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