The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B3b. Beijing 2008 
424 
(Ex x ,En x ,He x ,Ex 2 ,En 2 ,He 2 ,...,Ex m ,En m ,He m ) 
Expression Ex x , Ex~,,..., Ex is expected value, 
En x ,En 1 En m is entropy and He x ,He 2 ,...,He m is 
super-entropy. The mathematical expected hyper surface-MEHS 
of 171 -dimensional normal cloud is defined as following 1121 : 
{iJfR k 
(4) 
Set the average gray level of “actual part” as expected value, 
then Ex k — X R ^ . Suppose “fuzzy part” 
B k (k = has N B pixels in total, f k (i, j) is 
MEHS A (x x ,x 2 ,...,x m ) = exp 
I { x , Ex : ) 
2tT En t 2 
(1) 
The case discussed here expresses the YYl -dimensional normal 
cloud which irrelevant of dimensions. Whereas, it need to put 
forward the covariance matrix if there is compact correlation 
between dimensions. Express the variables and expected value 
in m -dimensional universe of discourse as matrix as following: 
the gray level of pixel, set jU k as membership of every pixel of 
“fuzzy part” ascribe to average gray level of “actual part”. Then 
Jfhjt-XR, 
1 255 
(k = 1,2= l,2,...,N Bk ) (5) 
Average gray level X B of “fuzzy part” and standard deviation 
X, 
Exj 
X, 
Ex 1 
z = 
Z 
E = 
Z 
EX m_ 
The mathematical expected hyper surface-MEHS of multi 
dimensional correlative normal cloud is defined as following: 
tT„ are: 
B k 
XB k 
^ B k (ijfB 
(J, 
(WEB 
(6) 
MES a = (x l ,x 2 ,...,x m ) = 
exp 
-±(Z-E) 7 'D-'(Z-E) 
(3) 
Because the multi-characters conversion to image has executed 
before the multi-dimensional cloud-space, the relativity between 
the bands have eliminated on the whole. So we only discuss the 
multi-dimensional cloud-space mapping model which irrelevant 
between the bands here. Suppose image C is a multispectral 
image which with m bands C x ,C 2 ,...,C m . In multi 
dimensional character space, after the pretreatment and the 
multi-characters conversion for the image C , the relativity 
between the bands have eliminated, so, we can dispose the 
multispectral image C as tfl single-band images. Each sub 
space correspond to a component of C after conversion that is 
a one-dimensional cloud-space. Because of fuzziness of cloud 
space object, an object can be divided to two parts, “actual part” 
and “fuzzy part ”. “Actual part” is the collection of inner pixels 
which membership of this object is 1. “Fuzzy part” is the pixel 
sets, which is except for “actual part” to edge, the membership 
of this object is less than 1 and has the rule that the farther to the 
object center, the smaller membership is. Obtain the ’’actual 
part ” R k (k = 1,2,..., w) of object in band k through 
region increasing algorithm, there are AL pixels in it. Suppose 
ft(ij) is the pixel level at point (/, j) in “actual part” of 
band k , The average gray level of “actual part” can be obtained 
by following function: 
Calculate parameter 
En ik - 
-{fk(Uj)-x Rk ] 
(k - 1,2,...,/72) 
(7) 
2 In (M ik ) 
Set En k = stdev(yf k (/J)) - (J Bk , 
He k - stdev (En ik ). 
Now we have 3m digital characters of object cloud as 
(Ec [ ,Ej,fE [ ,Ec 2 ,E%,Ek 2 ,...,Ev m ,Ei in ,iE m ) , based on the 
parameters, cloud drops can be achieved by the X-cloud 
generator. The normal stochastic numbers 
| Er\ j, EfjEn mj j which expected value 
is ( En x , En 2 ,..., En m j and standard deviation 
is [He x ,He 2 ,...,He m ) can be obtained by formula8. 
(En; j ,En 2j ,...,En mj ) = G(En x ,He l ,...,En m ,He m )W 
By formula9 we can calculate parameter jLl kj , and 
set as cloud dripping. 
{f'k{Uj)-Ex k ) 
M ki = exp 
2 Enl 
(9) 
This object-cloud is the multi-dimensional cloud that integrates 
the information of different band, to a discretionary object, it 
can be expressed as following form: 
C(C, (Ex x , En x , Efe x ), C 2 (Ex 2 , En 2 , He 2 ),...,