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Fig. 1.25
Illustration of the model adaptation procedure for the plane model. (
a
) Plane fit based
on repetitive structures. The 'wavelength' of the repetitive structures in scene space is denoted
by
s
.(
b
) Dependence of the disparity error
E
ME
according to (
1.135
) on the offset parameter
c
s
for scene 1 (fence with person) regarded in Sect.
1.6.4
1.6.1.2 Determination of Model Parameters
In three-dimensional scene space spanned by the world coordinates
x
,
y
, and
z
,the
plane with repetitive structures is determined based on modelling rays of light using
the previously determined wavelength information. These rays describe the relation
between the repetitive structures in the scene and their appearance in the image. The
coordinates
U
i,j
and
V
i,j
of the intersections of the rays with the image plane are
determined by
U
i,j
=
U
i,j
−
1
+
λ
h
(U
i,j
−
1
,V
i,j
−
1
)
(1.129)
V
i,j
=
V
i
−
1
,j
+
λ
v
(U
i
−
1
,j
,V
i
−
1
,j
),
(1.130)
where
i
denotes the index of the ray in a column,
j
the index of the ray in a row,
U
i,
0
=
0.
The connection between these intersection points and the optical centre leads
to modelled rays which are characteristic for the repetitive structure. Assuming
equidistant repetitive structures in the scene leads to the criterion that the mutual
distances between the intersection points on the plane have to be equal. At this point
we explicitly assume that these structures are repetitive in scene space and not just
a reasonably regular high spatial frequency pattern in image space. The distance pa-
rameter is denoted by
s
in Fig.
1.25
a. This condition yields the normal vector of the
plane in three-dimensional space. However, the offset parameter of the plane can-
not be determined based on the intersection point approach and has to be estimated
based on the initial three-dimensional point cloud.
We found by inspection of the measurement uncertainties of the pixel coordinates
of the three-dimensional points as well as their measured disparity values that they
0, and
V
0
,j
=
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