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The primary mechanism in fuzzy logic is a list of statements in the form /F inputl [AND input2 ...] THAN 
output, which are called rules. The rules, in this form, are used for describing the desired system response in 
terms of linguistic variables rather than mathematical formulas. All rules are evaluated in parallel, meaning that 
the order of the rules is not important. 
Each clause of the rules (i.e., input and output) is a declaration about a certain parameter of the data. Unlike 
usual rule-based systems, the correctness of the declaration is not necessarily a clear correct/wrong response, but 
a value of a membership function that ranges between 0 and 1. Thus, the response to an input declaration such as 
“the road segment is long” may be 0, which means “wrong,” 1, which means “right,” or any value in between. 
The value is determined by the membership function. In a similar way, another declaration may be “the road 
segment is short.” The output declaration in the case described here may be “segments are similar.” Figure 1 
shows the membership functions for these three examples. Additional examples are shown later in the paper. 
  
  
  
  
  
  
      
  
  
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dsigmf, P-[5 2 5 7] 
Figure 1: Examples of membership functions — *road segment is long" (increasing function, left); *road 
segment is short" (decreasing function, left); *segments are similar" (right). 
The calculation of the resulted value is performed in three stages: 
l.  Foreach rule, evaluating the fuzzy result of the left hand side. 
2. For each rule, selecting the area of the membership function of the right hand side underneath the 
value obtained in the first stage. 
3. Combining the selected areas of the graphs for all the rules to one result. This part is considered the 
defuzzication stage. 
The rules for defining the similarity measure are based on the following parameters (Figure 2): 
Il. The difference between the direction of the GIS road entity and the direction of the hypothesized 
segment ( da ). 
The length of the hypothesized road segment extracted from the image (4 ). 
The difference between the width of the road defined in the GIS and the average distance between 
the two potential road margins extracted from the image (dw). 
4. The distance between the GIS road entity and the hypothesized road segments, with respect to a 
common coordinate system ( d ). 
Ww IN 
Table I details the rules that are currently used for matching the features. These rules are based on common 
knowledge about how roads are represented in the image and in a database. When more knowledge is available, 
it can be easily incorporated to the system. It should be noted that the evaluation process requires that each rule 
should have its opposite, which calls for pairs of rules. 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 19