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discarded—the illumination conditions should therefore be chosen such that this
situation does not occur. The bright regions in the ratio images are segmented and
analysed using the binary connected component (BCC) analysis algorithm (Man-
dler and Oberländer,
1990
) which yields—among other information—the proper-
ties area, centre coordinates, and a pixel contour description for each segmented
region. This computation yields
n
1
regions in the first and
n
2
regions in the sec-
ond image. The extracted contours are smoothed by B-spline interpolation (Rogers,
2001
). Without loss of generality, it is assumed that the scene is illuminated along
the image rows. We thus calculate the
u
(column) coordinates at which the interpo-
lated contour intersects the rows in the
v
(row) range covered by the corresponding
B-spline in order to obtain subpixel accuracy (cf. Sect.
1.5.2.2
). Optionally, the B-
spline contours can be used as an initialisation to active contour techniques such as
the one introduced by Williams and Shah (
1992
) for further refinement. The con-
tours are represented as sets
c
(m)
c
(n)
{
1
,a
}
and
{
2
,b
}
of points for the first and the second
image, respectively:
=
ˆ
1
,a
,a
c
(m)
1
,a
u
(m)
v
(m)
1
,a
,
ˆ
=
1
,...,n
1
(3.2)
2
,b
=
u
(n)
2
,b
,b
=
c
(n)
2
,b
, v
(n)
1
,...,n
2
(3.3)
where
a
and
b
are the region indices in the images and
m
and
n
the point indices in
the respective contours. The values
u
(m)
1
,a
u
(n)
2
,b
and
are real numbers, while the values
v
(m)
1
,a
v
(n)
2
,b
denote image rows and therefore are integer numbers.
For each image row
v
in the range covered by a contour, the number of intersec-
tions between the contour and the image row is calculated. These intersection counts
are denoted by
e(v)
. Along with these values, the
u
coordinates of the intersections
u
(i)
(v)
with
i
ˆ
and
ˆ
=
1
,...,e(v)
are determined. They are known at subpixel accuracy
due to the B-spline representation of the contours. For each image row
v
, the inter-
sections are sorted in ascending order according to their respective
u
(i)
(v)
values
(Fig.
3.1
c). For extraction of ridges of surface features, image rows
v
with an odd
number
e(v)
of intersections are discarded. For the shadows in image 1 with illumi-
nation from the left-hand side, intersections
u
(i)
(v)
with even indices
i
are points at
which a shadow ends, while intersections
u
(i)
(v)
with odd indices
i
are ridges that
cast a shadow (Fig.
3.1
c). The situation is just the inverse in image 2 illuminated
from the right-hand side. Hence, the shadow lengths for image row
v
are
l
(j)
(v)
u
(j
−
1
)
(v)
with
j
even
.
(3.4)
Given the elevation angle
μ
of the light source with respect to the ground plane,
the shadow length
l
(j)
(v)
yields information about the difference in depth (in the
following denoted by
z
) at the corresponding pixel positions:
u
(j)
(v)
=
−
z
u
(j)
(v), v
−
z
u
(j
−
1
)
(v), v
=
l
(j)
(v)
tan
μ
with
j
even
.
(3.5)
The sign of the depth difference in (
3.5
) depends on whether the scene is illumi-
nated from the right-hand or the left-hand side. It is assumed that the incident light
is parallel and that the elevation angle
μ
of the light source with respect to the
(Δz)
shadow
=
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