In: Wagner W., Székely, B. (eds.): ISPRS TC VII Symposium - 100 Years ISPRS, Vienna, Austria, July 5-7, 2010, IAPRS, Vol. XXXVIII, Part 7B 
the objective to improve the TIN-models and to use the 
information about the order of the points of the point cloud 
available in the TIN-model. In this paper an algorithm is 
presented which covers the following tasks: 
The moving plane algorithm is extended to a polynomial 
approach, because (Thiel and Wehr, 2001) showed that DTMs 
can be modelled from ALS-data by using third order 
polynomials (s. Figure 4). 
a) Fusing GPS-RTK points with ALS-TIN-Model 
b) Fusing profiles with ALS-TIN-Model 
c) Fusing two models with different accuracy 
Figure 2. Model using profile line information 
2. FUSION ALGORITHM 
In this chapter the basic algorithm is presented which is applied 
in the three tasks mentioned in the introduction. A basic 
algorithm can be defined as the three tasks have in common, 
fusing 3D surveying points of an independent sensor with ALS- 
points (s. Figure 3) which corresponds directly with case a). 
The algorithm is funded on the moving plane algorithm of 
(Kraus, 2000) and the least square matching (LSM) based 
analysis presented in (Ressl a.l., 2008). In the following it is 
assumed that both data sets are well registered, so that only 
shifts in x, y and z direction remain. As all data are already 
modelled it is assumed furthermore that all data are available in 
a plane projection e.g. UTM-coordinates, so that the z- 
component corresponds to the elevation. 
too 110 120 130 »0 160 160 170 183 190 200 
Figure 4. With polynomial approximated surface 
surface line 
2.1 Fusion Process 
The procedure explained in the following was developed 
regarding Figure 3. If r is the vector to the i lh ALS point and 
l 0PSj the vector to the j lh surveyed GPS point, then look for each 
GPS point with j e {GPS points} all ALS points i e (ALS 
points} which satisfy the following condition: 
l^vLSi -X.J <e (1) 
The bound e should be larger than the expected shifts. If the 
number of identified ALS points for each GPS point satisfies 
the number of required points for a polynomial approximation 
the polynomial parameters are approximated by least square 
matching LSM. Accordingly to the empirical modelling in 
(Thiel and Wehr, 2001) and to Figure 4 seven parameters have 
to be computed so that more than 7 ALS points have to be 
identified for each GPS point. This leads to j surface patches 
each described by a polynomial: 
( 1 A 
x 2 
x 3 
y 
(2) 
S represents the elevations zj(x,y). The three dimensional shifts 
Ax, Ay and Az between the ALS-points and the j th GPS-point 
can be described by 
S, (x + Ax, y + Ay) = z GPS (x., y. ) + Az (3) 
The shifts can be determined by linear LSM. The corresponding 
observation equation derived from (3) is given by 
dS (x +Ax’,y. +Ay‘) 
hi =— r-^ — dx + 
dx 
3S.(x. + Ax*,y. + Ay*) 
dy 
dy+ dz 
(4) 
- (Sj ( x j + Ax*,y. + Ay*)-z ops (x.,y.)-Az") 
where Ax*, Ay* and Az* are the initial estimates for the shifts 
and hj are the elevation residuals. The derivatives of Sj are 
3S 2 
-J L = \ + 2a 2J -x J +3a, J -x ] 
as, , (5) 
= a. + 2a, . • y. + 3a,. ■ y. 
4j 5 j Sj 6j Sj 
The Gauss-Markov LSM formula is then 
¡; = (A t -A)-‘A t O (6) 
with 
■i 
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