Figure 1: The data of this example — a last pulse flight —
was provided in a grid. The shown view covers an area of
0.3km?. The upper half shows the original data, the lower
presents the filtered version. As it can be seen in this shading
there are still vegetation structures (trees and bushes) in the
data, though a filtering was performed in order to separate
the ground points from the off-terrain points. In this data
set negative errors occur, too. Notice the "holes" in the river
surface. The flying direction in this example is north-east.
Some methods have a hierarchic approach to the surface in-
terpolation or the classification step. Most approaches work
iteratively, for interpolation as well as for classification. Fil-
tering of measurement errors is not always performed. All
methods have in common that they stress the lower points
and assume that the higher points are vegetation (or more
generally, off-terrain) points.
Often, the measurments are provided in a grid. To this end,
a regular grid is generated and laid over the area of interest.
At each position the height is interpolated from the neigh-
bouring points (original points). This allows a considerable
data reduction because only the heights need to be stored.
However, one does not work with the original measurements
any more. The methods for this interpolation are not docu-
mented, nevertheless it can be assumed that this process also
favours the lower points. One solution is to take the height
for each grid point from the height of the lowest original point
inside a mesh centered on the grid point. For slanted terrain
this leads to a systematic height error of 0.5w tan a (w: mesh
width, tan a: terrain slope).
In fig. 1 a river scene is shown. It is a shading, the light source
is in the north. The river flows in direction north-north-east,
in the upper part a side arm can be seen. The water of this
side arm is standing still (more or less). This might explain
why no signal is received from the water surface (black area).
The upper part of fig. 1 shows the original data (to be more
precise, a 1 meter grid) and the lower part presents the fil-
tered version. It can be seen, that undesired structures are
still in the data. The vegetation on the left river side is not
eliminated completely. The data errors in the river (points
below the river surface) are enlarged in the filtered version.
International Archives of Photogrammetry and Remote Sensing, Vol. 32, Part 3W14, La Jolla, CA, 9-11 Nov. 1999
This is due to the stressing of the lower points (which are in
this case wrong).
2.2 Our method
In the method we proposed, linear prediction is used for the
DTM interpolation. The error distribution of laser scanner
heights with reference to the ground surface is no longer a
normal distribution but a skew distribution with a strong bias
towards off-terrain elevations. The points near the ground
are considered to be normally distributed whereas the vege-
tation points have only positive residuals with reference to the
ground. In the first interpolation step a rough surface approx-
imation is determined. All points, whether ground points or
vegetation points, have the same influence. Thus, the surface
obtained runs in an averaging way between the ground points
and the vegetation points. A modified weight function from
robust adjustment is used to compute weights from residuals.
Fig. 2 shows the residuals of the first interpolation step and
superimposed the weight function. Each measurement (i.e.
the height of each point) is given a weight according to its
residual. These weights can be considered in the next inter-
polation step. Points with heigh weights attract the surface,
points with low weights have less influence. Therefore, the
interpolating surface runs nearer to the ground, disregard-
ing the vegetation points. These vegetation points obtain a
residual even higher than in the previous step. This process is
called iterative robust interpolation. We use it to re-compute
the surface and to classify all laser measurements into ground
points versus off-terrain points (i.e. vegetation points in the
case of wooded areas). The classification is done on the basis
of a threshold value for the residuals. For a detailed descrip-
tion see [Kraus and Pfeifer, 1998] and [Pfeifer et al., 1999].
According to the characterisation of the methods mentioned
before, this approach is an iterative approach, filtering of
measurement errors is performed and the classification and
interpolation are performed simultaneously. Of course it can
also be applied to other data sources with an asymmetric
distribution of gross errors.
3 Performance of the algorithm for laser data
In the meantime, we have gained lots of experience with this
approach. Following is a list of advantages and deficiencies of
the algorithm. Some of the points are not only valid for our
approach but are valid for laser data processing in general.
Thus, this section also includes some general laser scanner
data characteristics.
Advantages:
1. The elevation model and the classification are per-
formed in one step. For steep terrain this is an advan-
tage. The classification is always performed relative
to the ground surface. The ground surface may be
distorted during the iteration steps, nevertheless the
trend of the terrain will always be captured. This is
an advantage over approaches which consider only the
height of a point.
2. The algorithm can either work on original data or it
can also be used to improve pre-classified data. An
improvement of the classification perform by the com-
pany supplying the laser scanner data results in a higher
quality of the digital terrain model derived from these
ground points. However, if the points are given in an
xy-grid, this is not exploited.
occurences
Figure 2: Resi
vegetation poi
(a z-measuren
weight functic
3. High de
of para
user.
4. There i
as well.
tion ne
less infl
shown i
of the 1
symmet
Howeve
as good
requirec
of nega
whereas
5. The gr
due to
On the
system
points.
patch-v
Deficiencies:
1. There i
Dense t
tion rat
tion wit
data so
of flying
be as le
mer tir
flect all
and [Ri
eas, las
Usually
situatio
such a
(or aga
tect an
hand, s
It depe
advant:
