3.4 FCM clustering segmentation 
For an image, clustering is a commonly used segmentation 
method, which usually employs spectral information of each 
pixel as feature vector and realize partition of the image in 
feature space by similarity measure. 
As a generalization of classical k-means clustering, Fuzzy 
C-Means (FCM) algorithm is also a partition-based clustering 
method, which realizes the soft partition of a data set by 
minimizing the objective function (Bezdek, 1981) 
N iC 
JUNI una? 
i=l k=l 
8 3) 
N= 1.4,20, 15s N 
k=l 
By solving the optimization problem (3), we obtain the 
following iterative formula (4) and (5) 
  
1 
Uy =r eu (4) 
S ki yn 
c=l da, 
N 
X ux, 
y, 2 LL — (5) 
where U = (ordeo and... (v,; jeu are membership 
matrix and cluster prototype matrix, respectively, and x; is the 
ith feature vector, d. is the dissimilarity measure between 
the ith feature vector and the kth cluster prototype, C is the 
number of clusters, N is the number of feature vectors, and m is 
a fuzzy factor (m >1). Note that for uc t0, hn. the Fuzzy 
C-Means (FCM) algorithm boils down to the hard c-means case 
(or classical k-means algorithm). 
Brrr 50.— 
  
For high resolution satellite images, clustering segmentation 
only using spectral information is difficult to obtain satisfactory 
results due to spectral variability. Spatial autocorrelation feature, 
as spatial information, may be incorporated into clustering 
segmentation algorithm to improve the segmentation quality. 
In this paper, segmentation experiments are conducted via the 
Fuzzy C-Means (FCM) algorithm, which incorporates both 
spatial autocorrelation features and Spectral features. The 
expected results are that spatial autocorrelation features can 
effectively improve the segmentation quality of high resolution 
satellite images. 
4. RESULTS AND DISCUSSIONS 
4.1 Semivariogram modelling 
This paper first selects three typical object classes (figure 3) 
from the original image of site 1 (figure 1(a)): vegetation, water 
and road, but the other small objects like ships are not 
considered. The omni-directional semivariograms of theirs are 
calculated in three bands, respectively (figure 4). 
      
(a) vegetation (b) water (c) road 
Figure 3. Typical object classes in site 1 
From figure 4, we know different object classes correspond to 
different semivariograms, and thus they have different spatial 
variabilities. Semivariograms of water and vegetation are quite 
simple and similar except in band 4, and their ranges are all 
about between 2~4 pixels by visual inspection. Comparing with 
water and vegetation, semivariogram of the road is relatively 
complex, which is continuously fluctuant and unstable when lag 
h exceeds the range, implying that roads have more complex 
variation structure. The range of its semivariogram is about 
between 8~9 pixels. The detailed range information of the three 
object classes in site 1 is listed in table 1. 
  
  
  
  
  
  
  
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Figure 4. Semivariograms of the three object classes in site 1 in three different bands 
Vegetation | Water | road Building 1 | Building 2 | Shadow | Vegetation | Bare land 
Band 4 2-4 2-4 | 8-9 Band4| 10-11 6-8 2-4 2-4 2-4 
Band 3 2-4 2-4 | 8-9 Band3 | 10-11 6-8 2-4 2-4 2-4 
Band 2 2-4 2-4 | 8-9 Band 2 10-11 6-8 2-4 2-4 2-4 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
Table 1. Ranges of object classes in site 1 
This paper focuses on ranges of these object classes, which can 
Table 2. Ranges of object classes in site 2 
provide a priori knowledge for the selection of neighborhood 
   
     
  
  
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