laser point to the exterior coordinate system. The laser
sensor system can be calibrated using these transforma-
tion parameters.
The applied method is similar to the photogrammetric
strip adjustment. The used mathematical model is a linear
drift model for positions and attitudes. Therefore for each
strip 12 unknown transformation parameters are estim-
ated. These are 6 offset parameters with AX (to), AY (fo),
A Z (to) representing an offset for the translation paramet-
ers, Aw(to), Av(to), A&(to) representing an offset for roll,
pitch and heading of the sensor system and 6 parameters
UX, VY, UZ, Vu, Vp, Ux representing a time-dependent drift
for each of the 12 parameters. With the variable £ repres-
enting the time of measurement, each estimated translation
results in the following three observation equations for the
unknown calibration parameters.
dX(t) & AX(to) + vx(t)+
F((Aw(to) + vu (1), (Ap(to) + ve (t)), (AK(to) + vs(t)))
dY (t) 2 AY (to) + vy (t)+
F((Aw(to) + vu (t)), (Ap(to) + ve(t)), (Ak(to) t v«(t)))
dZ(t) = AZ (to) + vz(t)+
F((Aw(to) + vu(t)), (Ap(to) + ve(t)), (AK(to) + vs(t)))
After the calibration of the airborne laser sensor system,
all measured laser points are defined in the same exterior
coordinate system.
i : =]
nl M m DX A DY 2 DZ us time
165 170 175 180 185 190
Distance between two windows: 10m
windowsize: 40m * 40m
Figure 4: Matching results after matching
The results of the matching procedure shown in figure 3, to
calibrate the laser data by performing a strip adjustmenr.
In order to evaluate and control the calibration process a
second matching process was applied afterwards. The res-
ults are shown in figure 4. The drifts and offsets, as seen
in figure 3 are eliminated. The RMS of the remaining X,Y
translations is about 0.7m (0.8 m in X and 0.5 m in Y).
Considering a laser point as a pixel with point size 3 m *
0.3 m (point distance), this value is better than 1/3 of a
pixel. This corresponds with the accuracy of the intensity
based image matching, which is given with 1/3 of a pixel.
The RMS of the remaining height translations is 0.3 cm.
This value corresponds to the given accuracy of the laser
distance measurement.
By the use of GPS for the positioning task and an high
precision INS for the attitude determination of an airborne
laser sensor system, which is state of the art in the present
system, the offsets and drifts could be reduced consider-
ably, compared to the results shown in figure 3. Especially
the X,Y offsets are small (« 2 m). Nevertheless especially
for high precision applications the calibration of the laser
sensor system described in this section still has to be per-
formed to eliminate remaining error influences —especially
the height offsets- and control the system.
3.3 Filtering of the measured laser points
Especially in forest and in build-up areas airborne laser
sensor systems are superior to conventional methods for
3D data capture. In areas covered with vegetation it is
advantageous to use a pulsed laser sensor, which is able
to measure the reflected part of a laser at different points
of time instead of a continuous wave laser sensor. For a
pulsed laser a certain amount of the emitted laser beam
is reflected at the tree canopy, while other parts penetrate
the canopy through gaps in the foliage and therefore reach
the ground. "Therefore the last reflected laser pulse, i.e.
the part which is received at last, will refer to the ground
surface. Nevertheless the laser beam is frequently reflec-
ted completely by the foliage, i.e. some measurements do
not reach the ground surface at all. The penetration rate,
i.e. the number of measurements reaching the ground sur-
face, that can be achieved for laser measurements in forest
areas depends on the season. In summer time, which is the
worst season due to the full foliage, still penetration rates of
about 25% in deciduous areas and of about 30% in conifer-
ous areas are reached. Especially in deciduous areas these
rates can be improved by flying in winter time [Ackermann
et al. 1994]. Nevertheless it can be shown that for all sea-
sons there is always a sufficient number of measurements
reaching the ground surface in forest areas which makes
it feasible to determine the topographical terrain surface
by the registration of the last reflected signal of the laser
beam, followed by further filtering and processing of the
measured laser points.
An important task while evaluating laser data is the sep-
aration of points on the topographical terrain surface from
topographical non relevant points, i.e. points reflected by
objects like trees or buildings. Figure 5 shows a Digital
Height Model computed using all measured laser points,
the surface represents a combination of the topographic
surface with objects rising from the terrain. To eliminate
these objects a process has to be applied, which can be
partitioned into the two essential parts:
> acquisition of approximate values for the ground sur-
face
p» filtering of measured points and modeling the ground
surface
The acquisition of approximate values to model the ground
surface is the first and essential part of the algorithm.
Therefore it is necessary to use a procedure, which provides
reliable approximate values for the ground surface out of
the data set of laser measurements. Due to the large
amount of laser measurements, this procedure should work
simple and consequently fast. Using the morphological op-
erator Opening for the processing of laser profiles, good
results could be achieved in the past. For this reason this
procedure was expanded to a 2D version to deal with the
scanner data. To perform the morphological opening, first
the deepest point inside a window of a certain size is de-
tected. Each point inside a band width above this deepest
386
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996
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