Geoscience Reference
In-Depth Information
Fig. 6
Angular observation ranges for hybrid scanner (a) and panoramic scanner (b)
z
.
þ
Dh
p
Vertical angle
;
h ¼ tan
1
x
2
þ
y
2
ð
5
Þ
where, Dr, Du and Dh are systematic error model for range, horizontal direction
and vertical angle, respectively.
Since this study involved panoramic scanners (Faro Photon 120), the angular
observations computed using Eqs. (
4
) and (
5
) must be modified. This is due to the
scanning procedure applied by panoramic scanner, which rotates only through 180
to provide 360 information for horizontal and vertical angles as depicted in Fig.
6
.
Based on Lichti (
2010
), the modified mathematical model for a panoramic
scanner can be presented as follows:
180
x
y
u ¼ tan
1
ð
6
Þ
z
.
p
h ¼ 180
tan
1
x
2
þ
y
2
ð
7
Þ
The modified models above Eqs. (
6
) and (
7
) are only applicable when the
horizontal angle is more than 180 as shown in Fig.
6
. Otherwise, Eqs. (
4
) and (
5
)
can be used, which means that panoramic scanner has two equations for both
angular observations.
In order to perform self-calibration bundle adjustment, the laser scanner
observations have to be expressed as functions of the position and orientation of
the laser scanner in a global coordinate system (Schneider
2009
). Based on rigid-
body transformation, for the jth target scanned from the ith scanner station, the
equation is as follows:
x
¼
R
11
ð
X
j
X
Si
Þþ
R
21
ð
Y
j
Y
Si
Þþ
R
31
ð
Z
j
Z
Si
Þ
y ¼ R
12
ð
X
j
X
Si
Þþ
R
22
ð
Y
j
Y
Si
Þþ
R
32
ð
Z
j
Z
Si
Þ
z ¼ R
13
ð
X
j
X
Si
Þþ
R
23
ð
Y
j
Y
Si
Þþ
R
33
ð
Z
j
Z
Si
Þ
ð
8
Þ
