The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B7. Beijing 2008 
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sensitive to edge characteristic named “Mexican hat mother 
wavelet” and the other is sensitive to the texture characteristic 
named “Morlet mother wavelet”. In literature, it had already 
proven that the combined mother wavelets have good 
characteristics as the independent wavelet (Szu etc., 2002). This 
combined wavelet transformation is the isotropic synthesis, 
with one-dimension definition in x and the y directions as 
follows: 
The most useful cloud models are the normal compatibility 
clouds because normal distribution have been supported by 
results in every branch of both social and natural sciences (Deyi 
etc. ,1998).A normal compatibility cloud characterizes the 
qualitative meaning of a linguistic atom with three digital 
characteristics: 
v 2 ¿ 
W(x) exp(—XI )+®p(— ) cos(Xa) = wtx)+ 
2 2 d) 
W(y)=exp(-^Xl -/)+exp(-¿) cos^) =rr(y)+M(y) 
2 2 (2) 
And then the two-dimensional isotropic combined wavelet filter 
can be constructed as below: 
A(E x ,E n ,H e ) 
(6) 
EE H 
Where x , " and e are the expected value, entropy and 
E E H 
deviation of the cloud respectively. A given set { *’ e j 
uniquely defines a particular compatibility cloud A. The MEC 
of the normal compatibility cloud to a linguistic atom A is: 
W(x,y) = exp(- —)(1 - x 2 )(1 - _y 2 ) 
x y 
+ exp(——) exp(- T-) cos (k 0 x) cos(/c 0 y) 
= m(x)m(y) + M(x)M(y) 
(3) 
MEC a {u) = exp[- 
(»-■EJ 2 -, 
2 Ej 
(7) 
Given x =0, n =3, e =0.1 and n=1000, the generated 
cloud can be described as figure 1. 
Where the first item describes the edge information and the 
second item describes the texture information. 
We suppose the image to be processed be to 
decompose it by the multi- resolution combined wavelet, which 
can be described: 
Figure 1. Cloud generated with CG(0,3,0.1,1 000) 
MW{f)(a,b) = 
f \f(t,uW(—,—)ddu 
J J a a 
(4) 
Where a is an alterable resolution and b= (bl, b2, ...) is a 
set of the displacements. 
3. CLOUD MODEL 
3.1 Cloud Generators 
Given three digital characteristics * , n and e to 
represent a linguistic atom, the forward generator could produce 
as many drops of the cloud as you like. All the drops obey the 
properties described above. Figure 2 shows a 1-D cloud 
generator. 
Cloud model is a model of the uncertain transition between a 
linguistic term of a qualitative concept and its numerical 
representation. In short, it is a model of the uncertain transition 
between qualitative and quantitative. 
Let U be the set U={u},as the universe of discourse, and T a 
term associated with U. The membership degree of u in U to the 
C T (u) 
term T, 1 , is a random number with a stable tendency. 
C T (u) 
1 takes the values in [0,1].A compatibility cloud is a 
mapping from the universe of discourse U to the unit 
interval[0,l].That is: 
C T (u) : U —> [0,1],\fu e u u —» C T (u) 
(5) 
♦<if0pú, ,u t ) 
Figure 2. 1-D forward cloud model generator 
It is natural to think about the generator mechanism in an 
inverse way, which is named backward cloud generator. Given 
drop Xu., u) 
a limited set of drops, , as samples of a 
E E 
compatibility cloud, the three digital characteristics *, n