In: Wagner W., Székely, B. (eds.): ISPRS TC VII Symposium - 100 Years ISPRS, Vienna, Austria, July 5-7, 2010, IAPRS, Vol. XXXVIII, Part 7B 
Figure 2: The range error SR due to the non-perpendicular scan 
ning geometry and the influence of SR on vertical and horizontal 
laser point positioning error. 
range R and knowing the beam width /3 from the laser scanner 
specifications, the range error SR is parameterized in terms of in 
cidence angle a as given in Eq. 2 (Lichti et al., 2005): 
(2) 
This range error SR is then propagated through the geo-referencing 
equation and the height precision of laser point i due to the (non 
perpendicular) scanning geometry crzi,SR (geometrical precision) 
is computed. 
Finally, the allover theoretical height precision of point i is writ 
ten as Eq. 3: 
a Zi = \J' a \i,m + a Zi,SR (3) 
2.3 Empirical relative quality of laser points 
In general the idea of validating the relative quality of laser data 
is based on checking the compatibility of laser points in areas, 
where data overlap (Kremer and Hunter, 2007). In (Habib et al., 
2008) some QC procedures are explained. However, the acquisi 
tion area discussed in this research, i.e. the sandy beach, does not 
include (many) steady points or lines, that are sufficiently well de 
fined in the laser LMMS point cloud. In other words, the beach 
area lacks artificial sharp edges or planes, which could be ex 
tracted from the laser points and used in a relative QC procedure. 
Besides, the terrain on the beach is changing smoothly. Thus find 
ing and aligning breaklines of beach morphology is not a promis 
ing method either. Instead, the advantage of high LMMS laser 
point density is used and a point-to-point comparison is made. 
Namely, the height differences between laser points that lie so 
close together that their footprints partly overlap, i.e. the height 
differences between so-called identical points, are analyzed. Not 
all measured laser points are considered in the process of finding 
those identical points. The next two conditions are set for laser 
points: 
• The footprint diameter might be unreasonably big in case 
the incidence angle is close to 90°. Therefore, just laser 
points that have an incidence angle less than 89.9° are con 
sidered: ap < 89.9°. • 
• Because just the vertical component Z of the two points is 
compared, points should lie on an almost horizontal plane 
in order to avoid the influence of surface slope on the height 
difference. This requirement is considered to be fulfilled, if 
the z-component of the normal N z , computed at each laser 
point as explained in Section 2), is: Np z fa 1. 
Now pairs of closest points in 3D are found using the kNN algo 
rithm (Giaccari, 2010), where k = 1. The closest point pair enters 
the set of identical point pairs, if the 3D distance dij between 
laser point Pi and its nearest neighbor Pj is smaller then the min 
imal size of their footprint radii. At the same time the 3D distance 
di,j should be smaller than 5 cm, thus: 
di,j < Min(min(rj, rj), 5 cm), (4) 
where i,j = 1.. .n 8z i ^ j and n the number of laser points. 
The height differences A Z between identical points are consid 
ered as an empirical quality measure. It is expected that the mean 
of signed height differences AZ equals approximately zero. 
LMMS is characterized by a high laser point density, compared to 
ALS. This high point density has several reasons. First, from an 
operational viewpoint, the drive paths can be arbitrary close to 
gether, resulting in overlapping drive-lines, while the vehicle can 
also scan at low driving speeds. Besides, usually more laser scan 
ners are mounted on a vehicle and measure at the same time. It 
is not clear a-priori that points from different drive-lines can have 
the same quality. That is because the acquisition time is different 
and the configuration of GPS satellites may have changed. Also 
different scanners may result in points of different quality. There 
fore the height differences AZ of identical points are investigated 
for three different cases: 
1. Identical points (IP) from the complete data set. 
2. Identical points (IP) belonging to different scanners (scanner 
overlap). 
3. Identical points (IP) belonging to overlapping drive-lines 
(drive-line overlap). 
For each case the height differences of identical points are ana 
lyzed in order to estimate noise levels and possibly identify sys 
tematic errors. Besides, the correlation with geometric attributes, 
i.e. the range and incidence angle, of laser points is investigated. 
2.4 DTM interpolation and quality 
There are many different algorithms to interpolate a DTM. The 
more common are Nearest Neighbor, Inverse Distance Weight 
ing, Moving Least Squares and Kriging (Shan and Toth, 2008). 
Many researches and books exist on those topics, however they 
are not discusses further in this research. The main emphasis is 
on the DTM quality estimation. 
In general the quality of a DTM depends on a number of individ 
ual influencing factors, see (Li et al., 2005, Huaxing, 2008). The 
ones investigated here are: the number of terrain points (FD1), 
height precision of individual terrain point (FD2), terrain point 
distribution (FD3), the terrain roughness (FR) and interpolation 
method (FI). When the DTM is constructed from the existing 
laser data, the first three influencing factors (FD1, FD2, FD3) 
are usually known or can be estimated. The fourth influencing 
factor, the terrain roughness (FR), is related to the interpolation 
method (FI). 
Following the research in (Kraus et al., 2006), a grid point ele 
vation and its precision are estimated by linear interpolation (FI). 
Rules of error propagation based on variances and co-variances of 
the original terrain laser points are applied, to estimate the quality 
of the grid points. The output is then strictly speaking the preci 
sion of a grid point, which is denoted by a standard deviation 
adtm• In other words, the systematic errors are assumed to be