m 
! 
f 
belows when k = 1,2,..., fl 
In each column, each number represent the membership of 
corresponding pixel belong to each class, as the same time 
restrained condition is as follows: 
n c 
I«*>o X u <* =1> 
k=1 /=1 
0 - u ik ^ 1 (* = 1,2,..., c; k = 1,2,...») (2) 
from above, membership U ik is fuzzy, U jk is arbitrary 
real number between 0 and 1, so each pixel can belongs to 
different class, but the sum of membership equal to 1, it is be 
true of real condition. The membership of hard 
classification method of k-mean clustering is always to be one 
a. if X k : £V i ( i — 1,2,...,C ), X k calculated 
by: 
x k * v i, 
(5) 
b. if for each V f , exist X k for X k = V ; , so for 
U :lr = 
c ( d ^ 
u ik 
I 
7=1 
\ d »J 
2 
m-1 
/ = 1,2,...,c 
or the other, in it the U jk is 0 or 1. 
the X k , we set U ik =■ 1 \U jk = 0(j ^ z), As a result, the 
The membership array U and clustering center V is confirmed 
when the aim function J m is minimum, 
in the aim function, 
4 = Ih-k 1C = fit - v iY A fr* - v,) 0) 
it represents Mahalanobis distance. Mahalanobis distance is a 
scale which can detect characteristic space for data muster of 
super ellipse structure. It suits to the real condition of pixels 
distributed., 171 G 1, go J introduced by Bezdek is fuzzy 
weighted index, it is also called as smoothness factor. It affect 
the fuzzy degree in the data partition, so it is necessary to 
select a optimum fuzzy weighted index. But the selection of 
the optimum fuzzy weighted index has no theory direction. 
When we find the optimum answer the aim function, 
interactive calculation is used by Laplacian theory because we 
must ascertain the two parameters U and V. The step of 
improved fuzzy c-mean clustering method is as follows: 
1) extracting the feature of samples, computing the average 
of them as the original clustering center. 
2) Initialization, setting the clustering number c, fuzzy 
weight index m, end error £ and the maximum iteration 
number. 
3) Initialization of the membership array U (0) . 
4) Start iteration, when iteration number is 
IT(IT = 0,1,1,...) , the C-mean vector is computed based 
on U (IT) . 
,(IT) _ 
f N 
£(“»)"**/ 
V*=i / 
i 1,2,..., c 
f n 
X («.)' 
V*=i 
)) 
(4) 
condition of consistency of clustering center and samples is 
removed, the membership is a real number between 0 and 1. 
6) If |U (IT) -t/ (/7M) I < £ or IT > LOOP ,the 
iteration is stopped, otherwise return to the step 3. 
The improved fuzzy c-mean clustering method can select the 
number of clustering freely, the result array U is c rows and n 
columns, each column represent the membership to the 
clustering classes of one pixel. On the basis of the rule of 
maximum membership, each pixel can be ascertained to a 
optimum class. 
3. LAND COVER CLASSIFICATION BY IMPROVED 
FUZZY C-MEAN CLASSIFIER 
With Satellite Liaoyang panchromatic image, improved fuzzy 
c-mean Classifier was used to land cover classification in this 
paper. The classification process was realized based on 
Matlab.The grayscale of panchromatic image is always 256, 
the data quantity is not vast, so it is easy to process by 
computer. The overall step of improved fuzzy c-mean 
classifier is as follows: 
F i g u r e. 1 the process of improved fuzzy c-mean clustering 
5) Replacing U UI) by U llT ’ rl) by the f ormu i a 
1) calculate the original clustering center