Farhad Samadzadegan 
  
This interest operator can be developed starting with elementary statistical texture parameters like local gradient 
variances in x- and y-direction. From this parameters a roundness measure and a weight is derived which defines (non) 
isotropy of texture in the window and the quality of point localisation, respectively. 
The selection process involves thresholding of both parameters, the roundness measures and the weights. If, in addition, 
classification between circular shaped features and junction points is taken into account a further sharp decision has ty 
be made by carrying out a statistical test. In consequence, the results of the detection and classification process of the 
interest operator might be different sets defined by all isotropic textured windows, by all highly weighted windows, by 
circular features, by junctions or by general isotropic textures, respectively. In fuzzy set theory these are considered 
classical sets with a crisp (well-defined or sharp) boundary rather than fuzzy sets. 
Theoretically the interest point detection process my be fuzzified by introducing fuzzy sets instead of classical sets ang 
fuzzy rules instead of rules with hard thresholds. But instead of working out exactly such an inference process we want 
to use additional basic texture measures, in particular, the grey value mean and the grey value variance. Those measures 
shall be merged with the Fórstner operator in a fuzzy reasoning system. In the following some of these criteria and rules 
are discussed as an example. 
Fuzzy Rules in the Detection Process 
The following fuzzy rules are applied to interest windows, i.e. only those windows which are already detected and 
selected by the interest operator by using low thresholds only. 
Rule 1: 
  
To avoid interest point extraction in predominantly dark or bright 
areas (which are also avoided if point selection is carried out by 
human operators) the mean grey scale in an interest. window 
should be higher than 30 and lower than 230 (Figure 2). 
  
1 
05 
0 
i N + + + i 1 
"T T T T T T T T Pr 
25 50 75 100 125 150 175 200 225 250 
  
  
  
Rule 1. IF Mean Is Central THEN Probably Key Point ELSE Figure 2: Membership function of mean 
Probably No Key Point 
  
  
  
  
Rule 2: 
For interest windows the grey scale standard deviation must be Si 
above a certain limit (Figure 3). The corresponding rule reads as ve iL} : ; 
10 20 30 Higher 
Rule 2. IF Variance Is High THEN Probably Key Point ELSE 
  
Probably No Key Point Figure 3: Membership function of variance 
Some further rules are formulated which relate to the roundness and the weight measures of the interest operator 
basically stating that the higher this measure are the higher is the probability for being an key point. 
For all these fuzzy if-then rules the linguistic output is "key point". Applying the implication and aggregation steps leads 
to the following membership function of key points (Figure 4). After defuzzification the resulting key point 
probabilities are determined. All key points with probabilities higher than 50% are considered as detected points and are 
plotted in Figure 5. Displayed are the detected points in three different levels of the image pyramid. 
  
P00 
ORO 
  
  
  
  
  
T : # ; 
SES AN A kk a RON WC ON © A 
Figure 5: Detected points based on implemented fuzzy 
reasoning 
  
Figure 4: Membership function of key points 
  
802 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 
    
  
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