Graphics Reference
In-Depth Information
This avoids problems with extremely tilted rigs and false positives next to the rig
(not shown here). Another run of the circle filter is performed to eliminate corners
which have become unconnected due to differences in length.
At this point the rig is assumed to be one component of the graph. The next step
is to identify the component which describes the rig. This is done by traversing the
graph component starting from all rig corner candidates. During the traversal each
square corner is assigned its presumed number (cf. Fig.
1.7
d). A single inconsistency
in this enumeration starting from different rig corners discards the complete image.
During the traversal the number of vertices per component is counted. The largest
component is assumed to be the rig. If the number of corners is not the expected
one, the complete image is discarded. If the rig is rectangular, the algorithm checks
for the correct size in both axes; i.e. a rig turned by 90
◦
is discarded.
The last step is to detect the direction marks on the rig and change the corner
enumeration accordingly. If marks are expected and cannot be found, the complete
image is discarded.
Definition of the Graph
The individual processing steps operate on a directed
graph
G
defined as
G
={
V,E
}
(1.69)
S
x
i
=
u
i
v
i
1
,...,N
v
V
=
i
=
(1.70)
=
e
i
=
E
(s
i
,t
i
,d
i
)
|
i
=
1
,...,N
e
;
s
i
,t
i
∈
1
,...,N
v
;
}
.
d
i
∈
D
={
left,right,up,down
(1.71)
The vertices
S
x
i
are estimated at subpixel accuracy as described in the following
section. The graph edges
e
i
contain the numerical identifiers of the source vertex
s
i
and target vertex
t
i
along with the symbolic direction
d
i
of the point from source to
target.
Extraction of Corner Candidates
Generating corner candidates from the image
is the most time-consuming processing step due to the iconic nature of the algo-
rithm. A fast implementation is crucial to the real-time application of the algorithm.
It is desired to find the corners by computing the correlation coefficient between
the image and the corner template. Since the correlation coefficient is a normalised
value, in terms of both brightness and contrast, the actual grey values of the tem-
plates are not important; they are chosen to be
1forthe
white parts. The empirical normalised cross-correlation coefficient is defined as
−
1 for the black parts and
+
i
=
1
x
i
y
i
−
n
(
i
=
1
x
i
)(
i
=
1
y
i
)
1
c
=
,
(1.72)
[
i
=
1
x
i
n
(
i
=
1
x
i
)
2
][
i
=
1
y
i
n
(
i
=
1
y
i
)
2
1
1
−
−
]
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