2.3 Model based on adaptive edge preserving filter 
The next step for the creation of an adaptive edge preserving 
filter is the consideration of a further structure information for 
the surface reconstruction. The system utilizes the direction of 
the local curvature maximum for the filtering of the DEM. For 
the first iteration phase of the DEM generation process the 
direction information is unknown and therefore introduced 
with the value of zero. Hence the result from the first iteration 
corresponds to a surface reconstruction process based on an 
edge preserving filter without an adaptive attribute. 
The information about the surface curvature properties for the 
location (i,j) {i=1,n/j=1,m} is fully contained in the so called 
Hessian matrix (Weidner, 1994). 
Lars id ] 
H(i,j) = | 3 Z au A Hu Hy | and H,=H, 
a4z aif | i Hy Hy 
For the evaluation of the structure direction for the (v +1). 
iteration we have to use the curvature information in the Hes- 
sian matrix of the v. iteration. The rotation of eigenvector of 
the maximum eigenvalue of the Hessian matrix represents the 
direction of the local curvature maximum. 
iml 2 Hy) x : n 
$(1,) =: arctan p = s $(1,) s +5 
H = Hessian-matrix elements in point (i,j) 
$(1j) = direction of local curvature maximum 
In the (v +1). iteration the implemented algorithm utilizes the 
directions of the local curvature maxima for the filtering of the 
DEM. If we introduce the mentioned angle in the convolution 
kemels of the curvatures and torsion (a,’, a,", a,") we get the 
principal curvatures for the filter process. The maximum cur- 
vature (a,"), the minimum curvature (a," ) and the torsion (a," 
with the expected value of about zero) do not correspond to 
the X- and Y-direction any more. 
Using an (5*5) window for the evaluation of the direction of a 
local curvature maximum allows an angle determination with 
an accuracy of about + 1°. The reliability of the direction de- 
termination depends on the spacing of the DEM posts and the 
roundness of the Hessian matrix. 
The mathematical background corresponds to chapter 2.2 ex- 
cept for the convolution kemels of the curvatures and torsion. 
Thus, the detection of local curvature maxima is not depending 
on the rotation of the structure direction against the object 
coordinate system. 
3 CONCEPT OF AUTOMATIC BREAKLINE 
DETECTION 
3.1 General remarks 
The scheduled concept for the automatic breakline detection is 
shown in figure 3.1 and represents the whole program flow of 
the system. All program steps will be executed during one 
pyramid level of the image pyramid used by MATCH-T. The 
number of pyramid levels depends on the image resolution and 
the image size and will be laid out automatically. 
948 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996 
  
DEM GENERATION 
-using edge preserving filter 
-provides DEM, approximate breakline 
points and breakline directions 
x 
VECTORIZATION 
-point connection of the 
approximate breakline 
  
  
  
  
  
FEATURE 
EXTRACTION 
extraction of gray value 
  
  
  
  
  
  
  
points to 3D polylines edges 
VERIFICATION 
-verification of the 3D polylines 
against the gray value edges 
  
$ 
FEATURE MATCHING 
-Matching of gray value edges 
  
next pyramid level 
  
i 
_ EVALUATION 
-evaluation of final breaklines by 
averaging splines 
  
  
  
  
  
  
  
Figure 3.1: Concept for automatic breakline detection 
After the DEM generation and the automatic breakline detec- 
tion for pyramid level (i) have finished, the result of the sys- 
tem (DEM, final breaklines) will be introduced as 
premeasured morphological information into the next pyramid 
level (1-1). Once all pyramid levels have been processed by 
using the automatic breakline detection the system provides a 
DEM which consider the surface structure more precisely. 
In breakline areas we are able to adapt the spacing of the DEM 
posts corresponding to the local surface areas of maximum 
curvature. The discrepancies between the DEM posts and the 
true terrain was minimized by using the breakline information. 
3.2 DEM Generation 
The use of the adaptive edge preserving filter for the DEM gen- 
eration in MATCH-T provides the DEM and approximations 
for breakline points with the corresponding breakline direc- 
tions. The implemented method detects local surface areas of 
maximum curvature and determines the direction of maximum 
    
  
    
    
    
    
  
   
  
      
   
   
    
  
   
    
   
   
    
  
   
    
      
    
    
    
    
    
   
   
   
   
   
  
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