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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