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
