d
=
u
(s)
u
(s)
1
−
1
−
u
(s
2
occurring in (
1.101
)
is termed 'disparity'. Accordingly, the depth
z
is characterised by an inverse propor-
tionality to the disparity.
1.5.2 The Determination of Corresponding Points
In this section it is assumed that the regarded pair of stereo images has been rectified
to standard geometry. Hence, the problem of three-dimensional scene reconstruction
basically becomes a problem of establishing point correspondences along epipolar
lines, i.e. corresponding image rows. Under these preconditions, the problem of
three-dimensional scene reconstruction is solved as soon as a disparity map has
been generated, i.e. disparity values have been determined for all image pixels or a
subset of them.
For selecting the correct correspondences from the multitude of possible cor-
respondences, certain constraints are applied by most stereo vision systems. Marr
and Poggio (
1979
) introduced the 'uniqueness constraint' and the 'continuity con-
straint'. According to the uniqueness constraint, a point in the first image can be
brought into correspondence with either one single point in the second image or no
point at all. The continuity constraint postulates that the disparity map should not
display abrupt changes (except at the borders of objects). According to the so-called
'monotonicity of edge order' introduced by Baker and Binford (
1981
), also known
as the 'ordering constraint', the relative positions of corresponding points along the
epipolar lines are the same in both images, i.e. the lateral sequential arrangement of
points in image 1 is the same as that of their corresponding points in image 2.
The following parts of this section describe a variety of classical as well as re-
cently developed methods for generating disparity maps.
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