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).