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Farhad Samadzadegan 
  
without a clearly defined boundary. The membership function defines how each point in the input is 
mapped to a membership value. 
Applying fuzzy operators. Yf-then rules are those conditional statements which make fuzzy logic useful. 
The if-part of the rule is called the antecedent (premise), while the then-part is called the consequent 
(conclusion). If the antecedent of a given rule has more than one part, the fuzzy operator is applied to 
obtain one number that represents the result of the antecedent for that rule. This number will then be 
applied to the output function, The output is a single truth value. 
Implication. Before applying the implication method, one must take care of the rule's weight, which is 
applied to the number given by the antecedent. The implication method is defined as the shaping of the 
consequent (a fuzzy set) based on the antecedent. It occurs for each rule. 
Aggregation of outputs. Aggregation is a matter of taking all the fuzzy sets that represent the output of 
each rule and combining them into a single fuzzy set. The unified output of the aggregation process is one 
fuzzy set for each output variable. 
Deffuzification. The final step is defuzzification. The input of the defuzzification process is the aggregate 
output fuzzy set and the output is a single number called the crispness. 
The illustration of this 5 steps is given in Figure 1. It shows fuzzy inference for the example of matching small 
patches or points using fuzzy conditions for correlation based similarity and conditions for expected and 
tolerated parallaxes in image space. 
  
Fuzzy Input Fuzzy Operation Implication 
Ir I I 
  
  
  
  
  
  
  
  
  
  
  
\ [A 
  
  
  
  
  
IF correlation is good AND Y parallax is excellent THEN certainly conjugate pt. 
  
  
nu 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
uoneso188 y 
  
  
IF correlation is good OR X parallax is good THEN probably conjugate pt 
  
  
  
  
  
Crispness «cmm 
Defuzzification 
  
  
  
  
  
  
  
  
Figure 1: Fuzzy reasoning diagram with an example based on fuzzy knowledge about 
image correlation and conditions for the X and Y parallaxes 
32 Detection of Key Points 
Key points are points in the images which may take a key role within the overall processing. In particular these are 
prominent points, edge points or other points which may represent significant texture. In the experiments interest points 
extracted by Fórstner's interest operator (Fórstner and Gülch, 1987) are used. Other points in particular edge points have 
to be integrated into processing at a later stage. 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 801