International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B1. Istanbul 2004 
  
  
  
  
  
  
  
  
  
Bnet 1 k 
| function Hoy = sea 3 and 
| — 1 k 1 . I Q1 i 
| Hoa m Uses, ike. ^ ? t$ 
: ds 1 1 
In the fuzzy inference identify the rules that apply to the current 
situation and compute the values of the output linguistic 
variable. The computation of the fuzzy inference consists of 
two components: 
“omputation of the IF pz " the rules, and 2) C ati > Mean s 
1) Computation of the IF part of the rules, and 2) Computation t Wu e N Mear Flu E 
o ® = > 
of the THEN part of the rules. For example: 
IF Mean == Good AND SD == Good THEN Gray- (a) e 
  
  
  
  
e 
Scale = Road T E 
| At the end of the fuzzy inference, the result is the value of a 
linguistic variable. To use it to the crisp value, it has to be 
| translated into a real value (Defuzzification). The relation 
| between linguistic values and corresponding real values is 
omatic | always given by the membership function definitions. In this E HA Gyr 
paper paper, the center of maximum (COM) is used for enum m 
ogram defuzzification. Let W, be the most typical values of the terms = 
omatic : ; 
mmon | with membership function, 44 ; (w) , then the defuzzification FIG. 2. The membership functions for the linguistic variables: (a) Mean; 
| (b) Standard Deviation; (c) Gray. Scale. 
| output is: * 
The values of Mean and SD before fuzification are 
SS ur (w i )w determined in two steps from histogram of the image. 
width 
; 
and “ | ; 
Step I: Histogram smoothing; Looking at histogram, scatterplot 
Strips. : sa ; s 
y (1) of the data may indicate that the data are not well fit by any of 
is for | > ud (w À the standard types of distributions. In this case, nonparametric 
| j techniques are needed for fitting an arbitrary density to a set of 
| samples. 
| One of the ways of obtaining an approximate density function 
| 3. IMPLEMENTATION AND RESULTS from sampled data is kernel method. Here, we used Gaussian 
| density function as kernel function which produce the estimated 
ed in density function for data. Choosing good width and SD for 
Wang 'The study area constitutes Spot image from an area of kernel function is a problem. If the width is too large, fine 
structure will be lost, but if the width is too small, the resulting 
remote | Iran in multispectral mode (Fig 1). 
system | approximation will not be sufficiently smooth. In this study, the 
| et al. | optimum width and SD of the kernel function is determined 3 
ication and 0.4 respectively. 
road Step 2: Objects detection. After the histogram is smoothed from 
the last step, the objects, the regions with similar properties, 
1i for should be detected from the smoothed histogram. That is done 
t, real by detection of the peak and valley points. The following rules 
guistic are applied to define the peak and valley points of the 
called histogram. 
i). The first derivative indicates peak and valley points of the 
histogram when the mask -1 1 is convolved with the smoothed 
histogram (points a, b, c and d in Fig. 3). 
es that 
on that 
  
  
ues as 
' terms ii). The mask -1 1 is convolved again on result i) to indicates 
the second derivative. If the second derivative will be greater 
than zero and the first derivative equal to zero then, the point is 
-prob- valley. If the second derivative will be less than zero and the 
first derivative equal to zero then, the point is peak. 
-prob- 
Road, Number 
pb 
4 ^ 
^8 f | 
| 2 1 f B X m 
| x 
shape, | ME s Boer NRL B , / n ; À S f 
[ X as | FIG. 1. The spot image for study area, 2 a "i : 
nclude | ^ T n C à 
every In last section, we used Mean and SD as linguistic variables and ^ H 2 
: . > . "M. 2 
ership II shape and Gaussian shape as membership functions for G al 
n = i rey scale 
  
segmentation in Fig. 1. Fig. 2 shows the membership functions 
for input and output linguistic variables.