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33 Matching of Corresponding Key Points Based on Fuzzy Logic 
Another important part of automatic feature based DTM generation is matching of key points. Fuzzy inference can be 
related to geometrical constraints and to radiometric constraints. Fusion of the constraints of both types leads to a fuzzy 
reasoning process for finding establishing correspondence. 
331 Geometric Constraints 
As outlined previously the matching process takes advantage of multilevel DTM generation and coarse-to-fine 
processing. The result of this is that an approximate location is predictable for establishing corresponding points. The 
fuzzy knowledge about the search space and the given orientation of the images can be use to formulate fuzzy matching 
rules for constraining the search space geometry. 
Rule 1: 
  
Given the predicted location of a certain feature point in the 
second image of an image pair the distance between the predicted *3 
locations and the location of extracted point in the search window 95 V ue 
in X-parallax direction should be small. For convenience this 9 ; ' + 
0 2 4 6 8 10 Higher 
distance is abbreviated as X-distance. A sample for a membership 
function is plotted in Figure 6. 
  
  
  
  
Figure 6: Membership function of X. Distance 
Rule 1. IF X Distance Is Short THEN Match ELSE Not Match 
  
  
  
Rule 2: 
Similar to rule 1 a second rule may apply for the Y-parallax of iru 
two points. But given the image orientation or epipolar line 14 
geometry the deviation orthogonal to the epipolar line (Y- 05 T p 
distance) must be near to zero. 0 1 2 3 Higher 
  
  
  
Rule2. IF Y. Distance Is Small THEN Match ELSE Not Match Figure 7: Membership function of Y. Distance 
332 Radiometric Constraints 
These constraints are based on the similarity of the grey values in the neighbourhood of extracted points in different 
images. Cross correlation values (CC) of the grey scale images and furthermore of local texture descriptions can be 
taken into account. But other features like local estimates of noise of the SNR are also of interest in this context. 
  
  
Rule 1: 
By correlating grey values, corresponding points should show up 3T. 00 R9 MG B M 
with high cross correlation values. A corresponding membership os nF 
function is plotted in Figure 8. 0+ + t + e 
0 02 04 | 05 . 08 1 Higher 
  
Rule I. IF CC Is High THEN Match ELSE Probably Not Match 
  
Figure 8: Membership function of CC 
  
  
  
Rule 2: 
Local estimates of the SNR should be similar to for corresponding 1^ 
points. For convenience the differences are abbreviated by S. diff 054 
(Figure 9). 
0 | + + | 
0 2 4 6 8 10 Hi 
Rule 2.1F S Diff Is Small THEN Probably Match ELSE Probably rer 
Not Match 
  
  
Figure 9: Membership function of S. Diff 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 803