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Mapping without the sun
Zhang, Jixian

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
x k * v i,
b. if for each V f , exist X k for X k = V ; , so for
U :lr =
c ( d ^
u ik
\ d »J
/ = 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
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 («.)'
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.
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