975 
The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part Bl. Beijing 2008 
meters dimension. A total of 7 scans were obtained by a FARO 
LS 880 laser scanner at a low resolution. The scanner was 
moved along an arbitrary trajectory that was manually 
measured later with respect to a reference 2D coordinate 
system. The performance of the localization algorithm was 
carried out on the basis of comparing the computed positions 
with the manually measured reference positions. Only the 
measured position and orientation of the scanner at the initial 
starting point was used in the localization algorithm. 
The segmentation algorithm was applied to the range images 
obtained at each scan. Fig. 5 depicts the segmented range 
images together with the original range images as well as the 
intensity images obtained at each scan. For each segmented 
image a list of the extracted planar surfaces with their 
parameters in the respective coordinate system of the scanner 
was generated. 
The extracted plane parameters were introduced to the 
localization algorithm. For every pair of successive scans a 
search space containing all the combinations of four planes in 
the two scans was formed. Inconsistent combinations were 
found and ruled out by comparing the orientation parameters of 
the planes. A threshold of 3 degrees was empirically found 
suitable for the selection of combinations that showed a 
consistent change of orientation angles in two successive scans. 
Table 1 illustrates the changes of parameter 0 of three planes in 
four successive scans. As can be seen, the planes exhibit 
changes of 0 in different scans, which are within the designated 
3 degrees of variation. In general, the comparison of 
parameters 0 and cp reduced the search space to less than 0.01% 
of its original size in the majority of cases. 
e, (60,) 
0 2 (50 2 ) 
03 (50 3 ) 
Scan 1 
149.6 
238.4 
61.3 
Scan 2 
157.3 (+7.7) 
246.2 (+7.8) 
68.5 (+7.2) 
Scan 3 
154.2 (-3.1) 
243.2 (-3.0) 
65.6 (-2.9) 
Scan 4 
153.3 (-0.9) 
239.6 (-3.6) 
64.3 (-1.3) 
memory. The CPU time required for the segmentation 
algorithm was in the order of a fraction of a second for each 
scan. The localization phase was performed on a Pentium D 
CPU with 3.2 GHz speed and 2.00 GB memory. The CPU time 
was 21.7 seconds for the entire sets of planes, which is in 
average 3 seconds for each scan. 
Fig. 6: The computed trajectory of the laser scanner as 
compared to the manually measured positions. 
Table 1: Changes of parameter 0 (in degrees) of three 
intersecting planes in four successive scans 
The position of the scanner at each scan was computed by 
intersecting the corresponding planes found in the search 
procedure. The computed positions were transformed to the 
reference coordinate system by using the initial position and 
orientation of the scanner and the average rotation between 
every two successive scans. These were then compared to the 
manually measured positions to provide a means for assessing 
the accuracy of the localization algorithm. Fig. 6 shows the 
computed positions plotted together with the manually 
measured positions. 
Table 2 summarizes the discrepancies between the computed 
and the manually measured coordinates of the laser scanner 
positions. As can be seen, the mean and the root mean square 
error measures are in the order of a few centimetres. 
The CPU times required for both the segmentation and the 
localization phases were measured to provide an estimate of the 
computational cost of the algorithms. The algorithms were run 
on two separate computers. The segmentation algorithm was 
run on a Pentium 4 CPU with 2.4 GHz speed and 1 GB 
x ref 
Y ref 
Z re f 
X C om 
Y 
A com 
7 
^com 
SX 
5Y 
SZ 
Si 
79 
248 
0 
79 
248 
0.0 
0 
0 
0 
s 2 
71 
300 
0 
71.2 
298.7 
0.0 
0.2 
-1.3 
0.0 
S 3 
98 
310 
0 
97.8 
309.1 
0.2 
-0.2 
-0.9 
0.2 
s 4 
114 
359 
0 
114.2 
359.2 
-0.9 
0.2 
0.2 
-0.9 
S 5 
88 
378 
0 
87.7 
376.7 
-0.9 
-0.3 
-1.3 
-0.9 
S 6 
72 
401 
0 
71.7 
399.2 
-1.8 
-0.3 
-1.8 
-1.8 
S 7 
132 
436 
0 
133.9 
432.1 
-1.4 
1.9 
-3.9 
-1.4 
Mean 
Error 
- 
- 
0.2 
-1.3 
-0.7 
RMSE 
- 
- 
1.9 
4.7 
2.6 
Table 2: Discrepancies between computed and manually 
measured coordinates of the laser scanner position in 7 scans 
(in centimetres).