In: Wagner W., Szekely, B. (eds.): ISPRS TC VII Symposium - 100 Years ISPRS, Vienna, Austria, July 5-7, 2010, IAPRS, Vol. XXXVIII, Part 7B
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navigation sensor is discussed.
Using laser LMMS it is in principle possible to quickly obtain
3D geo-referenced data of a large extended area, such as a beach.
High frequency laser pulse measurements enable high spatial res
olution. Besides, higher point density is expected, because the
measured ranges are smaller than in case of ALS. On the other
hand, more data voids might occur behind elevated features when
measuring from the ground. Besides, attention must be paid to the
intersection geometry of the laser beam with the relatively hori
zontal beach. If scanning a horizontal surface, the geometry gets
poorer further away from the trajectory. This decreases the laser
point positioning quality. In order to test the laser LMMS perfor
mance on the Dutch coast RWS initiated a pilot-project. Partic
ular interest of the RWS is the level of obtainable accuracy and
processing time of a final topographic product, which is a Digital
Terrain Model (DTM). The RWS requirements are twofold. First
a vertical DTM accuracy of at least 10 cm at a grid spacing of
lxl m is required, and, second, it is required that the results are
available close to real-time. In this research the quality of derived
LMMS laser point cloud and DTM is analyzed.
In general it is important to know the laser point quality, prior
to using points in further processing, like computing a DTM.
In quite some researches the theoretical or overall expected (a-
priory) quality of the derived 3D laser point cloud is estimated
by linearizing the geo-referencing equation. For equations of
the first order error model see e.g. (Ellum and El-Sheimy, 2002,
Glennie, 2007, Barber et al., 2008). The random errors of the
LMMS measurements (i.e. range, scan angle, IMU angles and
GPS position) and calibration parameters (i.e. lever-arms and
boresight angles) are propagated to obtain a-priori 3D laser point
precision. To verify those theoretical models and estimate an em
pirical (a-posteriori) quality of a laser point positioning, a proper
Quality Control (QC) is needed. In (Habib et al., 2008) the ex
isting QC procedures are explained in detail. However, standard
and efficient procedures for validating the quality of derived laser
points and further on the DTM are still missing.
In the following a procedure to evaluate the laser LMMS mea
surements of sandy Dutch beach morphology is described. In
Section 2 the methodology to estimate both the relative quality of
the LMMS laser point heights and the derived DTM is described.
In Section 3 the methodology is applied on the real data and re
sults of both quality evaluation procedures are presented. In Sec
tion 4 conclusions, which include recommendations for further
work, are given.
2 METHODOLOGY
In this section first the scanning geometry at the time of each
laser point acquisition is reconstructed by applying simple geo
metrical rules. The intersection geometry in general influences
the laser point positioning quality. Thus, this influence is consid
ered further on to compute the theoretical height precision. Here,
also the random errors of LMMS measurements and calibration
parameters specified for a LMMS are included.
Next, the methodology to evaluate the relative quality of LMMS
laser point heights is described. The relative quality describes the
relation between two points acquired in the same region in a short
time period (point-to-point quality) (Kremer and Hunter, 2007).
As stated already in the introduction, the quality of the whole
LMMS data depends on the quality of the system measurements
and calibration. The latter one varies depending on the experience
of the data processor. It is therefore impossible to give a-prior
relative quality quotes (Cox, 2009). For this reason here a real
laser LMMS data set is used and the empirical quality of point
heights is estimated employing a QC procedure.
Terrain laser points, which were extracted from the raw data by
provider Geomaat, are used to interpolate the DTM. The impor
tance of DTM applications makes it inevitable to provide DTMs
with adequate quality measures at a high level of detail, as it is
for example described in (Kraus et al., 2006). The idea is to in
form the user about the DTM quality and warn them of weakly
determined areas. Thus, in the following an approach to evaluate
the quality of each grid point height is described.
2.1 Reconstructing the scanning geometry
The instantaneous scanning geometry of a laser point can be de
scribed by the range and the incidence angle, which besides influ
ence the footprint size. Those geometric attributes are computed
for each measured laser point using point position and the trajec
tory position. Both data sets include the X, Y and Z coordinates
and the acquisition time.
The range R is the length of the vector p from the laser scan
ner position at time t to the laser point. It can be computed for
each laser point once the sensor position at the time t of the laser
point acquisition is known. The laser scanner position is linearly
interpolated using the consecutive trajectory positions. Here it is
assumed that the trajectory position directly represents the laser
scanner position.
The incidence angle a is the angle between the laser beam p
and the upward normal (n) of the surface at the laser point po
sition. When a beam hits a surface perpendicular to it, the inci
dence angle is 0° and when a beam is parallel to a surface the
incidence angle is 90°. The normal vector ft is computed as fol
lows. For each laser point the closest 4 points are determined
using a k Nearest Neighbor algorithm (Giaccari, 2010). A plane
is fitted to all 5 points using Least Squares. The result is the nor
mal n of a plane at a laser point. The number k = 4 of neighboring
laser points participating in plane fitting is chosen such that the
computed normals reflect just a local surface.
The laser footprint is the area of an illuminated surface and is
approximated by a circle. Thus, its diameter Df p is computed in
terms of the laser beam-width /3 and changing incidence angle a
and range R, as written in Eq. 1:
2.2 Theoretical quality of laser points
The theoretical models of error propagation through the geo-re-
ferencing equation are used to estimate an expected precision of
each laser point height ozi■ First the specified random errors
of LMMS measurements and calibration parameters are inserted
in the first order model of error propagation. Besides, the real
measurements as range, scan angle and the IMU angles are con
sidered in the computation. The result is the height precision
of laser point i due to L-MMS measurement errors azi,m (mea
suring precision). The value for the random range error used
here is valid when the laser beam falls perpendicular to the target
(Schwarz, 2009). In practice the incidence angle is changing over
the acquisition area and is usually non-perpendicular as shown in
Fig. 2. High incidence angles result in poor intersection geom
etry and affect the range measurements, (Soudarissanane et al.,
2009, Lichti and Gordon, 2004, Schaer et al., 2007, Alharthy et
al., 2004). For pulse laser scanners, which are used in this re
search, the approach in (Lichti et al., 2005) is used. At a given