ISPRS Commission III, Vol.34, Part 3A „Photogrammetric Computer Vision“, Graz, 2002
The effect of the elimination of off-terrain points can also be
seen in the comparison of the empiric variogramms computed
from all measured laser scanner points and from the classified
ground points. In the geostatistical literature the variogramm is
defined as the variance of the height difference between the
heights 7; and 7; (Var[zi-7;]) at the locations x; and X; =x; 1h
Under the hypothesis of 2™ order stationarity of the heights
(considering them as the realisation of a random function), the
variogramm does only depend on h and not on X; (Journel and
Huijbregts, 1978). This has also been described in sec. 3.1 for
the covariance function.
An example of such an empiric variogramm computed from a
dataset in a wooded area around Vienna (point distance of -3m)
is presented in fig. 7. For the classified terrain points we get, as
expected, a horizontal tangent in the origin, which corresponds
to a smooth (differentiable) surface and a nugget effect
(measurement variance) close to zero. On the other hand the
empiric variogram from all points shows a large nugget effect of
135m?, corresponding to a standard deviation of +12m for the
height difference of very close neighboured points.
Additionally, the tangent at the origin is not horizontal,
indicating a continuous but not differentiable surface.
Var[z;-2;] [m?]
ADD rrr etter se eee Le eh tra Le LL ==>
TT 7 et
0 10 20 30 40 50 60 70 80 90 100
+ classified terrain points
*- all original points
Figure 7: Empiric variograms of all original points and of the
classified terrain points
distance classes [m]
4.3 Hierarchic Robust Interpolation of Terrestrial Laser
Scanner Data
The generation of a DTM from terrestrial laser scanner (TLS)
data proceeds similar to ALS data. Again the task was to
eliminate points above the terrain surface and therefore the
weight function has to be asymmetric and must be shifted. The
difference to the ALS data lies in the point density. In the
neighbourhood of the sensor we have a point density of nearly
l000points/m? whereas for larger distances this density is
4points/m?. The laser scanner used is the Riegl LMS-Z210
(Riegl, 2002). Therefore the generation of data pyramids for
homogenisation is necessary.
The parameters for the hierarchical robust interpolation are
similar to the ALS case. The results from a test dataset of the
company ArcTron (2002) are presented in the figures 8 and 9.
The surface of this countryside area (~0.2km?) consists of
wooded and open terrain. A visual inspection and a difference
model showed that the algorithm did quite a good job. In the
centre of this test suite the DTM is rather rough, which can be
explained by the high point density, which allows a very
detailed description of the terrain.
For the computation of the DTM in the last step we used a
conditional data densification with the help of a distance
transformation (chamfering) (Borgefors, 1986). Therefore, the
ground plan locations of the terrain points are set as feature
pixels in a digital image with a pixelsize of 0.5m. The distance
transformation assigns each pixel the distance to its nearest
feature pixel (i.e. the nearest measured point). In areas within a
certain distance interval [1m,10m] we densified the terrain point
set to close data holes. The heights of these densification points
(1m grid) were sampled from a DTM, which was computed
from a thinned out (low resolution) data set of the classified
ground points. Therefore some extrapolation band exists around
the terrain points and small areas without data are closed in the
DTM of fig. 9.
<ont> Proc Operation mode Heb
jets. |
Figure 8: DSM of the thinned out TLS data (lowest point in
0.2m raster)
Figure 9: Shading of the DTM of the thinned out classified
terrain points with conditional densification
4.4 Elimination of Scan Errors in Satellite Laser Scanner
Data from Mars
The Institute of Photogrammetry and Remote Sensing is
participating as co-investigator in the “Mars Express” project of
the European Space Agency (ESA). Within this project, several
computations on the global Mars data from NASA's MOLA
(Mars Orbiter Laser Altimeter) sensor were performed. This
sensor can be characterized as a laser scanner profiler without a
deflection unit for the laser beam. Therefore only a very
inhomogeneous point distribution is available.
Presently the delivered MOLA data consists of about 640 mio.
surface points, which contain scan errors due to referencing
errors of the spacecraft. A DTM shading from a small part
(250000 points) of this dataset is presented in fig. 10, where
