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QUALITY MEASURES FOR DIGITAL TERRAIN MODELS
K. Kraus *', C. Briese * M. Attwenger *, N. Pfeifer
* Institute of Photogrammetry and Remote Sensing , Vienna University of Technology, GuBhausstrale 27-29,
A-1040 Vienna, Austria - (kk, cb, ma)@ipf.tuwien.ac.at
^ Department of Geodesy, Delft University of Technology, Kluyverweg 1,N-2629 HS Delft,
The Netherlands - n.pfeifer@citg.tudelft.nl
COMMISSION II, WG 11/2
KEY WORDS: DEM/DTM, Quality, Laserscanning, LIDAR, Photogrammetry
ABSTRACT:
In the last few years a lot of new possibilities for the acquisition of terrain data were developed. Next to new developments in the
area of digital photogrammetry due to automated image matching techniques, laserscanning has revolutionized the capturing of
topographic data. For digital terrain models (DTMs) derived from "traditional" photogrammetric techniques accuracy measures,
which were derived from theoretical but also from practical studies, are in use. With the upcoming of the new technologies the
question of quality “How accurate is the DTM?" has to be studied new. This paper gives several solutions for the computation of
different quality parameters. On the basis of these measures two different methods are presented. First, the empirical stochastic
approach, which is mainly dependent on the point density of the data set, the root mean square error (RMS) and the local curvature
of the DTM, is introduced step-by-step. Afterwards, a geometrically based approach is shown. It allows the computation of the DTM
accuracy based on the local curvature of the DTM and the distance from each grid point of the DTM to the original terrain point next
to it. The last quality measure helps to determine areas with unreliable surface description. The presented theories are independent
from the data source, the modelling process and the software. For the verification of the theory the quality measures were practically
tested with a typical airborne laserscanner data set. Additionally, the usability of the developed method was checked with
photogrammetric data. A final section gives a short summary and a short outlook on future research work.
1. INTRODUCTION
The idea of digital terrain models (DTMs) has been proposed
nearly 50 years ago by C. Miller of the Massachusetts Institute
of Technology, Boston, USA. In this realm, the decades to
follow have been characterized by searching for technologies of
(photogrammetric) data acquisition, and by developing
adequate software. Currently, DTMs constitute a fundamental
data base for geographical information systems (GISs). In
recent years airborne laserscanning (ALS), a new data
acquisition technique, gained special importance in digital
terrain modeling.
The importance and responsibility of DTM applications makes
it inevitable to provide DTMs with adequate quality measures.
Practical rules of thumb are nowadays available in a more or
less adequate and tested form (see, e.g, Kraus, 2004).
Furthermore, provided that the model has been computed by
software applying least squares algorithms, rules for error
propagation based on variances and co-variances can be applied
to estimate the accuracy of the points as interpolated from the
original terrain data. Applying this method has however the
disadvantage for users of applying a kind of a black box: the
user obtains detailed accuracy measures without any
information on individual factors of influence.
However, there is very little literature on deriving detailed
accuracy measures for DTMs in a post-processing phase, i.e. at
the stage of their application. Below, methods for deriving a
composite accuracy measure gradually, step-by-step will be
presented. All these steps and aspects are readily
comprehendible and well suited for individual visualization.
They can be applied to any DTMs existing beforehand,
independent of the methods applied in creating them. In the
description of the method we will make use of a DTM with
Corresponding author.
hybrid grid data structure (i.e. a grid augmented by meshed
breaklines) for deriving the quality measures.
2. THE EMPIRICAL STOCHASTIC APPROACH
It is assumed that the set of original data, as applied for
computing the DTM. is still available, with any blunders in data
acquired by photogrammetry eliminated; and in data from ALS,
all points not belonging to the terrain surface — i.e. all points on
trees or buildings — filtered out of the set.
In this approach, the height accuracy of the original set of data
will be estimated empirically, based on the set itself. Providing
an overall rough estimate of the accuracy of this set, o, ioi, 18
also useful.
2.1 Density n of the Original Set of Data
Terrain point density in the original set of data represents a
parameter fundamentally influencing the accuracy of DTMs
derived of them. We derive this density n in overlaying the
DTM with an analyzing grid; in counting the number of the
acquired terrain points in each cell of the analyzing grid; and
finally in dividing each of these numbers by the area of the
analyzing grid cell. Figure 1 displays the density n of terrain
points acquired by laserscanning; of these, a DTM has been
derived. In the area shown, the maximum point density is 4.64
points/m°. The high density of points is in the overlapping areas
of the ALS strips. In the areas shown white there are no points:
they have been removed by the program package SCOP as not
belonging to the terrain surface, e.g. positioned on trees or
buildings (compare Figure 9). (Literature to this method of
filtering: Kraus, Pfeifer, 1998: information concerning SCOP:
http://www.inpho.de,
