B 3b. Beijing 2008 
The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B3b. Beijing 2008 
427 
visional pixels sets 
He c |} (13) 
loud core of edge 
to multi under the 
mding element in 
l is not a value but 
r feature plane is 
: , En c , He c ) of 
d the membership 
^orithrn of normal 
<.el gray level in 
the mode 
al stochastic data 
tandard deviation 
be calculated by 
(14) 
/ of each pixel of 
obability of each 
irtition aggregate 
(i,j) is the gray 
r . Apparently, 
ivision of G . 
ion, the condition 
3 is 
L-\ 
i , (^ e )=ZM 
r=0 
Similarly, the condition entropy of natural fuzzy division Q under Rs is 
r =o p(Rs^j p(fc) r=o p(fo) p(Rs) 
p(K s ) = 1H('-M k )K 
r=0 
The entropy of fuzzy division P can be obtained by formula 18 
H{P) = H(Q\Re) + H($Rs) 
(17) 
pyRe J p[Rej p[Rs) P\R S ) 
(18) 
According to the max fuzzy entropy theory [l5] , for obtain the 
best expression of edge curves of gradient images, need to find 
the best membership jU k . The maximal fuzzy entropy principle 
must satisfy the following condition: 
H ^ = rJ^L-in (-“*)] 
(19) 
Set the best membership is ¡U , then, the best fuzzy feature 
tal characteristics 
plane 
Xy can be obtained by formula20. 
*)={/^}’ so ’ 
'Ai 
A 2 
P\N 
)wing forms: 
M22 
*.= 
P-2N 
(i = l,2,...,N;j = l,2,...,M) 
_Mm\ 
Pm 2 
Pmn _ 
(20) 
(15) 
Set ¡U is the 
probability of each pixel divided to Re , 1 — fil is 
the probability of each pixel divided to Rs . Calculate the 
entropy H of fuzzy division by formula 16 to20. The best 
membership jd can be obtained if H > // , 
then, H = H and set T — jd as the divided threshold. 
4.3 Integration for edge maps of all dimensions 
Different spatial object has different radiant capability, even a 
same object in different spectrum the radiant capability is 
possibly different. These differences lead to the number of the 
cloud in cloud-space corresponding to different bands 
unequally, so, the detailed degree of edge map that obtained by 
edge cloud is discordantly. For using the information of 
multispectral remote sensing image adequately, we need to 
integrate the different edge map of all components to obtain the 
edge information of spatial object in multispectral RS image. 
The method of matrix superposition is used to integrate the 
edge information of all components. Suppose there are m 
component of multispectral RS image after the eigenvector 
transform, the result of edge detection of each component is 
expressed as I Ek ,(k = 1,2,..., w) , element 1 in matrix is 
the edge and 0 is the background. Set the edge matrix of a 
certain component as the bottom matrix, add up the result of 
edge extract of each component pixel by pixel, if the 
accumulative total of a element is bigger than 1 or equal to 1, 
then set the value of this matrix element is 1, whereas is 0. To 
search the image thoroughly until every pixel is disposed. The 
method can preserving the map information in farthest, the 
probability of missing detect can be weakened. 
Execute edge detection for components 1-3 of multispectral 
image respectively, the edge image can be obtained by 
integrate the edge information of all component, the result as 
figure2: 
(16)