The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B5. Beijing 2008 
3. This algorithm starts from the classification of all points of 
the target into three classes according to their reflectivity. Once 
the classification is completed, classes are recognized by 
calculating the mean value of the points that are assigned to 
each one of them. Finally, the mean position with the largest 
mean reflectivity values is used. A carefull analysis of several 
targets measured by “fuzzypos” algorithm has revealed that the 
parts of the data that correspond to the highly reflective areas of 
the target are shifted w.r.t. the points whit lower intensity. This 
finding will be confirmated by other experimental tests 
described in Par. 4.2.1. 
In addition to methods above illustrated, a new algorithm called 
“intersect” has been designed to reduce the offset error. In a 
first step the cluster analyses is used to divide all points into 
three classes. For the class with the lower intensity, which 
belongs to the background surface around the RRT, a plane n is 
fitted using a RANSAC technique (Fischler & Bolles, 1981). 
The gravity centre G of the class with the largest intensity (i.e. 
the RRT itself) is computed. The target centre T c is computed 
as the intersection between n and a vector connecting G to the 
IRS centre. 
All discussed method has been tested on test-field adopted in 
Test Ex2.2 (Sub-sec. 3.2), but using only the scan from stand 
point 100. Residuals w.r.t. GCP are reported in table 3, which 
shows that some methods proposed give better results than the 
proprietary Riscan sofware algorithm (“riscan”), which is 
unknown. Moreover, the “intersect”, “fuzzypos” and “radcent” 
methods present approximately the same results, while 
“maxrad” and “maxrad4” have significant flaws. In the second 
part of the table, std.dev.s of georeferencing parameters 
computed on the basis of target measurement performed by 
different algorithms are reported. 
Algorithm 
RMSE of 
3-D 
residuals 
on targets 
[mm| 
Estimated georeferencing parameters (cr) 
Rotations of IRS [mgonj 
Position of 
IRS centre 
/mm/ 
n 
0 
K 
maxrad 
12.3 
7.2 
11.3 
6.2 
2.7 
maxrad4 
19.1 
19.6 
30.6 
17.0 
4.2 
radcent 
4.0 
6.4 
10.0 
5.3 
0.9 
fuzzypos 
3.9 
6.2 
9.6 
5.5 
0.9 
intersect 
3.8 
6.2 
9.1 
5.1 
0.9 
riscan 
5.0 
7.7 
11.9 
6.6 
1.1 
Table 3. Target residuals after scan georeferencing on GCPs 
and std.dev.s of georeferencing parameters 
4.2 Accuracy and repeatability on RR target measurement 
In this section results obtained from different tests have been 
organized in order to report different outlines and problems 
which have been observed. At the end, in Sub-sec. 4.3 an 
empirical model to compensate for errors in range measurement 
is then proposed, discussed and validated. 
4.2.1 Accuracy of target measurement 
In Test 1 the coordinate of target centres have been measured 
by proprietary algorithm of software Riscan Pro (“riscan”). To 
check the accuracy of their measurement, 6 parameters of a 3-D 
roto-translation between the Intrinsic RS (IRS) of the laser 
scanner and the GRS has been computed for all configurations, 
according to different distances and rotations. Table 4 shows 
the RMSE after the transformation. In general, the accuracy 
linearly decreases according to the distance. In this case, 
different incidence angles do not significantly influence the 
final results. 
The precision of single target declines when the beam footprint 
is larger than the size of target. Otherwise targets of large 
dimension have resulted in less accuracy in short range. For 
example, targets no. 5 and 6 have not given good results as far 
as a distance of 100 m. 
The data acquired do not present systematic error in range, 
horizontal and vertical angles corresponding to the computed 
target centre. However, a further problem has been outlined by 
computing a plane interpolating all points of the framework 
surface, after removing those points belonging to targets. 
Afterward, the orthogonal distance from each target centre to 
the plane has been calculated. The results have been 
summarized in Figure 5, showing a systematic bias in function 
of distance, i.e. the target centre has resulted closer to the 
scanner w.r.t. the interpolating plane. This problem is signed 
some time in literature (Pfeifer et. al., 2007). The large 
difference between the behaviour of off-planes at 10 m and the 
others can be imputed to the strategies adopted by Riscan Pro to 
scan RRTs. 
Framework 
rotations 
Distance laser scanner-framework [m] 
10 
50 
100 
200 
300 
Ortho [mm] 
2.8 
4.3 
5.1 
6.2 
9.7 
v30 [mm] 
4.6 
3.7 
5.6 
7.0 
n.a. 
h30 [mm] 
3.4 
4.2 
5.6 
7.5 
n.a. 
h45 [mm] 
3.2 
3.9 
3.8 
8.1 
n.a. 
Table 4. RMSE of target centres [mm] after roto-translation 
Figure 5. Target off-plane averaged on all targets of Test 1 in 
function of the distance, with std.dev showing the dispersion of 
biases 
In order to investigate the possible presence of the bias 
encountered in long-range measurements also in a close-range 
environment, coordinates of RRTs derived from Test Ex2.2 
have been used. After the computation of a 3-D rototranslation 
on the set of GCPs (see Sub-sec. 3.2), residuals in X, Y and Z 
have been computed. As shown in Figure 6, residuals present 
systematic errors in position, while a better accuracy has been 
achieved in elevation. Indeed, here the larger residuals on the 
height of target centres accounts for ±3 mm. The planimetric 
error fully agrees with the intrinsic accuracy of range measured 
by Riegl LMS-Z420i'. This is probably due to the extreme 
condition of measurement where incidence angles are ranging 
1 According to Lemmens (2007), LMS-Z420/' features a range accuracy 
of ±10 mm@50 m, and an angular accuracy of 0.0025 deg (1 a).