04 
  
the 
L). 
ker 
red 
an 
ling 
  
ling 
for 
tion 
iken 
ture 
have 
that 
riate 
. too 
nds 
ction 
ner 
ffset, 
ES. (s 
s the 
t line 
ess — 
icture 
n this 
ion of 
n this 
e this 
t from 
, then 
International Archives of the 
insert point 2 on this line at 33% of the line length, then 
duplicate this point in order to get point 3. Moving points 1 and 
3 new to their final position ends the process. In summary, the 
EGO for an offset is the following: 
IV 2 0.323 
DV 2 
MV 1 de dy 
MV 3 dx dy 
[n a similar way also the generalization operations for the other 
two events can be coded (for more details see [Brenner & 
Sester, 2003]). Figure 6 shows an example for the successive 
presentation of more and more details for four buildings 
(compare to Figure 4, where not appropriate Douglas-Peuker 
algorithm was used). Figure 7 shows some screenshots of a 
larger area of a city. 
        
Figure 6: Presentation of 
detail. 
N 
    
Í 
our buildings in different levels of 
        
Figure 7: Two screenshots with different generalization levels 
of buildings in city. 
5.3 Typification 
Typification involves that a group of objects is replaced by a 
new group with less objects. This means, that extreme changes 
occur between the different representations, as objects are 
eliminated and replaced by new ones. Coding this process in 
terms of EGO’s is simple: an object collapses and a new object 
emerges. This involves that a new geometry is created. 
5.4 Displacement 
The coding of the displacement operation in terms of SO's is 
very simple, as it only consists of move-operations (MV) of the 
Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B4. Istanbul 2004 
original points to their new positions. We use a least squares 
adjustment based approach for calculating the displacement 
between all objects in a scene ([Sester 2004]). Figure 8 shows 
an example for a spatial situation before and after displacement: 
it is obvious, that only in case where conflicts occur (red areas) 
5 
the objects change both position and also (partly) their shape 
(this is indicated in different shades of green in Figure 8). The 
resulting translations in the individual objects are coded in 
terms of SO's. 
  
  
  
  
  
  
   
(top) and solution after automatic displacement. 
5.5 Coding efficiency 
In order to compare the storage requirements of the coding in 
terms of EGO’s with the full presentation of several generalized 
instances of the object, the following estimation can be made. It 
is done in detail for the case of point reduction, but can be 
extended to the other operations mentioned here as well. 
A line consisting of n points is reduced to | point and then 
vanishes, or vice versa it comes into existence with 1 point and 
then iteratively is refined by including new points until its 
detailed structure is achieved. This means, that in the original 
representation 7 double values (x and y) have to be stored. 
Transmitting all the possible n representations would require 
1+2+3+...+n-1+n="%n (n+l) Points 
or twice the number of double values in terms of coordinates. 
Thus, the amount of data to be transmitted is in the order of n°. 
Storing this information in terms of SO’s requires two 
operations for each intermediate point (DV <int>, MV <float> 
<float>), which requires 
n points or 2*n coordinate differences 
In this case, float values can be used, as the coordinate 
differences <dx,dy>-values are typically small. In addition to 
1297